On a certain hot​ summer's day, 354 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $548.25. How many children and how many adults swam at the public pool that​ day?

2185 people make up the sample size.

What is proportion?

An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.

The formula used to determine sample size (n) is as follows:

n =  p(1 - p) (z²/ e² )

Where z = 1.96 with a 95% confidence interval (), p is the proportion, and e is the margin of error.

z = 1.96, p = 0.35, e = 0.02

n =  0.35(1 - 0.35) (1.96²/ 0.02²)

n = (0.2275)(9604)

= 2184.91

n ≈ 2185

2185 people make up the sample size.

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The integer value of x is 6.

What is a side of a triangle?

The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices.

Here, we have

Given,

the lengths of the sides of a triangle are x, 5, and 8.

x² + 5² < 8²

x² + 25 < 64

x² < 39, now perfect squares less than 39 are 36, 25, 16, 9, 4, 1.

x² + 5² = 8²

x² + 25 = 64

x²  = 39, No integer values.

x² + 5² > 8²

x² + 25 > 64

x² + > 39

Here the possible integer values are infinite.

Hence, the integer value of x is 6.

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If you have 29 pencils and gave 13 away to your friend, you subtract what you gave away from what you have.

[tex]29-13\\=\fbox{16}[/tex]

Equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0

What is the equation of the line?

A straight line's equation is y = mx + c, c is the height at which the line crosses the plane, and m is the gradient. y -axis, often known as the y -intercept. The gradient m is the slope of the line, which is the percentage increase in the y-coordinate relative to the x-coordinate.

Given:

Passing point of line , (-2,8)

Slope of the line = 2

Equation of the line having passing point (a,b) and slope m become

y - b = m (x - a)

Equation of the line ⇒ y - 8 = 2(x + 2)

⇒ y - 8 = 2x + 4

⇒ 2x - y + 4 + 8 = 0

⇒ 2x - y + 12 = 0

Therefore, equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0.

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Complete Question
What is the equation of a line that contains point(-2,8) and has a slope of 2?

In the kickball teams, Lee has the ability to put nine players on each team.

What does "greatest common factor" (GCF) mean?

The common number that each term in a group of terms shares, also known as the greatest common factor (GCF), is

All of the students who signed up for kickball teams from two classes are being put together into teams by Lee.

45 students from the one school have signed up to play on the kickball team. Let compose this number in factor structure as,

45 = 3*3*5

because both numbers contain the number three twice. Therefore, GCF = 3*3 GCF = 9 is the greatest common factor of two numbers.

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Full Question = Lee is forming kickball teams that include all of the students who signed up from two schools. Each team must have the same number of players and be from the same school. 45 students from the one school have signed up to play on the kickball team. What is the greatest number of players Lee can put on each team?

The upper bound for the area is 4527.7056 cm²  and the lower bound for the perimeter is 278 cm.

Area (upper bound) = 4527.7056 cm²

Perimeter (lower bound) = 278 cm

The length and width of the rectangle have been ROUNDED to the nearest tenth. Let's calculate what their actual measurements could be:

LENGTH: rounded to 87.3, actual is between 87.25 and 87.34

87.25 is the lowest number it could be that would round it UP to 87.3

87.34 is the highest number it could be that would round DOWN to  87.3

WIDTH: rounded to 51.8, actual is between 51.75 and 51.84

51.75 is the lowest number it could be that would round it UP to 51.8

51.84 is the highest number it could be that would round DOWN to 51.8

To find the Area of the upper bound, multiply the highest possible length and the highest possible width:

A = 87.34 × 51.84 = 4527.7056

To find the Perimeter of the lower bound, calculate the perimeter using the lowest possible length and the lowest possible width:

P = 2(87.25 + 51.75) = 278

The region is the quantity that expresses the volume of an area at the aircraft or on a curved floor. The vicinity of a plane region or aircraft place refers to the area of a shape or planar lamina, at the same time as floor region refers to the region of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of material with a given thickness that might be necessary to style a version of the shape, or the quantity of paint important to cover the surface with an unmarried coat. it's far the 2-dimensional analog of the length of a curve (a one-dimensional idea) or the extent of a stable (a three-dimensional idea).

The area of a shape can be measured by means of comparing the shape to squares of a hard and fast size. inside the worldwide system of devices (SI), the usual unit of the region is the square meter (written as m2), which is the region of a square whose sides are one meter long. A form with a place of three rectangular meters might have an equal area as 3 such squares. In arithmetic, the unit rectangular is described to have placed one, and the region of any other shape or floor is a dimensionless actual quantity.

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Complete question: -

The lengths of a rectangle have been measured to the nearest tenth of a centimeter they are 87.3cm and 51.8cm what is the upper bound for the area and the lower bound for the perimeter

Answer:

y= -1/2x+2

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

To find slope we use y2-y1/x2-1

I will use points (4,0) and (0,2) to show it

2-0/0-4)

2/-4

-1/2 is the slope

y= -1/2x+b

We also know the y intercept because the Line intersects the y axis when y=2

y= -1/2x+2

Hopes this helps

The probability that a teenage boy has a cholesterol level greater than 200 is 0.11507.

Let the distribution of teenage boys' cholesterol levels be x

According to the question,

X follows a Normal distribution with

mean = 170

Standard deviation = 25

Hence, the variance = 25² = 625.

Hence X ~ N(170,25)

Now we need to find P(X>200)

= 1 - P(X<200)

Now to find this we need to convert the problem to a standard normal distribution

for this, we use the formula

P(X<x) = P(Z<x-mean/sd)

Therefore,

P(X<200)

= P(Z<(200 - 170)/25)

= P(Z<30/25)

= P(Z<1.2)

According to Z table,

P(Z<1.2)

= 0.88493

Hence, P(X>200)

= 1 - 0.88493

= 0.11507

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The surface area of the resulting solid is 40 cm².

A cube is a three-dimensional figure that has 6 faces and 12 edges and 8 vertices. All of the edges of a cube are of the same length.

If the volume of each of the two cubes is 8 cm³, then the length of its edge is 2 cm.

V = e³

8 = e³

e = 2 cm

Two cubes are glued together. Either side by side or put on top of each other, the dimension of the resulting solid is 4 cm by 2 cm by 2 cm.

Hence, the surface area of the resulting solid is

SA = 2lw + 2lh + 2wh

SA = 2(4 cm)(2 cm) + 2(2 cm)(2 cm) + 2(4 cm)(2 cm)

SA = 40 cm²

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The retail price is $354.65.

What is retail price?

The price at which a product's manufacturer ostensibly recommends that a retailer sell it is referred to as the list price, also known as the manufacturer's suggested retail price, recommended retail price, or suggested retail price of a product.

Given: An import/export business marks up imported merchandise by 105%.

A wicker chair imported from Singapore originally costs from the manufacturer $173.

We have to find the retail price.

Retail price = [tex]= 173 + 173*\frac{105}{100} \\[/tex]

                   = 173 + 181. 65

Retail price  = 354.65

Hence,  Retail Price is $ 354.65.

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Lines b is parallel at an intersection at an angle of 89. 5 degrees.

In the above question, the two parallel lines will be b and d.

How do parallel lines work?

From the illustration, we can see that

Lines b and an intersect at an angle of 89. 5 degrees.

Lines c and an intersect at an angle of 91.5 degrees.

Lines d and an intersect at an angle of 89.5 degrees.

Lines e and an intersect at an angle of 88.5 degrees.

Lines f and an intersect at an angle of 90.5 degrees.

Since the angles created by lines b and an are equal, the result is 89.5.

Consequently, these two lines will never intersect.

However, other lines have different angles, so they can collide at a single location.

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Answer:

To find out how many miles per gallon the truck got, we can divide the number of miles it traveled by the number of gallons of gas it used: 84 miles / 4 gallons = <<84/4=21>>21 miles/gallon.

To find out how many miles per gallon the SUV got, we can divide the number of miles it traveled by the number of gallons of gas it used: 72 miles / 3 gallons = <<72/3=24>>24 miles/gallon.

To find out how many more miles per gallon the SUV got than the truck, we can subtract the number of miles per gallon the truck got from the number of miles per gallon the SUV got: 24 miles/gallon - 21 miles/gallon = <<24-21=3>>3 miles/gallon.

The SUV got 3 more miles per gallon than the truck.

Step-by-step explanation:

Answer:The SUV got 3 more miles per gallon than the truck.

Step-by-step explanation:

Answer:

4 x 10 + 5 x 1

Step-by-step explanation:

The expanded form of a number is written as a sum where each digit of the number is multiplied by its place value. Let's understand this concept with an example. To write the number 45 in the expanded form, we split the digits into tens and ones and write it as 4 x 10 + 5 x 1.

Answer:

Step-by-step explanation:

45 in expanded form;

(4x10)+(1x5)= 45

Total 205 students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval.

We have given that

Estimate of the proportion of students

= p

Confidence interval = 99%

As we know that the margin of error for the confidence interval is ,

MOE = Z ×√(p × (1-p)) / n

Where Z is z-score for

p --> estimate proportion confidence interval

n --> sample size

margin of error = 0 .09,

so we can set the equation as,

0.09 = Z×√(p×(1-p)) / n

Using the Z-table , the Z value for a 99% confidence interval is 2.575..

we will use p = 0.5 (since we are not given any information about value of p).

plugging all known values in above formula we get, 0.09 = 2.575√(0.5(0.5))/n

=> 0.0349 = √0.25/ n

=>0.00122 = 0.25/n

=> n = 204.6489

Since we get a decimal and we need our answer in number of students to sample, we round up to n = 205.

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After you dilate a figure , The figure gets bigger or smaller.

Dilation in mathematics is a process of changing the size of an object or a shape without changing its shape.

When you dilate any figure distance between the points changes.

Either the image gets enlarge or shrinks depends on the scale factor.

Things that don't changes are:

Only the size of an image changes not it's shape.

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The speed at which Marry was initially driving was 13 miles per hour and with that speed Marry drove 156 miles.

Given, Marry drove 156 miles at a constant rate.

If she had driven 99 miles/hour faster, she could have reduced her driving time by 45 minutes.

we have to find the speed at which Marry was driving.

Let the speed be, v

On using the distance formula, we get

Distance = Speed × Time

156 = vt

If she drive 99 miles/hour faster then her time reduced by 45 min.

156 = (v + 99)(t - 3/4)

156 = 156 + 99t - 3/4v - 297/4

396t = 3v + 297

396t = 468/t + 297

On solving the quadratic equation, we get

t = 12

and v = 13

So, the speed of marry was 13 miles per hour.

Hence, Initially the speed of marry was 13 miles per hour and with that speed Marry drove 156 miles.

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The vertex-form definition of the quadratic function is given as follows:

f(x) = −(x + 1)² + 25.

The roots of the quadratic function are defined as follows:

-6 and 4.

Hence the definition of the function is given as follows:

f(x) = a(x + 6)(x - 4)

f(x) = a(x² + 2x - 24).

When x = 1, y = 21, hence the leading coefficient a is obtained as follows:

21 = a(1 + 2 - 24)

-21a = 21

a = -1.

Thus the standard definition of the function is of:

y = -x² - 2x + 24.

The coefficients of the function are of:

a = -1, b = -2, c = 24.

Then the x-coordinate of the vertex is of:

x = -b/2a = 2/-2 = -1.

The y-coordinate of the vertex is of:

y = -(b² - 4ac)/4a = -((-2)² - 4(-1)(24))/-4 = 25.

Meaning that the vertex-form definition of the quadratic function is of:

f(x) = −(x + 1)² + 25

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Answer: B is the answer i got it right on the test

Step-by-step explanation:

The process to solve the linear  function problem is explained below .

In the question ,

we have been asked how can we solve a linear function problem .

we know that A linear function is a function that represents a straight line in the coordinate plane.

For Example, let the linear function problem be  f(x) = 3x - 2 ,

Step(1) :

to solve it we first have to equate the function to 0 ,

that is 3x - 2 = 0

Step(2) ;

we need to perform the necessary mathematical operation to find the value of x .

adding 2 on both sides of equation 3x - 2,

we get ,

3x = 2

dividing both sides by 3 ,

we have , x = 2/3 ,

the solution is x = 2/3 .

Therefore , the steps to solve a linear function is mentioned above .

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The distance between Chase and his younger sister is 12 feet. This is calculated by using Pythagoras' theorem.

The theorem that states "the square of the hypotenuse of a right triangle is equal to the sum of the squares on its other two sides" is said to be Pythagoras' theorem.

I.e., hyp² = opp² + adj²

It is given that,

Chase looks around at an assembly. He noticed that his younger sister was to his right and his elder brother is 16 feet ahead of him.

Chase's brother and sister are 20 feet apart, then the distance between Chase and his younger sister forms a right triangle as shown in the figure.

Where SB = 20 feet; CS = X feet; and CB = 16 feet;

According to the Pythagoras theorem, the distance between Chase and his sister is

SB² = CS² +CB²

⇒ (20)² = (x)² + (16)²

⇒ 400 = x² + 256

⇒ x² = 400 -256 = 144

⇒ x = √144 = 12

Therefore, the distance between Chase and his younger sister is 12 feet.

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To draw the area of a square, begin by drawing a square with four equal sides. Label the length of each side. Then, draw a triangle inside the square, connecting each corner. Label the length of each side.

Finally, calculate the area of the square by multiplying the length of the square by the length of the triangle.To find the area of any square, use the formula A= s2, where s is one of the sides' lengths.For example, if the length of each side of the square is 4, the area of the square would be 16 (4 x 4 = 16). To draw the area of the square, draw a 4x4 square and then draw a triangle inside it, connecting each corner. Label the length of each side of the triangle and the square. Then use the area formula to calculate the area of the square (A = s^2).

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The three ways of solving equations are graphing substitution and elimination.

To solve an equation by graphing, you essentially chart the given equations and discover the point(s) where they all meet. The arrangement of this point will grant you the values of the factors that you simply are tackling. The following method is substitution. Substitution is best utilized when one of the conditions is in terms of one of the factors such as y=2x+4, but the equations can continuously be manipulated. The primary step in this method is to solve one of the equations for one variable. Once an expression for the variable is found, substitute or plug within the expression into the other equation where the initial variable was to solve for the number esteem of the next variable. The final step is to substitute the number esteem that was found for its comparing variable within the original condition. The third method is the elimination, which involves adding the equations together in arrange to make an equation with as it were one variable. This will was done when the coefficients of one variable in both equations are alternate extremes and will cancel each other out once added together.

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Answer:

75/4

Step-by-step explanation:

I put all fractions in the same form and multiplied straight across

3/1 * 1/2 * 25/2 =

75/4

Answer: Mrs. Robinson

Step-by-step explanation:

Let's find Mrs. Robinson first

100% - 20% = 80% or 0.8

29.99 times 0.8% = $24

29.99 -24 = $5.99 off

Now Let's find Mr.Chang

100% - 10% = 90% or 0.9

25 times 0.9% = $22.50

25 - 22.50 = $2.50 off

So Mrs. Robinson received a better discount!

Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

Answer:

(35),(−3r),m=34(35),(−3),=3/4

Step-by-step explanation:

Cathy takes out a $167,000 mortgage. She plans monthly payments to pay it off in 40 years. At the end of the term, Cathy will have paid $401,294.40 total. The appropriate APR formula is APR=2(12)(401,294.4) / 167,000(480+1)

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money throughout the course of a loan or the revenue from an investment. This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.

Given,

Mortgage = $167000

Monthly plan = 40 years

End of the term, Cathy will have paid $401,294.40 total.

APR=2nf/P(N+1)

APR=2(12)(401,294.4) / 167,000(480+1)

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