The required interest rate would be 6.9% to the nearest tenth of a percent.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
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two unit squares share the same center. the overlapping region of the two squares is an octagon with perimeter $3.5$. what is the area of the octagon?
The area of the octagon is 0.875 units square.
Two unit squares share the same center. The overlapping region of the two squares is an octagon with perimeter 3.5.
Area of a triangle:
We need to know how to calculate the area of a triangle, in order to solve this question. The area of a triangle with base b and height h is [tex]\frac{hb}{2}[/tex]. An octagon is a 2D figure with 8 sides.
Let A, B, C, D, E, F, G, and H be eight consecutive vertices of the octagon. Let 0 be the common center of the square units.
Draw the segments OA, OB, OC, OD, OE, OF, OG and OH, connecting the vertices with the common center O of the squares.
The segments divide the octagon into 8 concurrent triangles.
Perimeter of the hexagon=(AB+BC+CD+DE+EF+FG+GH+HA)In these triangles, AB, BC, CD, DE,EF, FG, GH, and HA are the bases; the height is 12 of a unit in all the triangles.
Thus, the area of the octagon=[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2}[/tex]×(AB+BC+CD+DE+EF+FG+GH+HA)
=[tex]\frac{1}{4}[/tex]×(Perimeter of the hexagon)=14×3.5=3.54=0.875
Therefore, the area of the octagon is 0.875 units square.
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A chemical company make two brand of antifreeze. The firt brand i 60% pure antifreeze, and the econd brand i 85% pure antifreeze. In order to obtain 80 gallon of a mixture that contain 70% pure antifreeze, how many gallon of each brand of antifreeze mut be ued?
To obtain 80 number of gallons of a mixture that contains 70% pure antifreeze, you must use 56 gallons of the 60% pure antifreeze and 24 gallons of the 85% pure antifreeze.
1. Calculate the total amount of antifreeze needed to make 80 gallons of the 70% mixture.
80 gallons x 0.7 = 56 gallons of antifreeze
2. Calculate the amount of 60% pure antifreeze needed.
56 gallons x 0.6 = 33.6 gallons of 60% pure antifreeze
3. Calculate the amount of 85% pure antifreeze needed.
56 gallons x 0.85 = 47.6 gallons of 85% pure antifreeze
4. Subtract the amount of 60% antifreeze from the total amount of antifreeze needed to determine the amount of 85% antifreeze needed.
56 gallons - 33.6 gallons = 22.4 gallons of 85% pure antifreeze
5. Round the amounts to the nearest whole number.
33.6 gallons of 60% pure antifreeze and 24 number of gallons of 85% pure antifreeze.
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What is the distance between PQ? Explain. Best explanation gets brainliest
The length of the line segment is given by the distance equation
D = 7.2 units
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the distance of the line segment between two points be D
Now , the equation will be
Let the first point be represented as P ( 1 , 6 )
Let the second point be represented as Q ( 7 , 2 )
Now , distance between P and Q is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
D = √ ( 1 - 7 )² + ( 6 - 2 )²
On simplifying the equation , we get
D = √ ( -6 )² + ( 4 )²
D = √ ( 36 + 16 )
D = √ 52
D = 7.2 units
Hence , the distance is 7.2 units
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write an equivalent expression by distributing the “-“ sign outside the parenthesis: -(-0.1p+4)
The equivalent of the expression -(-0.1p+4) is 0.1p-4
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example: 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x² + 2y + 1) = 6x² + 12y + 6.
Similarly -( - 0.1p + 4) can be written in another for by multiplying the negative sign with every term in the parentheses.
therefore -1× -0.1p + -1×4 = 0.1p -4
This means -(-0.1p+4) and 0.1p -4 are equivalent
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cathy has obtained a sample mean of 0.7 and , but she cannot remember if the sample size was 20 or 25. she accidentally erased the data file. find the correct sample size.
The sample size of the data which has a sample mean of 0.7 is 20.
What is mean?
Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
Cathy has obtained a sample mean of 0. 7 and, but she cannot remember if the sample size was 20 or 25,
Calculate the sample size as shown below,
As we know that the variance would be positive,
s² ≥ 1 / (n - 1) [Σ xi²-nx²]
0 ≥ 1 / (n - 1) [Σ xi²-nx²]
[10 - n × x × 0.7²] ≥ 0
n × x × 0.7² ≤ 10
n ≤ 10 / (0.7)²
n ≤ 20.408
Thus, the sample size is 20.
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32 to 28 decrease percentage
Answer:
Step-by-step explanation:
To calculate a percentage decrease, first calculate the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100.
In this case, our difference is 32-28=4
4 divided by 32= 4/32, and multiplying by 100 gives us 400/32=12.5
Therefore, the percent decrease is 12.5%
PLEASE HURRY,TEST QUESTION,LIMITED TIME!
Question- Write the standard form equation of the circle given the center of (-1,0) and the circumference of 8π. Show all work using the equation editor to calculate the missing pieces of the equation.
Answer: (x+1)^2 + (y-0)^2 = 8pi^2
Step-by-step explanation:
7) Graph the systems of linear equations on your calculator
Part B
Here’s a different way to partition the same function. Write a description of the partitioned function using known function types. Include function transformations in your description
With a negative leading coefficient, quadratic polynomials, and the horizontal offset for a scaled 1/x function.
Section 1's wiggles might be attributed to a variety of distinct purposes. A fourth-degree polynomial is maybe the simplest. It would have to have a negative leading coefficient in order to have downward-trending end behavior.
The curve in section 2 appears to represent either an exponential function or a scaled and translated version of 1/x. We prefer a version of 1/x because the latter is anticipated to approach the horizontal asymptote more quickly than is depicted above.
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the london school of economics and the harvard business school have conducted studies of how chief executive officers (ceos) spend their time. these studies have found that ceos spend many hours per week in meetings that include conference calls, business meals, and public events. suppose that the data below show the time spent per week in meetings (hours) for a sample of 25 ceos. 14 15 18 23 15 19 20 13 15 23 23 21 15 20 21 16 15 18 18 19 19 22 23 21 12 (a) what is the least amount of time spent per week on meetings?
The least amount of time spent per week on meetings for the sample of 25 CEOs is 12 hours.
The least amount of time spent per week on meetings for the sample of 25 CEOs can be found by looking at the lowest value in the data set. The data set provided above lists the time spent per week on meetings for a sample of 25 CEOs, and the least amount of time spent is 12 hours per week.
This is the smallest value in the data set, and it represents the minimum amount of time spent on meetings among the CEOs in the sample.
Note that this data is a sample of 25 CEOs and not the entire population of CEOs, so it is not representative of all CEOs. Additionally, the time spent per week on meetings is a quantitative variable, and it is continuous. Therefore, it is recommended to use measures of central tendency (mean or median) and measures of dispersion (standard deviation, range) to make inferences about the population.
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Brittany opened a checking account with $50 she received for her birthday. She deposits $5 of her allowance each week.
If someone can help mee it would be great
Answer: Yes it's 15
Step-by-step explanation:
20/100 x 75 = 15
can you answer this? please
[tex]55 \times 35 = [/tex]
On multiplying 55 × 35, the answer is 1925.
The simplest way to start teaching multiplication is to establish the relationship between the concept and addition, which your pupils should already be familiar with. Make sure your students understand the first principle of multiplication—that it is just repeated addition—before continuing on.
Your youngster can learn that multiplication is actually just a means to repeatedly add multiple groups of the same number by using objects like blocks and small toys. For instance, ask your youngster to arrange the blocks into six groups of three by writing the issue 6 x 3 on a sheet of paper.
5 5
× 3 5
------------
2 7 5
+ 1 6 5 ×
--------------
1925
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Are the linear expressions equivalent? Select from the drop-down menus to correctly complete the statement. The expression 5(x−3)+1 Choose... to the expression 2+5x−16 .
The expression that would render the both the sides equivalent is 3x+2-2
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: The expression 2+8x-16
To find its equivalent we have an incomplete expression 5(x-3)+1
Now 5(x-3)+1=5x-15+1
=5x-14
Thus Adding 3x+2-2 to this expression we get
5x-14+3x+2-2=2+8x-16
Therefore, we can deduce that the missing term must be 3x+2-2
Hence, The missing expression is 3x+2-2
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Answer the following questions:
1. For a triangle oriented similar to the triangle in Example 3, find the value of h if a = 6 and b = 24.
2. Leo is inspecting a 1 cm ∶ 1.5 m scale floor plan of his new house. The dimensions of his bedroom in the scaled plan are 2 cm by 3 cm. What is the area of Leo’s actual bedroom in square meters?
3. You jogged 2.4 miles in 30 minutes. At that rate, how long will it take you to jog 3.2 miles?
4. An airplane flies 100 miles in half an hour. How far can it fly in 1 1⁄4 hours at the same speed?
5. The currency in Tajikistan is the Somoni. The exchange rate is approximately 0.17 Somoni = 1 Philippine peso. How much money in Somoni would you get with ₱500?
6. A map scale designates 1 inch = 25 km. The distance between the two towns on the map is 3 inches. If a liter of gasoline can last you for 50 kilometers, how many liters of gasoline would you need to drive from the first town to the second?
Answer: Using the formula for similar triangles, you can find the value of h by multiplying b by the ratio of corresponding sides. If a = 6 and b = 24, then the ratio of corresponding sides is 6/24 = 1/4. Therefore, h = b * (1/4) = 24 * (1/4) = 6
To find the area of Leo's actual bedroom in square meters, you can use the scale factor of 1 cm : 1.5 m and multiply the dimensions of the scaled plan by this factor. If the dimensions of the scaled plan are 2 cm by 3 cm, then the actual dimensions of the bedroom are 2 cm x 1.5 m/cm x 3 cm x 1.5 m/cm = 3 m x 4.5 m = 13.5 square meters
To find how long it will take to jog 3.2 miles at the same rate, you can use the formula distance = rate x time. If you jogged 2.4 miles in 30 minutes, then you can find the rate by dividing distance by time, which is 2.4 miles / 30 minutes = 0.08 miles/minute. Therefore, time = distance / rate = 3.2 miles / 0.08 miles/minute = 40 minutes
To find how far an airplane can fly in 1 1/4 hours, you can use the formula distance = rate x time. If the airplane flies 100 miles in half an hour, then the rate is 100 miles / 0.5 hours = 200 miles/hour. Therefore, distance = rate x time = 200 miles/hour x 1.25 hours = 250 miles
To find how much money in Somoni you would get with ₱500, you can use the exchange rate of 0.17 Somoni = 1 Philippine peso. Therefore, 0.17 Somoni x ₱500 = ₱85 Somoni
To find how many liters of gasoline you would need to drive from the first town to the second, you can use the map scale and
Step-by-step explanation:
Use the unit circle to find the value of sec (0°).
a. Sec (0°) =undefined
b. Sec(0°) = 1
C. Sec (0°) = 0
d. Sec (0°) = 2
Please select the best answer from the choices provided
By using the unit circle , we found that the value of Sec(0°) is (b) Sec(0°) = 1 .
The Unit Circle is defined as a circle that have a radius of 1 which is centered at the origin of a coordinate plane.
The angle in the unit circle are measured in radians.
The Secant function, denoted by Sec(x), is defined as 1/Cos(x) ;
we have to find the value of Sec(0°) ;
So , at 0 degrees, the point (1,0) lies on the unit circle and
the x-coordinate of this point is 1 which is the cos(0) and
the value of Sec(0) = 1/cos(0) = 1/1 = 1
Therefore , the value of Sec(0°) is = 1 .
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3.3.8 in a precourse, anonymous survey of students in her introductory statistics course, one of the authors asked her students how many hours per week they expected to spend studying statistics outside of class. forty-nine students responded to that question, with an average of 8.2 hours and a sd of 3.79 hours. the data were not strongly skewed. a) identify the observational unit for this study. b) identify the variable of interest and whether it is categorical or quantitative. c) use the theory-based inference applet to calculate and report the 95% confidence interval for the parameter of interest. d) in the context of this study, was it valid to use the theory-based (t-distribution) approach to find a confidence interval? explain your reasoning. e) interpret the 95% confidence interval reported in part (c) in the context of the study.
Above 95% confidence interval for population mean =(6.7149 to 9.2051)
Given that,
3.3.8 One of the writers asked her students how many hours a week they anticipated studying statistics outside of class in a pre-course, anonymous survey for her introductory statistics course. The average response time was 8.2 hours, with a standard deviation of 3.79 hours, from 49 students. Data were not significantly skewed.
To find : a) specify the study's observational unit. b) Determine if the variable is categorical or quantitative and the variable of interest. c) compute and present the 95% confidence interval for the parameter of interest using the theory-based inference applet. d) Was it appropriate to determine a confidence interval using the theory-based (t-distribution) technique in the setting of this study?
sample mean x= 7.960
sample size n= 36.00
sample std deviation s= 3.68
std error sx=s/√n= 0.6133
for 95% CI; and 35 df, value of t= 2.030
margin of error E=t*std error = 1.245
lower bound=sample mean-E = 6.7149
Upper bound=sample mean+E = 9.2051
from above 95% confidence interval for population mean =(6.7149 to 9.2051)
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a rectangle is 9 cm longer than it is wide. the width is one seventh of the perimeter. find the length and the width.
If the rectangle is 9 cm longer than it's width , and the width is 1/7th of perimeter , then the length of rectangle is 15 cm and width of rectangle is 6 cm.
let the rectangle's length be = l cm ;
and let the width of rectangle is = w cm ;
the length is 9 cm longer than its width , that means ;
⇒ l = w + 9 ...equation(1)
and the width is 1/7 of perimeter , then
⇒ w = (1/7)(2l + 2w)
⇒ w = 2/7(l + w) .....equation(2) ;
substituting value of equation(1) in equation(2) ;
we get ;
⇒ w = (2/7) × ( w + 9 + w ) ;
on simplifying ,
we get ;
⇒ w = 6 .
from equation(1) ⇒ l = 6 + 9 = 15 .
Therefore , the length is 15 cm and width is 6 cm .
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Solve the system of equations.
Answer: y,x = -2,3 is your answer. I hope this helps!
Step-by-step explanation:
the lifetime of a certain brand of car battery has an exponential distribution with a mean of 60 months. find the probability that a randomly selected battery of this kind lasts longer than 70 months (round off to second decimal place).
The probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104(rounded off to the second decimal place).
The cumulative distribution function of an exponential distribution with a mean of 60 months is given by:
F(x) = 1 - e^(-x/60)
The probability that a randomly selected battery lasts longer than 70 months is given by:
P(X > 70) = 1 - F(70) = 1 - (1 - e^(-70/60)) = e^(-70/60) = 0.104
So, the probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104 (rounded off to the second decimal place).
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A representative sample is one that accurately reflects a larger a) control group. Correct Response b) population. c) correlation coefficient. d) dependent variable.
The statement would e: A representative sample is one that accurately reflects a larger population.
The correct answer is an option (b)
We know that the sampling is used to find insights and observations about a population group.
A representative sample is nothing but a sample / a subset of a population that accurately reflect the characteristics of the larger group.
For example, consider a class of 50 students with 25 girls and 25 boys.
We can generate a representative sample that might include ten students: five girls and five boys.
As we know the samples contain smaller, manageable versions of the larger group, they are useful in statistical analysis when population size is large.
Thus, a representative sample is used for obtaining insights and observations of the targeted population group.
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The complete question is:
A representative sample is one that accurately reflects a larger
a. dependent variable.
b. population.
c. control group.
d. correlation coefficient.
The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?
For the function y = f (x), the average rate of change on the interval - 1 ≤ x ≤ 3 is -2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph of the function f(x) is graphed and the graph is given.
The average rate of change is a measure of how much the function changed per unit, on average, over that interval.
For a function f(x) at interval [a,b], the average rate of change is given as -
[f(b) - f(a)]/(b - a)
The interval values is given as - [-1,3]
The value for f(a) as seen in the graph is - 4.
The value for f(b) as seen in the graph is - -4.
Substitute the values in the equation -
Average rate of change = [f(b) - f(a)]/(b - a)
A = (-4 - 4)/[3 - (-1)]
A = -8/(3 + 1)
A = -8/4
A = -2
Therefore, the value for average rate of change is -2.
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a study that surveyed a random sample of otherwise healthy high school students found that they are more likely to get muscle cramps when they are stressed. the study also noted that students drink more coffee and sleep less when they are stressed. (a) what type of study is this? observational experiment correct: your answer is correct. (b) can this study be used to conclude a causal relationship between increased stress and muscle cramps? yes no correct: your answer is correct. (c) state possible confounding variables that might explain the observed relationship between increased stress and muscle cramps. (select all that apply.) extra-curricular activities caffeine lack of sleep classes
This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.
(a) What kind of research is this?
"Observational study" is the study's type.
Reason: This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.
Can this data be used to draw a causal conclusion about the link between elevated stress levels and muscle cramps?
No, an observational study was unable to draw any conclusions about the link between elevated stress levels and muscle cramps. The Chi-square test can be used to determine the relationship between increasing stress and cramps.
(c) Describe any potential confounding factors that could account for the correlation between greater stress and muscle cramps.
Muscle cramps may be impacted by the increased stress.
In this case, the factors under consideration are qualitative variables. Count the number of times that high school students have visited a doctor with a muscular ailment.
Confounding factors for stress may include anxiety over taking the exam, less sleep, spending more time studying, eating less, drinking more coffee, and other factors.
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To rent a certain meeting room, a college charges a reservation fee of $35 and an additional fee of $5.80 per hour. he history club wants to spend less than $69.80on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room?
The possible amounts of time for which they could rent the meeting room is 1.71 hours
How to determine the hours?The question states that
The college charges a reservation fee of $35 and an additional fee of $5.80 per hour.The history club wants to spend less than $69.80on renting the meeting roomThis implies that
35x + 5.80x ≤69.80
Solving the inequality to have
40.8x ≤69.80
Making x the subject of the relation we have
x≤1.71
In conclusion it takes the college 1.71 of time for them to rent the meeting room
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Let f(x) = 4x + 3 and g(x)=x²-x+1. Perform the function operation and then find the domain.
g(x)-f(x)
g(x)-f(x) = (Simplify your answer.)
The domain of g(x) - f(x) is all real numbers, or (-∞, ∞).
What is the domain?
The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value). In other words, it is the set of values for which the function is valid and can be used without producing any errors or undefined results.
To perform the function operation g(x) - f(x), we need to subtract the function f(x) from the function g(x).
g(x) = x² - x + 1
f(x) = 4x + 3
g(x) - f(x) = x² - x + 1 - (4x + 3)
g(x) - f(x) = x² - 5x - 2
The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).
For the function g(x) - f(x) = x² - 5x - 2, there are no restrictions on the input values, meaning that any value of x can be plugged into the function to produce a valid output.
Therefore, the domain of g(x) - f(x) is all real numbers, or (-∞, ∞).
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What is the value of 4.3x10^5
Answer: The value of 4.3x10^5 is 430000.
Step-by-step explanation:
To find the value of 4.3x10^5, you need to multiply 4.3 by 10 raised to the power of 5. This can be written as 4.310^5.
The value of 4.310^5 is 430000.
SOMEONE PLS HELP TYSM
The median of the given set of numbers is 82.
What is Median?Median is the middle element when the data set is arranged in an increasing or decreasing order.
Given is a stem and leaf plot.
We have to write each of the corresponding number in stem attached with each of the corresponding number in leaf plot.
So the numbers in the first row will be 71, 75, 77 and 78.
Numbers in the second row will be 80, 80, 81, 82, 84, 85, 86, 86, 87, 89.
Number in the third row will be 95.
Writing the numbers from the plot, we will get the values as,
71, 75, 77, 78, 80, 80, 81, 82, 84, 85, 86, 86, 87, 89, 95.
The numbers are already in the increasing order.
There are 15 number of data in the set.
Median is the middle element, that is 8th element, which is 82.
Hence the median of the data is 82.
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A batch of bread requires 3 cups of flour. How many batches can you make with 2 cups of flour?
Answer:
Step-by-step explanation:
To find out how many batches of bread you can make with 2 cups of flour, you need to divide the amount of flour you have by the amount of flour each batch requires.We know that a batch of bread requires 3 cups of flour. To find out how many batches you can make with 2 cups of flour, you can divide 2 by 3:2 / 3 = 0.67Therefore, you can make 0.67 batches of bread with 2 cups of flour. However, since you can't bake a fraction of a batch, you can't make any batches of bread with 2 cups of flour, as it is not enough. You will need at least 3 cups of flour to make a batch of bread.
Maggie wants to purchase songs from a streaming service. Each song has a cost of x dollars. Which situation can be represented by this inequality?
8 + 4x < 12 + 3x
The inequality says that the cost of each song is less than 4 dollars.
Which situation can be represented by this inequality?We want to see which situation can be represented by the inequality below.
8 + 4x < 12 + 3x
Where we know that each song costs x dollars.
The situation represented by that inequality can be:
"8 dollars plus 4 songs has less value than 12 dollars plus 3 songs"
We can also simplify the inequality to get:
8 + 4x < 12 + 3x
4x -3x < 12 - 4
x < 4
We also can see that the cost of each song is less than $4.
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If the playing surface of a carom bored is a square of length 28 inches, what is the diagonal length of the playing surface?
Answer:
To find the diagonal length, you can use the Pythagorean theorem.
If one side is 28 inches, and the board is a square, the other side must also be 28 inches.
a = side 1
b = side 2
c = diagonal length
a^2 + b^2 = c^2
(28)^2 + (28)^2 = c^2
784 + 784 = c^2
1568 = c^2
Square root both sides.
c = about 39.6 inches diagonal length