Swimming Pool On a certain hot summer's day, 240 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $510.75. How many children and how many adults swam at the public pool that day?

Using the roller coaster as an example, draw a right triangle.

Use h to symbolize the horizontal distance.

The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.

30² = h² + 25².

Assemble similar phrases.

h² = 30² - 25².

horizontal separation

In (a), there is:

h² = 30² - 25².

This results:

h² = 275

Take both sides' roots.

h = 16.58

Consequently, 16.58 feet are the horizontal distance.

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Answer:

Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.

Answer:

y=-3

Step-by-step explanation:

A line of symmetry is the line where a function can be folded in half evenly. Here it occurs at y=-3

line of symmetry, the line at which point the graph begins to mirror itself, Check the picture below.

The expression which has product of two binomials is (5-n)(n+7).

An expression is combination of variables, numbers and operators.

Binomials are expressions containing the sum (or difference) of two terms.

The expression (x + 3)(x + 2) is the product of two binomials.

(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y

(pq)(qp) is not the product of binomials because pq and qp are products.

3x(2x+5) is not the product of binomials because 3x is not a sum or difference.

6x-2y is also not because it is one binomial, not two multiplied together.

(5-n)(n+7) is the product of two binomials.

Hence, (5-n)(n+7) is the expression which has product of two binomials.

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The discount is $3.75 and the amount next week will be $21.25

This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.

The discount will be:

= 15% × $25

= $3.75

The amount next week will be:

= $25 - $3.75

= $21.25

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Answer:

Step-by-step explanation:

Answer:

y=-2/3x+4

Step-by-step explanation:

Rise/run (from the y-intercept to the next point you go down 2 and then to the right 3)

Y-intercept (where the line touches the y-axis) 4

Based on the above, the number of 3-points that they make is 25.

Simultaneous equation is a form of two equations that have to be solved at the same time. Thus, the number of 2 points made is 17, while that of 3 points is 25.

A set of equations that has to be solved simultaneously so as to determine the values of the unknown variables is termed simultaneous equation.

The given question would result to a simultaneous equation as follows;

let the number of 2 points made by represented by m, and that of 3 points by n.So that;

m + n = 42  ..................

i2m + 3n = 109  ...............

ii multiply equation 1 by 3 and equation 2 by 1 to have;3m + 3n = 126 ............

iii 2m + 3n = 109 .............

iv subtract eqaution iv from iii

m = 17

substitute the value of m in equation 1 to have:

m + n = 4217 + n = 42n = 42 - 17   = 25m = 17, n = 25

Thus the number of 2 points made was 17, while that of 3 points made was 25.

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Five water glasses each minute, one minute to fill the cooler.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

divide 150 by 30 equal 5

= 5

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A sampling error is the difference between a population parameter and a sample statistic.

Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.

Thus, the difference is defined as sampling error.

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if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.

To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.

Number of Classes = 720

Number of Rooms Required = Number of Classes = 720

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One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

The graph of the function has a horizontal asymptote at y = -3, hence:

c = -3.

For a and b, they can assume any non-negative values, hence we attribute these following values:

a = 1, b = 2.

The graph is given at the end of the answer.

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Answer:

2(x+8)=126

Step-by-step explanation:

GD is the bisector of CGE and 126 and the angle CGE are equal

Answer:

(8.25, 9.75)

Step-by-step explanation:

To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:

distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944

Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:

C = ¼ * A + ¾ * D

where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:

C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)

Therefore, the point C is located at the coordinates (8.25, 9.75).

The solution is given as,
Two-digit  numbers                 Multiples of 3             Three-digit numbers
     30                                      3,30, 333,                            333    

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333

Thus, It is shown that the numbers are placed in their appropriate positions.

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In  linear equation, He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.  

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Using linear function concepts, it is found that:

Seth starts closer to the school in the bus.

He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

From the graph of the bus, when he takes the bus, he is 13 miles from the school, as he starts at position 4 and ends at 17.

At his friend house, he is 13 miles from the school only after 3 minutes, which means that the bus will be closer.

The scenario with the greater speed is the one with the higher slope, that is, higher rate of change, which is the change in distance divided by the change in time.

In the bus, change of 13 miles in 24 minutes, thus

       mᵇ = 13/24 = 0.5417

   From the friend's house, change of 2 miles in 3 minutes, thus

   mf = 2/3 = 0.6667

Thus, he travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

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Answer:

554

Step-by-step explanation:

x + 2551 - 2551 = 3105 - 2551

x = 554

Answer:

[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]

Answer:

70.5%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of the 12-month-old baby boys are normally distributed:

[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]

where X is the weight of the baby boy.

To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).

Calculator input for "normal cumulative distribution function (cdf)":

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]

Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).

Step-by-step explanation:

A

for a linear function the slope ratio has to be the same between every pair of data points.

between (1, 4) and (2, 8) we have

x changes by +1 (from 1 to 2).

y changes by +4 (from 4 to 8).

the slope is

+4/+1 = 4

between e.g. (2, 8) and (3, 16) we have

x changes by +1 (from 2 to 3).

y changes by +8 (from 8 to 16).

the slope here is +8/+1 = 8.

which is not the same as 4.

so, it is not a linear function.

it is an exponential function.

B.

the function is actually

f(x) = y = 2^(x+1)

an exponential function is of the form

y = a^x

in our case we have

4 = a¹ = 2²

8 = a² = a¹×2 = 2² × 2 = 2^(2+1)

16 = a³ = a²×2 = a¹×2×2 = 2²×2×2

we see

f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)

C.

the average rate of change is

(the difference of the function results at the interval ends) / (the difference of the interval ends).

so, in our case

(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12

the average rate of change between stations 2 and 4 is 12 (or 12/1).

Answer:

Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to

Step-by-step explanation:

The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]

Given in the question,

The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]

The measure of an arc = is 36 inches.

According to the attached figure,

Let us consider the arc length = L

Let radius = r

As per the question L = 36'

Let the radius be

To calculate the length of the arc we need to use the formula,

L = r x θ

36 = r x θ

θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1

Now according to the area of the sector of the circle,

A = [tex]r^{2}[/tex] x θ / 2

121 = [tex]r^{2}[/tex] x θ / 2

[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )

[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex]  ----- equation 2

r = [tex]\frac{2 * 121 }{36}[/tex]

r = 6.72 cm.

Now if the radius is = 6.72 cm

Diameter = 2 x radius

= 2 x 6.72

= 13.44 cm

Area of the circle = [tex]\pi r^{2}[/tex]

= [tex]\pi[/tex] x 6.72 x 6.72

= 144.87 [tex]cm^{2}[/tex]

Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]

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Answer:

The value of n in this equation is 5.

Step-by-step explanation:

This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.

Answer:

I tried as I can to solve it

By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet

What is area of rectangle?

The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula

Area = [tex]l \times b[/tex]

Length of the median = 300 feet

Width of the median = 8 feet

Area of the median = 300 [tex]\times[/tex] 8 = 2400 sq. feet

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We require a more accurate and objective measure to determine the association between the two variables because visual exams are primarily subjective. We employ the linear correlation coefficient to express the degree and direction of the association between two variables:

[tex]r=\frac{\sum \frac{\left(x_i-\bar{x}\right)}{s_x} \frac{\left(y_i-\bar{y}\right)}{s_y}}{n-1}[/tex]

where the sample means and standard deviations of the x's are x and sx, respectively, and the y's are y and sy, respectively. n is the sample size. .

A different method of calculating the correlation coefficient is:

[tex]r=\frac{S_{x y}}{\sqrt{S_{x x} S_{y y}}}[/tex]

[tex]\begin{aligned}& \text { where } S_{x x}=\sum x^2-\frac{\left(\sum x\right)^2}{n} \\& S_{x y}=\sum x y-\frac{\left(\sum x\right)\left(\sum y\right)}{n} \\& S_{y y}=\sum y^2-\frac{\left(\sum y\right)^2}{n}\end{aligned}[/tex]

In honor of Karl Pearson, who created the linear correlation coefficient in the first place, it is also known as Pearson's product moment correlation coefficient. This metric quantifies the strength of the linear, or straight-line, relationship between the two variables as well as its positive or negative direction.

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Answer:

Your answer should be [tex]\frac{\pi }{7}[/tex]

Step-by-step explanation:

Looking at the x-axis we can say that is our b.

Period Formula: 2π/b.

x-axis is from 0 to 20.

b = 14 because of the rise to rise.

2π/14 = π/7

The segments in the blank provided is GH/FH=IH/JH so that the equation is true

Similar triangles differ in size but have the same form. Corresponding angles are identical in comparable triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.

The triangle similarity criteria are:

AA (Angle-Angle)

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

In the given question

<GHP=<IHJ (vertically opposite angles)

<JIH=<HPG (alternate angles)

From AA similarity critera

triangles JHI ~ triangle GHP

Hence

GH/FH=IH/JH

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The length of second lawn is found as the 36 sq. m.

For the stated question-

First lawn:

Area = length x width

A = 6 x 4 = 24 sq. m.

Second lawn:

A2 = length x width

6 x A = L x 4

6 x 24 = L x 4

L = 6 x 6

L = 36 sq. m

Thus, the length of the second lawn is found as the 36 sq. m.

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Answer:

Step-by-step explanation:

36 is the answer

The properties of the triangles created from the original triangle based on triangle congruency rules are as follows;

SSS: The triangle created using the lengths of the three sides of the original should have the same length and angles as the original

The triangle formed using SSS is a unique triangle and no other triangle has similar dimensions

SAS: The lengths of the sides and the measure of the angles should be the same

The triangle created using SAS is a unique triangle and there is not a way to have a third side that has a different length

ASA; The triangle formed using the ASA of the original triangle should have the same length as the same lengths and angles as the original triangle

The triangle formed using ASA is a unique triangle and there is not a way to create a triangle that has a different side length.

Two triangles are congruent if the lengths of the three sides of one triangle are congruent to the three sides of the other triangle or if they meet the other conditions of triangle congruency.

Length of first measured side of the triangle = 52 units

Angle made by the first measured side with the horizontal = 41°

Length of the second measured side of the triangle = 87 units

Angle the second measured side makes with the horizontal = 33°

Length of the third measured side of the triangle = 113 units

Angle the third side makes with the horizontal ≈ 6.5°

Let the vertices of the first side be A and B, we get;

∠A = 180° - (41° + 33°) = 106°

∠C = 33° - 6.5° = 26.5°

∠B = 41° + 6.5° = 47.5°

SSS: The SSS (Side-Side-Side) congruency postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Therefore, the lengths of the sides and the measures of the angles of the triangle created using the lengths of the three sides of the original triangle will be the same as the original triangle.

The SSS congruency postulate indicates that the triangle created using the same lengths of the three sides of the original triangle is a unique triangle and there are no other triangles having the same side lengths but different angles

SAS: The Side-Angle-Side, SAS, congruency postulate states that if the adjacent sides and an included angle of a triangle are congruent to two adjacent sides and an included angle of another triangle, then the two triangles are congruent.

Therefore, the triangle formed using two sides of the original triangle and the included angle between them will have the same length as the sides of the original triangle, and the triangle formed using the SAS of the original triangle is unique

The length of the third side of the triangle created using the SAS measurement is always the same as the length on the original triangle

ASA: The Angle-Side-Angle, ASA, congruency postulate states that if two angles and the included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.

The triangle formed using the ASA is a unique triangles and therefore and there is no way to create a triangle that has a different side length

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