**7 dollars per week**

Rate of change = change in balance (dollars)/change in weeks

for (0, 32) and (1, 39)

Rate of change = (39 - 32)/(1 - 0)

Rate of change = 7/1 = 7

For (1, 39) and (3, 53)

Rate of change = (53 - 39)/(3 - 1)

Rate of change = 14/2

Rate of change = 7

**Since the rate of change is constant from calculation, then the rate of change of the balance of the student savings account in dollars and cents per week is 7 dollars per week**

I just need to know what do I do when it says 2t but t is 10.M - t squared 2 / (M+p) + 2t

Solution:

Given the question in the image, the following are the solution steps to answer the question.

**STEP 1: Write the given expression**

**STEP 2: Write the given values**

**STEP 3: Substitute the values and simplify**

**We solve the bracket first:**

**We solve the division operator next:**

**We do the addition and subtraction simultaneously to have:**

**Hence, the result of the simplification gives 3**

what is math all about.

Mathematics is a branch of science that deals with numbers, quantities and shapes. It includes arithmetic, geometric, algebra, calculus and many more. It also refers to the study of relationship between numbers or items.

One example is counting numbers which we are using almost everyday in our life.

1, 2, 3, 4 and so on.

can you help me answer this please?This is condense each expression to a sinhle logarithm

**ANSWER**

**EXPLANATION**

Given;

[tex]\frac{\log _3x}{3}[/tex]Rewrite as;

[tex]\frac{1}{3}\log_3x[/tex]Simplify by moving 1/3 inside the logarithm;

[tex]\begin{gathered} \log_3x^{\frac{1}{3}} \\ \end{gathered}[/tex]Find the quotient of 24 and 3.

Please help

**Answer**

**8**

**Step-by-step explanation**

**we know that the term quotient means that we divided so we think backward if 24 is being divided by 3 what times 3 equals 24 the answer would be 8 because 3x8=24.**

Businesses deposit large sums of money into bank accounts. Imagine an account with $10 million dollars in it.

a. How much would the account earn in one vear of simple interest at a rate of

2.12067 Round to the nearest cent.

Answer:

21,206,700

explanation:

10,000,000 x 2.12067 = ____

This would mean the interest rate is ^ for one year. I’m not sure if you mean interest over months but that’s what it is with one over a year.

21,206,700

explanation:

10,000,000 x 2.12067 = ____

This would mean the interest rate is ^ for one year. I’m not sure if you mean interest over months but that’s what it is with one over a year.

275 x 56 using long multiplication

**Answer:**

**1****5****4****0****0**

**Step-by-step explanation:**

*Hope **it **helps **and **I **hope **you **have **a **nice **day**!**!**!** **:**)*

*BRAINIEST **is **appreciated **it **would **really **help!**!**!*

What’s the correct answer? I need help now

The correct answer would be B verhornend did the most

l need help with this please

**Answer:**

**Step-by-step explanation:**

y = 4 - 2x

simplified 4/16 (all fractions)

**Answer:**

The greatest common factor (GCF) of the numerator (4) and the denominator (16) is 4

GCF(4,16) = 4

4/16 = 4 ÷ 4/16 ÷ 4

= 1/4

hope it helps you

Find m

Which answer is correct

The value of** angle EFG **is 50°.

An angle results from the** intersection** of two **straight lines **or rays at a single terminal.

**Angles' Components**

**Vertex:** The intersection of two lines or sides at an angle is called a vertex.

**Arms**: The angle's two sides linked at a single end.

**Initial Side: **A straight line from which an angle is drawn, sometimes referred to as the reference line.

∵ exterior angle = sum of opposite interior angles

∴ 7x+18 = (6x-10) + 38

7x + 18 = 6x +28

x = 10°

∴∠EFG = 6*10-10

∠EFG = 50°

Option (B) is correct answer.

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Can you please show me how to check the answer to see if it is right.

We are given the equation;

[tex]-7=\sqrt[3]{9x-1}-3[/tex]Collect like terms

[tex]\begin{gathered} -4=\sqrt[3]{9x-1} \\ (-4)^3=(\sqrt[3]{9x-1})^3 \\ -64=9x-1 \\ -63=9x \\ x=-7 \end{gathered}[/tex]To check this, we insert the x value into the original equation, if it gives both sides equal, it is correct.

[tex]\begin{gathered} -7=\sqrt[3]{9x-1}-3 \\ -7=\sqrt[3]{9(-7)-1}-3 \\ -7=\sqrt[3]{-64}-3 \\ -7=-4-3 \\ -7=-7 \end{gathered}[/tex]**Therefore, the answer is -7**

THIS IS URGENT!!!! PLEASE HELP!!!

The amount of **flour **needed for 72** cookies **is 4.5 cups.

46 / 69 and 48/84 are** not proportional **because the fractions in their simplest forms are 3/4 and 4/7.

The **value** of x in 2/3 = 1.2 / x is 1.8.

The **value** of x in 8 / 15 = 24 / x is 45.

7 / 5 ≠ 15 / 10.

6 / 8 = 15/20

What are the solutions? In order to determine how many cups of flour is needed for 72 **cookies, **determine how many cups is needed for one cookies.

Amount of flour needed for one cookie = 3/48

Now, multiply this **fraction **by 72: 3/48 x 72 = 4.5 cups

If two fractions are **proportional, **when they are expressed in their simplest form, both fractions would have equal values.

46 / 69 = 2 / 3

48 / 84 = 4/7

Given this **equation **: 2/3 = 1.2 / x

In order to determine the value of x, cross multiply:

2x = 3 x 1.2

2x = 3.6

x = 3.6 / 2

x = 1.8

Given this **equation **: 8 / 15 = 24 / x

In order to determine the value of x, cross multiply:

8x = 24 x 15

8x = 360

x = 360 / 8

x = 45

7/5 and 15 / 10

7/5 = 15 /10

The **cross product**:

(7 x 10) = (5 x 15)

70 ≠ 75

6 / 8 = 15/20

The **cross product **: (6 x 20) = (8 x 15)

120 = 120

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The formula A = P +Prt represents the relationshipbetween the principal, P, interest rate, r, and amount ofmoney, A, in an account over a period of time, t.Solve the equation for P.

**Problem**

The formula A = P +Prt

**Solution**

We can take common factor and we got:

A= P(1+rt)

And we can divide both sides by 1+rt and we got:

**P = A /(1+rt)**

Pt 2. ROOTS OF QUADRATICS 50 PT!!!

Using the **discriminant **of a** quadratic function,** it is found that:

**6.** The **range **of values is of c ≤ 1/16.

**8. **The **range **of values of k is: -9 < k < -1.

**10.** The discriminant is never negative, hence the function has real roots for all values of k.

A quadratic function is **modeled **as follows:

y = ax² + bx + c.

The **discriminant **of the function is given as follows:

Δ = b² - 4ac

For** item 6,** the **function **is given as follows:

y = 2x² - 3x + (2c + 1).

The **coefficients **are given as follows:

a = 2, b = -3, c = 2c + 1.

The function is **positive **for **all values** of x if it has at most one real root, hence:

Δ ≥ 0

(-3)² - 4(2)(2c + 1) ≥ 0

9 - 16c - 8 ≥ 0

1 - 16c ≥ 0

16c ≤ 1

c ≤ 1/16

For** item 8,** the **function **is given as follows:

y = kx² - (k - 3)x - 1 = 0.

The **coefficients **are given as follows:

a = k, b = -k - 3, c = -1.

It has** no real roots **if:

Δ < 0

b² - 4ac < 0

(-k - 3)² - 4(k)(-1) < 0

k² + 6x + 9 + 4k < 0

k² + 10k + 9 < 0

Hence the **range **is:

-9 < k < -1.

For** item 10,** the **function **is given as follows:

y = kx² + (k - 2)x - 2 = 0.

The **coefficients **are given as follows:

a = k, b = k - 2, c = -2.

It has** no real roots **if:

Δ < 0

b² - 4ac < 0

(k - 2)² - 4(k)(-2) < 0

k² - 4k + 4 + 8k < 0

k² + 4k + 4 < 0

(k + 2)² < 0.

(k + 2)² is **always positive**, hence the function will always have real roots.

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**Answer**

Discriminant of a quadratic functio

A quadratic function is modeled as follows:

y = ax² + bx + c.

The discriminant of the function is given as follows:

Δ = b² - 4ac

For item 6, the function is given as follows:

y = 2x² - 3x + (2c + 1).

The coefficients are given as follows:

a = 2, b = -3, c = 2c + 1.

The fnction is positive for all values of x if it has at most one real root, hence:Δ ≥ 0

(-3)² - 4(2)(2c + 1) ≥ 0

9 - 16c - 8 ≥ 0

1 - 16c ≥ 0

16c ≤ 1

c ≤ 1/16

For item 8, the function is given as follows:

y = kx² - (k - 3)x - 1 = 0.

The coefficients are given as follows:

a = k, b = -k - 3, c = -1.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(-k - 3)² - 4(k)(-1) < 0

k² + 6x + 9 + 4k < 0

k² + 10k + 9 < 0

Hence the range is:

-9 < k < -1.

For item 10, the function is given as follows:

y = kx² + (k - 2)x - 2 = 0.

The coefficients are given as follows:

a = k, b = k - 2, c = -2.

It has no real roots if:

Δ < 0

b² - 4ac < 0

(k - 2)² - 4(k)(-2) < 0

k² - 4k + 4 + 8k < 0

k² + 4k + 4 < 0

(k + 2)² < 0.

(k + 2)² is always positive, hence the function will always have real roots.

**Step-by-step explanation:**

Solve the following problem. Give the equation using x as the variable, and give the answer.If 4 is added to five times a number, the result is equal to 7 more than four times the number. Find thenumber.Write the equation using x as the variable. Choose the correct equation below.O A. 4(5x) = 7(4x)O B. 5(x + 4) = 4(x + 7)O C. 5x + 4 = 7(4x)OD. 5x + 4 = 4x + 7O E. 4(5x) = 4x + 7The number is

**Answer**

**Explanation**

The variable given is x

**Five times the variable is 5x**

**When 4 is added, the expression becomes 5x + 4**, which gives the Left Hand Side of the equation.

For the Right Hand Side, **four times the number is 4x**

**7 more than 4x is 4x + 7**

Since the result on the Left Hand Side = Right Hand Side, then the required equation is

[tex]5x+4=4x+7[/tex]Now, to find the number x, we shall solve the above equation as follows

[tex]\begin{gathered} 5x+4=4x+7 \\ \text{Substract 4 from both sides} \\ 5x+4-4=4x+7-4 \\ 5x=4x+3 \\ \text{Substract 4x from both sides} \\ 5x-4x=4x+3-4x \\ x=3 \end{gathered}[/tex]Which is a perfect square?A:72B:81C:90D:99

**Solution:**

A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.

Hence, the number that can be expressed as a product of an integer by itself is;

[tex]81=9^2=9\times9[/tex]**Therefore, the perfect square is ****81.**

**OPTION B**** is correct.**

to put it in graphing form and then graphY=x^2-6x+3

We have the following:

[tex]\begin{gathered} y=x^2-6x+3 \\ f(x)=x^2-6x+3 \end{gathered}[/tex]now, we must give values to x, to be able to graph

[tex]\begin{gathered} f(-2)=x^2-6x+3=(-2)^2-6\cdot-2+3=19 \\ f(-1)=x^2-6x+3=(-1)^2-6\cdot-1+3=10 \\ f(0)=x^2-6x+3=(0)^2-6\cdot0+3=3 \\ f(1)=x^2-6x+3=(1)^2-6\cdot1+3=-2 \\ f(2)=x^2-6x+3=(2)^2-6\cdot2+3=-5 \end{gathered}[/tex]The grahp is:

What is the slope-intercept form(-2,-1),(-4,-3)

To solve the exercise, we can first find the **slope** of the line that passes through the given points using the following formula:

So, in this case, we have:

[tex]\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-4,-3) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-(-1)}{-4-(-2)} \\ m=\frac{-3+1}{-4+2} \\ m=\frac{-2}{-2} \\ m=1 \end{gathered}[/tex]Now, we can use the** point-slope formula**, and we solve for y:

Therefore, **the equation of the line that passes through the points (-2, -1) and (-4, -3) in its slope-intercept form is:**

3 people share one sandwich equally. what fraction of the sandwich will each person get? show work and write and equation. & solution

Let each person get portion "x".

So, 3 person would get "3x" and that would be equal to "1" sandwich.

Thus, we can write the equation:

[tex]3x=1[/tex]Let's solve for "x",

[tex]\begin{gathered} 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]Each person will get **one-third** of a sandwich.

1 devided for 3 people is 1/3 per person

It takes Anastasia 45 minutes to walk 2.5 miles to the park. At this rate, how

many minutes should it take her to walk 3 miles?

ANSWER: 54 minutes

WORK:

45/2.5 = 18

18 • 3 = 54

WORK:

45/2.5 = 18

18 • 3 = 54

45 divided by 2.5 equals 18

18 x 3=54

18 x 3=54

A Native American tepee is a conical tent. Find the number of skins needed to cover a teepee 10 ft. in diameter and 12 ft. high. Each skin covers 15 sq. ft. (use = 3.14)

Since it is conical, we need to find the surface area of the top of the conical shape.

If we unfold the top part of the cone, we will have a section of a circle:

The circunference of this section is the same as the total circunference of the base of the cone, which we can get from its radius (half its diamtere):

[tex]C=2\pi r=2\pi\cdot\frac{D}{2}=2\pi\cdot\frac{10}{2}=10\pi[/tex]If we visualize the cone by the side, we see that it forms a isosceles triangle which the same height and the base euqal to the diameter:

So, we can calculate "R", the radius of the unfolded cone, using the Pythagora's Theorem:

[tex]\begin{gathered} R^2=h^2+(\frac{D}{2})^2 \\ R^2=12^2+5^2 \\ R^2=144+25 \\ R^2=169 \\ R=\sqrt[]{169} \\ R=13 \end{gathered}[/tex]The circunference of a section of a circle is the circunferece of the total circle times the fraction of the section represents of the total circle. Let's call ths fraction "f", this means that:

[tex]\begin{gathered} C_{total}=f\cdot C \\ C_{total}=2\pi R=2\pi\cdot13=26\pi \\ C=10\pi \\ f\cdot26\pi=10\pi \\ f=\frac{10\pi}{26\pi}=\frac{5}{13} \end{gathered}[/tex]The area will follow the same, the area of the section is the fraction "f" times the total area of the circle, so:

[tex]\begin{gathered} A_{total}=\pi R^2=\pi13^2=169\pi \\ A=f\cdot A_{total}=\frac{5}{13}\cdot169\pi=65\pi\approx65\cdot3.14=204.1 \end{gathered}[/tex]So, the surface area of the top of the cone is 204.1 ft². Since each skin covers 15 ft², we can calculate how many skins we need by dividing the total by the area of each skin:

[tex]\frac{204.1}{15}=13.60666\ldots[/tex]This means that we need 13.60666... skins, that is, 13 is not enough, we need one more, so we need a total of **14 skins**.

Anyone know the question ?

The total** commission **earned by **Paun** is $14,000.

For the given question.

The** total sales** done by Paun is $50,000.

There is commission of 25% on **first **$2000.

There is commission of 30% on remaining that is 48,000.

The total** commission** will be 25% of $2,000 and 30% of 48,000.

25% of $2,000 = 25 × 2000/100

25% of $2,000 = $500

30% of 48,000 = 30 × 48,000/100

30% of 48,000 = $14,400

Total commission = $500 + $14,400 = $14,900.

Thus, the total commission earned by **Paun** is $14,000.

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If you would like to make $1323 in 7 years, how much would you have to deposit in an account that pays simple interest of 2%?

A = $13,366.37

A = P + I where

P (principal) = $10,000.00

I (interest) = $3,366.37

i need help with a test prep problem

The diameter = 2 times the radius

radius = diameter / 2

radius = 25.3/2

**radius = 12.65 cm**

**Result radius = 12.65 cm**

Would the answer be 2? I multiplied the coordinate (3, 6) by two and got ( 6, 12), I don't know if I'm right

Since we would need to multiply each coordinate by 1/2 to perform the transformation, then the scale factor would be 1/2. The answer is the first option.

Suppose you invest $5,000 at 4% annual interest. How much money would your investment be worth after 10 years? Round your answer to the nearest hundredth (2 places after the decimal).

**The investment will be worth $7,401.22 after 10 years **

Here, we want to calculate the amount the investment will be worth after 10 years

Mathematically, to get this, we will use the compound interest formula;

[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where A is the amount after 10 years

P is the amount invested which is $5,000

r is the interest rate which is 4%, same as 4/100 = 0.04

n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1

t is the number of years which is 10 in this case

Substituting these values, we have;

[tex]\begin{gathered} A\text{ =5000 (1 + }\frac{0.04}{1})^{1\times10} \\ \\ A=5000(1+0.04)^{10} \\ \\ A=5000(1.04)^{10} \\ \\ A\text{ = 7,401.22} \end{gathered}[/tex]Elijah earned a score of 64 on Exam A that had a mean of 100 and a standarddeviation of 20. He is about to take Exam B that has a mean of 600 and a standarddeviation of 40. How well must Elijah score on Exam B in order to do equivalentlywell as he did on Exam A? Assume that scores on each exam are normally distributed.

Notation:

μ = mean

σ = standard deviation

Exam A:

[tex]\begin{gathered} \mu=100 \\ \sigma=20 \end{gathered}[/tex]The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]Now, for X = 64:

[tex]Z=\frac{64-100}{20}=-1.8[/tex]Exam B:

[tex]\begin{gathered} \mu=600 \\ \sigma=40 \end{gathered}[/tex]Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:

[tex]\begin{gathered} -1.8=\frac{X-600}{40} \\ -72=X-600 \\ \therefore X=528 \end{gathered}[/tex]**The score on exam B should be 528 in order to do equivalently well as he did on Exam A**

(d) Find the domain of function R. Choose the correct domain below.

**Answer:**

last answer is right

( but x can be any number not just x>=0 )

Calculate the variance and standard deviation ofthe samples, using the appropriate symbols to label each

To determine the variance of a sample we can use the following formula:

[tex]s^2=\frac{\sum(x_i-\bar{x})}{n-1},[/tex]where

[tex]\bar{x}\text{ }[/tex]is the mean of the dataset.

The standard deviation is the square root of the variance.

Recall that the mean of a dataset is the sum of the number divided by the number of numbers, therefore, **the mean of the given dataset is**:

Substituting the above result in the formula for the variance, we get:

[tex]s^2=2.675.[/tex]Therefore, the standard deviation is:

[tex]s=1.6355427.[/tex]**Answer:**

Variance:

[tex]s^2=2.675.[/tex]Standard deviation:

[tex]s=1.6355427.[/tex]On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

**the length of the shadow is 30m**

hypotenuse = 50m

height of tree = 40 m

**To solve the question, we will use an illustration:**

To get the length of the shadow, we will apply **pythagoras' theorem:**

**Hypotenuse² = opposite² + adjacent²**

hypotenuse = 50m, opposite = 40m

50² = 40² + shadow²

2500 = 1600 + shadow²

2500 - 1600 = shadow²

900 = shadow²

**square root both sides:**

**Hence, the length of the shadow is 30m**

Question 3Read the excerpt from "Waste Not, Want Not."https://content.ebook.springboardonline.org/assessments/2332/printSeveral months earlier Papadopoulos had taken a break from a career as a business consultant to help manage his family's farm in Petaluma,California. He had repeatedly watched fresh, nutritious vegetables going into the compost pile.Which two words from the excerpt have the strongest positive connotation?
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