Alexa won 80 super bouncy balls playing horseshoes at her school's game night. Later, she gave two to each of her friends.
She only has 8 remaining. How many friends does she have?
Answer:
Alexa has 36 friends
Step-by-step explanation:
80 - 8 = 72, if she gives 2 to each friend...
that would mean 2 · x = 72
to find x, divide 72 by 2,
72 ÷ 2 = 36 friends
A store manager wants to determine how much to pay her employees. The number of hours the employees work is x, and the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation 10y-30x=20 . The business owner states that the employees should be paid a wage given by the equation 6y+30x=60. If the two equations were added then simplified to determine hourly wage, y, how much would the employees be paid?
Answer:
The employees will work for 1 hour, will earn $5 per hour and will be paid $5
Step-by-step explanation:
System of Equations
The number of hours the employees work is x.
And the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation
10y-30x=20
The business owner states that the employees should be paid a wage given by the equation
6y+30x=60
Adding both equations we have:
16y = 80
Dividing by 16:
y = 80/16 = 5
Substituting into the first equation:
10*5-30x=20
Operating and simplifying:
50-30x=20
50 - 20 = 30x
30x = 30
x = 30/30 = 1
Thus, the employees will work for 1 hour, will earn $5 per hour and will be paid $5
In 1984, the median family income was $26 433. In 1989, the median family income was $34 213. a) Determine the annual rate at which the median income is increasing. b) Determine the equation for the median family income given a particular year. c) Use the equation to predict the median family income in 2010.
Answer:
Step-by-step explanation:
a) To determine the annual rate at which the median income is increasing, we can use the formula:
annual growth rate = (final value / initial value) ^ (1 / number of years) - 1
Using 1984 as the initial year and 1989 as the final year, we get:
annual growth rate = ($34,213 / $26,433) ^ (1 / 5) - 1
annual growth rate ≈ 5.05%
Therefore, the median family income is increasing at an annual rate of approximately 5.05%.
b) To determine the equation for the median family income given a particular year, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the dependent variable (median family income), x is the independent variable (year), m is the slope (annual growth rate), and b is the y-intercept (median family income in the initial year).
Using the values from 1984 and 1989, we can find the values of m and b:
m = 0.0505
b = $26,433
Therefore, the equation for the median family income is:
y = 0.0505x + $26,433
c) Using the equation y = 0.0505x + $26,433, we can predict the median family income in 2010 by substituting x = 26 (since 2010 is 26 years after 1984):
y = 0.0505(26) + $26,433
y ≈ $39,360
Therefore, we can predict that the median family income in 2010 was approximately $39,360.
The radius of a semi circle is 5.2 what is the circles primeter
The perimeter of the circle is 16.33
What is perimeter of a circle?Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it. If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.
The perimeter of a circle is expressed as;
C = 2πr
C = 2 ×3.14 × 5.2
C = 32.66
since it is a semi circle, the perimeter of the semi circle = 32.66/2
= 16.33 unit
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The cost of an apple is $1.20. What is the cost of 5 apples?
Answer:
0.24
Step-by-step explanation:
$1.20 ÷ 5 = 0.24
To check that we are going to multiply \(5 x 0.24 = $1.20\\\)
I hope this helps and have a great day!
pls help me :) i really dont like math
Answer:
Yes!
Step-by-step explanation:
Yes, every diameter of a circle is also a chord because a chord of a circle is any line connecting 2 parts of the circle's circumference.
A walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the
equation that represents the new path.
Answer:
y = 1/3 x +4
Step-by-step explanation:
m = 1/3
3 = 1/3(-3) + b
3 = -1 +b
b=4
Is y=-x+5 proportional
Answer:
yes
Step-by-step explanation:
I'm not entirely sure what your question is, but x is directly proportional to y, meaning as as x increases at a constant rate, y also increases at a constant rate.
what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30
The proportional relationship is y = 3x.
What is the proportional relationship?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Here, we have
Given:
x: 2, 6, 8, 10
y: 6, 18, 24, 30
We have to find the proportional relationship between x and y.
So, we can see from inspection and visual observation that there is a proportional relationship between x and y.
6 = 3 2, 18 = 3 6, 24 = 3 8, 30 = 3 10.
Hence, The proportional relationship is y = 3x.
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The sales tax rate in Chicago is about 10.5%. Calculate the amount you would need to pay in tax below. How much would you need to pay with tax $10
Answer:
Including the tax, you would need to pay $11.05
Step-by-step explanation:
10.5/100 * 10 + 10 is the formula
The tax itself, if you had to pay $10 for something, is $1.05
The radius of a circle is decreasing at a constant rate of 0.2 mm/sec. In terms of the circumference, C, what is the rate of change of the area of the circle in mm2/sec
Answer:
\(-0.2Cmm/sec\)
Step-by-step explanation:
List given and unknown information
\(\frac{dr}{dt}=-0.2mm/sec\\ \\\frac{dA}{dt}=?\\ \\A=\pi r^2\\\\C=2\pi r\)
Differentiate area with respect to time and make proper substitutions
\(A=\pi r^2\\\\\frac{dA}{dt}=2\pi r\frac{dr}{dt}\\ \\\frac{dA}{dt}=C(-0.2)\\ \\\frac{dA}{dt}=-0.2C\)
Therefore, the rate of change of the area of the circle, in terms of the circumference, C, is \(-0.2Cmm/sec\)
We want to compare two brake lights in terms of reaction times by drivers. We run an experiment in which a random sample of drivers is tested on both lights (each driver is tested on both lights), and we find that 60% of drivers in the sample react quicker to the new light as compared to the old. Which of the following could be the correct 95% confidence interval for the proportion of drivers who react more quickly to the new light? (Note, there is only one possible correct answer here, and you should not be actually calculating the CI).
answer : (0.53,0.67)
show how to get answer
The correct 95% confidence interval for the proportion of drivers who react more quickly to the new light is (0.53, 0.67).
To calculate the confidence interval for the proportion of drivers who react more quickly to the new light, we can use the formula:
CI = p ± zα/2 √((p(1-p))/n)
where p is the proportion of drivers who react more quickly to the new light, n is the sample size, and zα/2 is the z-score for the desired confidence level (in this case, 95% corresponds to zα/2 = 1.96).
Substituting the given values, we get:
CI = 0.6 ± 1.96 √((0.6*0.4)/n)
Since we don't know the sample size, we can't calculate the exact confidence interval. However, we can see that the margin of error is proportional to 1/√n, which means that larger sample sizes will result in narrower confidence intervals.
Based on the given answer choices, we can see that the margin of error is 0.07, which corresponds to a sample size of around 200. So, if we assume that the sample size is large enough to use the normal approximation, we can calculate the confidence interval as:
CI = 0.6 ± 0.07
which gives us (0.53, 0.67) as the correct answer.
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when these equations are added together, what will the overall equation be? assume that no equations need to be reversed.
On adding the provided equations, 4x +7y= 17 and 9x + 13y = 46 the resultant equation we will be getting is 13x + 20y = 63.
In order to perform addition of two equations together, we are needed to add the left-hand side of each equation and the right-hand side of each equation separately. This gives us:
(4x + 7y) + (9x + 13y) = 17 + 46
Combining like terms on both the sides, we will be getting ,
13x + 20y = 63
Therefore, from the above calculations this inference can be drawn that the overall equation is calculated to be 13x + 20y = 63.
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The complete question is :
4x +7y= 17
9x + 13y = 46
when these equations are added together, what will the overall equation be? assume that no equations need to be reversed.
3:45 a.m. to 12:00 p.m.
Answer:
8 Hours 15 Minutes
Step-by-step explanation:
12:00 p.m - 3:45 a.m = 8 Hours 15 Minutes
I need help with this ASAP!
Answer:
0,10
9,7
10,6
3,10
7,8
1,4
10,8
0,3
0,5
7,6
Step-by-step explanation:
Select the correct answer.
Which is the simplified form of the expression
If you answer can you try and do it step by step so I can understand it better :)
Answer:
the answer is B
\(3( \frac{7}{5} x + 4) - 2( \frac{ 3}{2} - \frac{5}{4} x)\)
\((3 \times \frac{7}{5} x) + (3 \times 4) - 2( \frac{3}{2} - \frac{5}{4} x)\)
\( \frac{21}{5} x + 12 - 2( \frac{3}{2} - \frac{5}{4} x)\)
\( \frac{21}{5} x + 12 + ( - 2 \times \frac{3}{2} ) + ( - 2 \times ( - \frac{5}{4} x))\)
\( \frac{21}{5} x + 12 - 3 + \frac{5}{2} x\)
\( \frac{21}{5}x + \frac{5}{2} x + 12 - 3\)
\( \frac{67}{10}x - 9 \)
Solve the equation. 6k - 12 = -24
First, add 12 to both sides of the equation:
\(6k-12+12=-24+12\)\(6k=-12\)Finally, divide both sides of the equation by 6:
\(6k/6\text{=-12/6}\)\(k=-2\)The perimeter of a rectangle is 56 meters, and its length is 15 meters. Which equation can be used to find the width of the rectangle?
50 points
Answer:
Step-by-step explanation:
2(L+B)
Where L is the length and B is the breadth.
A ladder is leaning against a wall at an angle of 70° with the ground. The distance along the ground is 86cm. Find the length of the ladder
Answer:
\(\boxed{x = 251.4 cm}\)
Step-by-step explanation:
Part 1: Sketching the triangle
We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.
We can then sketch this triangle out to visualize it (attachment).
Part 2: Determining what trigonometric ratio can solve the problem
Now, we need to refer to our three trigonometric ratios:
\(sin = \frac{opposite}{hypotenuse}\)
\(cos = \frac{adjacent}{hypotenuse}\)
\(tan = \frac{opposite}{adjacent}\)
Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.
Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.
By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.
Part 3: Solving for the unknown variable
Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.
The cosine function is provided: \(cos( \alpha) = \frac{adjacent}{hypotenuse}\), where \(\alpha\) is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.
\(cos (70) = \frac{86 cm}{x}\), where x is the unknown side/the hypotenuse.
\(x * cos (70) = \frac{86 cm}{x} * x\) Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.
\(\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}\), Evaluate the second fraction because the first one cancels down to just the unknown, x.
\(\frac{86}{cos(70)} = 251.4\), round to one decimal place.
Your final answer is \(\boxed{x=251.4cm}\).
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $26.30. The oil change for the other car required 7 quarts of oil and cost $30.80. How much is the labor fee and how much is each quart of oil?
Answer:
5*26.30-7*30.8
Step-by-step explanation:
I think
1. The average commute times for employees of a large company is 27 minutes. The commute time of 12 employees are 31, 10, 13, 42, 20, 23, 23, 27, 25, 31, 18, and 13. a) Determine the sample mean and the population mean. b) What is the estimated margin of error of the sample population, using standard deviation?
2. There are 10 students who started precalculus in 11th grade and 10 students who started precalculus in 12th grade. The first group has a mean final grade of 88% and the second group has a mean final scored of 81. The line plot shows the difference after 15 randomizations. Determine the difference in the means of the two groups and whether the difference of means is significant based on the line plot. Explain your answer. (has a picture)
3. The results of a survey show that the percent of adults in a certain town who want to change the name of the town is in the interval [0.78 ,0.86].
What is the point estimate for the percent who want to change the town’s name?
What is the poll’s margin of error?
Do you think the town is most likely to change its name? Why?
1. The sample mean is 24 minutes. The population mean is 27 minutes. The estimated margin of error of the sample population is 3.5 minutes.
2. The difference in the means of the two groups is 7%. The difference in the means is not due to chance.
3. The point estimate for the percent who want to change the town's name is 0.82. The poll's margin of error is 0.04.
How to calculate tie value1a) The sample mean is calculated as follows:
(31 + 10 + 13 + 42 + 20 + 23 + 23 + 27 + 25 + 31 + 18 + 13) / 12 = 24 minutes
The population mean is calculated as follows:
(31 + 10 + 13 + 42 + 20 + 23 + 23 + 27 + 25 + 31 + 18 + 13) / 27 = 27 minutes
b) The estimated margin of error is calculated as follows:
z * s / sqrt(n) = 1.96 * 6.2 / sqrt(12) = 3.5 minutes
2. The difference in the means of the two groups is calculated as follows:
88% - 81% = 7%
The point estimate for the percent who want to change the town's name is calculated as follows:
(0.86 + 0.78) / 2 = 0.82
The poll's margin of error is calculated as follows:
(0.86 - 0.78) / 2 = 0.04
3. I think the town is most likely to change its name, because the point estimate is greater than 0.5 and the margin of error is small. This means that it is likely that the majority of adults in the town want to change the name.
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Write an expression that represents the volume of a cube with side length 2x^3. (For any cube with side length s, v = s^3 = s.s.s^.)
A. 6x^6
B.6x^9
C. 8x^9
D.8x^6
Answer:
C. 8x^9
Step-by-step explanation:
(2x³)³=8x^9
What is the product of −314 and −112?enter your answer as a mixed number,.
Answer: 314 -(112)
-314 -(112)= -314 * -112
Step-by-step explanation:
The function f(x) is shown on the graph
If f(x) = 0, what is x?
O 0 only
O-6 only
O-2, 1, or 3 only
O -6, -2, 1, or 3 only
If f(x) = 0, the value of x are -1, 2 and 3.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables—the independent and dependent variables. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have f(x)= 0
As we know that the solution of the graph can be predicted by the number of times the lines of the graph touches the x axis.
Here when f(x)= 0 which also means that y =0 then values of x are -2, 1 and 3.
Thus, the value of x are -1, 2 and 3.
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indeed some help me plz
Answer:
3
Step-by-step explanation:
15-2x=3x
or,3x+2x=15
or,5x=15
or,x=15/5
Therefore, x=3.
2. Choose the expanded form for: 5.673 *
(5 x 1) + (6 x 1/10) + (3 x 1/100) + (7 x 1/1000)
O five and six hundred seventy three thousandths
O (5 x 10) + (6 x 1/10) + (7 x 1/100) + (3 x 1/1000)
O (5 x 1) + (6 x 1/10) + (7 x 1/100) + (3 x 1/1000)
Simplify the polynomial. Then find its value for the given value of the variable.
(full question attached as image)
Answer:
simplified: xy²value: 4Step-by-step explanation:
The polynomial is simplified by combining like terms. Like terms are identified more easily if the variables in each term are written in the same order. We usually like to use alphabetical order. Two of the like terms have opposite coefficients, so they cancel. The result is ...
(3 1/2 -2 1/2)xy² +(-2 4/5 +2 4/5)x²y
= xy² . . . . simplified expression
__
For x = 1, y = -2, the value of the expression is ...
(1)(-2)² = 4
the middle number; put the values in order from lowest to highest, then find the number that is exactly in the middle
a​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.
A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
A random variable is defined as a variable that has posses a single numerical value, and determined for each outcome of an event. That is a variable whose value is either unknown or a function that assigns values to each of an experiment's outcomes. It can be either discrete (having specific values) or continuous (any value in a continuous range). Generally, random variables are represented by capital letters for example, X and Y. For example consider the tossing of coin event, then the values Heads = 0 and Tails= 1 and we have a Random Variable "X". Hence, required answer is random variable.
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Complete question:
a _______ variable is a variable that has a single numerical value, determined bychance, for each outcome of a procedure.
what are the coordinates?? please help!!
Answer:
-3 is on the x coordiante and 5 is in y coordinate
so, its always written as (x,y)
stay safe
can i have brainliest
Step-by-step explanation: