Mathematics College

## Answers

**Answer 1**

The **vector operations** defined for a position vector** **a and a velocity** **vector b are vector **addition** and **scalar multiplication**.

Simplified Vector expression is **(3u - 29) x u + (3u - 29) x v.**

**False, **as** **the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid **if v x a = 0**.

1.28: The **vector operations** defined for a position vector** **a and a velocity** **vector b are vector **addition** and **scalar multiplication**.

1.29: Using the properties of the **cross-product**, the simplified expression is:

3u x u + 3u x v - 29 x u - 29 x v

Using the fact that the cross-product is distributive over vector addition, we can write this as:

3u x u + 3u x v - 29 x u - 29 x v = (3u - 29) x u + (3u - 29) x v

So the **simplified vector** expression is (3u - 29) x u + (3u - 29) x v.

1.30: **False. **

The given equation,

v x (a x R) = 0,

can be simplified to a **scalar triple product**,

(v x a) · R = 0.

Since the scalar triple product is equal to the **determinant of a matrix **formed by the three vectors,

this equation implies that either v x a = 0 or R = 0.

Therefore, the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid **if v x a = 0**.

The **vector operations** defined for a position vector** **a and a velocity** **vector b are vector **addition** and **scalar multiplication**.

Simplified Vector expression is **(3u - 29) x u + (3u - 29) x v.**

**False **as** **the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid **if v x a = 0**.

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## Related Questions

Help me with this worksheet please

### Answers

The **trigonometry ratio **values are tan(50) = 1.19 and cos(70) = 0.34

The trigonometry ratio values

This can be calculated using a **calculator**

So, we have

tan(50) = 1.19 and cos(70) = 0.34

The measures of the angles

This can be calculated using a **calculator**

So, we have

sin(84) = 0.9945 and tan(75) = 3.7321

The trigonometry ratio values

Here, we make use of the laws of **cosines **and **sines**

So, we have

cos(X) = 15/17 = 0.8824

sin(C) = 36/45 = 0.8

The measures of the indicated angles

Here, we make use of the laws of **tangents **and **sines**

So, we have

tan(?) = 6/13 = 0.4615

? = 24.77

sin(?) = 41/59 = 0.6949

? = 44.01

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square root of 88 simplifying radicals

### Answers

**Answer:**

[tex]2\sqrt{22}[/tex]

**Step-by-step explanation:**

need help with my misisng he asap plss 30 points

### Answers

**Answer:**

y=4

x=3

**Step-by-step explanation:**

2y-4=y

y=4

4x=x+9

3x=9

x=3

Round 35.7 to the nearest ten

### Answers

**Answer: 40**

**Step-by-step explanation:**

I rounded to the nearest tens place. The 3 in the tens place rounds up to 4 because the digit to the right in the ones place is 5.

40

When the digit to the right is 5 or greater we round away from 0.

35.7 was rounded up and away from zero to 40

can i have ten dollahairs

### Answers

maybe if you ask politely

Find the area of the

trapezoid at the right

by decomposing it

into familiar shapes.

18 ft

8 ft

6 ft

### Answers

The **area **of the **trapezium **will be **168 ft²**.

What is a **trapezium**, exactly?

**Trapezoids **have two **parallel sides **and two oblique sides. Another term for it is a trapezium. A trapezoid is a four-sided closed form with a space-filling **perimeter**. It is a 2D figurine, not a 3D figure. The bases of a trapezoid are parallel to one another. Legs are non-parallel sides, sometimes referred to as lateral sides and height is the distance between the parallel sides.

The **area **of a trapezium is equal to** 1/2*(a+b)*h**.

where h is the distance or height between two parallel lines

Lines a and b are parallel.

Now,

As we can **decompose **given **trapezium **into a **rectangle **with length=18 ft and breadth=8 ft and a **triangle **with base=6 ft and height=8 ft.

Then** area of trapezoid**=**area **of **rectangle **+ **area **of **triangle**

=**l*b+1/2*b*h**

=18*8+1/2*6*8

=144+24

=168 ft²

Hence,

The **area **of the **trapezium **will be **168 ft²**.

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Which relation is a function?

### Answers

The **relation** that is a **function** is D (see image below).

How to Determine if a Relation is a Function Using the Vertical Line Test?

If any **vertical line **passes through more than one point on a graph, then the **relation **is not a **function**. Conversely, if every vertical line intersects the graph at most one point, then the **relation **is a **function**.

Applying the **vertical line test**, if we place a **vertical line** across each graph given, only the graph in option D (as shown in the image below) will have the the vertical line intersects it at most one point.

Therefore, the correct option is D. (see image below).

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￼ On Monday, Jack bought 2 burgers and 3 fries for $11.25. On Tuesday, he bought 7 burgers and 5 fries

for $32.50. Find the price of each item.

### Answers

The** burgers **is sold each for 3.75 dollars , while the** fries** is solde for 1.25 dollars each

How to solve for the equation

We would have to solve for the price of each of the items using the **simultaneous linear equation** method

2 burgers and 3 fries for $11.25

we would have:

Use the elimination method to solve the system of equations:

2 x+ 3 y = 11.25

7 x + 5 y = 32.50

Step 1 - Multiply Equation 1 by 7:

7 * (2x+3y=11.25) --> 14x + 21y = 78.75

Step 2 - Multiply Equation 2 by 2:

2 * (7x+5y=32.50) --> 14x + 10y = 65

Step 3 - s

14x + 21y = 78.75

-(14x + 10y = 65)

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

21y - 10y = 78.75 - 65

Step 4 - simplify and solve for y:

11y = 13.75

y = 13.75 / 11

y = 1.25

Step 5 - now that we have solved for y, let's rearrange Equation 1 to solve for x:

2x = 11.25 - 3y

Divide each side by 2

2x / 2 = 11.25 - 3y / 2

x = 11.25 - 3y / 2

Step 6 - we determined y = 1.25. Plug it into our Rearranged equation 1:

x = 11.25 - 3(1.25) / 2

x = 11.25 - 3.75 / 2

x = 7.5 / 2

x = 3.75

Since x is the **burgers** which is 3.75 dollars while y is the** fries** which is 1.25 dollars

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A colored spinner with eight equal sections is given.

spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow

Using the fair spinner, determine P(less than 4) when the spinner is spun once.

0.125

0.25

0.375

0.5

### Answers

The **Probability** (less than 4) when the spinner is spun once is 0.5, the correct option is D.

How to find the geometric probability?

When **probability** is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

E = favorable event

S = total **sample** space

Then:

P(E) = [tex]\dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for **event **E, and similar for A(S).

Given that;

Spinner is divide in eight sections that has 3blue, 1 red, 2 purple, 2 yellow

Now,

The coloured spinner is divided into = 8 colour sections

The P event;

=4/8

=1/2

=0.5

Therefore the **probability** of event will be 0.5.

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Thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%. Which of the following must be true?

I. The loan has a duration greater than one year.

II. The interest on Thomas’s loan is compounded more than once yearly.

III. The economy was strong when Thomas took out the loan.

a.

I and II

b.

II only

c.

I and III

d.

III only

Please select the best answer from the choices provided

A

B

C

D

### Answers

In the scanario where Thomas has a loan with a **nominal **interest rate of 6.4624% and an **effective **interest rate of 6.4715%; the statement true that occurs is that: II. The interest on Thomas’s loan is compounded more than once yearly.

Why is Statement II true based on the interest rated?

Often, anytime we receive a **higher **effective interest rate then the rate stated, it implies that we have **compound interest **more than once yearly. , so, the makes the **Statement II **is true.

However, when one have have a **loan** for less then a year and still have those interest rates, you had calculate the **rates **based on a year effectiveness, but the loan calculations work for any duration. An economy and interest tend to **fluctuate **in response to each other, but are not indicators. Therefore, the statements I and III are not necessarily true.

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A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6^{\circ}

∘

, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 13^{\circ}

∘

. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

### Answers

The required the** distance **from point A to point B is approximately 855.31** feet.**

Explain about angle of elevation.

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the **horizontal line.**

According to question:

Let's call the distance from point A to the** lighthouse** "x" and the height of the lighthouse "h" (h = 111 feet). We can use the tangent function to relate the angle of elevation to the distance and height:

tan(5°) = h/x

Solving for x, we get:

x = h/tan(5°) ≈ 1268 feet

Now let's call the distance from point B to the lighthouse "y". We can use the same tangent function to relate the **angle **of elevation from point B:

tan(15°) = h/y

Solving for y, we get:

y = h/tan(15°) ≈ 412.69 feet

The distance between** points** A and B is just the difference between x and y:

1268 - 412.69 ≈ 855.31 feet

So the** distance **from point A to point B is approximately 855.31 feet.

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Complete question:

A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 5º, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 15°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.

Mariene and her parents are baking a large batch of cookies for a fundraiser. There are 150 cookies and 62% of cookie and 62% of the cookies are chocolate chips.How many chocolate chip cookies did they make?

### Answers

93 chocolate chip cookies

this was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day

### Answers

The** **largest total number of **people **who attended 3 **matches **on the day was 17, 000 people.

How to find the number of people ?

The** largest total number **of **people **who attended 3 matches on the day would be the sum of the largest rounded attendance numbers for each match:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Rounding each **attendance **number to the nearest 1,000 gives us:

Match 1: 5,000

Match 2: 8,000

Match 3: 4,000

Adding these rounded numbers together gives us:

5,000 + 8,000 + 4,000 = 17,000

Therefore, the largest total number of people who attended the three matches on the day was 17,000.

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The full question is:

Match 1 - 5, 000 people

Match 2 - 8, 000 people

Match 3 - 4, 000 people

This was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day

HELP! ASAP!! What are the outputs?

### Answers

The completed **table **is,

Input (x) -1 0 1 2

**Output **(y) -6 -2 2 6

What is the function rule?

**Function **rule is the rule of writing the relationship between the two variables, one is **dependent **and another is independent.

We are given that, the output is 4 less than the input.

The table given in the problem is;

**Input **(x) -1 0 1 2

Output (y)

Thus we need to write such a **function**, which gives the value of (y) is 4 less than the value of (x), when we put this into the function.

y = 4x - 2

Complete the table using the above function rule;

At (x) equal to -1,

y = 4(-1)-2

y = -6

At (x) equal to 0,

y = 4(0)-2

y = -2

At (x) equal to 1,

y = 4(1)-2

y = 2

At (x) equal to 2,

y = 4(2)-2

y = 6

Hence, the function rule for the statement, "the output is 2 **less **than 4 times x the input is y = 4x - 2 and the completed table is,

Input (x) -1 0 1 2

Output (y) -6 -2 2 6

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Part B

Question

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the

average number of customers per hour. Create : inequality in standard form that represents the restaurant owner's

desired revenue.

Type the correct answer in each box. Use numerals instead of words.

### Answers

The inequality in **standard form** that represents the restaurant owner's

desired revenue is x² + 2x - 80 ≤ -65.

What are Inequalities?

Inequalities are defined as the **expressions **consisting of both variables and constants** **connected by inequality signs like ≠, >, <, ≤ and ≥.

Part A :

Cost : 10 + x

Customers : 16 - 2x

Part B :

Given that,

**Hourly revenue **= Price paid by each customer × average number of customers per hour.

**Price **paid by each customer = 10 + x

**Average **customers per hour = 16 - 2x

Given that the restaurant owner wants a **minimum revenue** of $130 per hour.

(10 + x) (16 - 2x) ≥ 130

(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130

160 + 16x - 20x - 2x² ≥ 130

-2x² - 4x + 160 ≥ 130

**Dividing **the equation throughout by -2,

x² + 2x - 80 ≤ -65

The inequality sign changes as we **multiply **or divide with a negative number.

Hence the required inequality is x² + 2x - 80 ≤ -65.

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The complete question is given below.

Noah manages a buffet at a local restaurant. He **charges **$10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average **number **of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Part A

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.

Part B

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.

Tim and Jessica plan to rent a camper van for a vacation. The can costs $183 per day. The rental includes 120 miles for free then charges $0.39 per mile.

The total price Tim and Jessica paid to rent the camper van is 598.74. An equation that models the cost of the van rental in terms of miles traveled, m, is 598.74 = 183 + 0.39 (m - 120)

Use the equation to determine how many miles Tim and Jessica tracked if they paid 598.74

### Answers

The **equation **that **represents **the **cost **of the van **rental **is $598.74 = 136.20 + $0.39m .

What is equation?

**Equations **are mathematical statements with **two algebraic** expressions flanking the equals (=) **sign **on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

**Coefficients**, **variables**, **operators**, constants, terms, expressions, and the equal to sign are some of the **components **of an **equation**. The "=" sign and terms on both sides must always be present when writing an equation.

The general form of **linear** **equations **is:

y = a + bx

Where:

a = **intercept**

b = **slope**

The **form **of the **equation **that **models **the cost is:

**Total cost **= cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

Thus, they **travelled **1186 **miles**.

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Solve for a and c 20A + 15C = 340

### Answers

**Answer:**

Below

**Step-by-step explanation:**

You have ONE equation and TWO unknowns, so there is infinite solutions for a and c......you cannot solve for a specific a and c unless you have another equation relating the two or a definition of one of them.

You **can** Solve for a

20a + 15 c = 340

20 a = 340-15c

a = ( 340 -15c) / 20 = 17 - 3/4 c

Similarly:

20 a + 15 c = 340

15c = 340 - 20 a

c = (340-20a)/15

6 Lola buys 2.5 meters of red fabric for $6.55 per meter. She buys 3.2 meters of

blue fabric for $5.25 per meter. How much money does she spend in all? 21

Round your answer to the nearest cent.

Show your work.

### Answers

The total **money** she spent in all is $34.00(nearest cent)

What is word problem?

A **word problem** is a math **problem** written out as a short story or scenario. Basically, it describes a realistic **problem** and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a **word** **problem**.

This **word problem** are interpreted into mathematical equation.

Lola bought 2.5 meters red for 6.55$ per yard

total for red = 2.5 × 6.55 = $16.4

She bought blue 3.2 meters for 5.25$

total for blue = 3.2 × 5.5 = $17.6

The total money spent = $17.6 + $16.4

= $34.00(nearest cent)

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Gold Corp. has an ROE of 12% and a payout ratio of 20%.

What is its sustainable growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

### Answers

The sustainable growth **rate** is calculated by subtracting the payout **ratio** from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth **rate** for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout **ratio** from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the **retention** ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable **growth** rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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26°

onotzib loinosho

er

11

### Answers

**Answer:chicken nuggets**

**Step-by-step explanation:**

chickemn nuggets

Let f : A → B be a function. Then, which of the following statements is/are equivalent to saying that f is onto

(a) 3x EA, Vy E B f(x) y

(b)y B, Vxe A f(x) y

(c) Vy e B, 3x A f(x) = y

(d) Væ E A, 3y B f(x) = y

(e) Vy e B, 3x E A, 3w E B f(x) = wɅy = w

Select all possible options that apply.

### Answers

Let f : A → B be a **function** and the equivalent of stating that f is onto is **statements** (a), (c), and (e) and they are, (a) 3x EA, Vy E B f(x) y, (c) Vy e B, 3x A f(x) = y, and (e) Vy e B, 3x E A, 3w E B f(x) = wɅy = w.

(a) 3x EA, Vy E B f(x) y denotes that at least one element x in A must exist for f(x) to equal y for every element **function** y in B. The meaning of onto is as follows.

(c) According to the formula Vy e B, 3x A f(x) = y, there must be at least one element x in A such that f(x) = y for each element y in B. Simply put, this is the same as **assertion** (a).

(e) Vy e B, 3x E A, 3w E B f(x) = wy = w indicates that at least one element x in A exists for every element y in B such that f(x) = y. The further requirement that g (x)

It is not equivalent to claim that f is onto based on statements (b) and (d).

(b) y B, Vxe A f(x) y denotes that there is at least one element in A such that f(x) = y for every element y in B. This is different from stating that f is onto because it does not imply that every element in B must actually be **mapped** to by f.

(d) According to the formula Vae E A, 3y B f(x) = y, there must be at least one element y in B such that f(x) = y for every element x in A. According to this definition, a function is total if it is specified for each element in **domain** A. The fact that f is assigned to some elements in B does not imply that f is necessarily onto those elements.

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Let x be a random variable that possesses a binomial distribution with p=0.6 and n=5. Using the

binomial formula or tables, calculate the following probabilities. Also calculate the mean and standard

deviation of the distribution. Round solutions to four decimal places, if necessary.

### Answers

**Answer:**

**Let X ~ B(0.6, 5) **

**Prob of success = 0.6 Prob of failure = 0.4**

**Amount of samples = 5**

**P(X **[tex]\geq[/tex] 3) = P(3) + P(4) + P(5)

** = (5C3 x (0.6)^3 x (0.4)^2) + (5C4 x (0.6)^4 x (0.4)) + (0.6)^5**

** = 0.6826 (cor to 4 dp)**

**P(X **[tex]\leq[/tex] 4) = P(0) + P(1) + P(2) + P(3) + P(4)

= 1 - P(5)

= 1 - (0.6)^5

= 0.9222 (cor to 4 dp)

P(X = 2) = P(2) = (5C2 x (0.6)^2 x (0.4)^3) = 0.2304

Mean = n x p = 5 x 0.6 = 3

Standard deviation = n x p x ( 1 - p) = 5 x 0.6 x (1 - 0.6) = 5 x 0.6 x 0.4 = 1.2

Rework Cantor’s proof from the beginning. This time, however, if the digit under consideration is 4, then make the corresponding digit of M an 8; and if the digit is not 4, make the associated digit of M a 4.

### Answers

M is not on the list, and thus the list cannot be a complete listing of all **real numbers **between 0 and 1.

What is inductive reasoning?

Inductive **reasoning **is defined as, **tempting judgments **by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to **precise conclusions**.

Here,

Georg Cantor's **diagonal** **argument **is proof by contradiction that shows that there are more real numbers than natural numbers. Here's how the proof can be reworked with the given modification:

Suppose that we have a list of all **real numbers **between 0 and 1, written in decimal form. We will show that this list cannot be a complete listing of all real numbers between 0 and 1.

Let M be a new real number whose decimal expansion is obtained by following the following rule: if the nth digit of the nth number on the list is 4, then the nth digit of M is 8; if the nth digit of the nth number on the list is not 4, then the nth digit of M is 4.

Since each number on the list has a unique decimal expansion, M is a real number between 0 and 1, and its **decimal expansion **is different from the nth number on the list in the nth digit for all n.

Therefore, M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.

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Use the commutative property of addition to collect like terms

### Answers

**Answer: The commutative property of addition states that changing the order of the terms being added does not change the sum. Therefore, we can rearrange the terms in an expression in any order we choose without changing the result.**

**For example, if we have the expression:**

**3x + 2y + 4x + 5y**

**We can use the commutative property of addition to rearrange the terms as:**

**3x + 4x + 2y + 5y**

**Then, we can collect the like terms (terms with the same variable and exponent) by combining the coefficients:**

**7x + 7y**

**So the simplified expression is 7x + 7y.**

**Step-by-step explanation:**

Complete the input-output table:

n 4n-5

### Answers

**Answer:**

4(1) - 5 = -1

4(2) - 5 = 3

4(3) - 5 = 7

**Step-by-step explanation:**

Replace variable "n" with values of "n".

4n-5 when n = 1 is 4(1) - 5

4(1) - 5 = -1

4(2) - 5 = 3

4(3) - 5 = 7

A box was made in the form of a cube. If a second cubical box has inside dimensions four times those of the first box, how many times as much does it contain?

(A) 4

(B) 8

(C) 16

(D) 64

(E) none of these

### Answers

64 when you have a box there are already for sides and the. It’s a cube so then 8 then you have 4 more dimensions

and you times 8 x 4, 4 times and you get 64

**Answer:**

Since the second box has inside dimensions four times those of the first box, its volume is $(4a)^3 = 64a^3$ times as much as the volume of the first box, whose volume is $a^3$. Therefore, the answer is (D) 64.

find mGHJ in degrees inscribed angles

### Answers

If the **measure** of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.

What is angle?

**Angel** is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

The measure of an inscribed angle in a **circle** is always equal to the measure of its intercepted arc. The measure of the arc intercepted by a central angle is determined by the formula, mGHJ = 360° - mJKH. Therefore, the measure of an inscribed angle in a circle with intercepted arc GHJ is equal to mGHJ = 360° - mJKH. This means that the measure of an inscribed angle in a circle can vary depending on the measure of its intercepted arc. For example, if the measure of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.

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The

accompanying

table shows the value

of a car over time that was purchased for

17100 dollars, where x is years and y is the

value of the car in dollars. Write an

exponential regression equation for this

set of data, rounding all coefficients to the

nearest hundredth. Using this equation,

determine the value of the car, to the

nearest cent, after 12 years.

Years (x) Value in Dollars (y)

0

1

2

3

4

LO

5

17100

14090

12240

11403

10369

9055

### Answers

The equation of the **exponential regression **is y = 17100[tex]e^{-0.194x}[/tex] and the value of a car after 12 years is $1667

What is an exponential regression?

It is a model that explains processes that experiences **growth **at a double rate. It is used for situations where the growth begins slowly but rapidly speeds up without bounds or where the **decay **starts rapidly but slows down to get to zero.

Given that, the given table shows the value of a car over time that was purchased** **for 14100 dollars, where x is years and y is the value of the car in dollars.

We need to find the **exponential regression** equation for this set of data,

We know that,

The **exponential regression** equation is : y = A₀eᵃˣ

Where A₀ is the coefficient of **exponential regression** and a is the constant.

For x = 0, the value of y will be $17100.

Therefore,

17100 = A₀e⁰

A₀ = 17100

Therefore, the equation will be =

y = 17100eᵃˣ

Find for a,

For x = 1, the value of y will be $14090.

14090 = 17100eᵃ

eᵃ = 14090/17100

Taking ln both sides, then we have,

a lne = -0.194

a = -0.194

Therefore, the **exponential regression** equation for this set of data is :

y = 17100[tex]e^{-0.194x}[/tex]

Finding the value of the car, after 12 years =

y = 17100[tex]e^{-0.194(12)[/tex]

y = 1667

Hence, the equation of the **exponential regression **is y = 17100[tex]e^{-0.194x}[/tex] and the value of a car after 12 years is $1667

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Which problem situation could be solved using the open sentence below?

24 - k = ?

A.Mrs. Garcia took 24 science papers home to grade. She graded k science papers before dinner. How many science papers did she have to grade after dinner?

B.Mrs. Garcia took 24 science papers and k reading papers home to grade. How many papers did she have to grade?

C.Mrs. Garcia had k science papers to grade. She now has 22 left to grade. How many papers did she grade already?

D. Mrs. Garcia has 22 science papers and 22 reading papers to grade. If she has k papers to grade in all, how many papers does she have to grade?

### Answers

The answer is A.

You use the deduction method - C and D clearly can't be the correct answers since there's only 22 papers there, somehow, so the only valid potential answers are A and B.

B cannot be it, since she took k papers at home and took extra 24, meaning that would be 24 + k.

So the only possible answer is A, since she has 24 papers and has already done k amount of papers, meaning it's reduction - 24-k = ?.

Hi. I have no idea what I’m doing so please someone that is experienced explain how and what to do here. And ofc answer the question. I will give you brainliest and report you to the head of Brainly saying that you are the best ever. Answer this question:

Based off the picture,

1. What is the absolute deviation? Round to the nearest tenth.

2. What is the median of the data?

3. What are the first and third quartiles of the data?

4. The standard deviation of the ages of class members is 14.8. Find the range of ages that are within one standard deviation of the mean age.

PLEASE HELP ME!!!!

### Answers

**Answer:**

1. To round to the nearest tenth, we'll need to look at the digit to the right of the tenths place, the hundredths place. Since there's a three in the hundredths place, we will round down to 4.9. The mean absolute deviation of these eight values rounded to the nearest tenth is 4.9.

2. 1

Order the numbers in the data set and find the median.

2

Subtract the median from each number in the data set.

3

Take the absolute value of each difference.

4

Add up all of the positive differences.

5

Divide this sum by the number of data points in the set.

3.The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

4.

**Step-by-step explanation:**