I need help with this question Write and expression that models the situation:Sarah has spent x dollars out of the 30 dollars she started with.

Answer: 6 hours

Explanation:

We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:

The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.

Now, we are told that "Together, their study time was 10 hours" so we have the following equation:

This will be our equation 2.

The next step is to substitute equation 1 into equation 2:

And we solve for J.

Combining like terms:

We add +2 on both sides of the equation to cancel the -2 on the left side:

And we divide both sides by 3:

Jackie studied for 4 hours.

Since we are asked for Ruth, we substitute J=4 into the equation 1:

Ruth studied for 6 hours.

Solution:

Given that;

For B∩C, i.e . common elements between bot sets

Then, A∪(B∪C), i.e. all the elements in A and B∩C

Hence, A∪(B∪C) is

Given the measure -845° we can find its coterminal measure on the interval, [0,360) below

Explanation

For angles measured in degrees

Answer: Option A

When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.

So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:

Then the total lateral surface is:

Then we need to find the volume of the truncated pyramid. This is given by the following formula:

Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:

In summary, the lateral surface is 46.2in² and the volume is 60.7in³.

i = P r T

interest: i

Principal = $350

Interest rate : 4.8% (in decimal form, 4.8/100 = 0.048)

time = t = days/365 = 150/360

Replacing:

i= 350 (0.048) (150/360) = 7

Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.

The given function :

In the graph of the f(x) , the least value of x of the given curve is : (-0.939)

and the f(x) at x = (-0.939) is -10.065

The absolute minimum value is (x,y) = (-0.939, -10.065)

To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)

Answer : (x, y) = (-0.94, -10.07)

The probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is .

in the question ,

it is given that

the waiting time is randomly distributed  between 0 and 6 minutes .

Since it is uniformly distributed , the Uniform distribution have two bounds a and b .

The probability of finding the value greater than x can be calculated using the formula .

P(X>x) = (b-x)/(b-a)

Given that , the waiting time is Uniformly distributed 0 and 6 minutes , we get a=0 and b=6,

Substituting the values in the Probability formula , we get

P(X>2.25) = (6-2.25)/(6-0)

= 3.75/6

= 0.625

Therefore , the probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is 0.625.

The given question is incomplete , the complete question is

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.

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Hence, the correct option is Option D. None of the choices are correct.

Answer:

v > -7.1

Step-by-step explanation:

Answer:  expect to lose 679.07 dollars

==========================================================

Explanation:

Assuming each free throw is independent of any other, the probability of making the next free throw is 359/449

The probability of making 3 in a row is (359/449)^3 = 0.511145 approximately which represents the probability of earning the $39

That must mean 1-0.511145 = 0.488855 is the approximate probability of losing $43

Let's make a table of outcomes and their associated probabilities.

X = amount of money the player earns (the person shooting the free throws)

[tex]\begin{array}{|c|c|} \cline{1-2}\text{X} & \text{P(X)}\\\cline{1-2}39 & 0.511145\\\cline{1-2}-43 & 0.488855\\\cline{1-2}\end{array}[/tex]

Then from here we'll multiply each X and P(X) value for each separate row.

Example: 39*0.511145 = 19.934655

Let's form a third column of these products

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{X} & \text{P(X)} & \text{X}*\text{P(X)}\\\cline{1-3}39 & 0.511145 & 19.934655\\\cline{1-3}-43 & 0.488855 & -21.020765\\\cline{1-3}\end{array}[/tex]

Add up everything in the X*P(X) column and you should get roughly -1.08611 which rounds to -1.09

The player expects, on average, to lose about $1.09 each time they play this game. Playing 623 times means they should expect to lose 623*1.09 = 679.07 dollars

Of course, given the nature of this random process, it's not a guarantee they will lose this amount. This is just the average of many attempts.

The distributive property of multiplication states the following:

So, for the given expression, we have:

There are eight students in each van and 38 students are in each bus.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Let the number of students fit into a van would be v

And the number of students fit into a bus would be b

School A:

2v + 6b = 244  ...(i)

2v = 244 - 6b

v = 122 - 3b

School B:

4v + 7b = 298  ...(ii)

Substitute the value of v = 122 - 3b in the equation (ii),

4(122 - 3b) + 7b = 298

Solve for b to get b = 38.

Substitute the value of b = 38 in equation (i),

2v + 6(38) = 244

2v + 228 = 244

2v = 16

v = 8

Therefore, eight students are in each van and 38 students are in each bus.

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Given:

David had $350. After shopping, he was left with $235.

Required:

If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.

Explanation:

We know c is the amount spent

So,

Available amount = Total amount - spent amount

235 = 350 - c

c= 350 - 235

c = 115

Answer:

Hence, David spent $115.

The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.

Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.

On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.

For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.

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We know that

• Ethan burns 650 calories per hour.

If he runs 5 hours we just have to multiply this time with the given rate.

Answer:

No

Step-by-step explanation:

3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe

she only has 1 cup

so does not have enough to triple her recipe

Answer:

No

Step-by-step explanation:

If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.

2 . 0 5 0

0 . 0 0 4

---------------------------------

8 2 0 0

+ 0 0 0 0

0 0 0 0

0 0 0 0

------------------------------

0 . 0 0 8 2 0 0 =

-----------------------------

Solution

Step 1:

Write the two given points:

p(4,2) and q(8,12)

Step 2

Find the distance between the two points:

Answer

Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.

What is Rational Function?

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.

So this will be a rational function with the vertical asymptotes given by the denominators:

(x + 5) and (x + 6).

The x-intercepts will be provided by the numerator,

which will be:

a(x + 3)(x + 4)

The letter an is a constant.

Given that (0,4) is the y intercept, we have:

4 = a(0+3)(0+4) / (0+5)(0+6)

4= 12a / 30

12a = 120

now,

a = 120/12,

a = 10,

and a = 1.

Now,

a(x+3)(x+4) / (x+5)(x+6) = 0

10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0

Hence, We have the following equation for a rational function:

10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.

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Given:

Required: First four terms

The nth term of a geometric sequence :

Hence, we can obtain the next four terms by substituting

From the question, we can derive the following:

Micheal earns 2x³ + 3x

His wife earns 3x² + 6

If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.

So we will have:

(2x³ + 3x) + (3x² + 6)

Adding up the two earnings:

2x³ + 3x² + 3x + 6

So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.

So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).

ANSWER

d < 200

EXPLANATION

If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.

A number which is 5 more than 8009998 is 8010003

In this question we need to find a number which is 5 more than 8009998.

Let x be a number which is 5 more than 8009998.

We get the required number by adding 5 to 8009998.

so, we write it down as:

x = 8009998 + 5

x = 8010003

Therefore, a number which is 5 more than 8009998 is 8010003

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The company estimates a residual value of $1,500 and a six-year service life.

It is given that,

Cost of truck delivery = $ 23100

Salvage value = $ 1500

Useful life = 6 years

Depreciation expenses by using the straight-line method are calculated as,

Substituting the value in the formula,

Thu

From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,

where x denotes the missing length. Then, our equation give us

By taking square root to both side, we have

Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft

Answer:125.431034

Step-by-step explanation:

Let

x -----> the missing number

we know that

80%=80/100=0.80

so

0.80x=20

solve the linear equation for x

Divide by 0.80 both sides

x=20/0.80

x=25

the answer is 25

Answer

D. (-3, 0) and (3, -4)

Explanation

Let the coordinate of the points be A(-9, 4) and B(9, -8).

We shall look for the gradient m of line using

m = (y₂ - y₁)/(x₂ - x₁)

Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8

m = (-8 - 4)/(9 - -9) = -12/18 = -2/3

From option A - D given, only C and D would have the same gradient of -2/3 as line AB

To know the correct option, we shall look for the equation of the line AB, that is,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)

(y -4)/(x + 9) = -12/18

(y - 4)/(x + 9) = -2/3 -----------*

Between option C and D, only D satisfies the equation *

That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3

Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3

Solution:

Given the amount invested, P; the rate, r, at which it was invested and the time, t, it was invested.

Thus,

Then, we would solve for the total amount, A, using the formula;

Thus;

ANSWER: $2,299.43