There are 15 true/false questions on the test and 5 multiple choice questions on the test.
Describe Equation?Equations can be written in many forms, but they all have the same basic structure: an expression on the left-hand side of the equals sign, and an expression on the right-hand side of the equals sign, with the equals sign itself indicating that the two expressions are equal.
Let the number of true/false questions be x and the number of multiple choice questions be y. We know that:
x + y = 20 (since there are 20 questions in total)
3x + 11y = 100 (since the test is worth 100 points)
We can solve this system of equations by substitution or elimination. Here, we'll use substitution:
x + y = 20 -> x = 20 - y
Substitute x = 20 - y into the second equation:
3x + 11y = 100
3(20 - y) + 11y = 100
60 - 3y + 11y = 100
8y = 40
y = 5
So there are 5 multiple choice questions on the test. To find the number of true/false questions, we can substitute y = 5 back into x + y = 20:
x + y = 20
x + 5 = 20
x = 15
Therefore, there are 15 true/false questions on the test and 5 multiple choice questions on the test.
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suppose you have a set of data with a mean of 50 and a standard deviation of 10. if you add 5 to each data point, what will happen to the mean and the standard deviation of the new set of data?
If you add 5 to each data point in a set of data with a mean of 50 and a standard deviation of 10, the mean of the new set of data will become 55. The standard deviation of the new set of data will remain the same at 10.
What is the standard deviation?The term standard deviation is frequently used in statistics to quantify the dispersion or spread of a set of data. The standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean. Standard deviation is denoted by the symbol s or σ (sigma).
What is the mean of a set of data?The term mean or arithmetic mean is used in statistics to refer to the value that represents the central tendency of a data set. It is computed by dividing the sum of all data values into a data set by the total number of data points. The formula for computing the mean is given as:
mean = (sum of data values) / (total number of data points)
When you add 5 to each data point in a data set with a mean of 50, the sum of all data values in the data set will increase by (5 * n), where n is the total number of data points. Consequently, the new mean will be given as:
new mean = (sum of new data values) / (total number of data points)
⇒ [(sum of old data values) + (5 * n)] / n ⇒ (50n + 5n) / n ⇒ 55
What is the effect of adding a constant to every data point in a data set?When you add a constant value to each data point in a data set, the measure of central tendency, i.e., mean, median, and mode will also be shifted by the same constant value. This is because the sum of all data values in the data set increases by the product of the constant value and the total number of data points, n.
The measure of variability or spread, i.e., range, interquartile range, variance, and standard deviation, however, remains the same because it is independent of the location of the data values in the data set. Therefore, adding a constant value to every data point in a data set does not change the spread of the data set but shifts the measure of central tendency to a new value.
Hence, the mean of the new dataset will increase by 5, from 50 to 55, and the standard deviation of the new dataset will remain the same at 10.
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PLEASE WORD ANSWER I CAN USE FAST
The area of the garden is given as follows:
A = 20.6925 ft².
How to obtain the area of the garden?The garden has a rectangular format, hence it's area is given by the multiplication of it's length l by it's width w, as follows:
A = lw.
From the image, converting the mixed numbers to decimal, the dimensions of the garden are given as follows:
l = 7.75 feet.w = 2.67 feet.Hence the area in feet squared is given by the multiplication of these two dimensions, as follows:
A = 7.75 x 2.67
A = 20.6925 ft².
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Sylvia's house has recently burned down, and fortunately, she has a homeowners insurance policy that
insures the market value of her home at $225,000. The policy provides coverage for personal belongings of 55% of the insured value of the house. Sylvia lost household and gargae items including: furniture, $75,000; appliances, $15,000; electronics, $9,500; and clothing and other personal items, $5,100; and garage (tools, lawn mower, snow blower, Christmas decorations), $10,750. Her personal property dductible is $500. Calculate the amount covered for personal belongs under Sylvia's homeowners policy
Therefore , the solution of the given problem of amount comes out to be Sylvia's homes insurance covers personal property up to a maximum of $123,250.
What is an amount?aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess
Here,
Sylvia's house is covered for $225,000. Accordingly, the coverage for personal belongings is as follows:
The policy offers coverage for personal belongings equal to 55% of the insured value of the home.
=> Personal property coverage = 0.55 x $225,000, or $123,750.
Sylvia, however, has a $500 personal property exemption. This implies that she is responsible for covering the first $500 of the insured loss.
So the amount covered for personal belongings under Sylvia's homeowners insurance is:
=> $123,750 - $500 is the amount insured for personal property, or
=> $123,250.
Sylvia's homes insurance covers personal property up to a maximum of $123,250.
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Let \underset{v}{\rightarrow}= (4, 2) and \underset{w}{\rightarrow}= (1, -3).
1. Find 7\underset{v}{\rightarrow} - 3\underset{w}{\rightarrow} and state the result in component form
2. State the exact magnitude (length) of \underset{v}{\rightarrow} and the exact magnitude of \underset{w}{\rightarrow}
3. State the dot product \underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}
4. Find proj_{\underset{w}{\rightarrow}}(\underset{v}{\rightarrow})proj_{\underset{v}{\rightarrow}}(\underset{w}{\rightarrow}) in component form. Give exact values. Show work.
5. Determine the angle between \underset{v}{\rightarrow} and \underset{w}{\rightarrow}. Show work. Write the exact angle as the arccosine of an appropriate number. Also, use a calculator to approximate the value of the angle, rounding the result to the nearest degree.
The approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree
\underset{v}{\rightarrow} - 3\underset{w}{\rightarrow} = (7 \cdot 4, 7 \cdot 2) - (3 \cdot 1, 3 \cdot -3) = (28, 12). The result in component form is (28, 12).
The exact magnitude of \underset{v}{\rightarrow} is $\sqrt{4^2 + 2^2} = \sqrt{20}$ and the exact magnitude of \underset{w}{\rightarrow} is $\sqrt{1^2 + (-3)^2} = \sqrt{10}$.
The dot product \underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow} is (4 \cdot 1) + (2 \cdot -3) = -10.
proj_{\underset{w}{\rightarrow}}(\underset{v}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{w}{\rightarrow} \Vert^2})\underset{w}{\rightarrow} = (\frac{-10}{10}) \cdot (1, -3) = (-1, 3).
proj_{\underset{v}{\rightarrow}}(\underset{w}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert^2})\underset{v}{\rightarrow} = (\frac{-10}{20}) \cdot (4, 2) = (-2, -1). The results in component form are (-1, 3) and (-2, -1).
The angle between \underset{v}{\rightarrow} and \underset{w}{\rightarrow} can be found using the formula $\cos\theta = \frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert \cdot \Vert \underset{w}{\rightarrow} \Vert}$.
Plugging in the values, $\cos\theta = \frac{-10}{\sqrt{20}\cdot\sqrt{10}} = -\frac{1}{\sqrt{2}}$. The exact angle is $\arccos(-\frac{1}{\sqrt{2}})$. Using a calculator, the approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree.
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Work out the value of 4 cubed - 6 squared.
help if can for 10+ points
Answer:
28
Step-by-step explanation:
4 cubed means 4 x 4 x 4, which is 64.
6 squared means 6 x 6, which is 36.
So,
4 cubed - 6 squared = 64 - 36 = 28.
Abox of apples weighs 270 kg 500 g. When the box is filled with oranges, it weighs 192 kg 500 g. The same basket when filled with guavas weighs 245 kg. If the fruits together weigh 690 kg, find the weight of the box alone. [some body help me i can't solve it
Answer:
The box alone weighs 6 kg
Step-by-step explanation:
Let, weight of Apple be x, Oranges be y, Guavas be z nd box a.
A box of Apple weighs 270kg and 500g i.e270.5kg
a+x =270.5---(1)
A box of oranges weighs 192.5kg
a+y=192.5---(2)
A box of guavas weighs 245
a+z=245---(3)
Fruits together weigh 690 kg
x+y+z=690---(4)
Combining (1),(2),(3), we get
3a+x+y+z=708---(5)
From 4&5
3a+690=708
3a=18
a=6
So the box weighs 6 kg
You have invested 50,000 dollars to start a donut shop. Your cost for raw materials is 0. 65 dollars per dozen and your overhead costs are 0. 55 dollars per dozen. How many dozen must you produce before your average cost per dozen drops to 2. 45 dollars?
50 dozen donuts should be produced before your average cost per dozen drops to $2.45
Let x be the number of dozen donuts produced.
The total cost to produce x dozen donuts is:
Total cost = cost of raw materials + overhead costs
Total cost = 0.65x + 0.55x
Total cost = 1.20x
The average cost per dozen can be expressed as:
Average cost per dozen = Total cost / number of dozens
2.45 = 1.20x / x
To solve for x, we can cross-multiply and simplify:
2.45x = 1.20x
x = 50
Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.
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Please help! I need this question to pass my class
Answer:
Step-by-,step explanation:
s.,s
What is the answer to this
16/20=?/10
Answer:
? is equal to 8
Step-by-step explanation:
16/20= 0.8
0.8x10= 8
8/10=0.8
OR YOU COUPLE DIVIDED 16 BY TO AND 20 BY 2
Answer:8/10
Step-by-step explanation:when you divide 16 by 20, you get 0.8. So turn 0.8 into a fraction with 10, you get 8/10. (I’m not that smart, mb if I get something wrong.)
Is the religious make-up of the United States Congress reflective of that in the general population? The following table shows the religious affiliations of the 435 members of the 114th Congress by proportion. Religion: Protestant Catholic Mormon Orthodox Jewish Other Unaffiliated Proportion: 0.572 0.307 0.030 0.009 0.052 0.011 0.019 The data below represent the religious affiliations of a random sample of 1500 adult Americans (based on data obtained from Pew Research). Test whether the distribution of religion among U.S. adults differs significantly from that among the 114th U.S. Congress. Use the α = 0.01 level of significance. Religion Frequency Expected Contribution Protestant 772 858.0 8.620 Catholic 368 460.5 18.580 Mormon 34 ? ? Orthodox 12 13.5 0.167 Jewish 46 78.0 13.128 Other 61 16.5 120.015 Unaffiliated 207 ? ?
The religious make-up of the United States Congress is reflective of that in the general population.
Answer:Yes, the religious make-up of the United States Congress is reflective of that in the general population.The steps to test whether the distribution of religion among U.S. adults differs significantly from that among the 114th U.S. Congress with an α = 0.01 level of significance are given below:First, calculate the expected frequencies for Mormon and Unaffiliated using the formula:Expected frequency = (total sample size) x (proportion)Expected frequency of Mormons = (1500) x (0.030) = 45Expected frequency of Unaffiliated = (1500) x (0.019) = 28.5Next, calculate the chi-square statistic using the formula:Chi-square = ∑ [(observed frequency - expected frequency)² / expected frequency]To find the observed frequency - check the frequency table below.Religion Frequency Expected Contribution Protestant 772 858.0 8.620 Catholic 368 460.5 18.580 Mormon 34 45.0 8.690 Orthodox 12 13.5 0.167 Jewish 46 78.0 13.128 Other 61 16.5 120.015 Unaffiliated 207 28.5 149.969The degrees of freedom for the chi-square test = (number of categories - 1) = 7 - 1 = 6Finally, compare the calculated chi-square statistic with the critical value from the chi-square distribution table with 6 degrees of freedom at α = 0.01 level of significance. If the calculated chi-square statistic is greater than the critical value, then the null hypothesis is rejected and we conclude that the distribution of religion among U.S. adults is significantly different from that among the 114th U.S. Congress. If the calculated chi-square statistic is less than or equal to the critical value, then the null hypothesis is accepted, and we conclude that the distribution of religion among U.S. adults does not differ significantly from that among the 114th U.S. Congress.
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Landon is going to invest in an account paying an interest rate of 6. 6% compounded daily. How much would landon need to invest, to the nearest dollar, four the value of the account to reach $3,250 in 18 years
Landon would need to invest approximately $1,150 to reach a future value of $3,250 in 18 years with an interest rate of 6.6% compounded daily.
To determine how much Landon needs to invest, we can use the compound interest formula, which is:
A = P(1 + r/n)^(nt)
where A is the future value of the account, P is the principal amount (the amount Landon needs to invest), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the interest rate is 6.6% or 0.066, the account is compounded daily, so n = 365, and t = 18. We want to find the principal amount, P, that will result in a future value of $3,250.
Substituting these values into the formula, we get:
3,250 = P(1 + 0.066/365)^(365*18)
Simplifying the right-hand side of the equation, we get:
3,250 = P(1.000181)^6,570
Dividing both sides by (1.000181)^6,570, we get:
P = 3,250 / (1.000181)^6,570
Using a calculator, we can evaluate this expression to find that:
P ≈ $1,150.52
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hw06-MoreProbability: Problem 9 (1 point) Employment data at a large company reveal that 59% of the workers are married, that 39% are college graduates, and that 1/5 of the college graduates are married. What is the probability that a randomly chosen worker is: a) neither married nor a college graduate? Answer =% b) married but not a college graduate? Answer = c) married or a college graduate? Answer = Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining.
The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married.
The probability that a randomly selected worker is neither married nor a college graduate is the complement of the probability that they are either married or a college graduate. The equation for the complement is 1 - P(A).1 - (0.59 + 0.39 - 0.2)1 - (0.78 - 0.2)0.22. The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married. The equation is P(A ∩ B) = P(A) × P(B|A).0.591 - 0.196 = 0.394.The answer is 0.394.c) To find the probability that a randomly selected worker is either married or a college graduate, we can use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).0.59 + 0.39 - 0.196 = 0.784.The answer is 0.784.
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A scale drawing of a living room is shown below. The scale is 1 : 40. A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 4 inches. What is the area?
find the area of a regular 12 sides polygon with radius 4 units Long
The area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.
What is polygon?
A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.
To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:
Area = (1/2) * perimeter * apothem
The perimeter of the polygon can be found by multiplying the number of sides by the length of each side. Since the polygon is regular, all sides are of equal length. Let's call this length "s".
s = 2 * r * sin(π/n) where r is the radius and n is the number of sides
s = 2 * 4 * sin(π/12)
s = 1.38 (rounded to two decimal places)
The perimeter of the polygon is:
P = 12 * s
P = 16.56 (rounded to two decimal places)
To find the apothem, we can use the formula:
apothem = r * cos(π/n)
apothem = 4 * cos(π/12)
apothem = 3.77 (rounded to two decimal places)
Now we can calculate the area of the polygon:
Area = (1/2) * P * apothem
Area = (1/2) * 16.56 * 3.77
Area = 31.28 square units (rounded to two decimal places)
Therefore, the area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.
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Julia teaches two dog training classes. The Level 1 class helps dogs learn the basics, while the Level 2 class focuses on more advanced commands. For each class, she kept track of the number of dogs that attended each session. These box plots show the results
On average, slightly more dogs attended the Level 2 class than the Level 1 class.The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48.
The box plots provided show the results of Julia's two dog training classes. The Level 1 class helps dogs learn the basics, while the Level 2 class focuses on more advanced commands. From the box plots, we can see that the Level 1 class was attended more consistently than the Level 2 class, with the majority of classes having between 5 and 10 dogs attending. The Level 2 class, on the other hand, had more variability in attendance, with some classes having up to 18 dogs and other classes having as few as 3. The median number of dogs attending the Level 1 class was 8, while the median number of dogs attending the Level 2 class was 10. The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48. This indicates that, on average, slightly more dogs attended the Level 2 class than the Level 1 class.
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complete the square for 3x²-12=9
The square form of the given equation as per quadratic equation is: x²=7.
What is the quadratic equation?
A quadratic equation is an equation where the variable has the highest degree of 2.
Given equation:
⇒ [tex]3x^{2} -12 =9[/tex]
⇒ [tex]3x^{2} -12 -9=0[/tex]
⇒ [tex]3x^{2} -21 =0[/tex]
⇒ [tex]3x^{2} =21[/tex]
⇒ [tex]x^{2} =7[/tex]
Therefore, the square form of the given equation is x² = 7
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A certain type of brass contains 65% copper. How many pounds of copper are contained in 120 pounds of the brass? Please help I’m doing a test I need help T^T
The amount of copper that is contained in 120 pounds of brass is equal to 78 pounds.
Let the amount of copper be C.
Given the following data:
Quantity of brass = 120 pounds
Percentage of copper = 65%
To calculate the amount of cooper that is contained in 120 pounds of the brass:
In this exercise, you're required to determine how many pounds of copper can be found in 120 pounds of brass. Thus, we would solve for the percentage of copper contained in this type of brass.
[tex]Copper=\frac{65}{100}*120\\\\Copper, c=78 ponds.[/tex]
This is correct because 65% of 120 pounds is equal to 78 pounds. 65% can be expressed as a decimal (0.65) and multiplied by 120 pounds to find the number of pounds of copper contained in 120 pounds of the brass.
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Find the value of x.
Answer:
x = -10
Step-by-step explanation:
Note that it is a isosceles triangle. This means that the base angles (the angles that are not forged by the congruent sides) are congruent.
It is given that one of the angle measurements are 67°, meaning that ∠A would also be equal to 67. Set the equation:
m∠A = x + 77
67 = x + 77
Isolate the variable, x. Subtract 77 from both sides of the equation:
67 (-77) = x + 77 (-77)
x = 67 - 77
x = -10
x = -10 is your answer.
~
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Jacob conducts another survey of students in the school in the Example. This time,
he surveys a random sample of 30 students.
a. In Jacob's sample, 24 students say they will vote for Garrett. Based on this
sample, about how many students in the school should Garrett expect to vote
for him? Show your work.
SOLUTION
Jacob's sample suggests that Garrett should expect approximately 80 percentage of the students in the school to vote for him.
Jacob's sample of 30 students suggests that 24 of them will vote for Garrett, which is an 80% ratio. Applying this ratio to the entire school population, Garrett can reasonably expect that 80% of the students in the school will vote for him. This means that out of the total student population, Garrett can expect approximately 24/30, or 80%, of them to vote for him. This is a useful estimate for how many votes Garrett can expect to receive from the student body. It is important to note, however, that this is only an estimate and may not accurately reflect the actual number of students who will vote for Garrett. Factors such as student opinion or external influences may affect the actual voting results.
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Matthew is training to run a marathon. He runs 20 miles his first week of training. Each week, he increases the number of miles he runs by 4 miles. How many total miles did he run in 8 weeks of training
Answer:
52 miles
Step-by-step explanation:
Matthew runs 20 miles in the first week. We want to increase this number by 4 each week. For this question we will use m for a variable for miles.
This will look like
20 + 4m = total miles ran
if he ran 8 miles, we will enter this number into the variable m.
20 + 4 × 8 = 52
The total miles Matthew ran was 52 miles after 8 weeks.
Please answer QUICKLY! -Bloom’s Nursery designed a plan for Mrs.Hartrick’s flower bed. What is the area of the flower bed?
Therefore , the solution of the given problem of area comes out to be 48 sq ft + 4.5π sq ft is flower bed area.
Define the area.Its total size can be determined by calculating how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. Something's total dimensions are determined by its surface area. The sum of the borders associated with each of a cuboid's six rectangular edges determines the internal water capacity of the object.
Here,
We must add the areas of the rectangular and semicircular regions to obtain the area of the flower bed visible in the picture.
The size of the rectangle, which is square and measures 8 feet by 6 feet, is:
=> A_rectangular
=> length * width
=> 8 ft × 6 ft = 48 sq ft
The radius of the semicircular area is 3 feet, and its diameter is 6 feet. Since this is only a semicircle, we must split by 2 in order to calculate the area of the semicircle using the formula A = r2.
=> A_semicircle = (πr^2)/2 = (π × 3^2)/2 = 4.5π sq ft
The area of the semicircular and rectangular parts combined gives us:
=>A_flower bed = A_rectangular + A_semicircle
= 48 sq ft + 4.5π sq ft
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A normal distribution has mean =μ57 and standard deviation =σ20. Find and interpret the z-score for =x50.
The z-score for =x50 is. So 50 is standard deviations ▼(Choose one) the mean =μ57
If a normal distribution has mean of 57 and standard deviation as 20, then the z-score for x=50 is -0.35 .
In order to find the z-score for x=50, we can use the formula : z = (x-μ)/σ ;
Where x is = 50, "μ" is = mean of the distribution , and "σ" is = standard deviation of the distribution ;
In this case , x = 50 , mean(μ) = 57 and standard deviation(σ) = 20;
Substituting in the values,
We get,
⇒ z = (50-57)/20,
Simplifying, We get,
⇒ z = -0.35
So, the z-score for x=50 is -0.35.
Interpretation of the z-score is that :
The z-score represents the number of standard deviations that a given value (in this case, x=50) is from the mean of the distribution (μ=57).
A negative z-score means that the value is below mean. In this case, x=50 is 0.35 standard deviations below the mean of 57.
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The given question is incomplete, the complete question is
A normal distribution has mean of 57 and standard deviation as 20. Find and interpret the z-score for x=50.
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Graphs allow us to show that the following is true: D. Both plans will be costing the same when 50 texts are sent is accurate.
Describe graphs?The graph is just a organised representation of the data. It helps in our understanding of the data. The numerical information gathered through observation is referred to as data.
The answer is that both plans are same in price when 50 texts are sent because both lines intersect at a cost of $22.5 for 50 texts, indicating that they are equal in price.
The other options are not right:
A-plan Hiroto's costs more than Emilia's plan when more than 50 messages are sent. This is untrue, as you can see from the graph that Emilia's line is higher after 50 texts, indicating that her plan is more expensive.
B-When 22 messages are sent, the cost of both plans is the same. This is false because when 22 texts are sent, the lines do not cross at the same spot.
C-When more than 22 SMS are sent, Emilia's is more expensive than Hiroto's plan. This is untrue because Hiroto's plan is more expensive until they send 50 messages, which is the only time they cost the same. At that moment, Emilia's plan costs about $15.5 and Hiroto's plan costs about $21.
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The complete question is:
Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
A. Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
B. Both plans cost the same when 22 texts are sent.
C. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
D. Both plans cost the same when 50 texts are sent.
Suki took $20 to the carnival she spent one half of her money on rides 1/4 of her money on food and 1/10 of her money on parking how much did Suki spend on rides on food and on parking
Suki spent a total of $17 on rides, food, and parking at the carnival.
The problem states that Suki took $20 to the carnival and spent some portion of it on rides, food, and parking. The first step is to figure out what fractions of her money she spent on each of these things.
The problem tells us that she spent one half of her money on rides, 1/4 of her money on food, and 1/10 of her money on parking. We can write this mathematically and use the multiplication :
Suki spent 1/2 x $20 = $10 on rides
Suki spent 1/4 x $20 = $5 on food
Suki spent 1/10 x $20 = $2 on parking
To find the total amount that Suki spent on rides, food, and parking combined, we simply add up these three amounts:
Total spent = $10 + $5 + $2 = $17
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A ball is dropped from a height of 10 ft. Assuming that on each bounce, the ball rebounds to one-fifth of its previous height, find the total distance traveled by the ball.
Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.
On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.
On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.
On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).
The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:
10 + 14 + 2 + 0.32 + ...
To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:
S = 10 / (1 - 1/5)
= 12.5
So the total distance traveled by the ball is 12.5 ft.
Step-by-step explanation:
A water sample shows 0. 066 grams of some trace element for every cubic centimeter of water. Shandra uses a container in the shape of a right cylinder with a radius of 5. 7 cm and a height of 13. 9 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Shandra collected? Round your answer to the nearest tenth
Shandra has cοllected apprοximately 93.67 grams οf the trace element.
How to Find Amοunt of trace element?The amοunt οf trace element refers tο the tοtal quantity οr mass οf a particular substance οr element that is present in a given sample οr substance. Tο find the amοunt οf trace elements, we can use the fοrmula:
Amοunt οf trace element = cοncentratiοn × vοlume
where the cοncentratiοn is the amοunt οf the trace element per unit vοlume, and the vοlume is the tοtal vοlume οf the sample.
Here we have
A water sample shοws 0. 066 grams οf sοme trace element fοr every cubic centimeter οf water.
Shandra uses a cοntainer in the shape οf a right cylinder with a radius οf 5. 7 cm and a height οf 13. 9 cm tο cοllect a secοnd sample
As we knοw the vοlume οf a right cylinder, V = πr²h
Substituting the given values, we get:
V = π(5.7 cm)²(13.9 cm)
V = 1419.34 cm³
Since the cοncentratiοn οf the trace element is 0.066 g/cm³,
Find the number οf trace elements in the sample by multiplying the vοlume οf the sample by the cοncentratiοn:
Amοunt οf trace element = cοncentratiοn × vοlume
Amοunt οf trace element = 0.066 g/cm³ × 1419.34 cm³
Amοunt οf trace element = 93.67 g
Therefοre,
Shandra has cοllected apprοximately 93.67 grams οf the trace element.
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Find the coordinates of the foci of the ellipse given by the equation 4x^2 + y^2 =64.
Answer: y=28
Step-by-step explanation:
The coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).
To find the coordinates of the foci of the ellipse given by the equation 4x² + y² = 64, we can compare it to the standard form of an ellipse:
(x²/a²) + (y²/b²) = 1
In this case, the equation 4x² + y² = 64 can be rewritten as:
x²/(8²) + y²/(8²) = 1
Comparing the equation to the standard form, we find that a = 8 and b = 8. The foci of the ellipse can be calculated using the formula:
c = sqrt(a² - b²)
For our ellipse, c = sqrt(8² - 8²) = sqrt(64 - 64) = 0.
Since c = 0, the foci coincide with the center of the ellipse. Thus, the coordinates of the foci are the same as the center of the ellipse.
Therefore, the coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).
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What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
We calculate the arc length to be 6.86 inches by rounding to the closest hundredth.
What is a Circle's Arc Length?The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
An arc with a radius of 18 inches and a centre angle of 22° can be calculated using the formula below:
Arc length = (central angle / 360°) × (2πr)
where r denotes the circle's radius.
Substituting the given values, we get:
Arc length = (22° / 360°) × (2π × 18 inches)
Arc length = (0.0611) × (2π × 18 inches)
Arc length ≈ 6.86 inches
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Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $70 for parts. The total was $395. Which equation or tape diagram could be used to represent the context if
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x represents the cost of labor per hour?
We get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's use the variable "y" to represent the cost of labor per hour.
The technician worked on the computer for 5 hours, so the cost of labor would be 5y. Additionally, the technician charged $70 for parts. The total cost was $395. We can set up the following equation to represent the context:
5y + 70 = 395
This equation represents the total cost Sadie paid for the repair, which includes the cost of labor and parts.
Alternatively, we can use a tape diagram to represent the context. We can draw a rectangle and divide it into two parts, one representing the cost of labor and the other representing the cost of parts. The length of the labor part would be Five times the cost per hour (5y), and the length of the parts part would be $70.
]The length of the whole rectangle would represent the total cost ($395). We can label the unknown cost per hour as "y".
Therefore, we get the equation as : 5y + 70 = 395 if the computer for 5 hours and charged her $70 for parts. The total was $395.
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Clty Line What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
The measure of the angle formed by the intersection of the River Line and the Northeast Line is equal to: C. 42°.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles:
60° + (8x - 18)° + (3x + 6)° = 180°
60° + 8x - 18° + 3x + 6° = 180°
11x = 180° - (18° - 6° - 60°)
11x = 180° - 48°
11x = 132°
x = 132/11
x = 12
For the intersection of the River Line and the Northeast Line, we have:
R = (3x + 6)°
R = 3(12) + 6
R = 36 + 6
R = 42°.
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Complete Question:
What is the measure of the angle formed by the intersection of the River Line and the Northeast Line?
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