On a certain hot​ summer's day, 560 people used the public swimming pool. The daily prices are $1. 50 for children and $2. 00 for adults. The receipts for admission totaled $991. 0. How many children and how many adults swam at the public pool that​ day?

The slope is of m = 7 and the y-intercept is of b = 10.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by one, y increases by 7, hence the slope m is given as follows:

m = 7.

Hence:

y = 7x + b.

When x = 1, y = 17, hence the intercept b is given as follows:

7 + b = 17

b = 10.

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The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

The given vector(v) is -3i+7j

The unit vector is found by dividing the vector by its magnitude

Unit vector of  [tex]$v=\frac{v}{\|v\|}$[/tex]

The formula of unit vector in the direction of a given vector is:

We have to find the magnitude first

So,

[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]

[tex]& \|v\|=\sqrt{58}[/tex]

The unit vector is:

The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,

[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]

Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

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The width of the mural (in feet) when it is finished is equal to 12.25 feet.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Scale factor = 2/5

For the width of the mural (in feet), we have:

2/5 = 4.9/x

x = (5 × 4.9)/2

x = 24.5/2

x = 12.25 feet.

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The required domain is x ≥ -4.So option(4) is correct.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

From the graph, we can see that curve is starting from -4 to infinity in x direction.

By baby curve method

x ≥ -4

Thus, required domain is x ≥ -4.So option(4) is correct.

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10 transactions have occurred in 2 months.

In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.

To create a frequency distribution:

Count the number of occurrences for each value (in this case, transactions).

Group the values into ranges (if applicable).

Tabulate the frequency (number of occurrences) for each value or range.

For this set of numbers, the frequency distribution is:

Transactions | Frequency

6 | 1

7 | 2

8 | 2

9 | 3

10 | 2

So, in 10 months, 10 transactions have occurred in 2 months.

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The volume of the cone with mentioned dimensions of height and diameter are 10,048 cubic inches.

The volume of come can be calculated by the formula -

V = πr²h/3, where V represents volume of the cone, r represents radius of the cone and h represents height of the cone. Furthermore, radius is half of the diameter. Hence, calculating radius first.

Radius = 40/2

Performing division on Right Hand Side of the equation

Radius = 20 inches

Keep the values in formula of cone to find the volume of the cone

Volume of the cone = (3.14 × 20² × 24)/3

Performing division on Right Hand Side of the equation

Volume of the cone = 3.14 × 20² × 8

Performing multiplication on Right Hand Side of the equation

Volume of the cone = 10,048 inch³

Thus, the volume of cube is 10,048 cubic inches.

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Answer:

14.16%

Step-by-step explanation:

[tex]=(\frac{44.27-38}{44.27} )(100)=(\frac{6.27}{44.27} )(100)=\frac{627}{44.27} =14.16[/tex]

Hope this helps

The greater ratio of boys to students in the class of Mrs. Henderson's class is, 0.67

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Mrs. Henderson has 16 boys in her class of 24 students

Mr. Gregory has 18 boys in his class of 30

Greater ratio = ?

Ratio in Mrs. Henderson =  number of boys/total students

                                         =   16/24

                                         =   2/3

                                         =    0.67

Ratio in Mrs. Gregory =  number of boys/total students

                                    =  18/30

                                    =   3/5

                                    =    0.6

Hence, the ratio is greater in Mrs. Henderson's class  0.67

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Answer: Number 2

Step-by-step explanation:

Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>

Answer:

15x-3

Step-by-step explanation:

Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:

Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

Given that,

One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level

To find: state the null and alternative hypotheses for the above scenario.

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

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Answer:373248

Step-by-step explanation:

72^3 = 373248

Answer:

Step-by-step explanation:

The rate of change, also known as the slope, between two points can be found using the formula:slope = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two points.To find the slope between the points (-1, 30) and (-6, 10), we can plug in the coordinates into the formula:slope = (10 - 30) / (-6 - (-1)) = -20/-5 = 4So the rate of change or the slope between the points (-1,30) and (-6,10) is 4.This means that the y-value of the second point is 4 units lower than the y-value of the first point for every unit you move to the left on the x-axis.

The solution to the inequality is (2, -2)

From the question, we have the following parameters that can be used in our computation:

y<-x and 2x+y>2

Express them as equations

So, we have

y = -x and 2x + y = 2

This gives

2x - x = 2

Evaluate

x = 2

Recall that

y = -x

So, we have

y = -2

Hence, the solution is (2, -2)

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Answer:

option (D) is the correct one ...

The missing interior angles of the hexagon is as follows:

∠X = 135 degrees

∠Y = 135 degrees

The polygon above has 6 sides. Therefore, the polygon is a hexagon. The sum of interior angles of a polygon is ( n − 2 ) × 180°.

where

The sum of interior angles in an hexagon is calculated as follows:

180(6 - 2) = 180(4) = 720 degrees

Therefore, the angles of x and y are congruent.

Hence,

let

∠x = ∠y = a

Therefore,

2a + 91 + 149 + 100 + 110 = 720

2a  = 720 - 450

2a = 270

a = 270 / 2

a = 135 degrees

Therefore,

∠x = ∠y = 135 degrees.

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The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

432 hamburgers.

We can write an equation to represent the information given.

Hamburgers + Cheeseburgers = 491

Cheeseburgers = Hamburgers - 59

Substitute the second equation into the first equation:

Hamburgers + (Hamburgers - 59) = 491

Solve for 'Hamburgers':

2Hamburgers - 59 = 491

2Hamburgers = 550

Hamburgers = 275

Since the question asks for the number of hamburgers, the answer is 275 hamburgers.

The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

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Answer: The percent was 12.5%

If 11 is Subtracted from both sides, the resulting inequality is 9 > -4

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

Initially, you have 11 > −2

If you subtract 11 from both sides, you will have:

11 -2 > −2-2

9 > -4

Thus, the resulting inequality will be 9 > -4

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When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .

A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.

if y=5 x

y= 7 and X = 4 , then

                         7= 5(4)

                          7 = 20

                         = 20/7

                      =     2.8

when Y =9 and X = 7 then,

                     9 = 5(7)

                         9 = 35

                          35/9

                      =    3.88

when Y = 6 and X = 4 then,

                          6= 5(4)

                           6= 20

                              20/6

                             = 3. 33

Missing function of table are 2.88 , 3.88,3.33

The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).

Incomplete question :

Create a table from y=5x. You can just do numbers like

Y 7. 9. 6

X 4. 7. 4 or sum I just need the table

Complete the table for the given rule.

Rule:y=5x

x, y

5,4,2

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As per the Pythagoras theorem, the width of the farmer's field  is 74.83 meters.

In math the term Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

The general form of the Pythagoras theorem is written as,

=> hypotenuse² = opposite side² + adjacent side²

Here we have know that a farmer is tilling his rectangular field.

Where the known length of the field is 54 meters and distance between opposite corners is 90 meters.

As we all know that here we have here is a triangle.

And then here we need to use Pythagorean Theorem is calculated as,

=> 50² + w² = 90²

When we simplify this one then we get,

=> 2500 + w² = 8100

=> w² = 5600

=> w = 74.83

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Answer:

which parallelogram?

Step-by-step explanation:

repost it and add a pic

Answer:  To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.

First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.

Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.

So, the slope-intercept form of Line A is y = -2x + 11

We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.

So, the slope-intercept form of Line B is y = 3x + 16

Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:

-2x + 11 = 3x + 16

Subtracting 3x from both sides:

-5x = 5

Dividing both sides by -5:

x = -1

Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:

y = -2(-1) + 11 = -2 + 11 = 9

So the point of intersection of Line A and Line

Step-by-step explanation:

Answer:

13 × 21=293

10/100×293=$29.3

If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.

The Rate Of Change is also known as "Slope" ,

The rate of change can be found by taking the derivative of the equation   ⇒ y = 7400x with respect to x.

The derivative of the equation "y = 7400x" with respect to x is  ;

⇒ dy/dx = d/dx(7400x) = 7400 .

Therefore ,  rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .

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CD is about 2.83 in length when C: (-3 , -4) D: (1 , -2) in coordinate geometry.

In coordinate geometry, the distance formula, which is the square root of (x2 - x1)2 + (y2 - y1)2, can be used to determine the length of CD.

In this instance, point C's coordinates are (-3, -4) and point D's coordinates are (1, -2). Using the distance formula with these values as input, we obtain:

√((1 - (-3))^2 + ((-2) - (-4))^2) = √(4 + 4) = √8 = 2.8284271247461903

In simpler terms, you can use the distance formula, which is the square root of the sum of the differences of their x- and y-coordinates squared, to determine the separation between two points in a coordinate plane.

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Answer:

Based on the weights assigned to these grades, Emily's weighted average in the class would be 77.6 marks.