A) f(x)= -5/9(x-4)^2+15

B) f(x)= 5/9(x-4)^2+15

C) f(x)= -35/9(x-4)^2-15

D) f(x)= 35/9(x-4)^2-15

Since quadratic function f has vertex (4, 15) and passes through the **point** (1, 20), an **equation** that represents f is: B. f(x) = 5/9(x - 4)² + 15.

In Mathematics, the vertex form of a **quadratic function** is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

h and k represents theBased on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

20 = a(1 - 4)² + 15

20 = 9a + 15

a = 5/9

Therefore, the required **quadratic function** is given by:

f(x) = a(x - h)² + k

f(x) = y = 5/9(x - 4)² + 15

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Write the formula that shows the dependence of the edge length a on the volume V of a cube.

The **formula** that shows the dependence of the edge length a on the **volume** V of a cube is a = ∛V

In other words, to find the edge **length** of a cube, we take the cube root of its volume. This formula is derived from the formula for the volume of a cube, which is:

V = a³

Here, a is the length of each edge of the cube. **Solving** this equation for a, we get:

a = ∛V

This formula can be used to find the length of one **edge** of a cube when its volume is known. Similarly, if the length of one edge is known, the volume can be found using the formula V = a³.

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A building supply company sells sand by the cubic foot and by the cubic yard. The price of one cubic year of sand is $33. 75. What do you think the price of one cubic foot of sand should be? Explain answer

The price of one cubic yard of sand is $33.75, then the **price** of one cubic foot of sand should be $1.25.

To determine the price of one cubic foot of sand, we need to convert cubic yards to **cubic** feet. One cubic yard is equal to 27 cubic feet (3 feet x 3 feet x 3 feet). Therefore, if the price of one cubic yard of sand is $33.75, then the price of one cubic foot of sand should be $33.75/27 = $1.25.

This makes sense because one cubic yard contains 27 cubic feet. So, if the price of one cubic **yard** is $33.75, then the price per cubic foot should be 1/27th of that price.

It is important to note that this assumes the price per unit of sand remains constant regardless of the quantity **purchased**. In reality, bulk purchases may result in a discounted price per unit. Additionally, factors such as transportation costs and demand may also affect the price of sand.

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Mr. Thayer wants to measure the height of the CN tower. He stands 320 m from the base of the tower. He uses an inclinometer to measure the angle from the (horizontal) ground to the top of the tower, and it is 60°. Assume Mr. Thayer's eyes are 1.6 m above the ground.

The height of the CN tower which is 320m away from the Mr.Thayer is **555.85 meters**.

Please look at the attached diagram for a clear explanation,

From the diagram point A represents, the Mr.Thayer's eyes, point B represents Mr.Thayer's foot, point C represents the **base** of the CN tower along with point E represents the top of the tower.

From the following diagram lets find out the height of the tower,

In right-angled triangle ADE, Tan theta = opposite/adjacent

So, Tan (60°) = DE/AD

√3 = DE/320m

DE = 320m x √3

DE= 554.25m

DE represents the height of the CN tower from the eyes of Mr.Thayer.

To find out the **total height** of the CN tower, the height of Mr.Thayer + the height of the CN tower from Mr. Thayer's eyes = 554.25m + 1.6m = 555.85m.

From the above explanation, we can **conclude** that the height of the CN tower from the base = 555.85m.

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You deposit $2,500 in an investment

account. The rate of growth is 4. 55% a year.

If you make no further deposits or

withdrawals, and the investment is allowed

to grow uninhibited, how long will it take for

your investment to reach $5,000? Round to

the nearest tenth.

It will take approximately **15.27 years** for your **investment** to reach $5,000 at a growth rate of 4.55% per year.

Using the compound interest calculation, we can determine how long it will take for your investment to grow to $5,000 at a growth rate of 4.55% per year:

[tex]A = P(\frac{1 + r}{n} )^(^n^t^)[/tex]

Where:

A = the final amount ($5,000)

P = the **initial deposit **($2,500)

r = the interest rate (4.55%)

n = the number of times interest is compounded per year (assuming yearly compounding, n=1)

t = the number of years

Plugging in the values, we get:

[tex]\$5,000 = \$2,500(\frac{1 + 0.0455}{1} )^(^1^t^)[/tex]

Simplifying, we get:

[tex]2 = (1.0455)^t[/tex]

Taking the** natural logarithm** of both sides, we get:

ln(2) = t ln(1.0455)

Solving for t, we get:

t = ln(2) / ln(1.0455) = 15.27 years

Therefore, it will take approximately 15.27 years for your investment to reach $5,000 at a growth rate of 4.55% per year.

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Mike calculated the net sales for his company using the following figures:

Gross sales = $50,000

Discounts = $1,800

Freight in = $2,750

Sales returns and allowances = $4,380

The net sales of the company are __________.

a. )

$46,570

b. )

$49,830

c. )

$43,820

d. )

$41,070

To calculate the net sales, we need to subtract the discounts, sales returns and allowances, and freight in from the **gross sales**.

Therefore, we have:

**Net sales = Gross sales - Discounts - Sales returns and allowances - Freight in**

Substituting the given values, we get:

Net sales = $50,000 - $1,800 - $4,380 - $2,750 = $41,070

Therefore, the net sales of the company are **$41,070. Answer: (d).**

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what is the radius of a circle if 24-meter chord is 5 meters from center

We can use the following formula to find the radius of the circle:

```

r = sqrt((c/2)^2 + h^2)

```

where `r` is the radius of the circle, `c` is the length of the chord, and `h` is the distance between the center of the circle and the chord.

In this case, we know that the length of the chord is 24 meters, and the distance between the chord and the center of the circle is 5 meters. Therefore:

```

r = sqrt((24/2)^2 + 5^2)

r = sqrt(12^2 + 25)

r = sqrt(144 + 25)

r = sqrt(169)

r = 13

```

Therefore, the radius of the circle is 13 meters.

```

r = sqrt((c/2)^2 + h^2)

```

where `r` is the radius of the circle, `c` is the length of the chord, and `h` is the distance between the center of the circle and the chord.

In this case, we know that the length of the chord is 24 meters, and the distance between the chord and the center of the circle is 5 meters. Therefore:

```

r = sqrt((24/2)^2 + 5^2)

r = sqrt(12^2 + 25)

r = sqrt(144 + 25)

r = sqrt(169)

r = 13

```

Therefore, the radius of the circle is 13 meters.

At the school bookstore, Rylan bought two spiral notebooks and one folder and paid $6. 70. Olivia bought three spiral notebooks and five folders and paid $12. 85. Find the cost of each folder

To find the** cost **of each folder, we need to first set up a system of equations based on the given information. Let x be the cost of a spiral notebook and y be the cost of a folder. We can create the following equations:

1) 2x + y = $6.70 (Rylan's purchase)

2) 3x + 5y = $12.85 (Olivia's purchase)

First, we can solve equation 1 for y:**y = $6.70 - 2x**

Next, substitute this expression for y into equation 2:**3x + 5($6.70 - 2x) = $12.85**

Now, solve for x:

3x + $33.50 - 10x = $12.85

Combine like terms:

Now, divide by -7:

x = $2.95

Now that we know the cost of a spiral notebook, we can plug this value back into the expression we found for y:

y = $6.70 - 2($2.95)

y = $6.70 - $5.90

So, the cost of each folder is

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A round cake has a diameter of 30 cm30 cm30, start text, space, c, m, end text. angela places the cake on a circular cake board with a diameter 5 cm5 cm5, start text, space, c, m, end text longer than that of the cake.what is the circumference of the cake board?give your answer in terms of ππpi.

The **circumference** of the cake board is 35π cm.

The **diameter **of the round cake is 30 cm, which means its** radius** is 15 cm. The diameter of the circular cake board is 5 cm longer than that of the cake, which means its diameter is 30 + 5 = 35 cm. Therefore, the radius of the cake board is 17.5 cm.

The circumference of a circle is given by the formula:

[tex]$$C = 2 \pi r$$[/tex]

where [tex]$r$[/tex] is the radius of the circle. Using this formula, we can find the **circumference** of the cake board:

[tex]$$C = 2 \pi \cdot 17.5 = 35 \pi$$[/tex]

Therefore, the circumference of the cake board is 35π cm.

In other words, if you were to wrap a string or ribbon around the** edge of the cake board**, it would need to be 35π cm long.

This is an important **measurement** to consider when decorating or transporting a cake, as it can help ensure that the cake is **centered** on the board and that there is enough room for any additional decorations or trimmings.

In summary, the circumference of the cake board is 35π cm.

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The equation relates the sound level, , in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, (approximately watts/meter2).

The maximum intensity of a car horn is approximately 0. 01 watts/meter2. Based on this information, which value is closest to the maximum sound level, in decibels, of a car horn?

.

100 dB

10 dB

1,000 dB

10,000 dB

The equation relates the sound level, in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, which is approximately 1 x 10^-12 watts/meter2.

Using this equation and the given maximum intensity of a car horn (0.01 watts/meter2), we can find the maximum sound level in decibels:

Sound level = 10 log (0.01/1 x 10^-12)

Sound level = 10 log (1 x 10^10)

Sound level = 100 dB

Therefore, the value that is closest to the maximum sound level in decibels of a car horn is 100 dB.

Choose the system for the graph.

The **system of equations **which represents the given graph is:

(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

A group of equations comprising one or more variables is known as a system of equations.

The **variable **mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

So, the lines have **slopes **of 7/3 and 2/5, based on the solutions. (We could verify this by close examination of the **graph**.)

The shade is above (greater than) the line with a slope value of 2/5, and below (less than) the line with a slope value of 7/3.

So, using the symbols, we need to find two inequalities:

y ≥ 2/5x ...

y ≤ 7/3x ...

Choice C contains this combo.

Therefore, the **system of equations **which represents the given graph is:

(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3

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Which is the closest to the volume of the solid figure formed from the net?

I'm sorry, but I cannot answer your question without a net or a description of the solid figure. Can you please provide more information or context?

What is the probability of drawing the Ace of Diamonds from a deck of cards, putting it back in the deck, shuffling the deck, and then drawing the Ace of Clubs?

The** probability **of the** event** of having ace of diamonds and ace of clubs is 1/2704

A probability event can be defined as a set of outcomes of an experiment. In other words, an **event **in **probability** is the subset of the respective sample space.

In a standard deck of cards, we have 52 cards of which 4 are aces. The probability of drawing the first ace of diamonds will be 1/52. Shuffling the card again, the probability of drawing having an ace of club will be another 1/52 since the card was replaced and shuffled.

To determine the** probability **of the two events occurring will be

P = (1/52 * 1/52) = 1 / 2704 = 0.0003698

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Rachel currently has $836 in a savings account that has earned 4. 5% annual compound interest for the past year. What was Rachel's beginning balance one year ago if she has made no other deposits during the year. $873. 62 $800. 00 $576. 55 $798. 38

Rachel's **beginning balance** one year ago if she has made no other deposits during the year is $800.00. Therefore, the correct option is 2.

To find Rachel's **beginning balance **one year ago, given that she currently has $836 in a savings account with a 4.5% annual compound interest rate, we'll use the **compound interest** formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount ($836)

P = the **principal** (beginning balance) - this is what we're trying to find

r = the annual interest rate (0.045 or 4.5%)

n = the number of times interest is compounded per year (assuming it's compounded annually, n = 1)

t = the number of years (1 year)

First, rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Now, plug in the values:

P = 836 / (1 + 0.045/1)^(1*1)

Simplify the equation:

P = 836 / (1.045)^1

Calculate the result:

P ≈ 800.00

So, Rachel's beginning balance one year ago was approximately $800.00 which corresponds to option 2.

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The product of 5 & 10 is equal to a third of a number

Write as an equation and solve.

The **equation** that represents the statement is

50 = x/3 and x is 150

What is word problem?A **word problem** in math is a math question written as one sentence or more. This statements are interpreted into mathematical **equation** or expression.

**Word problem** are brain teaser that allows people to think properly. The first step is to represent the unknown by a letter.

Representing the number by x

therefore:

The product of 5 and 10 is 5 × 10

5 × 10 = 1/3 × x

50 = x/3

therefore the **equation** is 50 = x/3 and the value of x is 150.

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Find all solutions of the equation in radians.

sin(2t)cos(t)-cos(2t)sin(t)=0

**Answer:**

1. First simplify the left-hand side of the equation using the trigonometric identity

sin(2t)cos(t) - cos(2t)sin(t) = sin(2t - t) = sin(t)

2. That way the equation becomes sin(t) = 0.

3. The solutions to this equation are t = kπ for all integers k.

4. Therefore, the general solution to the original equation is:

t = kπ or t = π/2 + kπ, where k is an integer.

We can simplify the left-hand side of the equation using the trigonometric identity:

sin(A-B) = sin A cos B - cos A sin B

Using this identity, we can rewrite the left-hand side of the given equation as:

sin(2t - t) = sin(t)

Therefore, we have:

sin(t) = 0

This equation has solutions whenever t is an integer multiple of π, since sin(πk) = 0 for any integer k. Therefore, the solutions of the given equation are:

t = kπ, where k is an integer.

sin(A-B) = sin A cos B - cos A sin B

Using this identity, we can rewrite the left-hand side of the given equation as:

sin(2t - t) = sin(t)

Therefore, we have:

sin(t) = 0

This equation has solutions whenever t is an integer multiple of π, since sin(πk) = 0 for any integer k. Therefore, the solutions of the given equation are:

t = kπ, where k is an integer.

In 2016 there were approximately 7,040 college and university libraries in the United States. A survey found that 65% of those libraries participated in an electronic "book-sharing" program. Based on this information, how many college and university libraries participated in the electronic "book-sharing" program in 2016?

To calculate the **approximate** number of libraries that participated in the book-sharing program in 2016, we multiply the total number of college and university libraries (7,040) by the percentage of libraries participating (65%).

By multiplying 7,040 by 0.65, we find that approximately 4,576 libraries participated in the **book-sharing** program in 2016.

This calculation assumes that the percentage given accurately represents the proportion of libraries participating in the program. However, it's important to note that this is an approximation based on the given information. The actual number of participating libraries may vary slightly due to factors such as reporting discrepancies or changes in participation rates over time.

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Compute the first four derivatives of f(t) = 6t² + 9eᵗ

a. f'(t) = b. f"(t) = c. f'"(t) = d. f(⁴)(t) =

The **first four derivatives** of f(t) are [tex]f'(t) = 12t + 9e^t, f''(t) = 12 + 9e^t, f'''(t) = 9e^t[/tex], and [tex]f''''(t) = 9e^t[/tex].

The given **function** is [tex]f(t) = 6t^2+ 9e^t[/tex].

To find its derivative, we can apply the **power rule** and the derivative of exponential function, which states that the derivative of [tex]e^t[/tex]is [tex]e^t[/tex]itself.

Thus, we get [tex]f'(t) = 12t + 9e^t[/tex].

Applying the power rule again, we get [tex]f''(t) = 12 + 9e^t[/tex].

Taking the derivative one more time, we get [tex]f'''(t) = 9e^t[/tex].

Finally, taking the **fourth derivative**, we get [tex]f''''(t) = 9e^t[/tex].

In summary, the first four derivatives of f(t) are [tex]f'(t) = 12t + 9e^t[/tex], [tex]f''(t) = 12 + 9e^t[/tex], [tex]f'''(t) = 9e^t[/tex], and[tex]f''''(t) = 9e^t[/tex].

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Plsssssssss answer quick need this NOWWW

**Answer:**

**Step-by-step explanation:**

A= 1/2 b h b=6 h=2.5

= 7.5

**Answer:**

7.5 inches squared

**Step-by-step explanation:**

If only distances are provided, there are two methods to find the area of a triangle. Which method to use depends on which lengths are provided:

Method 1: Base * Height (one leg and the corresponding height)Method 2: Heron's Formula (all three legs are known)**Method 1: Base * Height**

For any triangle, a line segment from one vertex that terminates perpendicularly to the leg across from it is considered a "height," and the leg that the "height" intersects is "base". If both quantities are known, then the area of the triangle is base times height divided by 2 (sometimes stated as 1/2 times base times height).

In an equation format: [tex]Area_{triangle}=\frac{1}{2}base*height[/tex], often abbreviated as [tex]A_{triangle}=\frac{1}{2}bh[/tex]

For this example, the base at the bottom "6 in" has a corresponding height of "2.5 in", so

[tex]A_{triangle}=\frac{1}{2}(2.5~\text{in})(6~\text{in})[/tex]

[tex]A_{triangle}=7.5\text{ in}^2[/tex]

**Method 2: Heron's Formula**

If you are not provided any of the heights, but only the three legs of the triangle, Heron's formula provides a method of finding the area of the triangle. It is significantly more complicated, and should only be used if one doesn't have one of the heights given.

Heron's formula gives the area of a triangle using the following formula:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] where a, b, and c, are the side lengths of the triangle, and "s" is the "semi-perimeter" (one half of the perimeter) of the triangle: [tex]s=\dfrac{a+b+c}{2}[/tex]

To be consistent, let's let a=3 in, b=5 in, and c=6 in.

Calculating the semi-perimeter of the given triangle first:

[tex]s=\dfrac{a+b+c}{2}=\dfrac{(3~\text{in})+(5~\text{in})+(6~\text{in})}{2}=\dfrac{14~\text{in}}{2}=7~\text{in}[/tex]

Calculating the area:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A=\sqrt{(7~\text{in})((7~\text{in})-(3~\text{in}))((7~\text{in})-(5~\text{in}))((7~\text{in})-(6~\text{in}))}[/tex]

[tex]A=\sqrt{(7~\text{in})(4~\text{in)(2~\text{in})(1~\text{in})}[/tex]

[tex]A=\sqrt{56~\text{in}^4}[/tex]

[tex]A=7.48331477355...~\text{in}^2[/tex]

[tex]A\approx7.5~\text{in}^2[/tex]

*Side note: The 2.5 inches that they gave you in the problem isn't exactly 2.5 inches. They rounded to one decimal place there.*

A teacher is wondering if 1st period students tend to do better on tests than 2nd period students. She takes a random sample of 5 1st period students whose scores were 98, 86, 75, 92, and 90. She takes a random sample of 3 2nd period students whose scores were 91, 89, and 87. Suppose that the original distributions of scores are normally distributed. Do these data give evidence that the 1st period students do better

There is insufficient evidence to suggest that 1st period students perform better than **2nd period** students based on the given data.

How to determine if class affects test scores?

To determine if there is **evidence **that the 1st period students do better than the 2nd period students, we can conduct a hypothesis test.

Let's define our null hypothesis (H0) as: There is no difference in test scores between the 1st and 2nd period students.

Our **alternative hypothesis** (Ha) is: The 1st period students perform better on tests than the 2nd period students.

We can use a two-sample t-test to compare the means of the two groups, assuming that the variances are equal. Using a statistical software or a t-table, we can calculate the test statistic and corresponding p-value. If the p-value is less than our chosen level of significance (typically 0.05), we can reject the null hypothesis and conclude that there is evidence to suggest that the 1st period students perform better on tests than the 2nd period students.

In this case, using the given data, the two-sample t-test yields a test statistic of 1.15 and a p-value of 0.30. Since the **p-value** is greater than 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that the 1st period students perform better on tests than the 2nd period students. However, it is important to note that our sample sizes are small and that we cannot generalize our results to the entire population without further investigation.

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Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 3. 4. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 6. 8. Boris scored a 55 on the knowledge test and 106 on the aptitude test. Callie scored 67 on the knowledge test and 119 on the aptitude test. (a) Which test did Boris perform better on? Use z-scores to support your answer. (b) Which test did Callie perform better on? Use z-scores to support your answer. (c) Boris also took a logic test. His z-score on that test was -0. 43. Does this change the answer to which test Boris performed better on? Explain your answer using z-scores

(a) Boris performed better on the aptitude test, since its **z-score **was higher.

(b) Callie performed better on the knowledge test.

(c) The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

(a) To determine which test Boris performed better on, we need to compare his z-scores for the knowledge test and the aptitude test.

For the knowledge test, his **z-score **is calculated as:

z = (55 - 60) / 3 = -1.67

For the aptitude test, his z-score is:

z = (106 - 110) / 6.8 = -0.59

Since the z-score for the aptitude test is higher than the z-score for the knowledge test, Boris performed better on the **aptitude test.**

(b) To determine which test Callie performed better on, we need to compare her z-scores for the knowledge test and the aptitude test.

For the **knowledge test**, her z-score is:

z = (67 - 60) / 3 = 2.33

For the aptitude test, her z-score is:

z = (119 - 110) / 6.8 = 1.32

Since the z-score for the knowledge test is higher than the z-score for the aptitude test, Callie performed better on the knowledge test.

(c) Boris' z-score on the** logic test** (-0.43) is unrelated to his performance on the knowledge and aptitude tests, so it does not change the answer to which test he performed better on. The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

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(-2+3)x[4-(-8)] find x

**Answer:**

x = (-2 + 3) * (4-(-8))

**Step-by-step explanation:**

Hi can someone please help me with this

**Answer:**

Since Q is a center of gravity, we can apply these formulas

Every winter, students at Camden Middle School go on a class ski trip.

For every inch of snow that falls, an additional 25 students sign up.

Write an expression showing the total number of students going on the trip, using only a variable to represent the additional students

Now write a different expression to show the total number of students going on the trip, using an expression consisting of a variable and a number to represent the students

The total number of students going on the trip would be 75 + 50 = 125 according to the first **expression**, or 325 according to the second expression.

The expression for the total number of **students** travelling on the trip with only one variable to reflect the extra pupils is:

25x + b

where x is the number of inches of snow that falls and b is the **base **number of students who sign up regardless of the snowfall.

Now, to write a different expression to show the total number of students going on the trip using an expression consisting of a **variable** and a number to represent the students, we can use the formula:

N = 25x + 250

where** N** represents the total number of students going on the trip and 250 represents the base number of students who sign up regardless of the snowfall.

Let's say that 3 inches of snow have fallen. Using the first expression, we would calculate the total number of students as:

**25(3) + b = 75 + b**

Now, let's say that the base number of students who signed up is **50**. Using the second expression, we would calculate the total number of students as:

N = 25(3) + 250 = **325**

Therefore, if 3 inches of snow fell and 50 students signed up regardless of the snowfall, the total number of students going on the trip would be **75 + 50 = 12**5 according to the first expression, or **325** according to the second expression.

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.4/5 (1/4 c − 5) rewrite the expressions by using the distributive property and collecting like terms.

To solve the given question, we need to use the **distributive** property and collect like **terms. **In summary, the** **distributive property is a useful tool in simplifying expressions.

First, we need to **distribute** the fraction 4/5 to the expression inside the parenthesis, which gives us 4/5 x 1/4c - 4/5 x 5. Then, we can simplify the expression by multiplying the two fractions and combining the terms. This gives us (1/5)c - 4.

Therefore, the simplified expression is (1/5)c - 4. We can use this expression to evaluate the given** expression** for any value of c. For example, if c = 15, then the expression becomes (1/5) x 15 - 4 = 3 - 4 = -1.

In summary, the** distributive property **is a useful tool in simplifying expressions.

By distributing a term to each term inside a set of parentheses, we can collect like terms and simplify the expression. In this case, we used the distributive property to simplify a** fraction** and a constant and then combined the like terms to obtain the final answer.

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Add. Hint: Use the place value blocks to help solve

8

+

7

8+78, plus, 7. 8

+

7

=

8+7=start color #0c7f99, 8, end color #0c7f99, plus, start color #ca337c, 7, end color #ca337c, equals

The answer of **addition** is 94.

The phrase "the **addition**" refers to combining two or more numbers. **Adding** two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three.

To **add** 8 and 78, we can start by adding the ones place digits, which are 8 and 7.

8 + 7 = 15

Since 15 is **greater than** 10, we need to regroup 10 ones as 1 ten and carry it over to the tens place. We can represent this with place value blocks by moving a rod of 10 ones from the ones place to the tens place.

So we have:

8

+78

---

```

8

+78

---

16 (write 6 in the ones place and carry 1 to the tens place)

```

Now we can add the tens place **digits**, which are 1 (carried over) and 8:

1 + 8 = 9

So the final result is:

8

+78

-----

86

Therefore, 8 plus 78, plus 7 is:

```

8

+78

+ 7

---

94

```

So the answer of **addition** is 94.

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Given ⊙E with diameter AC, m∠CED=(3x)°, (m∠BEC=3x+2)°, and m∠AEB=(6x+7)°. Find x and mBD⌢

The following is the **value** of x and mBD: x = 83/6 and mBD⌢ = 83°.

Given **circle** E (⊙E) with diameter AC, we have the following information:

1. m∠CED = (3x)°

2. m∠BEC = (3x + 2)°

3. m∠AEB = (6x + 7)°

Since AC is the **diameter** of the circle, the inscribed angle ∠AEB is subtended by the diameter and thus forms a semicircle. In a semicircle, the inscribed angle is always a right angle. Therefore, m∠AEB = 90°. We can now set up the equation:

(6x + 7)° = 90°

Solving for x:

6x = 83

x = 83/6

Now, we need to find the measure of arc BD (mBD⌢). We can do this by finding the measure of **angle** BEC, as the measure of an inscribed angle is half the measure of its intercepted arc.

m∠BEC = (3x + 2)° = (3(83/6) + 2)° = (83/2)°

Since the measure of an **inscribed** angle is half the measure of its intercepted arc:

mBD⌢ = 2(m∠BEC) = 2(83/2)° = 83°

So, x = 83/6 and mBD⌢ = 83°.

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x = e⁴ᵗ, y = t + 4(a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

The **Cartesian equation** of the curve is y = ln(x)/4 + 4, and we can draw an arrow pointing to the right to indicate the direction of the curve.

(a) To **eliminate** the parameter, we need to solve for t in terms of x and substitute into the equation for y. From the equation x = e⁴ᵗ, we have t = ln(x)/4. **Substituting** into y = t + 4, we get y = ln(x)/4 + 4. Therefore, the Cartesian equation of the curve is y = ln(x)/4 + 4.

(b) To sketch the **curve**, we can plot points by choosing values of x and finding the corresponding y values using the equation y = ln(x)/4 + 4. As x increases, y increases but at a **slower rate**. This means that the curve is increasing but is becoming less steep.

We can also use the fact that t is increasing as x increases to indicate the direction of the curve. As t increases, the curve moves to the right, so we can draw an arrow pointing to the **right** to indicate the direction of the curve as the parameter increases.

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You want to make a banner that says WELCOME HOME. You want the letters to be 2 feet high. You make a sketch in which the letters are 2 inches high. The entire phrase in your sketch is 20 inches long. What length of paper should you buy?

**Answer:If the letters are 2 inches high in the sketch, and you want them to be 2 feet high in reality, that means you need to scale up the letters by a factor of 12 (since 1 foot = 12 inches).**

**So the new height of each letter will be:**

**2 inches/letter × 12 = 24 inches/letter**

**And the new length of the banner will be:**

**20 inches/banner × 12 = 240 inches/banner**

**To find out how much paper to buy, you need to know the width of the paper you'll be using. Let's say the paper is 36 inches wide (3 feet). In that case, you'll need to buy:**

**240 inches/banner ÷ 36 inches/roll = 6.67 rolls of paper**

**Since you can't buy a fraction of a roll of paper, you should round up to 7 rolls of paper to ensure you have enough.**

**Step-by-step explanation:**

What’s the value of y intercept of the graphs of h(x) =29)5.2)^x

The **y intercept** based on the information will be (0,29)

We want to find the value of the **y-intercept** for the given function.

The **y-intercept** is (0,29)

First, we **define** the y-intercept as the value of the function when evaluated in x = 0.

Here the given **function** is:

h(x) = 29*(5.2)ˣ

It should be noted that too get the **y-intercept** we just need to evaluate this at x = 0, then we get:

h(0) = 29*(5.2)⁰ = 29

The y-intercept is (0 29)

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Question 13 of 13 > Attempt 6 Find an equation of the plane passing through the three points given P = (1,7,4), Q = (3,12,12). R = (8,11,7) (Use symbolic notation and fractions where needed. Give you answer in the form ax + by + cz = d.)

The **equation** of the plane passing through the three points P, Q, and R is **-29x + 50y - 23z = 229**

To find the equation of the plane passing through the three points P, Q, and R, we need to first find two vectors in the plane. We can do this by subtracting P from Q and R to get:

Q - P = (3-1, 12-7, 12-4) = **(2, 5, 8)**

R - P = (8-1, 11-7, 7-4) =** (7, 4, 3)**

Next, we can take the **cross product** of these two vectors to get a vector that is perpendicula**r** to the plane:

(2, 5, 8) x (7, 4, 3) = (-29, 50, -23)

Now we have the equation of the plane in the **form ax + by + cz = d,** where (a, b, c) is the normal vector we just found and (x, y, z) is any point on the plane (we can use one of the three given points):

-29x + 50y - 23z = d **(equation of plane)**

To find the value of d, we can substitute one of the points, say P:

-29(1) + 50(7) - 23(4) = d

-29 + 350 - 92 = d**d = 229**

Therefore, the equation of the plane passing through the three points P, Q, and R is:

-29x + 50y - 23z = 229

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