A theater is selling tickets to a ''preview night'' of their new musical. The tickets cost $12 per adult and $7. 50 per child. Due to limit on seating, they can sell no more than 150 tickets. However, they would like to make at least $675 from ticket sales

78

Step-by-step explanation

by adding all the number and divide by the number of number

Answer:

78

Step-by-step explanation:

add all and divide by 7

Answer:

Selling Price= $180

Step-by-step explanation:

100%×90=90

90+90=180

The graph that represents the situation is required.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Graphs are a popular tool for graphically illuminating data connections. A graph serves the objective of presenting facts that are either too many or complex to be fully expressed in the text while taking up less room.

Here the  X- axis denotes the number of hours and

Y- axis denotes the pounds of ice.

The given ordered pair is

\(\left(\frac{1}{2}, 1 \frac{1}{2}\right)=(0.5,1.5)\)

At zero hours the ice produced will be zero so, the third and fourth options are incorrect.

The only graph where the line passes through (0.5,1.5).

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Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Here, we want to match what we have on the left with the expressions on the right.

(-4^9)^2

= -4^18

(4^6)^-3

= 4^-18 = 1/4^18 according to laws of indices

(4^0)^-9 = 4^0

(4^-3)^-3

= 4^9

Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Answer:

from formula

slope(M)=Y2-Y1

X2-X1

you already have slope which is 3

3=Y-(-3)

X-1

then cros multiplication

3X-3=Y+3

from formula

Y=Mx-c

Y=3X-6--is answer

Plug in the values to solve this problem.

\(5x-2y+(7x-y), x=7, y=-2\)

\(5(7)-2(-2)+(7(7)-(-2))\)

\(35+4+(49+2)\)

\(39+51\)

\(90\)

Hope this helps.

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The probability was broken by Bob is, 0.003 or 3%.

What is probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Alonzo, Bob, and Casper are each assigned three chances to bus tables and to fix any broken dishes, respectively.

P(Alonzo bussing tables) = 50% = 0.5

P(Bob bussing tables) = 15% = 0.15

P(Casper bussing tables) = 35% = 0.35

P(Alonzo breaking a dish) = 6% = 0.06

P(Bob breaking a dish)  = 2% = 0.02

P(Casper breaking a dish)  = 4% = 0.04

As the likelihood of dish breakage does not change with the busing of the tables, this is all about independent events.

Consequently, P(A and B) = P(A) + P (B)

So, if a dish is broken, the likelihood that Bob broke it is;

P(Bob breaking dishes and busing tables) = P(Bob busing tables) x P (Bob breaking a dish)

                                                                       = 0.15 x 0.02

                                                                       = 0.003

P(Bob breaking dishes and busing tables)  = 0.003 0r 0.3%

Hence, the probability was broken by Bob is, 0.003 or 3%.

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The distinct peaked stars that can be formed with the given N values, it's not clear what is meant by "peaked stars" in this context.

To find φ(N), we need to calculate Euler's totient function for each given value of N (15, 28, 42, 64, 84, 89, and 100). The distinct peaked stars that can be formed depend on the prime factorization of N.

Euler's totient function, denoted as φ(N), calculates the count of positive integers less than or equal to N that are coprime (relatively prime) to N. In other words, it determines the number of positive integers less than N that do not share any common factors with N.

a) N = 15:

15 = 3 * 5, so φ(15) = (3 - 1) * (5 - 1) = 2 * 4 = 8.

b) N = 28:

28 = 2^2 * 7, so φ(28) = (2^2 - 2^1) * (7 - 1) = 4 * 6 = 24.

c) N = 42:

42 = 2 * 3 * 7, so φ(42) = (2 - 1) * (3 - 1) * (7 - 1) = 1 * 2 * 6 = 12.

d) N = 64:

64 = 2^6, so φ(64) = 2^6 - 2^5 = 64 - 32 = 32.

e) N = 84:

84 = 2^2 * 3 * 7, so φ(84) = (2^2 - 2^1) * (3 - 1) * (7 - 1) = 4 * 2 * 6 = 48.

f) N = 89:

89 is a prime number, so φ(89) = 89 - 1 = 88.

g) N = 100:

100 = 2^2 * 5^2, so φ(100) = (2^2 - 2^1) * (5^2 - 5^1) = 4 * 20 = 80.

Regarding the distinct peaked stars that can be formed with the given N values, it's not clear what is meant by "peaked stars" in this context.

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The life cycle of a product represents the stages a product goes through from its introduction to its decline. It is depicted on a graph called the product life cycle curve, which shows the pattern of sales or revenue over time.

The product life cycle consists of four main stages: introduction, growth, maturity, and decline. In the introduction stage, sales start low as the product is launched and consumer awareness is limited. As the product gains traction, it enters the growth stage, characterized by rapid sales growth and increased market competition. The maturity stage follows, with sales leveling off as the product reaches market saturation. Finally, the decline stage occurs when sales and profits decline due to obsolescence or intense competition.

When drawn on a graph, the life cycle curve starts with a low point in the introduction stage, gradually rises during the growth stage, plateaus during maturity, and then declines in the decline stage. The duration and shape of the curve can vary depending on the product and market dynamics.

The life cycle graph helps businesses understand the trajectory of their products, plan marketing strategies, make pricing decisions, and anticipate future challenges and opportunities. It provides a visual representation of a product's market performance over time.

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Answer:

x=10

Step-by-step explanation:

As the two triangles are similar, the value of x = 10.

The volume of the composite solid is 4095 cubic yd.

A trapezoidal prism is a three-dimensional object that contains rectangular cross-sections in one direction and trapezium cross-sections in the other. This implies that the prism has two congruent trapezoids that are joined to one another by four rectangles. On the top and bottom of the prism, or bases, are these congruent trapezoids. The trapezium prism's lateral sides are the four rectangles. There are six faces, eight vertices, and 12 edges on a trapezoidal prism.

The volume of the composite solid is the addition of all the solids in the figure.

The volume of the trapezoid prism is:

V1 = (a+b)h(l) / 2

Substituting the values we have:

V1 = (19 + 30)(10)(9) / 2

V1 = 2205 cubic yd.

The volume of the rectangular prism is given as:

V2 = lwh

V2 = 7(30)(9)

V2 = 1890 cubic yd.

The total volume of the composite solid is:

V = V1 + V2

V = 2205 + 1890

V = 4095cubic yd.

Hence, the volume of the composite solid is 4095 cubic yd.

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If φ = arccos(-5/13), then cos(φ) = -5/13. Since this is negative, you know φ is an angle that terminates either the second or third quadrant.

arctan(x) has a range of -π/2 < arctan(x) < π/2, which is to say that arctan(x) is an angle that terminates in either the first or fourth quadrant.

These quadrants don't overlap, so there is no solution to the equation.

Answer:

Step-by-step explanation:

You can tell how to isolate a variable by listing the operations done to it, as prescribed by the order of operations. Then, you work backwards up the list performing inverse operations as you go.

__

Additional comment

Where mixed powers of the variable are involved, as in polynomials of degree higher than 1, there is generally not an inverse operation you can use to isolate the variable. Rather, special forms are used that facilitate isolating the variable. The variable in a quadratic, for example, can be isolated by "completing the square." Similar procedures are available for solving cubic and quartic equations, though those tend to be somewhat more complicated.

There are many kinds of equations in which there are no methods for isolating the variable. In general, any mix of polynomial terms and logarithmic, exponential, or trigonometric function terms are in that category: x +sin(x) -3 = 0, for example. (A graphing calculator shows the solution is near x=2.18, where the angle is in radians.)

Answer:

5.7

Step-by-step explanation:

cos 18° = x / 6

0.9511 =x / 6

cross multiply

x = 5.70666

To 1 decimal place

ANSWER = 5.7

Have a nice day !

Answer:

5.7 =x

Step-by-step explanation:

cos theta = adjacent side/ hypotenuse

cos  18 = x /6

6  cos 18  = x

5.706339098 =x

Rounding to the nearest tenth

5.7 =x

In a scatter plot, if all data points were aligned along a 44º angle, the correlation would be 0. The correct answer is D.

In a scatter plot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

When all data points are aligned along a 44º angle, it means that the points are distributed randomly and do not follow a clear linear pattern. There is no consistent increase or decrease in one variable as the other variable changes. Therefore, the correlation between the variables is 0, indicating no linear relationship or strength of association.

In other words, the angle of 44º suggests that the variables are unrelated and have no linear dependency on each other.

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The tangent line to the parabola y = x² at the point (6, 36) is (0.141, 1.68)

The equation of the tangent line at the point (6, 36) can be found using the derivative of the function and the point-slope form of a line:

f(x) = x²

f'(x) = 2x

y = f'(x) * (x - 6) + 36

Substituting f'(x) = 2x,

y = 2x * (x - 6) + 36

Now, we can find a unit vector that is parallel to this line by finding a non-zero multiple of the direction vector of the line, which is (1, 2x), and normalizing it.

To normalize, we divide by the magnitude, which is sqrt(1^2 + (2x)^2) = sqrt(1 + 4x^2).

Let's use x = 6:

y = 2 * 6 * (x - 6) + 36

y = 72

So, the direction vector is (1, 12) and its magnitude is sqrt(1 + 144) = sqrt(145) = 7.07.

The unit vector that is parallel to the tangent line is (1/7.07, 12/7.07) = (0.141, 1.68).

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The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

The total amount that they have to spend on parking and admission = $89.50

The parking cost = $7.75

The ticket cost including tax = $27.25

Consider the number of people who can go to amusement park as p

Then the equation will be

7.75 + 27.25p = 89.50

Subtract both side of the equation by 7.75

27.25p + 7.75 - 7.75 = 89.50 - 7.75

27.25p = 81.75

Divide both side of the equation by 27.25

27.25p / 27.25 = 81.75 / 27.25

p = 3

Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

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using angle sum property

we get

110+35+(x+12)=180

(x+12)=180-145

(x+12)= 35

x= 35-12

x= 23

Answer:

Angles in a triangle are sum up to 180 degrees.

35 + 110 + (x+12)=180

145+x+12=180

157+x=180

x=180-157

x=23 degrees

Answer:

is that a question I'm confused

Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

Answer:

C. 42

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

add all the sides:

(3x - 4) + (15 - x) + (3x + 6) = 32

simplify - collect like terms:

5x + 17 = 32

5x = 15

x = 3

The expression 25⁻³/₂ can be simplified to 1/√25³, which further simplifies to 1/125.

To simplify the expression 25⁻³/₂, we can rewrite 25 as 5² and use the properties of exponents. The expression becomes (5²)⁻³/₂.

Now, we can apply the power of a power property, which states that (aⁿ)ᵐ is equal to aⁿᵐ. In this case, 5² raised to the power of -³ is equal to 5²*(-³).

Next, we use the reciprocal property of exponents, which states that (aⁿ)⁻ᵐ is equal to 1/(aⁿᵐ). Applying this property, we get 1/(5²*³).

Simplifying further, we have 1/(5⁶), since 5²*³ is equal to 5⁶.

Finally, we can write the expression as 1/5⁶ or 1/125, since 5⁶ is equal to 15625.

Therefore, the simplified form of the expression 25⁻³/₂ is 1/125.

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The type of interference is this :

Comparing proportions from 2 independent samples

Given,

In the question:

Complete question is this:

Do upperclassmen (Seniors and Juniors) spend more money on alcoholic beverages then underclassmen (Freshman and Sophomores)? What type of inference is this?

a. Comparing proportions from 2 independent samples

b. One proportion

c. Comparing means from dependent samples

d. Comparing means from 2 independent samples

e. Comparing proportions from dependent samples

f. One mean

Now, According to the question:

Hence, The type of interference is this :

a. Comparing proportions from 2 independent samples

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The formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

The formula =IF(A1="A",1,IF(A1="B",2,IF(A1="D",4,5))) is a nested IF statement that checks the value of cell A1 and returns a corresponding value based on the conditions.

In this case, the value of A1 is "C". Therefore, the first condition, A1="A", is not true, so the formula moves on to the second condition, A1="B". This condition is also not true, so the formula moves on to the third condition, A1="D". However, this condition is also not true, because the third condition has a typo, where there is an extra space before the "D". Therefore, the formula evaluates the final "else" option, which is 5.

Thus, the formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

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Answer:

180 D

Step-by-step explanation:

Answer:

We're no strangers to love

You know the rules and so do I

A full commitment's what I'm thinking of

You wouldn't get this from any other guy

I just wanna tell you how I'm feeling

Gotta make you understand

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

We've known each other for so long

Your heart's been aching but you're too shy to say it

Inside we both know what's been going on

We know the game and we're gonna play it

And if you ask me how I'm feeling

Don't tell me you're too blind to see

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

No, I'm never gonna give you up

No, I'm never gonna let you down

No, I'll never run around and hurt you

Never, ever desert you

We've known each other for so long

Your heart's been aching but

Never gonna give you up

Never gonna let you down

Never gonna run around and desert you

Never gonna make you cry

Never gonna say goodbye

Never gonna tell a lie and hurt you

No, I'm never gonna give you up

No, I'm never gonna let you down

No, I'll never run around and hurt you

I'll never, ever desert you

Step-by-step explanation:

The equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6). Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

The equation given is 3x₁ + 5x₂ = 30. To find the axis intercept, we need to determine the points at which the line intersects the x₁ and x₂ axes. To find the x₁-axis intercept, we set x₂ = 0 and solve for x₁ 3x₁ + 5(0) = 30 3x₁ = 30
x₁ = 10

So, the x₁-axis intercept is (10, 0) which corresponds to point D in the given options. To find the x₂-axis intercept, we set x₁ = 0 and solve for x₂: 3(0) + 5x₂ = 30 5x₂ = 30 x₂ = 6 Therefore, the x₂-axis intercept is (0, 6) which corresponds to point C in the given options. To summarize, the equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6).

In the given options, option A (10, 6) is not an intercept on either axis. Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

Remember, the x₁-axis intercept is found by setting x₂ = 0, and the x₂-axis intercept is found by setting x₁ = 0 in the equation.The correct answer is option D

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Answer:

the slope is 1/2 and part b is no hes not its 0.5 gallon per minute

Answer:

k= -5

Step-by-step explanation:

The equation for slope is rise over run which is also (y2-y1)/(x2-x1)

with the given coordinate being (x,y)

So, we just plug the given values into the equation in order to solve for k.

(9-k)/(-6-1)= -2

First let's simplify the denominator:

(9-k)/(-7)= -2

then we get rid of the denominator by multiplying it on both sides:

(9-k)= (-7)*(-2)

(9-k) = 14

-k = 5

k=-5