Question
DIG DEEPER A group of friends visits a movie theater.

A menu of Royal Cinemas shows cost of tickets and refreshments. The cost of daytime and evening tickets are 5 dollars and 7.50 dollars respectively. The cost of small, medium, and large drinks are 1.75 dollars, 2.75 dollars, and 3.50 dollars respectively. The cost of small and large popcorns are 3 dollars and 4 dollars respectively.

Each person buys a daytime ticket and a small drink. The group shares 2 large popcorn. What is the average cost per person when there are 4 people in the group?

The slope calculations she can use to correctly show that △PQR is a right triangle are

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

The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).

This means that

P = (-2,5),

Q = (-1,1)

R = (7,3).

The slope of the points are calculated using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4

Also, we have

Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4

Hence, the equations are (a) and (d)

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The height of the tower is 2358 feets.

David is standing 500 feet away from the base of a cell phone tower.

The angle of elevation from his eyes to the top of the tower is 78°. David eyes are 6 feet above the ground . The height of the tower can be found as follows:

This situation forms a right angle triangle. Therefore,

using trigonometric ratios,

tan 78° = opposite / adjacent

tan 78° = x / 500

cross multiply

x = 500 tan 78°

x = 500 × 4.70463010948

x = 2352.31505474

Therefore,

height of the tower = 2352 + 6

height of the tower = 2358 ft.

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Answer:the answer is 319.857 and round to 320

Step-by-step explanation:

Answer: $1750

Step-by-step explanation:

7000x$0.25 = $1750

The total charge /cost c of taxi company's for a trip of d miles will be

c = 0.6 d + 1.2

What is mile with example?

Let c be the cost/charges and d be the miles.

Let $3/mile be the basic charge as well as the cost for the distance covered.

For 6 mile trip , the cost is $ 4.80 , then the cost of 3 miles is

          $ 4.80 - $ 3.00 = $ 1.80

Therefore, the cost for 1 mile is $ 1.80 / 3 = $ 0.60

The basic fee for hiring the cab is $ 3.00 - $ 1.80 = $ 1.20.

Therefore the total charge /cost c of taxi company's for a trip of d miles will be

 Total cost = cost for 1 mile + basic fee for hiring the cab

                c = 0.6 d + 1.2

If the formula is correct we get the given cost :

For 3 miles , then the cost c = 0.6(3) + 1.2 = $ 3.00

For 6 miles , then the cost c = 0.6(6) + 1.2 = $ 4.80

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Constant of variation for the direct function is y = [tex]\frac{2 x}5}[/tex]

Direct variation in mathematics is the general form of formula  y = k x  where x and y are variables (numbers that change) and k is a constant

Convert to slope intercept form

2x -5y =0

Add 5y to both sides

2x-5y +5y =5y

2x=5y

divide both sides by 5

[tex]\frac{2x}{5}[/tex]  =[tex]\frac{5y}{5}[/tex]

Cross multiply to solve for y

5(2x) =5(5y)

y = [tex]\frac{2 x}5}[/tex]

Therefore, the constant of variation y = [tex]\frac{2 x}5}[/tex]

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The total number of buttons they have is 4033.

A system having more than two equations is known as a system of equations.

Given that, Sebastian and Zoey had 3068 buttons, Sebastian and Valeria had 2103 buttons, and Valeria has half as many buttons as Zoey.

The equations corresponding to the statements are:

S + Z = 3068         (1)

S + V = 2103          (2)

V = Z/2                   (3)

Subtract equation (2) from equation (1):

Z - V = 965

Substitute V = Z/2 into the above equation:

Z - Z/2 = 965

Z/2 = 965

Z = 1930

Substitute Z = 1930 into equation (3):

V = 1930/2

V = 965

Substitute V = 965 into equation (2):

S + 965 = 2103

S = 1138

The total number of buttons is:
S + V + Z

= 1138 + 965 + 1930

= 4033

Hence, the total number of buttons they have is 4033.

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Answer:

√2 is irrational.

Step-by-step explanation:

√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1). Thus, p and q have a common factor 2. This statement contradicts that 'p' and 'q' have no common factors (except 1). We can say that √2 is not a rational number.

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Answer:

B and D

Step-by-step explanation:

A - check to see IF the relationship is proportional by dividing each y by its associated x:

     2 2/3 ÷ 3 = 8/9

     1 2/3 ÷ 3 = 5/9

     2/3 ÷ 3 = 2/9

none of these match, so not even proportional

B - CoP is the coefficient of x (2)

C - not proportional because of the +2

D - do the same as A

     6/3 = 2

     12/6 = 2

both are the same and equal to 2

{2, 3, 4, 5, 5, 7, 7, 9, 10} is the required dataset to represent the boxplot.

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

Given,

boxplot with the minimum of 2

lower quartile value of 3,

median of 5,

upper quartile of 9,

and maximum of 10

In the given data sets {2, 3, 4, 5, 5, 7, 7, 9, 10} represents boxplot with the minimum of 2, lower quartile value of 3, median of 5, upper quartile of 9, and maximum of 10

Hence,  {2, 3, 4, 5, 5, 7, 7, 9, 10} is the required dataset to represent the boxplot.

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If his employer pays 60% of the cost. The annual premium amount for Jonathan's group health insurance is $2,550.

Annual premium can simply be defined as the premium a person is expected to pay per year or annually.

First step is to find the cost

Cost = $85/ (1-.60)

Cost = $85/.40

Cost = $212.5

Now let find the annual premium amount

Annual premium amount = Cost × 12 months

Annual premium amount = $212.5 × 12 months

Annual premium amount = $2,550

Therefore the annual premium amount  is the amount of $2,550.

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Answer: -21

Step-by-step explanation:

[tex]x+2=-19\\\\What\ value\ of\ x\ will\ make\ the\ left\ side\ equal\ to\ -19?\\\\Well,\ if\ we\ subtract\ 2\ from\ both\ sides,\ we\ get\ our\ answer...\\\\x+2-2=-19-2\\\\The\ 2\ and-2\ on\ the\ left\ cancel\ out\ leaving\ us\ with\\\\\boxed{x=-21}[/tex]

We can check our work by plugging back in -21 for x and getting -19 = -19

The time it takes for the projectile to reach its maximum height would be 0.77 s. The time it takes for the projectile to hit the ground is 2.67 s.

The horizontal range ∆x would be 20.3 m.

To determine the time it takes for the projectile to reach its maximum height, we can use the formula:

t = (vi sin(θ)) / g

where t is the time, vi is the initial velocity, θ is the angle of launch, and g is the acceleration of gravity.

In this case, the initial velocity has a horizontal component of 7.5 m/s, so we can assume that the initial velocity is 7.5 m/s and the angle of launch is 90 degrees (since the projectile is launched horizontally). Therefore, the time it takes for the projectile to reach its maximum height would be:

t = (7.5 m/s × sin(90)) / 9.8 m/s2 = 0.77 s

To determine the time it takes for the projectile to hit the ground, we can use the formula:

t = (2 ∆y) / (vi sin(θ))

where t is the time, ∆y is the maximum height, vi is the initial velocity, and θ is the angle of launch.

Since we know that the projectile rises to a maximum height of ∆y above the end of the cannon's barrel, the initial velocity has a horizontal component of 7.5 m/s and the angle of launch is 90 degrees, we can calculate the time it takes for the projectile to hit the ground as follows:

t = (2 ∆y) / (7.5 m/s x sin(90)) = (2 ∆y) / 7.5 m/s = 2.67 s

To determine the horizontal range ∆x of the shot, we can use the formula:

∆x = (vi × t) cos(θ)

where ∆x is the horizontal range, vi is the initial velocity, t is the time, and θ is the angle of launch.

In this case, we know that the initial velocity has a horizontal component of 7.5 m/s, the time it takes for the projectile to hit the ground is 2.67 s, and the angle of launch is 90 degrees.

Therefore, the horizontal range ∆x would be:

∆x = (7.5 m/s × 2.67 s) × cos(90) = 20.3 m.

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The investment amount is $37263.09.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

P(t) = P₀ [tex]e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the Alang is going to invest with the continuous compound interest rate 5.7%.

Using the formula of continuous compound interest rate,

P(t) = P₀ [tex]e^{rt}[/tex]

P(t) = $113000 x    [tex]e^{(5.7)(5)}[/tex]

P(t) = $37263.09

Therefore, the investment amount is $37263.09.

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The slope of C and D in the picture shows that ΔPQR is a Right Triangle.

What is slope of line?

Slope of line is defined as the angle of line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂).

If the product of slopes of any two sides is equal to -1, then those two sides are perpendicular

Given,

The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).

Slope of PQ = (y₂ - y₁)/(x₂ -x₁ )

                    = (1 - 5)/(- 1 - (-2)

                    = -4/1

                    = - 4

Slope of QR = (y₂ - y₁)/(x₂ -x₁ )

                    = 3 -  1/7 - ( -1)

                    = - 1 / 4

The product of Slope of PQ and QR is  - 1. It means lines PQ and QR is perpendicular to each other consequently △PQR is a right triangle.

Therefore,The slope of C and D in the picture shows that ΔPQR is a Right Triangle.

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Step-by-step explanation:

the answer

(3x-2)(4y-3)

Answer: (3x-2)(4y-3)

Step-by-step explanation:

If Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of nickels then 0.15 Nickels does Lianne has.

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

Given,

Lianne has some dimes and nickels with a total value of $4.60.

The number of dimes she has is 4 more than 3 times the number of nickels.

We need to find number of nickels

From the given information

N+D=4.60

D=3N+4

N+3N+4=4.60

4N=4.60-4

4N=0.6

Divide both sides by 4

N=0.15

Hence, 0.15 Nickels does Lianne has.

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Step-by-step explanation:

divide 15 by 2 to get the radius which is 7.5

then 7.5² = 56.25 x3.15=177.1875 round and its A=177.188

if this is incorrect someone else correct me

For the initial fee, Bob charges less than Ginny.

A unit rate means a rate for one of something.

Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.

Ginny initial charge = $80

Bob initial charge =$60

Hence, For the initial fee, Bob charges less than Ginny.

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Hence, the  decimal equivalent of students who passed the test is [tex]0.33[/tex].

What is the decimal values?

Decimals are a set of numbers lying between integers on a number line.

Here given that,

Three out of nine students passed the SHSAT test.

So,

[tex]\frac{3}{9}=0.33[/tex]

Hence, the  decimal equivalent of students who passed the test is [tex]0.33[/tex].

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The domain and the range of the function are given as follows:

The domain of a function is the set containing all the values assumed by the input of a function, hence on the graph it is given by the values of x for which the function is defined.

The range of a function is the set containing all the values assumed by the output of a function, hence on the graph it is given by the values of y which the function assumes.

In this problem, the horizontal line is given as follows:

y = -3.

Hence the lone value assumed by output is of 3, meaning that the range is given as follows:

{3}.

In {} notation because it is a single element, not an interval.

The values of x, that is, the values of the horizontal axis assumed by the function are between -3 and 3, hence the domain is given by the following interval:

[-3, 3].

Which is a closed interval due to the closed circle.

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The normal distribution based on the graph is:

a) The mean is 91.

b) The standard deviation is 1.

c) 68 % of the data values are between 90 and 92.

e) 99.7 % of the data values are between 87 and 94.

What is the normal distribution?

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value.

From the graph the mean is (x¯) = 91

a) The mean is 91

and  Standard Deviation (σ)= (∑(x - x¯)²)  

= (70-91)²+ (77-91)² +(84-91)²+(91-91)²+(98-91)²+(105-91)²+(112-91)²

= 1372 / 1371

= 1.0007293946

σ = 1

b) The standard deviation is 1.

if x¯ is the mean and σ is the standard deviation of the distribution, then 68% of the values fall in the range between (x¯−σ) and (x¯+σ).

= (91 -1) (91+1)

= 90 to 92

c) 68 % of the data values are between 90 and 92.

About 95% of the values lie within two standard deviations of the mean, that is, between (x¯−2σ) and (x¯+2σ).

(91-2) to (91+2)

89 to 93

d) 95 % of the data values are between 89 and 93.

About 99.7% of the values lie within three standard deviations of the mean, that is, between (x¯−3σ) and (x¯+3σ) .

(91-3) to (91+3)

87 to 94

e) 99.7 % of the data values are between 87 and 94.

Hence, the normal distribution based on the graph is:

a) The mean is 91.

b) The standard deviation is 1.

c) 68 % of the data values are between 90 and 92.

e) 99.7 % of the data values are between 87 and 94.

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Answer:

36.2/4=length of each sandwich piece

The time period of the loan was 1 year.

The intercepts of x-axis for the given polynomial function is (1. 0)

The intercepts of y-axis for the given polynomial function is (0, -3) and the graph is attached below:

A function of a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain in a function is the set X, and the codomain of the function is the set Y.

The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability.

Given function is,

f(x)=x³+2x²-3

The graph of the polynomial function is plotted below:

The intercepts of x-axis for the given polynomial function is (1. 0)

The intercepts of y-axis for the given polynomial function is (0, -3)

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1. An equation that finds the number of car washes for which the costs of Plan A and Plan B are the same is 12n = 16 + 8n.

2. The solution of the equation shows that the number of car washes for which the cost of each plan is the same is 4.

Equations are mathematical statements claiming that two or more mathematical expressions are equal or equivalent when solved.

Equations use numbers, constants, variables, and the equation symbol (=) to depict the equality of the mathematical expressions.

                                 Plan A     Plan B

Cost per cash wash  $12           $8

Fixed cost                  $0           $16

Mathematical Expressions for the Carwash Plans:

Let Plan A = 0 + 12n

Let Plan B = 16 + 8n

The number of car washes when the two plans' costs are equal can be derived by equating the two mathematical expressions above:

12n = 16 + 8n

12n - 8n = 16

4n = 16

n = 4

= 4 car washes

Check:

Plan A = 0 + 12n

= 12(4)

= 48

= $48

Plan B = 16 + 8n

= 16 + 8(4)

= 16 + 32

= 48

= $48

Thus, solving the equation, we can conclude that choosing Plan B will take 4 car washes to equal the cost of Plan A.

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The interest rate for a ​$6000 deposit accumulating to ​$​6957, compounded annually for 6 years is r=2.49%.

The interest rate is the amount charged by the lender to the borrower over and above the principal amount. In terms of the receiver, a person who deposits money in any bank or financial institution obtains additional revenue due to the time value of money, which is referred to as interest received by the depositor.

Here's a simple interest formula: Interest = P x R x T, P = Principal Amount (the beginning balance).

Given, Amount=6957, P=6000, t=6 years

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

6957=6000(1+(r/1))[tex](1+(r/1))^{6}[/tex]

[tex](1+(r/1))^{6}[/tex]=6957/6000

=1.1595

ln[tex](1+(r/1))^{6}[/tex]=ln(1.1595)

6(1+(r/1))=ln(1.1595)

(1+(r/1))=ln(1.1595)/6=0.0246

(1+(r/1))=[tex]e^{0.0246}[/tex]

1+r=1.02490508

r=0.02490508

r=2.49%

The interest rate for a ​$6000 deposit accumulating to ​$​6957, compounded annually for 6 years is r=2.49%.

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Answer:

3/4n = 5/8

Step-by-step explanation:

your…. welcome……

I don’t trust meself so I might be wrong

Step-by-step explanation:

10-8b

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