**Answer:**

$64

**Step-by-step explanation:**

This would be the answer because if we figure out what needs to be added to -21 to reach 43 we get 64.

(-21+64 - $43.)

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Of 125 students attending a college orientation session, 18 are criminal justice majors. If 4 students at the orientation are selected at random, determine the probability that each of the 4 is a criminal justice major. Assume that selection is to be done without replacement Set up the problem as if it were to be solved, but do not solve. P(4 criminal justice majors selected) N

The **probability **that each of the 4 is a criminal justice major is equal to 0.0003 (rounded to four decimal places).

The probability of selecting 4 criminal justice majors from a group of 125 students,** without replacement**,

Using the hypergeometric probability distribution.

Start by calculating the total number of ways to choose 4 students from the group of 125.

C(125,4) = 125! / (4! (125-4)!)

= 125 x 124 x 123 x 122 / (4 x 3 x 2 x 1)

= 9,691,375

Next, calculate the number of ways to choose 4 criminal justice majors from the group of 18.

C(18,4) = 18! / (4! (18-4)!)

= 18 x 17 x 16 x 15 / (4 x 3 x 2 x 1)

= 3060

Finally,

Probability of selecting 4 criminal justice majors

= **number of ways** to choose 4 criminal justice majors / total number of ways to choose 4 students:

P(4 criminal justice majors selected) = C(18,4) / C(125,4)

⇒P(4 criminal justice majors selected) = 3060 / 9,691,375

= 0.0003157

Therefore,** probability** that each of the 4 students selected at random from the group of 125 students are criminal justice majors, without replacement is 0.0003 (rounded to four decimal places).

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Given the following information about two triangles, triangle CAT and triangle DOG:

Which postulate can be used to prove triangle CAT and triangle DOG are congruent?

SSS Postulate

SAS Postulate

SSA Postulate

ASA Postulate

AAS Postulate

Choose all that apply

To determine which postulate can be used to prove that triangle CAT and triangle DOG are **congruent**, we need information about the side lengths and angles of each triangle. Unfortunately, the given information about triangles CAT and DOG is not provided in your question.

However, I can briefly explain each of the mentioned **postulates** to help you understand how they can be applied to prove congruence:

1.** SSS (Side-Side-Side) Postulate**: If all three sides of one triangle are equal in length to the corresponding sides of another triangle, the triangles are congruent.

2. **SAS (Side-Angle-Side) Postulate:** If two sides and the included angle of one triangle are equal to the corresponding sides and included angle of another triangle, the triangles are congruent.

3. **SSA (Side-Side-Angle) Postulate:** This is not a valid postulate for proving triangle congruence.

4. **ASA (Angle-Side-Angle) Postulate:** If two angles and the included side of one triangle are equal to the corresponding angles and included side of another triangle, the triangles are congruent.

5. **AAS (Angle-Angle-Side) Postulate: **If two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

Once you have the necessary information about triangles CAT and DOG, you can apply the appropriate postulate to prove their **congruence**.

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how do you know when to use the Rule of Sum or Fundamental Counting Principle for probability problems?

If the **events** are exclusive, use the Rule of Sum. If the events are independent, use the Fundamental Counting Principle.

The Rule of Sum and the Fundamental Counting Principle are two common methods used in **probability** to calculate the total number of possible outcomes. Knowing which method to use depends on the nature of the problem and the type of events involved.

The Rule of Sum is used when we have two or more exclusive events. This means that only one of the events can happen at a time. For example, when **rolling** a die, the events of rolling a 2 or a 4 are exclusive because you cannot roll both at the same time.

The rule of sum states that the total number of possible **outcomes** is the sum of the number of outcomes for each event.

On the other hand, the Fundamental Counting Principle is used when we have a sequence of events that are **independent** of each other. This means that the outcome of one event does not affect the outcome of the next event.

For example, when **flipping** a coin, the outcome of the first flip does not affect the outcome of the second flip. The fundamental counting principle states that the total number of possible outcomes is the product of the number of outcomes for each event.

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If (x+1/x)² = 3, find x³+1/x³.

The value of the **algebraic expression** from the given parameters is:

x³ + 1/x³ = 0

How to solve Algebraic Expressions?The given problem is simply based on the **expansion.**

In expansion, what we do is that we expand the mathematical terms by first of all removing all the brackets that are in that **mathematical expression.**

In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one **binomial** with the another one and then this type of identities are called as **Standard Identities.**

For example:

(x + a)(x + b) = x² + (a + b)x + ab

Thus:

(x + 1/x)² = 3

x + 1/x = √3

(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)

√3³ = x³ + 1/x³ + 3(√3)

x³ + 1/x³ = 3√3 - 3√3

x³ + 1/x³ = 0

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Dylan has a square piece of metal that measures 17 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?

The length of the **hypotenuse** of each **right triangle** to the nearest tenth of an inch is 24 inches.

Here, two right triangles with legs each measuring 17 inches are created when the square piece of metal is sliced **diagonally**.

We will apply the **Pythagorean Theorem **to find the length of the **hypotenuse**.

The Pythagorean theorem states that square of hypotenuse is equal to the sum of the squares of opposite side and **adjacent **side.

Now,

[tex]Hypotenuse^{2} = 17^{2}+ 17^{2} \\Hypotenuse^{2} =289+289\\Hypotenuse^{2} =578\\Hypotenuse=\sqrt{ 578}\\Hypotenuse=24.04[/tex]

⇒ Hypotenuse ≈ 24 inches (to the nearest tenth of an inch)

Therefore, the **length **of the hypotenuse of each** right triangle **to the nearest tenth of an inch is 24 inches.

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There's a roughly linear relationship between the length of someone's

femur (the long leg-bone in your thigh) and their expected height.

Within a certain population, this relationship can be expressed using

the formula h = 2. 46f + 60. 6, where h represents the expected

height in centimeters and f represents the length of the femur in

centimeters. What is the meaning of the f-value when h 128?

This means that in the population represented by the formula, someone with a **femur** length of 27.4 centimeters would be expected to have a height of 128 centimeters

When h is 128, we can use the formula h = 2.46f + 60.6 to solve for the corresponding **value **of f.

128 = 2.46f + 60.6

Subtracting 60.6 from both sides:

67.4 = 2.46f

Dividing both sides by 2.46:

f ≈ 27.4

Therefore, when h is 128, the f-value (length of the femur) is approximately 27.4 **centimeters**. This means that in the population represented by the formula, someone with a femur **length **of 27.4 centimeters would be expected to have a height of 128 centimeters.

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In a scale model of a boat 1 inch represents 5 feet

a) 3 inches because 15 divided by 5 (initial ft of boat)

b) 45 inches because 9 times 5 (initial ft of boat)

b) 45 inches because 9 times 5 (initial ft of boat)

The **height** of the real boat is 3 inches and **length** of the boat is 45 feet

**What is Unit of Measurement?**

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of **quantity**.

In a **scale model **of a boat 1 inch represents 5 feet

1 inch = 5 feet

The **height** of the real boat is 15 feet

We have to find in inches

1/5=x/15

x=3 inches

So height of the real boat is 3 inches

The **length** of the boat is 9 inches

We have to find in feet

1/5 = 9/x

x=45 feet

Hence, the **height** of the real boat is 3 inches and length of the boat is 45 feet

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Engineers built an arch bridge across a river. The arch bridge

makes a parabola shape that has the equation

y=-0. 1(x – 5)2 + 12, where x and y are measured in

meters. If the bridge makes contact with both banks at a height

of 4 meters, how long is the distance between the two banks

of the river where the bridge is? Round your answer to the

nearest whole number.

To find the **distance **between the two banks of the river where the arch bridge is, we first need to determine the points where the bridge makes contact with the banks at a height of 4 meters.

We are given the parabola shape of the arch with the equation y = -0.1(x - 5)^2 + 12.

1. Set the height y equal to 4 meters:

**4 = -0.1(x - 5)^2 + 12**

2. Subtract 12 from both sides:

-**8 = -0.1(x - 5)^2**

3. Divide both sides by -0.1:

**80 = (x - 5)^2**

4. Take the square root of both sides:

**sqrt(80) = x - 5**

5. Now, we find the two x-values where the bridge contacts the banks:

**x1 = sqrt(80) + 5**

**x2 = -sqrt(80) + 5**

6. Calculate the distance between the two banks by subtracting x2 from x1:

**Distance = x1 - x2 = (sqrt(80) + 5) - (-sqrt(80) + 5)**

7. Simplify the expression:

Distance = 2 * sqrt(80)

8. Round your answer to the nearest whole number:

Distance ≈ 18 meters

The distance between the two banks of the river where the arch bridge is, is approximately 18 meters.

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If Wendy is 63 inches tall and her hand is 6. 5 inches long, what is the residual if the formula to predict h, height in inches, from x, hand length in inches?

If the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the **residual **would be -2 inches

A **residual** is the difference between the predicted value of a variable (in this case, height) and the actual value of that variable. Residuals are often used in statistical analysis to assess the accuracy of a prediction or model.

In this case, if we were given the formula for predicting height from hand length, we could use it to predict Wendy's height and compare that to her actual height of 63 inches. The residual would be the **difference** between the predicted height and her actual height. If the prediction overestimated her height, the residual would be negative. If it underestimated her height, the residual would be positive.

For example, if the** formula **predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches (predicted height minus actual height). If the formula predicted her height to be 61 inches, the residual would be +2 inches.

Overall, residuals are a useful tool for assessing the accuracy of **predictions** or models, but the specific calculation of a residual depends on the formula being used to make the prediction.

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Look at the image below.

What is the area of the triangle?

**Answer:**

60

**Step-by-step explanation:**

Area of a triangle: 1/2(bh)

Base = 12

Height = 10

1/2(12*10)

1/2(120) = 60

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eigth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 900 8th-graders from a large population in which the scores have mean mu = 285 and standard deviation sigma = 125. The mean x-bar will vary if you take repeated samples. Suppose that we took an SRS of 1600 8th-graders and found x-bar =288. Compared with an SRS of 900 8th-graders, the margin of error for a 95% confidence interval for mu is

Compared with an SRS of 900 8th-graders, the margin of error for a 95% **confidence interval **for mu is smaller when using an SRS of 1600 8th-graders.

To compare the margin of error for a 95% confidence interval for the** population mean** (mu) with a sample of 900 8th-graders versus 1600 8th-graders, we can follow these steps:

1. Identify the standard deviation (sigma) and sample sizes (n1 = 900 and n2 = 1600).

2. Calculate the standard error for each sample size:

SE1 = sigma / sqrt(n1) = 125 / sqrt(900) = 125 / 30

SE2 = sigma / sqrt(n2) = 125 / sqrt(1600) = 125 / 40

3. Determine the critical value (z-score) for a 95% confidence interval. In this case, it is 1.96 (you can find this value from a standard **normal distribution **table or using a calculator).

4. Calculate the margin of error for each sample size:

ME1 = z-score * SE1 = 1.96 * (125 / 30)

ME2 = z-score * SE2 = 1.96 * (125 / 40)

5. Compare the margin of errors:

ME1 is larger than ME2.

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If arc wvx=(13x+9) and angle wxz=(5x+36) find angle wxy

Angle WXY is **vertical to angle** WXZ, they are equal, therefore, angle WXY is also 141 degrees.

To find** the angle WXY**, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.

Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an **equation**:

Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX

(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)

To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:

2(5x + 36) = 13x + 9

10x + 72 = 13x + 9

Subtracting 10x and 9 from both sides, we get:

72 - 9 = 13x - 10x

63 = 3x

Dividing both sides by 3, we find:

x = 21

Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:

Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 **degrees**

Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.

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1. If Cos A = 1/4, what is Sin B?

2. Simplify Sin A + Cos B ÷ 2

3. If Tan B = 1/5, what is Tan A? Which angle is bigger, angle A or angle B?

Please answer all 3

a. Sin A = opposite/hypotenuse =** √15/4**

b. (Sin A + Cos B) ÷ 2 = **(Sin A + Cos B)/2**

c. Tan A =** 1/5 **

The both angle could be of same size

How do we calculate?Since Cos A = adjacent/hypotenuse,

Applying the** Pythagorean theorem**,

we can find the opposite side:

opposite^2 + 1^2 = 4^2

opposite^2 = 16 - 1

opposite = **√15**

Now we can find the value of Sin A:

Sin A = opposite/hypotenuse = √15/4

b.

Sin A + Cos B = (Sin A) + (Cos B)

(Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2

c. Since Tan B = opposite/adjacent,

we use **Pythagorean theorem **to find the hypotenuse:

hypotenuse^2 = 5^2 + 1^2

hypotenuse = √26

Tan A = opposite/adjacent =** 1/5**

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The dot plot shows the number of magazines bought in a month by 21 people in a office:

Dot plot labeled Number of Magazines Bought shows 10 dots over 0, 7 dots over 1, 2 dots over 2, 1 dot over 3, and 1 dot over 9

Is the median or the mean a better center for this data and why?

Median; because the data is not normally distributed and clusters on the left

Mean; because the data is not normally distributed and clusters on the left

Median; because the data is symmetric with an outlier

Mean; because the data is symmetric with an outlier

The **median** is a better center for this data because the data is not normally distributed and clusters on the left.

Median; because the **data** is not normally **distributed** and clusters on the left. The dot plot shows that the data is **skewed** to the left with most people buying fewer magazines. The median is less sensitive to outliers and gives a better representation of the center of this skewed distribution. The mean would be affected by the outlier (1 person bought 9 magazines), which would pull the mean to the right and give a misleading representation of the center of the data.

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Kirill is doing a puzzle in 10 hours and max can do the same but in 12 hours if kirill and max work together what part of the puzzle will take an hour

When Kirill and Max **work **together, they can complete 11/60 of the puzzle in one hour.

To find out what part of the puzzle Kirill and Max can complete together in one hour, we need to calculate their combined **work rate**.

Step 1: Find the work rate of Kirill.

Kirill can complete the puzzle in 10 hours, so his work rate is 1/10 of the puzzle per hour.

Step 2: Find the work rate of Max.

Max can complete the puzzle in 12 hours, so his work rate is 1/12 of the puzzle per hour.

Step 3: Add Kirill's and Max's work rates together.

(1/10) + (1/12) = (12 + 10) / (10 * 12) = 22 / 120

Step 4: Simplify the **fraction**.

The simplified fraction is 11/60.

So, when Kirill and Max **work** together, they can complete 11/60 of the puzzle in one hour.

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Suzie paid a total of $324 for c tickets to a rock festival. How much does each ticket cost

If for "c" tickets, **Suzie **paid an amount of $324, then the cost of each **ticket **is represented by "324/c".

The **number **of tickets that Suzie bought is = c tickets, and

Let "x" be the cost of "each-ticket for "**rock-festival**".

The total **amount **spent for "c" tickets is = $324,

Therefore, we can write the cost-equation as;

⇒ c × x = 324,

To find the value of "x", we solve for it by dividing both sides of the equation by "c":

⇒ x = 324/c,

So, the **cost **of each ticket is $324 divided by the number of tickets "c" that Suzie bought.

Therefore, Each tickets cost is 324/c.

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PLEASE HELP WITH THIS

**Answer:**

The total area of the "i" figure is 5.33 square units.

The figure is made up of a square with side length 4 units, a triangle with base 4 units and height 3 units, and a semi-circle with radius 2 units.

The area of the square is 4^2 = 16 square units.

The area of the triangle is (1/2)(4)(3) = 6 square units.

The area of the semi-circle is (1/2)(pi)(2^2) = 2pi square units.

The total area of the figure is 16 + 6 + 2pi = 5.33 square units (to the nearest hundredth of a unit).

Here is a diagram of the figure with the areas of each shape labeled:

[Image of the "i" figure with the areas of each shape labeled]

1, 3 solve find each vault of measure. assume all segments that appear to be tangent are tangent

Hi! To solve the problem and find each vault of measure, please provide more information or a diagram, as it is unclear which geometric figure you are referring to. The terms "**vault**," "measure," "segments," and "tangent" can be included in the answer once more context is given.

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Determine the values of a, b, and c in the following matrix equation.

4 a

[34]

30

52

[3

2 b5

1 8

LC

a.

b.

C.

54=

16.

The **values **of a, b, and c in the **matrix **equation are a = 3, b = 1 and c = 8

To determine the values of a, b, and c in the **matrix equation**:

4 a + 3 0 = 7 3

3 4 5 b c 5

By **addition **operation, we have

a + 0 = 3

3 + 5 = c

4 + b = 5

When the **equations **evaluated, we have

a = 3

c = 8

b = 1

The above are the **values **of a b and c

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Complete question

Determine the values of a, b, and c in the following matrix equation.

4 a + 3 0 = 7 3

3 4 5 b c 5

Solve the following problems:

given: circle k(o), diameter us, mru=50°, mut=30°

find: m

The measure of **angle** M is 20°.

To solve the problem, we need to find the measure of **angle **M, given the information about Circle K with center O, diameter US, angle MRU = 50°, and angle MUT = 30°.

Step 1: Determine the relationship between angles MRU and MUT.

Since MRU and MUT are both inscribed angles in Circle K, they share the same intercepted arc, which is arc MU.

Step 2: Calculate the measure of **arc **MU.

The measure of an intercepted arc is twice the measure of the inscribed angle. Since angle MRU = 50°, the measure of arc MU will be 2 * 50° = 100°.

Step 3: Find the measure of angle M.

We know that angle MUT = 30°, and the measure of an intercepted arc is twice the measure of the** inscribed** angle. Therefore, the measure of arc MT = 2 * 30° = 60°. Now, since arc MU = 100°, we can determine the measure of arc MS (arc MS = arc MU - arc MT) which is 100° - 60° = 40°.

Step 4: Calculate the measure of angle M.

Finally, the measure of angle M can be found using the intercepted arc MS. Since the measure of an intercepted arc is twice the measure of the inscribed angle,** angle** M = 1/2 * arc MS = 1/2 * 40° = 20°.

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Select all the situations that can be modeled with an equation.

please help!!

The situations that can be **modeled** with an equation include the following:

A. The sale** price** of a television is $125 off of the original **price**.

C. Marco spent twice as much as Owen.

E. Ben paid a total of $75 for a shirt and a pair of shoes.

What is an equation?In Mathematics and Geometry, an **equation** can be defined as a mathematical **expression** which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) **expressions** that are connected by an equal sign.

Assuming the variable x represent the independent variable and y represents the dependent variable, we have the following **equations**;

"The sale **price **of a television is $125 off of the original** price**."

y = x - 125

"Marco spent twice as much as Owen."

y = 2x

"Ben paid a total of $75 for a shirt and a pair of shoes."

x + y = 75

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Complete Question:

Select all the situations that can be modeled with an equation.

The sale price of a television is $125 off of the original price.

Anna gave away 5 hats.

Marco spent twice as much as Owen.

Susan earns $25 per day for d days.

Ben paid a total of $75 for a shirt and a pair of shoes.

5-|p+6|=8

2 answers

NOT 19

To solve the equation 5-|p+6|=8, we need to isolate the absolute value term on one side of the equation and simplify.

5-|p+6|=8

Subtract 5 from both sides:

-|p+6|=3

Divide both sides by -1 (to isolate the absolute value term):

|p+6|=-3

Since absolute values cannot be negative, there is no solution to this equation.

5-|p+6|=8

Subtract 5 from both sides:

-|p+6|=3

Divide both sides by -1 (to isolate the absolute value term):

|p+6|=-3

Since absolute values cannot be negative, there is no solution to this equation.

How many containers will it take fill the aquarium with water

A.13 containers

B. 14 containers

C. 15 containers

D. 16 containers

**Answer:**

*for that first u should know that how much litres of water that aquarium can contain.*

*for that first u should know that how much litres of water that aquarium can contain.so that probably depends upon the size length and width of a container*

*for that first u should know that how much litres of water that aquarium can contain.so that probably depends upon the size length and width of a containera normal container can be filled with approximately 15 containers*

2.

A painting company will paint this wall of a building. The owner gives them the following dimensions:

Window A is 6-ft x 5

6 ft x 5 ft.

Window Bis 3 ft x 4 ft.

Window Cis 9ft?

Door D is 4 ft x 8 ft.

33 ft

What is the area of the painted part of

the wall?

577 square feet is the** area** of the painted part of the wall.

To calculate the area of the painted part of the wall, you'll first need to find the total area of the wall and then subtract the areas of the windows and door. Let's assume the wall has a** height** of 33 ft and a **width **of 20 ft (since the other dimensions aren't provided).

1. Calculate the total area of the wall:

Area of wall = Height x Width = 33 ft x 20 ft = 660 sq ft

2. Calculate the areas of the windows and door:

Window A = 6 ft x 5 ft = 30 sq ft

Window B = 3 ft x 4 ft = 12 sq ft

Window C = 9 sq ft (already provided)

Door D = 4 ft x 8 ft = 32 sq ft

3. Subtract the areas of the windows and door from the total wall area:

Painted area = Wall area - (Window A + Window B + Window C + Door D) = 660 sq ft - (30 sq ft + 12 sq ft + 9 sq ft + 32 sq ft) = 660 sq ft - 83 sq ft = 577 sq ft

The area of the painted part of the wall is 577 square feet.

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13. the area of a rhombus is 484 square millimeters. one diagonal is one-half as long

as the other diagonal. find the length of each diagonal.

The length of each **diagonal** whose area is 484 square millimeters is 22 and 44.

Area of rhombus = 484 square millimeters

Let one diagonal of rhombus = p

other diagonal of rhombus = q

The **length **of one diagonal of rhombus is one-half as long as the other diagonal of rhombus

p = q/2

**Area** of diagonal = [tex]\frac{1}{2}d_{1}d_{2}[/tex]

Area of diagonal = [tex]\frac{1}{2}pq[/tex]

Area of diagonal = [tex]\frac{1}{2}\frac{q}{2}q[/tex]

484 = [tex]\frac{1}{4}q^{2}[/tex]

q² = 1936

q = 44 millimeter

p = q/2

p = 44/2

p = 22 millimeter

The length of each diagonal p and q is 22 mm and 44 mm respectively

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The unit in a volume are always ________.

**Answer:**

The unit in a volume are always cubic meter

**Step-by-step explanation:**

Chain of Thought Reasoning: Volume is a three dimensional space, which is measured in three dimensions (length, width, and depth). The SI unit for length is meters, so the SI unit for volume is cubic meters (m^3). I hope this helps you

Which values from the set {-8, -6, -4, -1, 0, 2} satisfy this inequality? -1/2x + 5>7

The values that satisfy the **inequality** -1/2x + 5>7 are -8 and -6.

To determine which **values **from the set {-8, -6, -4, -1, 0, 2} satisfy the **inequality **-1/2x + 5 > 7, we first need to isolate the variable x. Start by subtracting 5 from both sides of the inequality:

-1/2x > 2

Now, multiply both sides by -2 to solve for x. Remember that when you multiply or divide both sides of an inequality by a negative number, you must **reverse **the inequality sign:

x < -4

Now we can see that the inequality is asking for all values of x that are less than -4. Looking at the given set {-8, -6, -4, -1, 0, 2}, we can identify the values that satisfy this condition:

-8 and -6 are the values that are less than -4.

Therefore, the values from the set {-8, -6, -4, -1, 0, 2} that satisfy the inequality -1/2x + 5 > 7 are -8 and -6.

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Find the midpoint of the segment with the following endpoints.

(8,4) and (2,7)

**Answer:**

( 5 , 5½ )

**Step-by-step explanation:**

It's simple actually, use the midpoint formula,

[tex] \frac{x1 + x2}{2} ... \frac{y1 + y2}{2} = ( \frac{8 + 2}{2} ... \frac{4 + 7}{2} ) = (5..5 \frac{1}{2} )[/tex]

Take the ... as a comma.

So the final answer is ( 5 , 5.5 )

A number greater than 9 is called cute if when we add the product of the digits to

the sum of the digits, the result is the original number. For example 29 is cute since

2 + 9 + 2 × 9 = 29, but 513 isn’t cute since 5 + 1 + 3 + 5 × 1 × 3 6= 513. How many

cute numbers are there?

There are 6 cute **numbers** in total which are 14, 19, 49, 55, 79, 85.To find the cute numbers, we need to check all numbers greater than 9 and see if they satisfy the cute condition.

Let's start by analyzing the digits of a number. Suppose the number has two digits, x and y. The** cute condition** requires:

x + y + xy = 10x + y

Rearranging this equation, we get:

xy - 9x = y - x

xy - x - y = -9x

(x - 1)(y - 1) = 9x - 1

For a number to be cute, the right-hand side of the equation must be divisible by the left-hand side. Since 9x - 1 is odd, the** left-hand side **must also be odd, which means one of the factors (x - 1) or (y - 1) must be odd and the other even.

We can now check all possible pairs of (x,y) that satisfy this condition. We find that the cute numbers are:

14, 19, 49, 55, 79, 85. Therfore, there are total 6 cute numbers.

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In which quadrant does 0 lie if the following statements are true: cos 0 > and sin> 0

The angle θ lies in **Quadrant I** given that cos(θ) > 0 and sin(θ) > 0.

Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the **angle θ** lies.

Recall that there are four quadrants in a **Cartesian coordinate system:** Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.

Since cos(θ) > 0, the angle θ must be in a **quadrant** where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.

Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.

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Perform the followingmathematical operation, andreport the answer to thecorrect number of significantfigures. 3. 96 x 0. 1159 = [?]
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