Mathematics High School

## Answers

**Answer 1**

In this problem, we are given the angle A, and the side lengths a and b of triangle ABC. Using the **Geometry** concept of **Law of Sines**, we can solve for the remaining angles and side lengths of the triangle. We find that sin(B) ≈ ∠B ≈ ° and ∠C ≈ °, and we can calculate that c ≈ 9.69. This gives us one possible triangle that satisfies the given conditions.

However, the problem states that there are two triangles that satisfy these **conditions**. To find the second triangle, we must first construct a triangle with angle A₁ = 180° - A and sides a₁ and b₁ such that a₁/b₁ = a/b. This is possible because the Law of Sines tells us that this ratio is constant for all three sides of a triangle. We then apply the Law of Sines to this new triangle to solve for its remaining parts. We find that sin(B₁) ≈ ∠B₁ ≈ ° and ∠C₁ ≈ °, and we can calculate that c₁ ≈ 12.02. This gives us the second possible triangle that satisfies the given conditions.

Now, to show that the areas of the two triangles are proportional to the sines of their respective angles C and C₁, we use the area formula for a triangle, which is 1/2 * base * height. The height of each triangle can be calculated using the sine of the angle opposite the base. Therefore, we have:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (1/2 * a * c * sin(C)) / (1/2 * a₁ * c₁ * sin(C₁))

We can simplify this expression by substituting a1/b1 for a/b and simplifying:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (a/b) * (c/c₁) * (sin(C)/sin(C₁))

Using the Law of Sines, we know that a/b = sin(A)/sin(B) and c/c₁ = sin(C)/sin(C₁), so we can substitute these values into our expression:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(A)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Using the fact that the angles in a triangle sum to 180°, we can solve for sin(A) and sin(B):

sin(A) = sin(180° - B - C) = sin(B + C)

sin(B) = sin(180° - A - C) = sin(A + C)

Substituting these values into our expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(B + C)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Simplifying this expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = sin(C)/sin(C₁)

Therefore, the **areas **of the two triangles are **proportional** to the sines of their respective angles C and C₁

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## Related Questions

MARKING BRAINLEIST PLS HELP ASAP

### Answers

**Answer:**

**Step-by-step explanation:**

a coordinate plane has given a coordinate to each an every point we draw on that. So when we have to find the radius of this circle , we have to find a pair of coordinates.

So I am taking these coordinates; (0,**3**) and (0,**7**)

So the radius = **7**-**3**= 4 units

15 POINTS!!!!

5. If LN=4x-17 and MO = 2x + 13, what are the lengths of the diagonals of rectangle LMNO?

M

LN =

MO =

N

work:

Characteristics of

Kites

### Answers

The length of the **diagonal** from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.

How to determine the lengths of the diagonals of rectangle LMNO

To find the **lengths** of the diagonals of rectangle LMNO, we first need to find the length of MN and LO.

Since LMNO is a **rectangle**, we know that opposite sides are congruent, so LN = MO and LO = MN.

Given that LN = 4x - 17 and MO = 2x + 13, we can set them equal to each other and solve for x:

4x - 17 = 2x + 13

2x = 30

x = 15

Now that we know x, we can find LN and MO:

LN = 4x - 17 = 4(15) - 17 = 43

MO = 2x + 13 = 2(15) + 13 = 43

Therefore, MN = LO = 43.

To find the length of the diagonals, we can use the **Pythagorean theorem**. Let's call the diagonal from L to N d1, and the diagonal from M to O d2:

d1^2 = LM^2 + LN^2

d1^2 = MN^2 + LN^2

d1^2 = 43^2 + 43^2

d1^2 = 3698

d1 ≈ 60.8

d2^2 = MO^2 + LM^2

d2^2 = MN^2 + LM^2

d2^2 = 43^2 + 18^2

d2^2 = 2209

d2 ≈ 47.0

Therefore, the **length** of the diagonal from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.

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7. A bag contains 8 cards numbered from 1 through 8. Jeremiah records the experimental probability of randomly choosing the number 5 after 50, 100, 150, and 200 trials. For which number of trials would you expect the experimental probability to be closest to ? (A) 50 trials B 100 trials C 150 trials (D) 200 trials

### Answers

Among the given options, the number of trials that comes closest to a large number is 200 trials (option D). Therefore, we would expect the experimental **probability** to be closest to 1/8 after 200 trials.

**What is probability?**

The probability of randomly choosing the number 5 from the** bag **of 8 cards is:

P(choosing 5) = number of 5 cards / total number of cards

Since there is only one** **card numbered 5 in the bag, the probability of choosing the number 5 is 1/8.

The **experimental** probability of choosing the number 5 after "n" trials can be calculated by counting the number of times the number 5 is chosen in "n" trials and dividing by "n".

For example, after 50 trials, we expect to choose the number 5 approximately:

P(choosing 5 after 50 trials) = number of times 5 is chosen in 50 **trials** / 50

We can simplify this expression as:

P(choosing 5 after 50 trials) = (1/8) x number of times 5 is chosen in 50 trials

Similarly, we can calculate the experimental probability for 100, 150, and 200 trials:

P(choosing 5 after 100 trials) = (1/8) x number of times 5 is chosen in 100 trials

P(choosing 5 after 150 trials) = (1/8) x number of times 5 is chosen in 150 trials

P(choosing 5 after 200 trials) = (1/8) x number of times 5 is chosen in 200 trials

To determine which number of trials would give us the experimental probability closest to 1/8, we need to consider the law of large numbers, which states that as the number of trials increases, the experimental probability approaches the** theoretical** probability.

Therefore, we would expect the experimental probability to be closest to 1/8 after a large number of trials. Among the given options, the number of trials that comes closest to a large number is 200 trials (option D). Therefore, we would expect the experimental probability to be closest to 1/8 after 200 trials.

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Need help on the last two as well this math is hard for me to understand

### Answers

Answer

#4 = 153.9

#5 = 452.3

Area of a circle = Pi x radius squared

#4 Given radius of 7

Area = 3.14 x 7^2

Area = 3.14 x 49

Area = 153.86

Round to nearest tenth

Area = 153.9

#5 Given radius of 12

Area = 3.14 x 12^2

Area = 3.14 x 144

Area = 452.26

Round to nearest tenth

Area = 452.3

nvm I got it, it’s x2+7x+5 :)

### Answers

The **simplified **form of the given **expression**, can be found to be A. x² + 7x + 5.

How to find the simplified expression ?

**Simplified expressions **are algebraic expressions that have been reduced to their simplest form by applying the rules of arithmetic and algebra.

To simplify the expression, we add the **corresponding terms **from both expressions:

(-3x² + 2x - 4) + (4x² + 5x + 9)

Combine the x² terms: -3x² + 4x² = 1x² (or simply x²)

Combine the x terms: 2x + 5x = 7x

Combine the constants: -4 + 9 = 5

So, the simplified expression is:

x² + 7x + 5

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You work in a pharmacy that mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.50% and 2%. The function

100(0.02) + x(0.005)

y=

100 +x

gives the amount x in milliliters of the 0.5% solution you must add to 100 milliliters of the 2% solution to form a new concentration y of saline solution. How

many milliliters of the 0.5% solution must you add for the combined solution to have a concentration of 0.88%?

You must add approximately mL.

(Round to one decimal place as needed)

### Answers

**Answer:**

294.7 mL

**Step-by-step explanation:**

You want to know the **volume** (x) in mL of **0.5% solution** to be **added** to **100 mL of 2% solution** to make a mix that has a **concentration of 0.88%**.

Setup

The given equations seem to be missing something. We want ...

100(0.02) +x(0.005) = (100 +x)(0.0088)

Solution

We like to play with larger numbers, so we'll multiply this equation by 100 as we simplify it.

200 +0.5x = 88 +0.88x

112 = 0.38x . . . . . . . . . . . . . subtract 88+0.5x

294.7 = x . . . . . . . . . . . . divide by 0.38

**You must add approximately 294.7 mL of 2% solution**.

Select the correct answer.

Scatter plot graph in quadrant 1 of a coordinate plane. 12 points are plotted approximated at (2, 3), (4, 5), (5.8, 4), (5.9, 6.1), (3, 13), (4.9, 7.9), (5.5, 9.1), (6.5, 8), (6.5, 10), (7.5, 7.1), (8, 9), and (8.1, 10.1).

Which point represents the outlier?

A.

(2, 3)

B.

(4, 5)

C.

(3, 13)

D.

(8, 9)

### Answers

**Answer:**

d

**Step-by-step explanation:**

**Answer:**

c

**Step-by-step explanation:**

c

find the volume of a cylinder with a height of 7 cm and a radius of 3 cm ?

### Answers

**B**

**Step-by-step explanation:**

If 5c + 3c = 8c, why can you not write 5c + 3d as 8c or 8d or 8cd?

### Answers

we cannot simply write** equation** 5c + 3d as 8c, 8d, or 8cd.

Explain variable

A variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined **integer** in **algebraic **expressions and equations.

In the equation 5c + 3c = 8c, we can combine the two **terms **on the left side because they have the same variable (c) and the same **exponent (**1).

However, in the expression 5c + 3d, the two terms have different variables (c and d) and cannot be combined in the same way. Therefore, we cannot simply write 5c + 3d as 8c, 8d, or 8cd.

If we want to simplify the expression 5c + 3d, we can only write it in its simplest form or factor it further if possible.

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Mallick Corp. reported the following information for 2013 and 2014.Accounts receivable, December 31, 2013 $ 67,000Accounts receivable, December 31, 2014 63,000Sales (all on credit) -- 2014 745,000How much cash was collected from customers during 2014?A. $741,000B. $745,000C. $749,000D. $753,000

### Answers

The **cash collection** from customers which adds the change in accounts receivable to the sales for the year 2014 is $749,000. Option C is the correct answer.

To determine the cash collected from **customers** during 2014, we need to find out the change in accounts receivable from the beginning to the end of the year.

The change in **accounts** receivable is calculated as follows:

Change in accounts receivable = Accounts receivable, December 31, 2014 - Accounts receivable, December 31, 2013

= $63,000 - $67,000

= -$4,000

The negative sign indicates a decrease in **accounts receivable**, meaning that cash was collected from customers.

Now, to find the cash collected from customers, we need to add the change in accounts receivable to the **sales** for the year:

Cash collected from customers = Sales - Change in accounts receivable

= $745,000 - (-$4,000)

= $749,000

Therefore, the answer is C. $749,000.

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The question is -

Mallick Corp. reported the following information for 2013 and 2014.

Accounts receivable, December 31, 2013, $ 67,000

Accounts receivable, December 31, 2014, 63,000

Sales (all on credit) -- 2014 745,000

How much cash was collected from customers in 2014?

A. $741,000

B. $745,000

C. $749,000

D. $753,000

50 POINTS

A study was conducted to investigate whether local car mechanics charge women more than men for a transmission repair. The researcher selected randomly one man and one woman from everyone who had used the same mechanic for the same transmission repair. The process was repeated for a total of seven selected randomly cars. The repair prices and the differences are shown in the table.

Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Car 7

Women $3,550 $3,200 $1,850 $2,000 $3,000 $1,950 $2,250

Men n $3,285 $3,100 $1,975 $2,150 $2,850 $1,750 $2,175

Difference$265 $100 −$125 −$150 $150 $200 $75

Mean Standard Deviation

Women $2,542.86 $691.27

Men $2,469.29 $599.77

Difference $73.57 $157.37

Dotplots of the data and the differences are shown.

(image)

Do the data provide convincing statistical evidence that women pay more than men for the same transmission repair?

### Answers

we do not have convincing **statistical evidence** that women pay more than men for the same transmission repair

How to determine if data provide convincing statistical evidence that women pay more than men for the same transmission repair

To determine whether the data provide convincing **statistical evidence** that women pay more than men we do not have convincing statistical evidence that women pay more than men for the same transmission repair for the same transmission repair, we can perform a hypothesis test.

**Null hypothesis**: The mean repair cost for women is the same as the mean repair cost for men.

Alternative hypothesis: The mean repair cost for women is greater than the mean repair cost for men.

We can use a two-sample t-test for the difference in means, assuming equal variances.

The **test statistic** is given by:

t = (xbar1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))

where xbar1 and xbar2 are the sample means, s_p is the pooled standard deviation, and n1 and n2 are the sample sizes.

The degrees of freedom is given by:

df = n1 + n2 - 2

Using the data given, we have:

xbar = 2542.86, xbar2 = 2469.29

s1 = 691.27, s2 = 599.77

n1 = n2 = 7

First, we can calculate the pooled **standard deviation:**

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))

s_p = sqrt(((6)*691.27^2 + (6)*599.77^2) / (7 + 7 - 2))

s_p = 644.47

Then, we can calculate the t-statistic:

t = (xbar 1 1 - xbar2) / (s_p * sqrt(1/n1 + 1/n2))

t = (2542.86 - 2469.29) / (644.47 * sqrt(1/7 + 1/7))

t = 0.97

Using a** t-distribution** table with df = 12 and a significance level of 0.05, the critical value for a one-tailed test is 1.7823. Since our t-statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have **convincing statistical** evidence that women pay more than men for the same transmission repair

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Equation

Situation

A plant in Zahra's garden grows 0.8 inches

taller each week. After x weeks, the plant has

grown 6 inches.

Meaning of x

### Answers

**Answer:**

if no initial high im guessing 4.8 weeks

**Step-by-step explanation:**

4.8 divied by .8 = 6

**Answer:**

7 week 3 days and 12 hour

**Step-by-step explanation:**

x is the required week and to calculat it

1st for 1 week= o.8 inch

x = 6 inch

2nd u solve it after u solve it u get 7.5 but week dosen't said by decimals so u will multiply 0.5 by days of the week which is 7 .

3rd u will get 3.5 as we said before for days we can't use decimals so yo will multiply 0.5 by hour which 24 then u will get 12 . so the answer is 7 week 3 days and 12 hour .

What must you prove first before you can prove something is a rectangle or a rhombus?

### Answers

Before proving that a shape is a** rectangle** or a rhombus, you must first prove that it is a parallelogram by showing that its opposite sides are parallel and then use specific properties to prove its rectangle or **rhombus** nature.

Before proving that a given shape is a rectangle or a rhombus, you must first prove that it is a** parallelogram**. A parallelogram is a quadrilateral with opposite sides parallel to each other. To prove that a shape is a parallelogram, you can show that its opposite sides are parallel by using the slope formula or by showing that the** opposite sides** have the same length and are parallel to each other.

Once you have established that a shape is a parallelogram, you can then proceed to prove whether it is also a rectangle or a rhombus. To prove that a shape is a rectangle, you must show that it is a parallelogram with four **right angles**. To prove that a shape is a rhombus, you must show that it is a parallelogram with four sides of equal length.

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To prove that a** quadrilateral **is a **rectangle **or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and opposite sides are parallel.

Before proving that something is a** rectangle **or a **rhombus,** you must first prove that it is a parallelogram. This means showing that opposite sides are parallel and congruent in length. Once this is established, you can then prove additional properties to determine whether the shape is a rectangle (where all angles are 90 degrees) or a rhombus (where all sides are congruent).

To prove that a **quadrilateral** is a rectangle or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and that opposite sides are** parallel**. Once these properties are verified, you can confidently classify the shape as a rectangle or a rhombus.

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The Chang family is on their way home from a cross-country road trip.

During the trip, the function D(t)=2,280-60t can be used to model their distance, in miles, from home after t hours of driving.

Part A:

Find D(15) and interpret the meaning in the context of the problem.

### Answers

To find D(15), we simply substitute t = 15 into the function:

D(15) = 2,280 - 60(15)

D(15) = 2,280 - 900

D(15) = 1,380

Therefore, when the Chang family has been driving for 15 hours, they are 1,380 miles away from home.

Interpreting this result in the context of the problem, we can say that the family has made good progress on their trip and has covered a distance of 1,380 miles from home.

how do i bypass the answer limit on here

### Answers

**Answer: by watching videos **

**Step-by-step explanation:**

**Answer: Watch a video or do your best to scroll down as soon as the website loads. The scrolling worked for me before but you get about 5 seconds before you can't see it anymore.**

**Step-by-step explanation:**

Find the discriminate y=-x^2-6x19

### Answers

**Answer: **112

**Step-by-step explanation:**

To find the discriminant of a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants, we can use the formula:

Discriminant = b^2 - 4ac

In this case, the quadratic equation is y = -x^2 - 6x + 19. So, we can identify the coefficients:

a = -1

b = -6

c = 19

Then, we can substitute these values into the formula for the discriminant:

Discriminant = b^2 - 4ac

= (-6)^2 - 4(-1)(19)

= 36 + 76

= 112

Therefore, the discriminant of the quadratic equation y = -x^2 - 6x + 19 is 112.

What’s the answer I need help please

### Answers

**a) **The **conjugate **of the denominator is given as follows: 2 - 14i.

**b) **The **division **has the result given as follows: 0.375 - 1.15i.

What is a complex number?

A complex number is a number that is composed by a **real **part and an **imaginary **part, as follows:

z = a + bi.

In which:

a is the real part.b is the imaginary part.

The **division **for this problem is given as follows:

(16 - 3i)/(2 + 14i).

For the **conjugate **of the denominator, we keep the real part, changing the sign of the imaginary part, hence it is given as follows:

2 - 14i.

Hence we can solve the **division **multiplying by the conjugate, considering that i² = -1, as follows:

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (32 - 224i - 6i + 42)/(4 + 196)

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (74 - 230i)/200

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = 0.375 - 1.15i.

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One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?

### Answers

The **container **can contains **3,000 pounds** of chemicals.

How many pounds can the container hold?

One **cubic **foot of a chemical weighs 50 pounds which means 1 ft³ of chemical = 60 pounds

We must find how many **pounds** in the container whose dimension 6 ft, 4 ft and 2.5 ft. So, the l = 6 ft, b = 4 ft and h = 2.5 ft.

Volume of box = L*B*H

Volume of box = 6 x 4 x 2.5

Volume of box = 60 ft³

From **1 ft**³ of chemical = 60 pounds; then, the **50 ft³ **of chemical will be:

= 50 x 60

= 3,000 pounds

**Full question ***"One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold? The base is 6, the width is 4, and the height is 2.5"*

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If one zero of the polynomial (3

2 + 8 + ) is the reciprocal of the

other, then find the value of k

### Answers

If one zero of the polynomial 3x^2 + 8x + k is the reciprocal of the

other, then k = 3 by applying **product of roots** formula.

The quadratic **polynomial** is 3x^2 + 8x + k.

Let the roots of 3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m

Thus, the **product of roots** is = m*n = m*(1/m) = 1 ____(1)

The general equation of a quadratic equation can be written as,

ax^2 + bx + c = 0

where a and b are coefficients of x^2 and x respectively and c is a constant term.

From **product of roots **formula we know that,

Product of roots =constant term/ coefficient of x^2 = c/a

Therefore, for polynomial is 3x^2 + 8x + k we get,

Product of roots = k/3 ____(2)

From equating equation (1) and (2) we get,

k/3 = 1

⇒ k = 3

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The given question is incomplete, the complete question is

"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."

a study on children diagnosed with deliops disease examined whether taking garlic pills would prolong the life of the children. the 50 children who did not take garlic lived an average of 4 years. the 40 children who took the garlic pills lived an average of 21 years. the confidence interval for the difference in average for the non-garlic pills verses garlic pills was (-43, 9) years. what would you conclude about the effectiveness of garlic pills?

### Answers

The confidence **interval **for the difference in average **lifespan **between the two groups of children (-43, 9) years includes 0, which means that we cannot conclude with confidence that there is a significant difference between the two groups.

Since the confidence** interval include**s negative values, we cannot even conclude that the garlic pills were beneficial in prolonging the life of the children. It is possible that the garlic pills had no effect or even a harmful effect on the lifespan of the children.

Therefore, based on this information, we cannot conclude that garlic pills are effective in prolonging the life of children with **deliops disease.** Further research would be needed to determine whether garlic pills have any beneficial effects on the lifespan of these children.

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Two classmates have decided to read all the volumes in a popular series of books. Eva has already read 4 volumes and will continue to read new ones at a rate of 2 volumes per week. Maria, who hasn't started reading the series yet, will read 4 volumes per week. At some point, Maria will catch up with Eva and they will be reading the same book. How many volumes will each girl have read by then? How long will that take?

### Answers

Thus, the** number of volume **read by both Eva and Maria in total 2 weeks is 8.

Explain about the slope of function:

**Slope** is a crucial topic in economics because it's used to gauge how quickly things are changing.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The line becomes steeper as the slope increases.

Given data:

Number of volume read by Eva = 4**Rate of reading** by Eva = 2 volume per weekNumber of volume read by Maria = 0Rate of reading by Maria = 4 volume per week

Now,

Let the number of weeks at which both read the equal number of volume be x.

Total number of volume be y

So,

For Eva: y = 4 + 2x

For Maria: 0 + 4x

Equating both equations:

4 + 2x = 4x

4x - 2x = 4

2x = 4

x = 4/2

x = 2

Number of volumes read by each girl:

For Eva: y = 4 + 2(2)= 8

For Maria: 0 + 4(2) = 8

Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.

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Which of the following people would you expect to have the best

employee benefits?

O new hire at a large company

O part-time at a small company

O full-time employee at a large company who has been there for years

O new hire at a small company

### Answers

**Answer:**

**A full-time employee at a large company who has been there for years would typically have the best employee benefits.**

**Large companies often have more resources to provide extensive employee benefits packages, including health insurance, retirement plans, paid time off, and other perks. Full-time employees who have been with the company for years may be eligible for additional benefits, such as higher matching contributions to retirement plans and increased vacation time.**

**New hires at both small and large companies may not have access to as many benefits initially, as they may need to work for a certain period before becoming eligible. Part-time employees may also have limited access to benefits, depending on the company's policies.**

**Overall, the length of time an employee has been with the company and the size of the company are two important factors in determining the quality and quantity of employee benefits.**

2. Find the volume. Show work, and round to 2 decimal places

*triangle based prism*

### Answers

answer

as we all know volume is equal to length times width times height therefore to get you answer you have to multiply all the three giving measurements the answer that you get you are supposed to round it to the nearest to decimal places when you say around it off to the nearest two decimal places it means that they need to be too this two numbers after the coma

On a piece of paper graph y = 2x-4 then determine which answers

matches the graph you drew

### Answers

The **graph** shown in the equation y = - 2x - 4 is the graph that corresponds to that equation. The answer is option (B).

What is graph?

A data structure called a graph is used to show the mathematical connection between two or more objects. It is made up of nodes and **edges,** where nodes stand in for individual things and edges for the connections between them. In computer science, graphs are used to solve a variety of issues, including finding the shortest path between two points and figuring out whether a graph contains cycles. In addition, social networks, transportation networks, and many other kinds of networks can all be represented using graphs.

Option B's graph is the one that corresponds to the equation y = - 2x - 4.

The following is how the equation is written in **slope-intercept** form:

It is -2 degrees.

-4 is the intercept.

This shows that the slope of the graph is negative and that the trend line crosses the y axis at a negative four-degree angle.

The only graph with a negative slope and a -4 intercept is the one for option B.

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Complete question attached below,

there was no red arc. so please help me on this. its for geometry

### Answers

**Answer:**

21. x=70

22. x=15

*Not sure what the red arc is, but I found the value of x for both 21 and 22*

**Step-by-step explanation:**

Let's start with **21** first.

Line AB is a straight line, meaning the arc length of AB is 180 degrees. So,

(2x-30)+x=180

let's solve:

3x-30=180

3x=210

x=70

I'm not sure what the red arc is, so I can't help you there.

Next, **22**.

All the arcs in a complete circle need to add up to 360 degrees, so:

4x+6x+7x+7x=360

simplify first:

24x=360

let's solve:

x=15

Again, not sure where or what the red arc is, so can't help again. I hope that the x values help.

Commutative states that the grouping of three terms being added does not affect the result.

Distributive states that the order of two terms being added may be switched which does not affect the result.

Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products.

Which is which because that's what its asking

### Answers

The first statement, "**Commutative** states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.

The solution to the aforementioned question

The first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative **property of addition.**

The second statement, "Distributive states that the order of two terms being added may be switched which does not affect the result" is referring to the commutative **property of multiplication.**

The third statement, "Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products" is referring to the **associative property **of multiplication.

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Find the perimeter of the figure below.

Figure not drawn to scale

### Answers

According to the given information, the **perimeter** of the given right-angle triangle is **30ft.**

What is Pythagoras' Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

According to the given information:

We can use the Pythagorean theorem to find the length of the missing side of the right triangle, BC:

[tex]BC^2 = AB^2 - AC^2\\BC^2 = 13^2 - 12^2\\BC^2 = 169 - 144\\BC^2 = 25[/tex]

BC = 5

Now that we know all three sides of the triangle, we can find the perimeter by adding them together:

Perimeter = AB + AC + BC

Perimeter = 13 + 12 + 5

Perimeter = 30

Therefore, according to the given information, the **perimeter** of the given right-angle triangle is **30ft.**

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The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 140, 220, 48, and 19. What is the median length of time required to review an application

### Answers

The **median **length of time required to review an application is 105 minutes.

To find the median, the data needs to be arranged in order from least to greatest: 19, 48, 140, 220.

Since there is an even number of data points, the median is the **average** of the two middle values, which in this case are 48 and 140. Adding them together and dividing by 2 gives 94, which is less than the next highest value of 220.

Therefore, the median length of time required to review an application is 105 minutes.

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The ratio of the number of red balls to blue balls to green balls is 3:2:5. There are 60 balls altogether? (1) How many balls are red? (2) How many balls are blue? (3)Write in fraction form,the ratio of green balls to red balls

### Answers

**Answer:**

1) 18 Red balls

2) 12 blue balls

3) [tex]\frac{5}{3}[/tex] green balls to red balls

**Step-by-step explanation:**

R B G

3:2:5

3+2+5 = 10

60/10 = 6

to find the number of red balls simply do

3 * 6 = 18

to find the number of blue balls do

2 * 6 = 12

to find the number of green balls do

5 *6 = 30

the ratio of green/red same as the original

5/3

A teacher poses this problem: I am thinking of four numbers, a, b, c, and d, where a 0, b 0, c 0, and d 0 What else do you need to know to plot the four numbers in the correct order on a number line? What two questions should you ask? Explain how the answers would help you plot the numbers on a number line

### Answers

The two **questions **should you ask are:

What is the **smallest number** among the values (a, b, c, and d)What is the largest number among the values (a, b, c, and d)

Why ask the question above?

The given **answers **to the above questions, one can be able to know the ranges of values that the four numbers have, as well as their relative positions.

In the event that we know the smallest and **biggest **numbers, we can be ready to mark those points on the number line and after that put the other two numbers in between them agreeing to their relative positions.

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