Ricky Bobby currently has $500 in his savings account, and figures that he will add $25 per week from his
job. He realizes that he can use the equation
S=25w+500 where S is the amount in savings and w= number of weeks from now.
a. How much will he have saved in 15 weeks
b. When will Ricky Bobby have $1200?

To factor this polynomials, we will use the method "slide and divide".

First, we will multiply the first numerical coefficient 10 to the last term 12, so the expression becomes:

Our next step here is to find factors of the last term -120 that when added, the result is the middle term 7.

The possible factors of -120 are:

-1 and 120

1 and -120

2 and -60

-2 and 60

3 and -40

-3 and 40

4 and -30

-4 and 30

5 and -24

-5 and 24

6 and -20

-6 and 20

8 and -15

-8 and 15

10 and -12

-10 and 12

After determining all the possible factors of -120, let's add the pairs and see which pair would give us the middle term +7.

-1 and 120 = 119

1 and -120 = -119

2 and -60 = -58

-2 and 60 = 58

3 and -40 = -37

-3 and 40 = 37

4 and -30 = -26

-4 and 30 = 26

5 and -24 = 19

-5 and 24 = 19

6 and -20 = -14

-6 and 20 = 14

8 and -15 = -7

-8 and 15 = 7

10 and -12 = -2

-10 and 12 = 2

As we can see above, the factors of -120 that gives us +7 is -8 and 15. Hence, the possible factors of x² + 7x - 120 are:

Remember that we multiplied the first term 10 to the last term -12. Our next step here is to divide -8 and +15 with 10 and simplify if needed.

Since the coefficient is a fraction, let's simplify it further.

Hence, the factors of 10x² + 7x - 12 are (5x - 4) and (2x + 3).

The ODE

y''' - 7y'' + 8y' + 16y = 0

has characteristic equation

r ³ - 7r ² + 8r + 16 = 0

which can be factorized as

(r - 4)² (r + 1) = 0

Then the characteristic solution to the ODE is

y(x) = C₁ e ⁴ˣ + C₂ x e ⁴ˣ + C₃ e ⁻ˣ

Answer:

AB =  4.9cm

Step-by-step explanation:

We know

AC is 9.1 centimeters, and BC is 4.2 centimeters.

Find AB

We take

9.1 - 4.2 = 4.9cm

So, AB = 4.9cm

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

Work Shown:

A = probability 1st satellite sends weak signal

A = 3/7

B = probability 2nd satellite sends weak signal, assuming event A happens earlier

B = 2/6 = 1/3

C = probability both A and B happen at the same time

C = A*B

C = (3/7)*(1/3)

C = 3/21

C = 1/7

Note: The fraction 3/7 has both numerator and denominator decrease by 1, to get 2/6, due to the "no replacement" condition.

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

Answer:

-22

Step-by-step explanation:

h(5)=-5•5+3

h(5)=-25+3

h(5)=-22

Answer:

-22

Step-by-step explanation:

Replace x with 5 and multiply tge -5 by 5 wich equals -25 and add 3 which would make -22

Answer:

Step-by-step explanation:

In order to properly fit the website for Faria mobile devices such as tablets and smartphones, the company will need to make sure that the website is optimized for different screen sizes. The original website was designed for a screen dimension of 16" x 9", but mobile devices have varying screen sizes. The company can use the dimensions listed in the table to ensure that the website looks and functions properly on the five mobile devices they are researching.

Answer:

18.8 cubic inches

Step-by-step explanation:

1. Solve for the volume of Cup A. (volume of a cone = 1/3πr² · h)

1/3 · 3.14 · 1² · 3 = 3.14 in³

2. Solve for the volume of Cup B (volume of a cylinder = πr² · h)

3.14 · 1² · 7 = 21.98 in³

3. Subtract the volume of Cup A from Cup B

21.98 - 3.14 = 18.84

4. Round 18.84 to the nearest tenth

18.84 → 18.8 in.³

Answer:

18 .8

Step-by-step explanation:

got it right on test

Answer:

I have attached a really rough graph!!

Step-by-step explanation:

The point that does not fit in the proportional relationship is (6,2) when we plot the other three points and join the points they will give us a staright line but the point (6,2) isnt lying on that staright line.. Therefore, it does not fit in the proportional relationship!

Answer:

(6,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

ΔABC = ΔCDA

Step-by-step explanation:

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

the answer would be e because you can't determine the side length

Answer: (B)

Step-by-step explanation:

Step 1: Find minimum values of the third side.

53-17 = 36

Step 2: Find maximum values of the third side.

17+53 = 70

Step 3: Find equation

36 < x < 70

Using probabilities, it is found that the expected profit of one round of this game is of $0.

A probability is the number of desired outcomes divided by the number of total outcomes.

Hence, since the coin and the dice are independent, the probability of winning is:

\(p = \frac{1}{2} \times \frac{2}{6} = \frac{1}{6}\)

The expected value is the sum of each outcome multiplied by its respective probability.

In this problem:

Then:

\(E(X) = 30\frac{1}{6} - 6\frac{5}{6} = 5 - 5 = 0\)

The expected profit of one round of this game is of $0.

A similar problem is given at https://brainly.com/question/24855677

Answer:

3¹² is answer

Step-by-step explanation:

3^(2+4+6)

3^12

We can prove the formula given in the question as a theorem using the truth table method.

A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.

Let A, B, and C represent propositions. We construct a truth table as follows:

A B C (A → (B − C)) (B → (A → C))

T T T T T

T T F T F

T F T T T

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.

Learn more about Truth Table at:

brainly.com/question/28605215

#SPJ4

Answer: Andre should buy Car 2. Brainliest?

Step-by-step explanation:

To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.

For Car 1: y = 25x

This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).

For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:

For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).

For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).

For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).

For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).

For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).

Therefore, Car 2 has a consistent gas mileage of 30 mpg.

From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.

Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.

Answer:

0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean and standard deviation of 486.9 and 24.01, respectively.

This means that \(\mu = 486.9, \sigma = 24.01\)

What is the probability that on a given day the supermarket will sell between 477 and 525 gallons of milk?

This is the p-value of Z when X = 525 subtracted by the p-value of Z when X = 477.

X = 525

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{525 - 486.9}{24.01}\)

\(Z = 1.59\)

\(Z = 1.59\) has a p-value of 0.9441

X = 477

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{477 - 486.9}{24.01}\)

\(Z = -0.41\)

\(Z = -0.41\) has a p-value of 0.3409

0.9441 - 0.3409 = 0.6032

0.6032 = 60.32% probability that on a given day the supermarket will sell between 477 and 525 gallons of milk

2(z+10)

2z+20

Answer:

2z+20

Answer: The third one

Step-by-step explanation:

That system has the same equation, but a different solution, meaning the lines can never intersect.

We can also convert it into slope-intercept form.

y = -2x + 9

y = -2x + 5

Different slope and same y-intercept = NO SOLUTION

Answer:

2x + y = 9

2x + y = 5

Step-by-step explanation:

No solutions for 2 lines will only happen when the lines are parallel and never touch.  So there are no solutions.

Lines are parallel when slopes are the same.

The equations cannot be the same just the slopes are the same.  

Let's rearrange this set of equations into y=mx+b so we can see what the slope m is:

2x + y = 9           and               2x + y = 5

y= -2x +9                                 y= - 2x +5

You can see the lines are different but have the slopes so they are parallel and no solutions.

Answer:

17/1000

Step-by-step explanation:

0.017 as a decimal- in simplest form as a fraction is 17/1000

Answer:

1 7/10 or 17/10

Step-by-step explanation:

the number after the decimal point is over ten

the number before the decimal point is a whole number

Answer:

It means Progressing

In Progress

Step-by-step explanation:

Answer:

I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.

Step-by-step explanation:

The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.

Answer:

Part A: Which point represents the origin?

Part B: Starting from the origin, explain how to plot the following three points accurately (1,-1) (-1.1.25) (-2,3).

Reference point is the origin for below.

Answer:

62 miles per hour

Step-by-step explanation:

620mile/10hrs

62miles/hr

62 miles per hour