you want to organize a group of friends to go to a karaoke studio friday night. you must pay $30 to reserve a room plus $5 for each person in the group. You also want to have snacks for the group at a cost of $2 per person. how Many people can be in the group in order for the total cost to be $114

how do you solve this????

Answer:

Number B: 4x+1

Step-by-step explanation:

I used synthetic division instead, But hope this helps.

(4x² - 7x - 2) ÷ (x-2)

I have placed the terms corresponding to each variable, for x squared I put 4, for x - 7 and for c (constant) I put - 2.

We go down 4, which will multiply to 2.

¿Why 2?

This is obtained by matching the denominator to 0.

\(x-2=0\rightarrow \boxed{x=2}\)

Then we multiply 4 by 2, give us 8, add this value to the variable x (- 7), we have 1.

Multiply 1 by 2, give us 2, add this value to the constant (- 2), we have 0. ¡Finish!

Answer: 4x + 1

The total surface area of the triangular prism is 756 meter²

Given,

A triangular prism and its net.

We have to find the surface area of the triangular prism.

First we can consider the right angled triangle.

Height = 9 meter

Base = 12 meter

Hypotenuse = 15 meter

Area of the right angled triangle = (1/2 bh)

Here,

Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²

Now, area of right rectangle.

Area of rectangle = length × breadth

Here, the breadth of the rectangle is the height of the triangle = 9 meter

Length = 18 meter

Area = length × breadth = 9 × 18 = 162 meter²

Then, area of middle rectangle.

Length = 18 meter

Breadth = 12 meter

Area = length × breadth = 18 × 12 = 216 meter²

Next, area of left rectangle.

Length = 18 meter

Breadth = Hypotenuse of the triangle = 15 meter

Area = length × breadth = 18 × 15 = 270 meter²

Now, lets calculate the total surface area of the triangular prism.

Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²

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Given information: In the PGA, on par 3 holes, golfers hit the green in one shot 80% of the time. In fact, 20% of the time, they hit the green in one shot and then need only one putt to complete the hole. So 60% of the time, they hit the green in one shot but are unsuccessful on their putt.

Let G be the event that the golfer hits the green in one shot. Let P be the event that the golfer needs one putt to make the hole. Probabilities listed in the problem: Probability of hitting the green in one shot

.= 80% = P(G)Probability of hitting the green in one shot and needing only one putt = 20% = P(G ∩ P)Probability of hitting the green in one shot but are unsuccessful on the putt = 60% = P(G ∩ P')Where P' denotes not P or the complement of P. In other words, P' means that the golfer needs more than one putt to make the hole.

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Answer:

Step-by-step explanation:

the measure to the nearest degree is 567.98

Answer:

The answer is A because there are no coefficients which is a letter and 1 term.

Answer:

2 to 10 or 1 to 5

Step-by-step explanation:

there are 2 footballs and 10 balls in total.

Answer:

7

Step-by-step explanation:

1x2=2x3/1/2= 7

Answer:

7

Step-by-step explanation:

I did the question

Answer:

The domain is all real number

a) The effort level E MSY to get the maximum sustainable yield is 0.

b) The effort level E OA is not constrained.

(a) To calculate the size of the biomass S MSY for the maximum sustainable yield (MSY), we need to find the stock level where the growth rate G(S) is equal to the harvest rate H(E,S).

G(S) = H(E,S)

0.4S(1−10000/S) = 0.01ES

S(1−10000/S) = 0.01E

S - 10000 = 0.01E

S = 0.01E + 10000

To find S MSY , we need to set the growth rate G(S) equal to zero:

G(S) = 0.4S(1−10000/S) = 0

0.4S(1−10000/S) = 0

S(1−10000/S) = 0

S = 0 or S = 10000

Since S cannot be zero in this context, the size of the biomass S MSY for the maximum sustainable yield is 10,000.

To find the corresponding effort level E MSY , we substitute S MSY into the equation:

S = 0.01E + 10000

10000 = 0.01E + 10000

0.01E = 0

E MSY = 0

(b) In an open access fishery, there are no restrictions on the amount of effort that can be applied. Therefore, the effort level E OA is not constrained.

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The given sequence is an = n/(42+3n).

To determine whether it converges or diverges, we can use the limit comparison test. Taking the limit as n approaches infinity of the ratio of an and n, we get lim n→[infinity] an/n = lim n→[infinity] n/(n(42/ n+3)) = lim n→[infinity] 1/(42/ n+3) = 1/42.

Since the limit is a finite positive number, the sequence converges. To find the limit, we can use the fact that the sequence converges to the same limit as an = 1/(42/ n+3).

Taking the limit as n approaches infinity of 1/(42/ n+3), we get lim n→[infinity] 1/(42/ n+3) = 0. Therefore, the limit of the given sequence is 0.

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Complet question:

determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an =  n/(42+3n) lim n→[infinity] an =

The given sequence is an = n/(42+3n).

To determine whether it converges or diverges, we can use the limit comparison test. Taking the limit as n approaches infinity of the ratio of an and n, we get lim n→[infinity] an/n = lim n→[infinity] n/(n(42/ n+3)) = lim n→[infinity] 1/(42/ n+3) = 1/42.

Since the limit is a finite positive number, the sequence converges. To find the limit, we can use the fact that the sequence converges to the same limit as an = 1/(42/ n+3).

Taking the limit as n approaches infinity of 1/(42/ n+3), we get lim n→[infinity] 1/(42/ n+3) = 0. Therefore, the limit of the given sequence is 0.

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Complet question:

determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an =  n/(42+3n) lim n→[infinity] an =

Answer:

5.25

Step-by-step explanation:

"The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average"

in that case

1.6, 3.2, 3.6, 4.6 , 4.7 , 5.2 , 5.3,  5.4 , 6.1 , 7.8 , 9.0 , 9.5 ,

1st  2nd 3rd 4th  5th    6th  7th .  8th . 9th  10th 11th 12th

as you can seem 5.2 and 5.3 are both in the middle. that means you take the average of those two numbers. so 5.25

Answer:

The median is 5.25

Step-by-step explanation:

Median is found in the middle of numbers.

First you arrange the number from descending to ascending order:

1.6, 3.2, 3.6, 4.6, 4.7, 5.2, 5.3, 5.4, 6.1, 7.8, 9.0, 9.5

There are 12 numbers.

Then find the number that is in the center. In this case, 5.2 and 5.3 are the numbers in the center. You add them together and divide them by 2:

5.2+5.3 = 10.5/2 = 5.25

The median is 5.25

Answer:

A tiny cat named Tiny sits all day in the window and watches people pass by.

Step-by-step explanation:

A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.A tiny cat named Tiny sits all day in the window and watches people pass by.

Wouldn't it still just be 84 with or without the distributive property? :0

2(5+5)+2(16+16)

Step-by-step explanation:

lol and ignorw this wifnsnsjwjs

Answer:

Step-by-step explanation:

A

y = 7 - x

y = 7 - 2

y = 5

B

y = x^2 - 1

y = (2)^2 - 1

y = 2*2 - 1

y = 4 - 1

y = 3

C

y = x + 14

I'm going to assume that you mean (x + 14)^3

y = (x + 14)^3

y = (2 + 14)^3

y = 16^3

y = 4096

If you really do mean what it says, then

y = 2 + 14^3

y = 2744 + 2

y = 2746

Answer: x= -8 and y = -20

Answer:

\( \frac{1}{2} (48 \div6) - 2 + 5 \\ \frac{1}{2} (8) - 2 + 5 = 4 - 2 + 5 \\ = 2 + 5 \\ = 7\)

Answer:

The slope is 6

Step-by-step explanation:

The rise is 6 and the run is 1. 6/1

x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

\(f(x) = \frac{1}{4}(x - 1)(x + 7)\)

Let,

\(y = \frac{1}{4}(x - 1)(x + 7)\)             ..(1)

To find x - intercept, plug y = 0 in above equation,

\(\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7\)

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

\(x = \frac{-7+1}{2} = \frac{-6}{2} = -3\)

Plug x = -3 in equation (1)

\(y = \frac{1}{4}(-4)(4) = -4\)

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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Answer:

1 911.484916 square units

Step-by-step explanation:

Area of the rectangle = 50 * 14 = 700 square units

thanks to the given informations we can find the height of the triangle by using sine.

sin = opposite/hypotenuse

opposite = hypotenuse * sin = 50 * 0,969188 = 48,459397

Area of the triangle = (50 * 48,459397)/2 = 1.211,484916 square units

Total area = 1.211,484916 + 700 = 1.911,484916 square units

Answer:

x-intercept: 8; the number of hours

y-intercept: 400; distance to be covered

Answer:

total angles in triangle = 180

180 = 44+56+ y

y = 180-44-56

y = 80°

now to find z and x

we know the 2 straight lines are parallel (indicated by arrows)

x = 56°

z = 44°

how?

alternate angles theorem

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Answer:

B

Step-by-step explanation:

1 4/5

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

To determine if a function is linear, we need to verify if it satisfies the linearity property, which states that for any x and y in the domain of the function and any scalars α and β, the function should satisfy f(αx + βy) = αf(x) + βf(y).

Let's examine each function and determine if it is linear:

f(x) = 3x - 2

To check linearity, we need to verify if f(αx + βy) = αf(x) + βf(y). Let's substitute the values:

f(αx + βy) = 3(αx + βy) - 2

= 3αx + 3βy - 2

On the other hand:

αf(x) + βf(y) = α(3x - 2) + β(3y - 2)

= 3αx - 2α + 3βy - 2β

Comparing the two expressions, we can see that they are not equal, so the function f(x) = 3x - 2 is not linear.

f(x) = 2x²

Using the same logic, let's check linearity:

f(αx + βy) = 2(αx + βy)²

= 2(α²x² + 2αβxy + β²y²)

= 2α²x² + 4αβxy + 2β²y²

On the other hand:

αf(x) + βf(y) = α(2x²) + β(2y²)

= 2αx² + 2βy²

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

In conclusion, neither of the given functions is linear since they do not satisfy the linearity property.

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The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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The side x of the right angle triangle is 6√3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sides of a right triangle is named according to the position of the angle. The side of a right triangle are as follows:

The hypotenuse side is the longest side of a right triangle.

Therefore, let's find the x side of the right triangle using trigonometric ratios.

tan 60 = opposite / adjacent

opposite side = x

adjacent side = 6

tan 60 = x / 6

cross multiply

x = 6 tan 60

x = 6 × √3

x = 6√3

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Answer:

4.96 dollars

Step-by-step explanation:

20-5.12=14.88

14.88/3= 4.96 dollars

so each pair of socks costs 4.96$