At an amusement park, only 17 people are allowed on a ride at the
same time. There are 157 people waiting in line. How many groups
of riders will there be?
Show your work.

Answer:

3.25

Step-by-step explanation:

To find the arithmetic mean of a set of data, you add up all of the values in the set and then divide by the total number of values.

In this case, the set of data is {6, 1, 5, 1} and the total number of values is 4.

To find the arithmetic mean, we add up all the values:

6 + 1 + 5 + 1 = 13

then divide by the total number of values:

13 / 4 = 3.25

So the arithmetic mean of the set of data {6, 1, 5, 1} is 3.25.

Answer:

d = 4 and a₁ = 12

Step-by-step explanation:

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₆ = 32 and a₁₀ = 48 , then

a₁ + 5d = 32 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 4d = 16

4d = 16 ( divide both sides by 4 )

d = 4

substitute d = 4 into (1) and solve for a₁

a₁ + 5(4) = 32

a₁ + 20 = 32 ( subtract 20 from both sides )

a₁ = 12

The square root of a number is only defined for non-negative numbers, since the square root of a negative number is not a real number.

For the expression sqaure root of -(6-x) to make sense mathematically, the expression inside the square root must be non-negative.

So, we need to find the values of x that make -(6-x) non-negative.

-(6-x) is non-negative when -(6-x) ≥ 0

Simplifying this inequality, we get 6-x ≤ 0

x ≤ 6

So, for x ≤ 6, the expression sqaure root of -(6-x) is defined and makes sense mathematically. This is the domain of the expression.

In summary, the domain of the expression sqaure root of -(6-x) is x ≤ 6.

Reasons:

The give figure shows;

The preimage figure = P

The image figure = Q

The image P is larger than the preimage Q, therefore, the figure, Q is a

dilation of the preimage P

The center of dilation is found with the formula;

[tex]& x_0=\frac{\mathbf{k} \cdot \mathbf{x}_1-\mathbf{x}_2}{\mathbf{k}-1} \\[/tex]

[tex]& y_0=\frac{\mathbf{k} \cdot \mathbf{y}_1-\mathbf{y}_2}{\mathbf{k}-\mathbf{1}}[/tex]

Where;

[tex]$\left(x_1, y_1\right)=$[/tex]A point on the preimage, [tex]$P=(2,3)$[/tex]

[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=$[/tex]The corresponding point on the dilated image, [tex]$\left.Q=\mathbf{( 4}, \mathbf{9}\right)$[/tex]

k= The scale factor

Therefore;

[tex]x_0=\frac{3 \times 2-4}{3-1}=1[/tex]

[tex]$y_0=\frac{3 \times 3-9}{3-1}=0$[/tex]

The center of dilation, [tex]$\left(x_0, y_0\right)=(1,0)$[/tex]

Therefore;

Shape P is transformed into shape Q through a single transformation that involves dilation by a scale factor of 3 with a center of dilatation at (1,0).

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The age of the older brother is 13

From the information given, let their ages by x and y

This is represented as;

x + y = 22

(x - 6) (y -6) = 21

From equation (1), make x, the subject of formula

x = 22 - y   (3)

Substitute equation (3) in equation (2), we get;

(22 - y- 6)(y - 6) = 21

expand the brackets

(16 - y)(y-6) = 21

16y - 96 - y² +6y = 21

collect iike terms

-y² + 22y - 96 - 21 = 0

subtract like terms

-y² + 22y - 117 = 0

y²- 22y + 117 = 0

Find the pairs factors of 117 and substitute the values

y² - 13y - 9y + 117 = 0

(y² - 22y) - (9y + 117) = 0

factorize

y(y - 22) - 9(y - 22) = 0

Then y = 9 and y = 22

The older brothers age = x = 22 - y = 22- 9 = 13

Hence, the value is 13

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The complete question:

The sum of the ages of two brothers is 22 years. Six years ago, the product of their ages was 21 years. What is the age of the elder brother?

The amount that Cameron plans to give his parents every month as a way to pay them back for the bicycle is called an Installment.

A loan installment is a fixed payment that a borrower makes to a lender over a period of time, usually on a regular basis, until the loan is fully paid off. The payment typically includes both the principal amount borrowed and the interest charged on the loan.

Loan installments are related to annuities in that they are both financial products that involve a series of regular payments. An annuity is a financial contract in which an individual gives an insurance company a lump sum of money or a series of payments in exchange for a stream of payments over a period of time.

This means therefore, that the amount that Cameron plans to pay his parents every month for the money borrowed to buy a bicycle, is called a loan installment.

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The full question is:

Cameron owes his parents money that he narrowed to buy a bicycle. He plans on paying them back by giving them amount of money each month. What is this amount called?

Answer:

y = -x - 3

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:

y - 5 = -1(x + 8)

Simplifying, we get:

y = -x - 3

This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.

Step-by-step explanation:

area of square=length×length

=25ft²

area of rectangle=length × breath

=2×9

18ft²

area of the figure=25 +18

=43ft²

Answer:

The answer is option A.

Step-by-step explanation:

To find the rate at which the questions were answered correctly on the first try, we can divide the number of questions answered correctly by the total number of questions.

Let's call the rate of correct answers on the first try as R

R = (number of questions answered correctly) / (total number of questions)

Substituting the given values:

R = 67 / 74

R = 0.905

So, the rate of correct answers on the first try is 0.905.

Answer:

Step-by-step explanation:

The question answered correctly in fraction will be 67/74.

67/74 equals 67÷74, which is 0.9054054054...

0.9054054054... round to the nearest thousand is 0.905.

So the answer is A, 0.905.

The  age of the older brother is 21 years

Two or more expressions with an Equal sign is called as Equation.

Six years ago, the sum of the ages of two brothers was 22

x+y=22

The product of their ages is 21

xy=21

y=21/x

x+21/x=22

x²+21=22x

x²-22x+21=0

Factorize the equation

x²-21x-x+21=0

x(x-21)-(x-21)=0

(x-1)(x-21)=0

x=1 and x=21

21+y=22

y=1

Hence, the  age of the older brother is 21 years

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The solution of the given differential initial value problem is

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}

In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.

Given is the initial value problem -

y' = y² - 6y + 5

We can write the -

y' = y² - 6y + 5

Dividing both sides by {y² - 6y + 5}, we get -

y'/y² - 6y + 5 = 1

Integrating -

∫(y'/y² - 6y + 5) dx = ∫1 dx

- 1/4 log(1 - y) + 1/4 log (5 - y) = x + c{1}

Solving for y{x}, we can write -

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}

The given differential equation can be solved and written as -

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}

Therefore, the solution of the given differential initial value problem is

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}.

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For the local salesman to have a monthly income of $3,000, using mathematical operations, he would need to sell $20,045 worth.

The sales revenue that the local salesman should generate to reach his monthly income target is determined by working backward with the mathematical operations of subtraction, division, multiplication, and addition.

Firstly, the base salary is deducted from the expected monthly earnings to obtain the amount of the sales commission.

The sales commission is equated to its commission percentage through division and multiplication operations.

The result is added to $500 to arrive at the expected sales revenue.

The monthly base salary = $850

Commission = 11% on sales above $500

Needed monthly income = $3,000

Sales commission = $2,150 ($3,000 - $850)

11% = $2,150

100% = $19,545 ($2,150/11% x 100%)

$19,545 = Sales above $500

Total target sales = $20,045 ($19,545 + $500)

Thus, if the salesman expects a monthly income of $3,000, he must generate monthly sales revenue of at least $20,045.

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Answer:

The solution set of x^2 + 4x - 21 ≤ 0 is (-7, -3)

Step-by-step explanation:

To solve this inequality, we first set x^2 + 4x - 21 = 0 and factor it to get (x + 7)(x - 3) = 0. This gives us x = -7 and x = 3 as the solutions.

To find the solution set of x^2 + 4x - 21 ≤ 0, we need to determine the values of x that make the expression on the left-hand side non-positive. Since x^2 + 4x - 21 is a quadratic function, it is non-positive when x is less than -3 or x is greater than -7.

Therefore, the solution set of x^2 + 4x - 21 ≤ 0 is the set of all x such that x ∈ (-7, -3).

Answer:

Step-by-step explanation:

You want to use the graph to evaluate the compositions ...

where f(x) = x² -2x -3, and g(x) = x -2.

To find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.

Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:

  f(x) = (x -2)x -3

  f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45

The value of f(g(f(1))) is 45. The equation must be used for this.

Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.

The value of g(f(g(0))) is 3.

__

Additional comment

A suitable calculator or spreadsheet can evaluate these expressions for you.

Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get 4.

According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the shapes are congruent to each other,” asserts the transitive property of congruence.

We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or divide both sides of an equation.

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The trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle WVX, WV=24, WX=51 and VX=45

We know that, sinθ = Perpendicular/Hypotenuse and cosθ = Base/Hypotenuse

Here, sin X= 24/51

sin X= 8/17

cos W= 24/51

cos W= 8/17

Therefore, the trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

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Answer : 165/2

To do this, we just have to add 82 and 1/2. However, the question asks for an improper fraction, so we turn 82 into 164/2. Now, we add 1/2 to 165/2 which equals 164+1/2 = 165/2.

Answer:

4x + 36 = 100

Step-by-step explanation:

Considering how you have already earned 36 points, there will be no variable for it present. The x stands for the amount of times you go see a movie in the theater.

Answer:

You need to see 16 more movies to earn 100 points.

Step-by-step explanation:

you earn 4 advantage points every time you see a movie at the theater.

You need to earn 100 points to get a free movie pass.

Currently, you have 36 advantages points.

If you watch m movies you get = 4m points

You have 36 points so you need = 100 - 36 more points

So the equation will be = 4m = 100 - 36    [after combining like term]

4m = 64 [divide both side by 4]

m = 16

You need to see 16 more movies to earn 100 points.

Answer:

Question 1

The model is an exponential model that describes the relationship between the number of weeks since the first data point and the closing price of the stock. It is calculated by using the given data points and finding the best fit for the data. The model can be used to make predictions about the closing prices of the stock by plugging in the value of x, which represents the number of weeks since the first data point.

One week from today, the stock is predicted to close at $67,034.37, one month from today, the stock is predicted to close at $66,327.75, and one year from today, the stock is predicted to close at $76,584.35 according to the model.

Question 2

It is difficult to say whether the model is a good predictor of the future closing price of the stock because it depends on how accurately the model describes the underlying relationship between x and y. However, since the model is based on historical data and has a high R-squared value, it could be a good predictor of the future closing price of the stock.

The ratio for each product, so that they can be compared to the new brand, is given as follows:

The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.

Hence, for the products in this problem, the ratio of protein to carbs is applied by the division of the amounts of protein by cards.

For each product, the ratios are obtained as follows:

Hence they can be compared to the new product, as all the ratios have a denominator of one.

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The required system of equation has no solution.

The more physical interpretation of the idea of two linear equations having a linear equation is that it will always have a singular solution regardless of whether the lines are parallel or coinciding.

We have,

4x + 10y = 57---------------(1)

2x + 5y = 38

Multiply 2

4x + 10y = 76----------(2)

So, above equation (1) and (2) has no solution.as values of x and y are not same for both the equation.

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The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15

You should note the following about FOIL method

It stands for "First, Outer, Inner, Last"

It is the sum of:

· multiplying the First terms,

· multiplying the Outer terms,

· multiplying the Inner terms, and

· multiplying the Last terms

That is  (a+b)(c+d) = ac + ad + bc + bd

Use FOIL (First, Outside, Inside, Last)

The give expression is

x(x²) = x³

x(-3x) = -3x²

5(x²) = 5x²

5(-3x) = -15x

Combine like terms:

x³ - 3x² + 5x² - 15x

x³ + 2x² - 15

Therefore the FOIL method is x³ + 2x² - 15

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Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour

The equation representing t in hrs and odometer reading after noon in y is

y = 6852 + 52t

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The reading in odometer =6852 miles at 12:00

The reading in odometer = 7034 miles at 3 :30 pm

Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour

An equation representing t in hrs and odometer reading after noon in y is

y = 6852 + 52t

The point is (5,7112)

for t = 5

y = 6852 + 52*5 = 7112 (proved)

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Answer: 360

Step-by-step explanation:

If 10% of people were 55 or older, than 90% of people were younger than 55.

This is 9 times the number of people that were 55 or older.

Therefore, the answer is 360.

Answer: -7.05

Step-by-step explanation: a calculator is very helpful for problems like these if you can use one in your class!

Answer:

Amount = $ [tex]2080[/tex]

Step-by-step explanation:

Given ,

To Find : The Amount

We can derive the SI i.e the Simple Interest by the formula,

[tex]SI = \frac{PRT}{100}[/tex]

Applying the values into the given equation we get,

[tex]SI = \frac{2000X8X5}{100}[/tex]

Substituting we get,

[tex]SI = 80$[/tex]

[tex]Amount =[/tex] [tex]SI + Principal[/tex]

[tex]Amount = 80 + 2000[/tex]

[tex]Amount = $2080[/tex]

Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

u = 2n² - 5n + 3

u = 45

2n² - 5n + 3 = 45

2n² - 5n - 42 = 0

(2n - 7)(n + 6) = 0

2n - 7 = 0 or n - 6 = 0

n = 7/2 or n = 6

Answer: 6

Answer:

B

Step-by-step explanation:

A quadratic function is a polynomial function which has a degree of 2, and is generally expressed in standard form: [tex]ax^2+bx+c\text{ where }a\ne 0[/tex]. The degree of a polynomial function can be determined by looking at which term has the largest exponent.

By looking at both options, B would be the correct option as it is a polynomial function with degree 2, while option A is a polynomial function with degree 1, also known as a linear equation.

Answer:

i think the answers are m=4 and n=10

Answer:

A segment is congruent to another segment if and only if they have the same length.

Answer:

Segments are congruent if and only if they have the same length.

Segments have the same length if and only if they are congruent.

Step-by-step explanation:

Biconditional statement

A biconditional statement is a combination of a conditional statement and its converse.  It is conditional in both directions:

Write the given statement as a conditional statement:

Write the given statement as a converse of the conditional statement:

Both the conditional and converse statements must have the same truth value to produce a biconditional statement.  Therefore, as both are true, we can write the biconditional statements: