The problem is asking us to calculate the probability that less than 200 of 500 cell phone calls selected at random will be spam, given that First Orion estimates 45% of all cell phone calls in 2019 will be spam. To solve this problem, we can use the normal approximation to the binomial distribution.
First, we need to find the mean and standard deviation of the binomial distribution. The mean is given by:
μ = n * p
where n is the number of trials (500) and p is the probability of success (i.e., a cell phone call is spam) on a single trial (0.45):
μ = 500 * 0.45 = 225
The standard deviation is given by:
σ = sqrt(n * p * (1 - p))
σ = sqrt(500 * 0.45 * (1 - 0.45)) = 11.79
Next, we can use the normal approximation to calculate the probability that less than 200 of the 500 cell phone calls selected at random will be spam. We need to standardize the value of 200 using the mean and standard deviation of the binomial distribution:
z = (x - μ) / σ
where x is the number of successes (i.e., spam calls) we're interested in (200):
z = (200 - 225) / 11.79 = -2.12
We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.12. This probability is approximately 0.017.
Therefore, the probability that less than 200 of the 500 cell phone calls selected at random will be spam is approximately 0.017 or 1.7%.
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Mark wanted to buy a new car for $43,500. The salesman told him that with rebate and discounts he could lower the price by 15%. What is the sale price of the car? What is the final cost of the car if Kentucky sales tax of 6% is added ?
The sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.
The sale price of the car after a 15% discount can be calculated as:
Sale Price = Original Price - Discount
Sale Price = $43,500 - 0.15($43,500)
Sale Price = $43,500 - $6,525
Sale Price = $36,975
The final cost of the car including 6% sales tax can be calculated as:
Final Cost = Sale Price + Sales Tax
Final Cost = $36,975 + 0.06($36,975)
Final Cost = $36,975 + $2,218.50
Final Cost = $39,193.50
Therefore, the sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.
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The orthogonal trajectories of s = 3a sin 0 is, where a is an arbitrary constant O 3 = csin Ота =ccos e O 73 = c cose T=csin e
Hi! To find the orthogonal trajectories of the given curve s = 3a sin θ, we first need to determine its differential equation by eliminating the arbitrary constant, a. The orthogonal trajectories should have slopes that are the negative reciprocal of the original curve's slopes.
1. Differentiate s with respect to θ:
ds/dθ = 3a cos θ
2. Solve for a:
a = (ds/dθ) / (3 cos θ)
3. Substitute the expression for a back into the original equation:
s = 3((ds/dθ) / (3 cos θ)) sin θ
4. Simplify:
s = (ds/dθ) tan θ
5. Find the orthogonal trajectories by taking the negative reciprocal of the original slope:
-1 = -ds/dθ / s
6. Rearrange to find the differential equation for the orthogonal trajectories:
ds/dθ = s
7. Integrate with respect to θ to find the orthogonal trajectories:
s(θ) = c * e^θ, where c is an arbitrary constant.
So, the orthogonal trajectories of the given curve s = 3a sin θ are s(θ) = c * e^θ.
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Define the set S = {a, b, c, d, e, f, g}. Give an example of a 4-permutation from the set S. Give an example of a 4-subset from the set S. How many subsets of S have two or more elements?How many subsets of S have 3 or 4 elements?
Set S has 840 permutations and 70 subsets of 4 elements, and [tex]2^7[/tex] - 7 - 1 = 120 subsets of 2 or more elements an example of a 4-permutation are {b, e, f, c}, and an example of a 4-subset is {a, d, g, e}.
An example of a 4-permutation from the set S would be {a, b, c, d}. An example of a 4-subset from the set S would be {a, c, e, g}.
To find how many subsets of S have two or more elements, we need to subtract the empty set and the singleton sets from the total number of subsets. The total number of subsets of S is [tex]2^7[/tex] = 128. There is only one empty set, and there are seven singleton sets. Therefore, the number of subsets of S with two or more elements is 128 - 1 - 7 = 120.
To find how many subsets of S have 3 or 4 elements, we can use the combination formula. The number of 3-element subsets of S is C(7,3) = 35, and the number of 4-element subsets of S is C(7,4) = 35 as well. Therefore, there are 35 + 35 = 70 subsets of S that have 3 or 4 elements.
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Solve
a. 0.00032x500 / 2,000,000
___ x 10 ^--
b. 15,000 x 0.0000007 / 0.005
___ x 10 ^--
The solution of the a) part is 8 x 10⁻⁸ and the solution to the b) part is 2.1 x 10⁰.
Simplify simply means to make an expression simple.
In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form.
a. To get the solution of 0.00032 x 500 / 2,000,000, follow these steps:
1. Multiply 0.00032 by 500, which equals 0.16.
2. Divide 0.16 by 2,000,000, which equals 8x10⁻⁸.
So, 0.00032x500 / 2,000,000 = 8 x 10⁻⁸.
b. To solve 15,000 x 0.0000007 / 0.005, follow these steps:
1. Multiply 15,000 by 0.0000007, which equals 0.0105.
2. Divide 0.0105 by 0.005, which equals 2.1.
So, 15,000 x 0.0000007 / 0.005 = 2.1 x 10⁰, since 10⁰ equals 1, and 2.1 remains the same.
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Q2: Find a root, using Bisection method and false position methods of an equation • f(x)=2x³-2x-5 between 1 and 3 (5 iteration) • f(x)=2*cos(x)-x between 1 and 3 (5 iteration) Hint(Solution correct upto 5 digit)
a = 1.25, b = 1.375, c = (a + b)/2 = 1.3125
f(c) = 2(1.3125^3) - 2(1.3125) - 5 = -0.04983520508
f(b)*f(c) = (2(1.375^3) - 2(1.375) - 5)(-0.04983520508)
Bisection Method for f(x) = 2x³-2x-5:
In this method, we first check if the function has opposite signs at the endpoints of the given interval. If yes, then we can be sure that there is at least one root in the interval. Then, we find the midpoint of the interval and check the sign of the function at the midpoint. Based on the sign, we either consider the left half or the right half of the interval for the next iteration.
Using this method with 5 iterations, we get:
Iteration 1:
a = 1, b = 3, c = (a + b)/2 = 2
f(c) = 2(2^3) - 2(2) - 5 = 1
f(a)*f(c) = (2(1^3) - 2(1) - 5)(1) = -5
Since f(a)*f(c) < 0, the root lies in the interval [1, 2]
New interval: a = 1, b = 2
Iteration 2:
a = 1, b = 2, c = (a + b)/2 = 1.5
f(c) = 2(1.5^3) - 2(1.5) - 5 = -1.375
f(b)*f(c) = (2(2^3) - 2(2) - 5)(-1.375) = 2.875
Since f(b)*f(c) > 0, the root lies in the interval [1, 1.5]
New interval: a = 1, b = 1.5
Iteration 3:
a = 1, b = 1.5, c = (a + b)/2 = 1.25
f(c) = 2(1.25^3) - 2(1.25) - 5 = -0.859375
f(b)*f(c) = (2(1.5^3) - 2(1.5) - 5)(-0.859375) = -1.94921875
Since f(b)*f(c) < 0, the root lies in the interval [1.25, 1.5]
New interval: a = 1.25, b = 1.5
Iteration 4:
a = 1.25, b = 1.5, c = (a + b)/2 = 1.375
f(c) = 2(1.375^3) - 2(1.375) - 5 = -0.2373046875
f(b)*f(c) = (2(1.5^3) - 2(1.5) - 5)(-0.2373046875) = 0.8305053711
Since f(b)*f(c) > 0, the root lies in the interval [1.25, 1.375]
New interval: a = 1.25, b = 1.375
Iteration 5:
a = 1.25, b = 1.375, c = (a + b)/2 = 1.3125
f(c) = 2([tex]1.3125^3[/tex]) - 2(1.3125) - 5 = -0.04983520508
f(b)*f(c) = (2([tex]1.375^3[/tex]) - 2(1.375) - 5)(-0.04983520508)
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Suppose that a particular brand of 5 inch candles has an average life of 27 hours with a standard deviation of six hours. If all possible samples of 4 candles were selected in the average life of the samples was determined, what would the mean of the distribution of the sample means be?
5
3
4
27
The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.
This is because the sample means would be expected to be centered around the population mean.
The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:
standard deviation of sample means = standard deviation of population / square root of sample size
In this case, the standard deviation of sample means would be:
6 / square root of 4 = 3
So the answer is 3.
So, the mean of the distribution of the sample means would be 3. Your answer: 3.
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In a recent school year, 91,863 of the students were girls and 80,492 of the students were boys. Among the girls, 19,598 dropped out of school, and among the boys, 31,419 dropped out. A student is chosen at random. Create a table to help you answer the question. Boys Girls Total Dropped Did not drop Total Given that the student is male, what is the probability that he did not drop out? Write your answer as a decimal rounded to 2 decimal places.
The probability that a male student did not drop out of school is 0.28 (rounded to 2 decimal places).
To answer the question, we need to use conditional probability. We are given that a student is male, and we need to find the probability that he did not drop out of school.
From the information given, we can fill in the table:
The probability of a student being a boy is:
P(boy) = number of boys / total number of students = 80,492 / 172,355 = 0.4666 (rounded to 4 decimal places)
The probability that a boy did not drop out is:
P(did not drop | boy) = number of boys who did not drop out / total number of boys = 49,073 / 80,492 = 0.6100 (rounded to 4 decimal places)
Therefore, the probability that a student is male and did not drop out of school is:
P(male and did not drop) = P(did not drop | boy) * P(boy) = 0.6100 * 0.4666 = 0.2847 (rounded to 4 decimal places)
So the probability that a male student did not drop out of school is 0.28 (rounded to 2 decimal places).
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What is the slope intercept equation of the line shown below
The slope of the given line is -1.
Given is a line passing through the points (-2, 3) and (4, -3) we need to find the slope of the line,
Slope = y₂ - y₁ / x₂ - x₁
Here, (x₁, y₁) and (x₂, y₂) are (-2, 3) and (4, -3),
So, the slope of the line =
Slope = -3-3 / 4+2
= -6 / 6
= -1
Hence, the slope of the given line is -1.
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The following polygons are similar find the scale factor of the small figure to the large figure 1-2
Answer:
1.5 and 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original.
1
scale factor = [tex]\frac{DF}{AC}[/tex] = [tex]\frac{21}{14}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
2
scale factor = [tex]\frac{8}{2}[/tex] = 4
A budget estimator predicts that a family of 4 will need $18,946 per
year to support the first person and $4,437 to support each additional
person. If Natalia works 38 hours per week for 50 weeks per year,
what is her minimum hourly wage to support her family of 4? (Round
your answer to the nearest cent.)
Answer:
$17 per hour
Step-by-step explanation:
Given,
The amount required to support first-person is $18,946 per year.
The amount required to support each additional person is $4,437 per year.
So, The amount required to support 3 additional people = $13,311
Total amount required to support 4 people = $18,946 + $13,311
= $ 32,257
Total number of hours Natalia works in a year = 38×50
= 1900 hours
The minimum required hourly wage for Natalia =
total yearly expenses÷ total working hours in a year
$32,257 ÷ 1900 = $16.97 per hour
≈$17 per hour
Natalia's minimum hourly wage to support her family of 4 is $17.00/hour.
To solve this problemWe must first assess the total annual cost of supporting the family in order to determine Natalia's minimum hourly income to support her family of four.
The budget estimator estimates that it will cost $18,946 per year to support the first person and $4,437 per year to sustain each additional person. Natalia has a total of four family members, so her total yearly support expenses would be as follows:
$18,946 + ($4,437 x 3) = $32,257
The annual salary of Natalia must then be determined based on her working hours. She would put in the following number of hours if she worked 38 hours per week for 50 weeks in a year:
38 hours per week x 50 weeks in a year = 1,900 hours.
By dividing the entire annual cost of providing for her family by the number of hours she works per year, we can determine her minimum hourly wage:
1,900 hours / $32,257 = $17.00/hour.
Therefore, Natalia's minimum hourly wage to support her family of 4 is $17.00/hour.
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if bruce and bryce work together for 1 hour and 20 minutes, they will finish a certain job. if bryce and marty work together for 1 hour and 36 minutes, the same job can be finished. if marty and bruce work together, they can complete this job in 2 hours and 40 minutes. how long will it take each of them working alone to finish the job?
Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.
Let's assume the job takes x hours for Bruce to complete alone, y hours for Bryce to complete alone, and z hours for Marty to complete alone.
From the first piece of information, we can create the following equation based on the work completed in 1 hour and 20 minutes (4/3 hours):
1/x + 1/y = 3/4
From the second piece of information, we can create the following equation based on the work completed in 1 hour and 36 minutes (8/5 hours):
1/y + 1/z = 5/8
From the third piece of information, we can create the following equation based on the work completed in 2 hours and 40 minutes (8/3 hours):
1/x + 1/z = 3/8
Solving these equations simultaneously, we can find that x = 5, y = 8, and z = 10.
Therefore, Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.
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Let a, b, c ∈ Z be arbitrary with 3 | a, 3 | b, and c
≡ 2 (mod 3). Prove ax + by ≡ c (mod 3) has no solution.
The solution for the equation ax + by ≡ c (mod 3) does not exist. Hence, it has no solution.
We need to prove that the equation ax + by ≡ c (mod 3) has no solution.
Since 3 | a and 3 | b, we know that a ≡ 0 (mod 3) and b ≡ 0 (mod 3).
Now let's look at the left side of the equation ax + by. Since a and b are both divisible by 3, their product with any integers x and y will also be divisible by 3.
Therefore, ax + by will always be divisible by 3 and can be written as ax + by ≡ 0 (mod 3).
However, we know that c ≡ 2 (mod 3), which means that c is not divisible by 3. Therefore, we can conclude that ax + by can never be congruent to c (mod 3), as their remainders when divided by 3 are different.
In other words, the equation ax + by ≡ c (mod 3) has no solution.
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please help! I have faith in you guys!
The probabilities and the expected values are calculated below
Evaluating the probabilities and the expected valuesNext cereal box wll contain blue or yellow
Here, we have
Yellow or blue = 15 + 5 = 20
Total = 50
So, we have
P(Yellow or blue) = 20/50
P(Yellow or blue) = 2/5
Arrival time before 7:30 am
Here, we have
Arrival time before 7:30 am = 7
Total time = 20
So, we have
P(Arrival time before 7:30 am) = 7/20
Team least likely
Convert the probabilities to decimal
So, we have
Nets = 0.67
Rockets = 0.5
Bucks = 0.8
Warriors = 0.375
This means that the team least likely to play in the championship game is 0.375
Section 7 in the game
Here, we have
P(7) = 35/250
In 150 times, we have
n(7) = 35/250 * 150
n(7) = 21
So, the number of times is 21
Expected students to eat chicken nuggets
Here, we have
P(Chicken) = 14/40
In 840 students, we have
n(Chicken) = 14/40 * 840
n(Chicken) = 294
Hence, the expected number of students to eat chicken nuggets is 294
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Describe all numbers x that are at a distance of 3 from the number 10. Express this using absolute value notation.
The numbers that are at a distance of 3 from the number 10 are 7 and 13.
To describe all numbers x that are at a distance of 3 from the number 10, we can use the absolute value notation. The distance between two numbers is given by the absolute value of their difference. So, the numbers x that are 3 units away from 10 can be expressed as:
| x - 10 | = 3
This means that the absolute value of the difference between x and 10 is equal to 3. To find the values of x that satisfy this equation, we can solve for x as follows:
x - 10 = 3 or x - 10 = -3
Adding 10 to both sides of each equation, we get:
x = 13 or x = 7
Therefore, the numbers that are at a distance of 3 from the number 10 are 7 and 13.
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When hired at a new job selling jewelry, you are given two pay options: Option A: Base salary of $19,000 year with a commission of 12% of your sales Option B: Base salary of $28,000 a year with a commission of 8% of your sales How much jewelry would you need to sell for option A to produce a larger income?
To calculate how much jewelry you would need to sell for option A to produce a larger income than option B, you need to set up an equation. Let's call the amount of jewelry sold "x".
Option A:
Base salary = $19,000
Commission = 12% of sales
Total income = $19,000 + 0.12x
Option B:
Base salary = $28,000
Commission = 8% of sales
Total income = $28,000 + 0.08x
To find out when option A produces a larger income than option B, we need to set the two equations equal to each other and solve for x:
$19,000 + 0.12x = $28,000 + 0.08x
0.04x = $9,000
x = $225,000
So, you would need to sell $225,000 worth of jewelry for option A to produce a larger income than option B.
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Use the range rule of thumb to identify the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high. A test is used to assess readiness for college. In a recent year, the mean test score was 21.6 and the standard deviation was 5.4. Identify the test scores that are significantly low or significantly high. What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice. A. Test scores that are between and (Round to one decimal place as needed. Use ascending order.) B. Test scores that are less than (Round to one decimal place as needed.) C. Test scores that are greater than (Round to one decimal place as needed.)
Previous question
Using the range rule of thumb:
A. Test scores that are between 10.8 and 32.4 (rounded to one decimal place) are neither significantly low nor significantly high.
B. Test scores that are less than 10.8 (rounded to one decimal place) are significantly low.
C. Test scores that are greater than 32.4 (rounded to one decimal place) are significantly high.
The range rule of thumb states that we can identify significantly low or high values by looking at data points that are more than two standard deviations away from the mean.
In this case, the mean test score is 21.6 and the standard deviation is 5.4.
To find test scores that are significantly low, we need to subtract two standard deviations from the mean:
21.6 - (2 x 5.4) = 10.8
Therefore, test scores that are significantly low are less than 10.8. The answer is B. Test scores that are less than 10.8.
To find test scores that are significantly high, we need to add two standard deviations to the mean:
21.6 + (2 x 5.4) = 32.4
Therefore, test scores that are significantly high are greater than 32.4. The answer is C. Test scores that are greater than 32.4.
Test scores that are neither significantly low nor significantly high are between 10.8 and 32.4. The answer is A. Test scores that are between 10.8 and 32.4.
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A battery is shaped like a cylinder. It has a height of 5.5 inches and a base radius of 2.2 inches. What is the volume of the battery? Round to the nearest tenth.
Answer:
The volume is 83.6 cubic inches.
Step-by-step explanation:
We know that the battery is cylindrical, so we can use the formula:
[tex]\pi r^{2} h[/tex]
We can use 3.14 for [tex]\pi[/tex], and we know that the radius is 2.2 with a height of 5.5.
Let's set up the equation:
3.14 · 2.2² · 5.5= volume
=83.5868, which rounded to the nearest tenth would equal 83.6.
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A mayor running for re-election claims that during his term, average municipal taxes have fallen by $200. A conscientious statistician wants to test this claim. He surveys 36 of his neighbors and finds that their taxes decreased (in dollars) as follows: 150, 205, 108, 188, 186, 195, 154, 169, 270, 190, 168, 185, 142, 267, 157, 218, 183, 200, 192, 250, 100, 234, 182, 231, 209, 235, 182, 173, 197, 171, 191, 150, 174, 206, 200, 171 The statistician assumes a population standard deviation of $43. Do you think the statistician should reject the mayor's claim? Why or why not?
We do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.
Step 1: Hypotheses Set-Up:
H0: The average tax decrease during the mayor's term is not $200 (μ ≠ 200)
Ha: The average tax decrease during the mayor's term is $200 (μ = 200)
Step 2: The significance level α = 0.05
Step 3: Compute the test statistic:
We will use a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30.
The formula for the t-test statistic is:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size
Substituting the values, we get:
t = (186.6 - 200) / (43 / √36)
t = -1.98
Step 4: Testing Procedure:
The test is a two-tailed test since we want to determine whether the average tax decrease is significantly different from $200, not just whether it is greater or less than $200.
At a significance level of 0.05 with 35 degrees of freedom, the critical values for a two-tailed test are ±2.03.
The p-value for the test is the probability of getting a t-value as extreme or more extreme than -1.98, given the null hypothesis. From a t-distribution table, we find that the p-value is approximately 0.057.
Step 5: Decision:
Since the calculated t-value (-1.98) is less than the critical value (-2.03) and the p-value (0.057) is greater than the significance level (0.05), we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.
Step 6: Interpretation:
At a 5% significance level, we do not have enough evidence to reject the null hypothesis that the average tax decrease is not $200.
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Question 4 (1 point) In his Ted Talk, James Lyne presents the following statistic(s) in his TedX talk about malware and cybercrime. There are 30,000 new infected websites every day. 8 new internet users join every second. 250,000 new pieces of malware appear every day. All of the above. Question 2 (1 point) Why is traditional supply chain management (SCM) ineffective for e-commerce? It is based on manual processes and separation of functions It is based more on manufacturing, whereas e-commerce is mostly retail distribution E-commerce is gnerally more specialized and is not a good fit for traditional SCM It usually doesn't include e-procurement functions.
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
4)
We have,
James Lyne mentions that there are:
- 30,000 new infected websites every day
- 8 new internet users join every second
- 250,000 new pieces of malware appear every day.
All the above are statistics.
2)
E-commerce is generally more specialized and requires a more integrated approach to supply chain management. Additionally, traditional SCM is based on manufacturing, whereas e-commerce is mostly retail distribution.
Finally, traditional SCM usually doesn't include e-procurement functions, which are essential for e-commerce supply chain management.
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
Thus,
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
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Dakota earned $15.75 in interest in Account A and $28.00 in interest in Account B after 21 months. If the simple interest rate is 3% for Account A and 4% for Account B, which account has the
greater principal? Explain.
The account that has the greater principal is account B.
Which account has the greater principal?
Simple interest is a linear function of the amount invested (the principal), the interest rate and the duration of the investment.
The formula that can be used to determine simple interest is:
Interest = principal x time x interest rate
Principal = interest / (time x interest rate)
Principal in account A = $15.75 / (0.03 x (21/12)) = $300
Principal in account B = $28 / (0.04 x (21/12)) = $400
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A boy who is flying a kite lets out 300 feet of string which makes an angle of 52 with the ground. Assuming that the string is stretched taut, find, to the nearest foot, how high the kite is above ground.
The height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.
We can use trigonometry to solve this problem. Let h be the height of the kite above the ground. Then, the opposite side of the triangle formed by the kite string and the ground is h, and the adjacent side is 300 feet. The angle between the ground and the kite string is 52 degrees.
We can use the tangent function to find the value of h:
[tex]tan(52) = h/300[/tex]
Multiplying both sides by 300, we get:
h = 300 t[tex]an(52)[/tex]
Using a calculator, we find:
h ≈ 433.76 feet
Therefore, the height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.
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Compound i street at what was an investment made that obtains $136.85 in interest compounded quarterly on $320 over four years
The interest rate of an investment made that obtains $136.85 in interest compounded quarterly on $320 over four years is 69.44%.
How to determine the interest rate?In Mathematics and Financial accounting, the compound interest on an investment can be calculated by using this mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n} )^{nt}[/tex]
Where:
A represents the future value.r represents the interest rate.n represents the number of times compounded.P represents the principal.T represents the time measured in years.By substituting, we have the following:
[tex]136.85 = 320(1 + \frac{r}{4} )^{4 \times 4}\\\\136.85 = 320(1 + \frac{r}{4} )^{16}[/tex]
136.85/320 = (1 + 0.25r)¹⁶
136.85/320 = (1.25r)¹⁶
0.42765625 = (1.25r)¹⁶
r = 0.6944 = 69.44%
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Complete Question:
At what interest rate was an investment made that obtains $136.85 in interest compounded quarterly on $320 over four years?
For what value of A, the binary number 1000A12 represents 35?
The value of A such that the binary number is 35, must be A = 1.
How to find the value of A?We want to find the value of A such that:
1000A1 represents the number 35.
Remember that each of these numbers are the coefficient of the correspondent powers of 2, then we can write:
1000A1 = 1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵
Solving that we will get:
1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵ = 1 + 2A + 32
And that must be equal to 35, then:
1 + 2A + 32 = 35
2A = 35 - 33
2A = 2
A = 2/2 = 1
That is the value of A.
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Could you please help me find x
Answer:
x = 3√3
Step-by-step explanation:
You want the middle-length side of a 30°-60°-90° triangle whose short side is 3.
Special trianglesThere are two "special" triangles in trigonometry. The ratios of their side lengths are used in many algebra, trig, and geometry problems.
30°-60°-90° triangle has sides in the ratios 1 : √3 : 2
45°-45°-90° isosceles right triangle has sides in the ratios 1 : 1 :√2
ApplicationThe triangle shown in this problem is a 30°-60°-90° right triangle with a short side of length 3. You want the middle-length side (x), which the above tells us is √3 times the length of the short side.
x = 3√3
__
Additional comment
You can use the trig relation ...
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
For this triangle, this means ...
x = 3/tan(30°)
x = 3/(1/√3) = 3√3
A suitable calculator can show this in the desired format.
QUESTION 14 During oxygen consumption measurement the participants V2 was t.minand coa was. Umin What was the participants at that point in time ove your answer to decimal places QUESTION 15 The follo
Measurement is the process of obtaining the quantity or size of something, usually expressed in numerical values. It is a crucial aspect in various fields, including science, engineering, and mathematics. When it comes to measuring physical activity or exercise, oxygen consumption measurement is a commonly used method. It involves measuring the amount of oxygen that an individual consumes while exercising, which provides insight into their metabolic rate and energy expenditure.
In the given scenario, the participant's V2 was measured in units of t.min, and their coa was measured in units of Umin. To determine the participant's oxygen consumption rate at that specific point in time, we need to use the formula VO2 = V2/((t2-t1) x (coa-cob)). Here, t1 and t2 represent the start and end time of the measurement, while cob and coa represent the initial and final carbon dioxide levels.
Since we do not have information about the start and end times or the carbon dioxide levels, we cannot accurately determine the participant's oxygen consumption rate. Therefore, we cannot provide a decimal value as requested in the question.
In regards to Question 15, there seems to be incomplete information, and therefore, we cannot provide a response. However, it is essential to note that accurate and precise measurements are crucial in obtaining reliable data and making informed decisions in various fields.
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Which expression is equivalent to 3218y = 8√3y, if y+0?
O A. 12V/2y²
OB. 46
O c. 4√/15y
O D. 46y
The equivalent expression to 3218y = 8√3y is 4√(15) / 15y when y is not equal to zero. Option C is the correct answer.
To find an equivalent expression to 3218y = 8√3y when y is not equal to zero, we can start by dividing both sides of the equation by 8y, giving us:
3218y / 8y = 8√3y / 8y
Simplifying the right-hand side, we get:
3218 / 8 = √3
Squaring both sides, we get:
(3218 / 8)² = 3
Simplifying the left-hand side, we get:
130071.25 = 3
Dividing both sides by 3, we get:
y = 4√(15) / 15
Therefore, the expression that is equivalent to 3218y = 8√3y when y is not equal to zero is an option (C) 4√(15) / 15y. Option (D) 46y is not equivalent to the original expression because it does not involve the square root of 3. Option (A) 12V / 2y² and option (B) 46 are also not equivalent to the original expression because they involve different values and operations than those in the original expression.
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Find the interest earned. Then, find the balance.
P = $500
r = 3.5%
t = 3 years
The balance after 3 years is $552.50.
We have,
To find the interest earned, we can use the simple interest formula:
I = Prt
where I is the interest earned, P is the principal (starting amount), r is the interest rate (as a decimal), and t is the time (in years).
Substituting the given values, we get:
I = 500 x 0.035 x 3
I = $52.50
Therefore, the interest earned is $52.50.
To find the balance, we need to add the interest earned to the principal:
Balance = Principal + Interest
Balance = $500 + $52.50
Balance = $552.50
Therefore,
The balance after 3 years is $552.50.
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Determine which of the values is a solution of 4t+6≤10
The values that are solution of stated inequality expression are -8,-4,0 and 1.
The stated expression represents inequality. Hence, the solution will provide a range rather than a specific number as a resultant value. We will solve it in similar method to inequality.
Rearranging the expression in terms of 4t
4t ≤ 10 - 6
Subtracting the digits on Right Hand Side of the expression
4t ≤ 4
Rewriting the expression
t ≤ 4/4
Dividing the value on Right Hand Side of the equation
t ≤ 1
The values will be 1 or less than 1. Thus, the solution values are -8,-4,0 and 1.
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The complete question is -
Determine which of the values is a solution of 4t+6≤10
Values = -8,-4,0,1,3,7
Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.
Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of
To predict the value of y when x=10 is an example of Extrapolation. So, the correct answer is (b) extrapolation.
Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.
In this case, using the equation y = –3x + 21 to predict the value of y when x = 10 is an example of extrapolation because 10 is outside the range of the original x-values.
Using a line of best fit with the equation y = -3x+21 to predict the value of y when x = 10 is an example of extrapolation in statistics.
Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.
Ricardo's next step to construct the circumscribed circle for △XYZ would be to construct the perpendicular bisector of YZ
In this case, constructing the perpendicular bisector of YZ would give Ricardo the center of the circumscribed circle, which is equidistant from the three vertices of the triangle.
Complete Question:
Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.
Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of
a) correlation
b) extrapolation
c) causation
d) intrapolation
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If z is a standard normal variable, find the probability. Round your answer to four decimal places. The probability that z lies between -0.55 and 0.55 O A. 0.9000 OB. -0.9000 O C. -0.4176 OD. 0.4176
The probability that z lies between -0.55 and 0.55 is 0.4176. So, the correct option is option OD. 0.4176.
To find the probability that z lies between -0.55 and 0.55 for a standard normal variable, we'll use the standard normal table (also known as the z-table).
Step 1: Look up the z-score of -0.55 in the z-table. This gives us the area to the left of -0.55, which is 0.2912.
Step 2: Look up the z-score of 0.55 in the z-table. This gives us the area to the left of 0.55, which is 0.7088.
Step 3: Subtract the area to the left of -0.55 from the area to the left of 0.55 to find the probability between the two z-scores: 0.7088 - 0.2912 = 0.4176.
Therefore, the probability that z lies between -0.55 and 0.55 for a standard normal variable is approximately 0.4176 (rounded to four decimal places).
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