at a vacation resort, you can rent a jet ski for $35 per hour plus a $20 rental fee. your bill came to $90.
write an equation that can be used to represent this situation?

The probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.

The mean of the four grand prizes is (34+54+74+94)/4 = 64. Therefore, the probability of selecting two envelopes and receiving an average of exactly 84 thousand dollars is the same as the probability of selecting two envelopes and getting a sum of 168 thousand dollars (since the sum of two values divided by two is equal to their average).

There are six possible combinations of two envelopes, as stated in the question. To find the probability of getting a sum of 168 thousand dollars, we need to find the number of combinations that add up to 168. These combinations are (74,94) and (94,74). Therefore, the probability of getting a sample mean grand prize of exactly 84 thousand dollars is 2/6, which reduces to 1/3.

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Answer:

\((f-g)(x)= x^2-4x-5\)

Step-by-step explanation:

We have the two functions:

\(f(x)=x^2-3x-10\text{ and } g(x)=x-5\)

And we want to find (f-g)(x).

(f-g)(x) is equivalent to f(x)-g(x).

Therefore:

\(\begin{aligned} (f-g)(x)&=f(x)-g(x)\\ &=(x^2-3x-10)-(x-5)\end{aligned}\)

Simplify:

\(\begin{aligned} &=x^2-3x-10-x+5 \\ &=(x^2)+(-3x-x)+(-10+5) \\ &=x^2-4x-5\end{aligned}\)

Therefore:

\((f-g)(x)= x^2-4x-5\)

Answer:

x^2 -3x+5 = 0

Step-by-step explanation:

Answer:

between 4 and 20......................

The number should be bigger than difference of both sides and smaller than sum of both sides.

So

12+8=20

12-8=4

So it should be 4<x<20

which means between 4 and 20

Do you really have brown eyes?

Answer:

4 < x < 20

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

12 - 8 < x < 12 + 8

4 < x < 20 ← range of values for third side

The (⍺3β3) oligomer of ATP synthase can have 3 different functional conformations.

The (⍺3β3) oligomer of ATP synthase, which consists of three α-subunits and three β-subunits, can exhibit three different functional conformations. These conformations are known as "open," "loose," and "tight" states. The binding change mechanism describes the sequential transition of the catalytic sites within ATP synthase as they alternate between these conformations, facilitating the synthesis of ATP.

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That the nimber value i

Answer: \(49.79\ m\)

Step-by-step explanation:

Given

The volume of the spherical solid is \(V=123,456\ m^3\)

It is melted to form a solid cube

Suppose the edge length of the cube is \(a\)

The volume of the sphere is  \(\frac{4}{3}\pi r^3\)

\(\Rightarrow 123,456=a^3\\\Rightarrow a^3=123,456\\\text{Factorising 123,456}\\\Rightarrow a^3=2^6\times 3\times 643\\\\\Rightarrow a=\sqrt[3]{2^6\times 3\times 643} \\\\\Rightarrow a=4\sqrt[3]{ 3\times 643}\\\\\Rightarrow a=49.79\ m\)

The equation for function g is given by using translational ideas:

g(x) = 7x/3 + 1.

According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or stretching vertically or horizontally, and reflecting over the x- or y-axis.

Given that f(x) exists, obtaining f is equal to compressing horizontally by a factor of a. (ax).

The function in this issue is as follows:

f(x) = 7x + 1.

We have the following for a horizontal compression of 1/3:

g(x) = f(1/3x) = 7x/3 + 1.

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(21)(x^6)(y^5) / (14)(x^2)(y^9)

Step 1: Coefficients

---This is just like simplifying fractions!

21 / 14 = 3 / 2

Step 2: Variables with exponents

---Remember to subtract exponents because this is division!

x^6 / x^2 = x^4 / 1

y^5 / y^9 = 1 / y^4

Answer: (3)(x^4) / (2)(y^4)

Hope this helps!! :)

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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Answer:

SSS

Step-by-step explanation:

Answer:

WZY congruent to WXY

Step-by-step explanation:

by SSS theorem

The number of different orders of top-three finishers in the free throw contest depends on the total number of participants. The specific number of participants is not provided in the given information.

To determine the number of different orders of top-three finishers, we need to know the total number of participants in the free throw contest. The order of finishers can be calculated using the concept of permutations, where the order matters.

If there are "n" participants, the number of different orders of top-three finishers can be calculated using the formula nP3, which represents the number of permutations of "n" objects taken 3 at a time. However, since the total number of participants is not provided in the given information, we cannot determine the exact number of different orders of top-three finishers.

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Answer:

x + y + z = 360

Answer:

x + y + z = 360°

Step-by-step explanation:

I presume that the attached image is what you are trying to achieve.

x + y + z = 360°

Answer: I gotta say forever 21, American eagle, rue21, and Aeropostale.

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

4x is going to be the answer because he bakes 4 cobblers and they need c cups of flour so c is going to be the variable x. :)

The objective function is "min 2m + 3b" which represents the cost of making m units and buying b units. To find the optimal solution, we need to minimize this cost. To begin, we are given that the total number of units needed is 4000. This implies that m + b = 4000.

Now, let's solve for m and b separately.
1. Solving for m:
We want to minimize the cost of making m units, which costs $2 per unit. Therefore, the cost of making m units is 2m dollars.
2. Solving for b:
We want to minimize the cost of buying b units, which costs $3 per unit. Therefore, the cost of buying b units is 3b dollars.

To summarize:
- The cost of making m units is 2m dollars.
- The cost of buying b units is 3b dollars.
- The total number of units needed is 4000, so m + b = 4000.

The objective function "min 2m + 3b" represents the total cost. We want to minimize this cost.

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The equation in point-slope form:  y - y₁ = m(x - x₁)

slope:  m = -2

point:   (4, -5)   ⇒   x₁ = 4, y₁ = -5

Therefore, the equation of the line in point-slope form:

The equation in slope-intercept form:   y = mx + b

Parallel lines has the same slope, so:

y = 4x + 2     ⇒    a = 4

If a line passes through the point (x₁, y₁) then the equation y₁ = mx₁ + b is true.

(4, 6)  ⇒   x₁ = 4, y₁ = 6  

So:   6 = 4·4 + b  ⇒   b = -10

Therefore the equation:  

a = 3

(-1, 1)  ⇒   x₁ = -1, y₁ = 1  

So:   1 = 3·(-1) + b  ⇒   b = 4

The equation:  

The product of slopes of perpendicular lines is -1.

2x - 7y = 1    ⇒  7y = -2x + 1   ⇒  y = -²/₇x + ¹/₇

-²/₇×m = -1    ⇒   m = ⁷/₂

(0, -4)  ⇒   x₁ = 0, y₁ = -4  

-4 = ⁷/₂·0 + b   ⇒   b = -4

The equation:

Answer:

What?

Step-by-step explanation:

Okay.

Answer:

13 2/3 yds

Step-by-step explanation:

We know that there are 3 ft in 1 yd

41 ft * 1 yd / 3ft = 41 / 3  yds

Changing to a mixed fraction

39/3 + 2/3 yds

13 + 2/3 yds

13 2/3 yds

13 and 2 feet

Step-by-step explanation:

there are 3 feet in every yard.

For the first problem, we can interpret the confidence interval as follows:

We are 95% confident that the true mean commuting time for workers who drive to work is between 27.74 and 30.06 minutes.

This means that if we were to repeat the sampling process many times and construct a 95% confidence interval each time, about 95% of those intervals would contain the true mean commuting time.

For the second problem, we can use the following formula to find a 95% confidence interval for the true mean length of long distance telephone calls:

\(CI = X ± t*(s/sqrt(n))\)

Where X is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with n-1 degrees of freedom for a 95% confidence interval.

Plugging in the values given, we get:

\(CI = 1.68 ± t*(5.2/sqrt(45))\)

To find the value of t, we can look it up in a t-distribution table or use a calculator. For a 95% confidence interval with 44 degrees of freedom, we get t = 2.015.

Plugging this value in, we get:

\(CI = 1.68 ± 2.015*(5.2/sqrt(45)) = (0.86, 2.50)\)

So we can interpret the interval as follows:

We are 95% confident that the true mean length of long distance telephone calls made by customers of this company is between 0.86 and 2.50 minutes longer or shorter than the sample mean of 1.68 minutes.

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we must use the slope formula

where (x2,y2)is a point right from (x1,y1)

so on this case

(x2,y2)=(2,5)

and

(x1,y1)=(-8,-4)

the slope is 9/10

9514 1404 393

Answer:

  A

Step-by-step explanation:

If the price of a hot dog is x, then the price of two hot dogs is 2x, and the price of 3 of them is 3x.

If the price of a drink is y, then the price of 2 drinks is 2y.

So, we have the price of 2 hotdogs and 2 drinks is 4.75.

  2x + 2y = 4.75

And the price of 3 hot dogs and 1 drink is 7.75.

  3x + y = 7.75

This pair of equations matches those in choice A.

_____

Comment on the question

We know right away that something is screwy here, because the cost of two hotdogs and 2 drinks should be an even number. 4.75 is not an even number. If we solve this set of equations, we find the cost of a drink is negative—not something you're likely to see in the real world.

So, this is an exercise in writing equations. It has nothing to do with finding real prices.

Let's talk......................

..........

Answer:

798

Step-by-step explanation:

Answer:

Part A: total pizza cost = 2.50s + 2.25t + 18

Part B: 30 dollars

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks"!

Answer:

Part A: 18 + 2.25t + 2.50s

Part B: $30

Step-by-step explanation:

Let t= each additional topping

Let s=each side

First we add the cost of one pizza ($18)

Then we add each additional topping (t) multiplied by its cost (2.25 dollars)

Finally we add each side (s) multplied (2.50 dollars)

Part B:

Plug in 2 for t and 3 for s into the expression from earlier and simplify:

Expression: 18 + 2.25(2) + 2.50(3)

=18+ 4.50 + 7.50

=30

And there you have it- the total cost is $30.

Hope this helps and good luck in your studies :)

Answer:

From the given graph, it is clear that at x = 4, the corresponding y-value of the graph is y = 1

Therefore, we conclude that:

Step-by-step explanation:

Given:

A graph is given

To determine:

g(4) = ?

In other words, from the given graph, we need to determine the value of y at x=4

Finding g(4)

From the given graph, it is clear that at x = 4, the corresponding y-value of the graph is y = 1

Therefore, we conclude that:

Answer:

Yes, it is greater.

Step-by-step explanation:

15/3 is equal to 5.

5 is a positive number, while -4.75 is a negative number. Therefore, 15/3 is greater than -4.75.

Answer:

Yes!

Step-by-step explanation:

any positive fraction/decimal no matter the number will always be greater than a negative number!

Answer:

-1/2

Step-by-step explanation:

Exact form:-1/2

Decimal form: -0.5

Hope that helps.

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Thank you

19NBoli