Sam surveyed his classmates to find out if they played a sport after school or practiced in the
school band
- 14 of his classmates played a sport
- of those 14 who played, 5 participated in the school band
- 8 students played in the school band, and out of those 8, 3 did not play sports
- there were 10 students who did not play a sport nor participate in the school band
Create a two way table to represent the data and answer the following questions

Answer:

12 mph

Step-by-step explanation:

First we're going to start by finding the difference in miles from the first route to the second route.

The first route is 120 miles and the second is 20% more than the first. To find the difference you should first multiply the 120 by 20%.

120*0.2=24

You then need to add the additional 24 miles to the original 120 to find the distance of the second route.

120+24=144

After we will begin to find the mph expected speed for both routes.

The first route was 120 miles and it was expected to take 2 hours to get there. This means you need to divide 120 by 2 to find out how many miles they were traveling within one hour.

120/2=60

So the expected mph for the first route would be 60.

We want to repeat the same thing for the second route.

144/2=72

The mph for the second route was 72.

Now you need to find out how much faster the mph was for the second route than the first by subtracting the first from the second.

72-60=12

The second route was 12 mph faster than the first.

Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). It is called by GEMS.

An effective acronym for teaching pupils the hierarchy of operations is PEMDAS.

The PEMDAS rule explains to pupils how to solve multi-step arithmetic problems and in what sequence to complete the operations to arrive at the right solution.

Groupings, Exponents, Multiplication or Division, Subtraction or Addition is referred to as GEMS. All grouping symbols, including parentheses, brackets, and braces, are referred to as groupings. The acronym GEMS has been adopted to take the role of PEMDAS. These can be used in place of one another.

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The amount of time he spent on the bicycle is 5.5 hours.

Jim began a 167​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking.

The whole trip took 6 hours. Jim walks at a rate of 4 miles per hour and rides at 30 miles per​ hour.

The amount of time he spent on the bicycle can be calculated as follows;

speed = distance / time

distance = speed × time

Therefore, total distance is as follows:

let

x = time spent walking

167 = 4x + 30(6 - x)

167 = 4x + 180 - 30x

167 = -26x + 180

167 - 180 = -26x

x = -13 / -26

x = 1 / 2

Time spent on bicycle = 6 - 0.5 = 5.5 hours.

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Answer:

x = 9

Step-by-step explanation:

x = the missing side

24/8 = x/3

8(x) = 24(3)

8x = 72

x = 9

====================================================

Explanation:

The slanted left-most sides of the figures are 24 and 8, when moving from left to right.

Let's reverse the direction and move from right  to left. The jump from 8 to 24 is "times 3", which is the scale factor when moving from the smaller figure to the larger figure.

The smaller figure has 3 up top. Apply the "times 3" scale factor to get 3*3 = 9 as the top side length of the larger figure.

In other words, every side of the smaller figure is tripled to get the larger figure.

----------------

Here's another way to solve.

24/8 = x/3

24*3 = 8*x .... cross multiplying

72 = 8x

8x = 72

x = 72/8

x = 9 is the final answer.

The measure of angle B crossing the river perpendicularly is 110°.

When the sum of the two angles is 180° they are said to be supplementary.

When the sum of the two angles is 90° they are said to be complementary.

Given, Bridge A crosses the river at an exterior angle of (2x),  Bridge B crosses at an angle of (4x-6) and these two angles are supplementary.

So, The sum of these two angles are 180°.

Therefore,

4x - 6 + 2x = 180°.

6x = 174°.

x = 174°/6.

x = 29°.

So, The measure of the angle B is (4(29) - 6)°.

= 116 - 6.

= 110°.

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It will take 7 years for the account balance to reach $11,688.69.

To find how long will it take for the account balance to reach $11,688.69

we will use the compound interest formula that is

[tex]$ \text A = \text P(1 + \frac{\text r}{\text n})^{\text {nt}}[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Given that, P = $7,171

A = $11,688.69

r = 7%

n = 12

t = to find

Substitute the details in the formula and we get

[tex]$11688.69 = 7171(1 + \frac{0.07}{12})^{12t}[/tex]

[tex]$ \text t=\frac{\log _{\frac{1207}{1200}}\left(\frac{1168869}{717100}\right)}{12}[/tex]

t = 7.000003 = 7 years

Thus, It will take 7 years  for the account balance to reach $11,688.69.

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Answer:

-----------------------------

Use compound interest equation:

Substitute the given to find the value of t:

Answer:

Step-by-step explanation:

second one

The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

A quadratic equation is a second-order equation written as ax² + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

To solve two order system of equations using substitution, follow these steps:

Step 1. Choose one equation and solve it for either of the one variables.

Step 2. In the other equation, substitute the value get from step 1.

Step 3. Solve the new equation.

Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.

Step 5. Check the solution in both original equations.

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Customer #2 has the smallest total bill, including tax and tip.

From the information, three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3.

For customer #1:

(1.06(12.95))(1.15) = 15.79;

The tip is 0.15(1.06(12.95)) = 2.06.

For customer #2:

1.06x = 11.65; x = 10.99; 20%

The tip = 0.2(10.99) = 2.20;

total = 11.65+2.20 = 13.85.

For customer #3:

1.06(11.50) + 0.18(11.50) = 14.26;

The tip is (0.18)(11.50) = 2.07.

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Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.

1. Which customer has the smallest total bill, including tax and tip?

Answer:

15

Step-by-step explanation:

x/3+10=15

(x+30)/3=15

x+30=15×3

x+30=45

x=45-30

x=15

Answer:

First you need to put the variable, x, in a fraction

     [tex]\frac{x}{3} + 10=15[/tex]

In this case, 10, is a positive integer, so because its a whole number, we put it with 15 on the other side of the equal sign. Then the +10 will become -10.

   [tex]\frac{x}{3} =15-10[/tex]

Then its easier to calculate, 15 - 10 is 5.

     [tex]\frac{x}{3} =5[/tex]

After that you put 5 over 1 and crisscross the equation.

    [tex]\frac{x}{3} =\frac{5}{1}[/tex]

x times 1 is x itself, and 3 times 5 is 15

   [tex]x=15[/tex]

So in the end x = 15

Have a wonderful day! :-)

The average rate of change of g over the interval −8 ≤ t ≤ 2 is equal to -0.5 or -1/2.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(t) over the interval [-8, 2]:

a = -8; g(a) = 1

b = 2; g(b) = -4

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (-4 - 1)/(2 - (-8))

Average rate of change = -5/10

Average rate of change = -0.5 or -1/2.

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Complete Question:

What is the average rate of change of g over the interval −8 ≤ t ≤ 2?

Answer:

B) -3

Step-by-step explanation:

(y - y₁) / (x - x₁) = slope

(8-2) / (m-5) = -3/4

cross-multiply to get:

-3(m-5) = 24

distribute -3 to get:

-3m + 15 = 24

subtract 15 from each side to get:

-3m = 9

m = -3

The solution for 4ˣ⁺³ = 7 using change of base formula is -1.596

To solve 4ˣ⁺³ = 7 using change of base formula log base b of y equals log y over log b, we are going to use logarithm rules.

If f(x) = g(x), then ln(f(x)) =  ln(g(x)). Thus,

ln( 4ˣ⁺³) = ln(7)

Using log rule:

[tex]\log _{a} x^{b} = b \log _{a}(x)[/tex]

ln (4ˣ⁺³) = ln(7)

(x+3) · ln(4) = ln(7)

(x+3) · ln(2²) = ln(7)

(x+3) · 2ln(2) = ln(7)

x+3 = ln(7) / (2ln(2))

x  = [ln(7) / (2· ln(2))] - 3

x = -1.596

Thus, the solution is x = -1.596

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Answer:

Did he round up?

Step-by-step explanation:

Constant variance, also known as homoscedasticity, is a statistical property where the variance of a variable is equal across all values of the variable.

This means that the variability of the variable is consistent, no matter what the value of the variable is. Mathematically, this is expressed by the formula:

Var(X) = σ^2

where Var(X) is the variance of the variable X, and σ^2 is the same across all values of X.

For example, if we look at the heights of a group of people, we may find that the variance of their heights is equal to 25 cm, no matter what the heights are. In this case, the variance of the heights is 25 cm, and this variance (25 cm) is the same for all the heights in the group.

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Gender inequality refers to the unequal distribution of rights, opportunities, and resources between individuals based on their gender. There are many forms of gender inequality, but some common ones include economic inequality, educational inequality, health inequality, political inequality, violence against women, social inequality and intersectionality.

Economic inequality: This refers to the unequal distribution of wealth, income, and resources between men and women. This can manifest in various forms, such as the gender pay gap and lack of representation in leadership positions.

Educational inequality: This refers to the unequal access to education and the resulting disparities in literacy rates and educational attainment between men and women.

Health inequality: This refers to the unequal access to healthcare and the resulting disparities in health outcomes between men and women.

Political inequality: This refers to the underrepresentation of women in politics and leadership positions, as well as the lack of policies and laws that promote gender equality.

Violence against women: This refers to the widespread problem of physical, sexual, and emotional abuse against women.

Social inequality: This refers to the unequal distribution of social status, power, and privilege between men and women, which can manifest in various forms of discrimination, prejudice, and bias.

Intersectionality: This refers to the ways in which gender inequality intersects with other forms of inequality, such as race, class, and sexuality, creating complex and interconnected forms of disadvantage for certain individuals and groups.

It's important to note that Gender inequality can manifest in various forms and it can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life. Therefore, it's crucial to understand and address gender inequality in all its forms.

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Students have 52.5 lb. weight in water.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A student weighs = 70 lb.

And, About 3/4 of a person's weight is water.

Since, A student weighs = 70 lb.

Hence, Students weighs in water = 3/4 of 70 lb.

                                                   = 3/4 × 70

                                                   = 52.5 lb.

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The value of the expression of the percentage as the friend details is; 0.04888....... and as such the friend is not correct

Percentages are usually calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Now, we are given the number 4.8% with 8 having a bar over it.

A bar over a number is called  vinculum  and it means that the number is being repeated indefinitely after a decimal point.

This tells us that our given number can now be expressed as;

4.888.....%

This is because from the definition of  vinculum , 8 is repeated indefinitely. Thus, this can be simplified as;

4.888...../100 = 0.04888.......

Thus, the friend is not correct in conclusion.

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The three numbers are: 23, 25, 27, The boy is 140 cm tall, the father is 140 + 30 = 170 cm, and the sister is 70 cm tall.

In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

The terms 3x + 5 and 14 are separated by the word "equal" in the equation 3x + 5 = 14. The three main formats for linear equations are the slope-intercept form, standard form, and point-slope form.

Two expressions are combined with an equal sign to form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. It is possible to solve this equation, and the answer reveals that the value of the variable x is 7.

Let the the first number is : x

So, the other two numbers are :x+2, x+4

a) x+(x+2)+(x+4)=75

3x+6=75

3x=69

X=23

The three numbers are: 23, 25, 27

b)The sister's height is denoted as x. Two times, since the boy is twice as tall. His height is 2x + 30 because the father is 30 centimeters taller than the boy. The total height is 3.8 meters, or 380 centimeters. You can now create an equation.

x + 2x + 2x + 30 = 380

assemble similar terms

5x = 350

x = 70

The boy is 140 cm tall,

the father is 140 + 30 = 170 cm,

and the sister is 70 cm tall.

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The slope of the line that contains points (2, -3) and (8, -2) is equal to 1/6.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 - (-3))/(8 - 2)

Slope (m) = 1/6

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The volume of a rectangular solid tool box would be 2,052 cubic inches.

Rectangular solids are three-dimensional shapes with six equal rectangles for sides. To find the volume of the rectangular solid tool box, we can use this following formula:

Volume = length x breadth x height

In this case, we are given that:

The length of the tool box = 19 in

The breadth of the tool box= 12 in

The height of the tool box= 9 in

We can find the volume by using the formula above:

Volume = 19 in x 12 in x 9 in

Volume = 2052 in³

As the result, the volume of the rectangular tool box would be 2052 cubic inches.

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The left side of the equations is equal to the right side for the values (3/14,5/14).

What is a system of equations?

A system of equations is a set of two or more equations that contain multiple variables. The goal is to find the values of the variables that make all the equations in the system true at the same time. There are different methods to solve a system of equations, such as substitution, elimination, and graphing.

To solve the system of equations given, we can use the substitution method:

1-s = 3r

7s = 4 - 6r

We can start by solving the first equation for one of the variables.

1-s = 3r

s = 1 - 3r

Now we can substitute this expression of s into the second equation

7(1 - 3r) = 4 - 6r

7 - 21r = 4 - 6r

-14r = -3

r = 3/14

Now we can substitute this value of r into either equation to find the value of s

s = 1 - 3r

s = 1 - 3(3/14)

s = 1 - 9/14

s = 5/14

So, the solution of the system of equations is (r,s) = (3/14,5/14)

We can check by substituting the solution into the original equations.

3r = 1 - s = 1 - 5/14 = 9/14

7s = 4 - 6r = 4 - 6(3/14) = 4 - 18/14 = -14/14 = -1

The solution is correct, since the left side of the equations is equal to the right side for the values (3/14,5/14)

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The value of x in the square is 5√2 centimetres.

A square is a quadrilateral with 4 sides equal to each other. The square has side length 5 times x centimetres and the diagonal length is 50 centimetres.

Therefore, the side x can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore,

50² = (5x)² + (5x)²

2500 = 25x² + 25x²

2500 = 50x²

divide both sides by 50

x² = 2500 / 50

x² = 50

square root both sides of the equation

x = √50

x = √25 × 2

x = 5√2 centimetres

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Answer:

1=yes

2=no

3=no

4=no

5=yes

6=yes(im not sure on this last one)

Step-by-step explanation:

If no vertical line can intersect the curve more than once, the graph does represent a function.

Answer:

Graph 1= It's a function

Graph 2= No

Graph 3= No

Graph 4= No

Graph 5= Yes

Graph 6= Yes

Step-by-step explanation:

Answer: The measure of the third side of a triangle, when the measures of the other two sides are 13 in and 27 in, must be greater than the difference between the measures of the other two sides (which is 27 in - 13 in = 14 in) and less than the sum of the measures of the other two sides (which is 27 in + 13 in = 40 in).

This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.

Therefore the range of the measure of the third side of a triangle with side lengths 13 in and 27 in is:

(14 in < x < 40 in)

or

[x > 14 in and x < 40 in].

It is also important to note that any value of x within this range will produce a valid triangle, however any value less than 14 in or greater than 40 in will not.

Step-by-step explanation:

The resulting quadrilateral have the following vertices: A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5), D'(x, y) = (1, 1). (Correct choice: B)

Herein we have the case of a quadrilateral, that is, a polygon with four vertices: A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2), D(x, y) = (4, 4), whose image is the result of a dilation with a scale factor of 1 / 4 about the origin on Cartesian plane. The polygon is contracted by contracting each of five vertices, whose formula is shown below:

P'(x, y) = k · P(x, y)

Where:

If we know that k = 1 / 4, A(x, y) = (- 4, 6), B(x, y) = (- 2, 2), C(x, y) = (4, - 2) and D(x, y) = (4, 4), then the coordinates of the resulting polygon:

A'(x, y) = 0.25 · (- 4, 6)

A'(x, y) = (- 1, 1.5)

B'(x, y) = 0.25 · (- 2, 2)

B'(x, y) = (- 0.5, 0.5)

C'(x, y) = 0.25 · (4, - 2)

C'(x, y) = (1, - 0.5)

D'(x, y) = 0.25 · (4, 4)

D'(x, y) = (1, 1)

The vertices of the resulting quadrilateral are A'(x, y) = (- 1, 1.5), B'(x, y) = (- 0.5, 0.5), C'(x, y) = (1, - 0.5) and D'(x, y) = (1, 1).

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The line that passes through (12, 5) and (12, 9) is a vertical line, and its equation is:

x = 12

We know that we have a line that passes through points (12, 5) and (12, 9).

Notice that the x-value of the two points is the same one, then we will have a vertical line of the form:

x = a

The x-value in both points is 12, then the constant value of the line is 12, thus the equation for the line that passes through these two points is:

x = 12.

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Step-by-step explanation:

Solution

The correct option is A Yes, it is.

Given Line:

2

x

+

3

y

=

5

Standard Line :

a

x

+

b

y

=

c

Given line has two variables

x

and

y

where both

x

and

y

have power of

1

similar to standard form of line. So,

2×+3y=5 is a line in two variables.

The y-intercept indicates the y-value when the x-value is 0.

What does the y-intercept look like?

When a linear equation is expressed in slope-intercept form (y=mx+b), the constant variable b stands in for the y-intercept. As an illustration, the variable b corresponds to the number 8 in the equation y=6x+8. The y-intercept is shown here.

In regression, what does the y-intercept stand for?

In regression analysis, the point at which the regression line crosses the y-axis is known as the constant term. The y-intercept is another name for the constant.

                       The easiest way to depict the overall picture of what the collected data is indicating is with a straight line, which is what a linear regression does. It aids in our ability to determine whether the two things under investigation are related or have a correlation.

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To solve the inequality -1/2 > 3/5, we can start by multiplying both sides of the inequality by the least common multiple of the denominators, which is 10, to get rid of the fractions. This gives us:

-1/2 * 10 > 3/5 * 10

-5 > 6

This inequality is not true, since -5 is not greater than 6. So the solution set is the empty set, or { }.