**Answer:**

**Step-by-step explanation:**

To find the interest rate on an investment of $470 for seven years with an ending balance of $683.85, you can use the formula for simple interest:

I = P * r * t

Where I is the interest earned, P is the principal amount ($470), r is the interest rate, and t is the number of years (7).

Rearranging the formula to solve for r:

r = I / (P * t)

Substituting the given values:

r = (683.85 - 470) / (470 * 7)

r = 213.85 / 3290

r = 0.0649 or 6.49%

So, the interest rate on the investment of $470 for seven years with an ending balance of $683.85 is 6.49%.

A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, how far away is where it is tied to the base of the flag pole? Round your answer to the nearest hundredth

The** distance **of the rope to the base of the **flagpole** is 27.05 ft.

A rope is tied from the top of a **flag pole** to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, the distance of the rope to the base of the flag pole can be calculated as follows:

The situation forms a** right angle triangle**.

Hence,

using **trigonometric ratios**,

cos 15° = adjacent / hypotenuse

cos 15° = x / 28

cross multiply

Therefore,

x = 28 cos 15

x = 28 × 0.96592582628

x = 27.0459231361

x = 27.05 ft

Therefore,

distance of the flagpole to the base of the ground = 27.05 ft

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What is the value of x?

What is the value of y?

What is the value of z?

**Answer:**

X=63

Y=63

Z=72

**Step-by-step explanation:**

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what is the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy)

By **factorizing** the polynomials, the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy) is 3.

HCF or** Highest Common Factor** is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

To obtain the HCF of algebraic expression, take the common of all the **prime** factors of two polynomials.

We first **factorize** the given algebraic expressions:

3(x - y)^2 = 3 × (x - y) × (x - y)

12x^2(x^2+y^2+2xy) = 12x^2(x + y)^2

12x^2(x + y)^2 = 2 × 2 × 3 × x × x × (x + y) × (x + y)

so, the highest common **factor** between the both expressions is 3.

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Let f(x) = 2√3x and g(x) = -4√3x. Find (f-g)(x), then evaluate when x = 12.

The **function operation **(f-g)(x) in the **functions** f(x) = 2√3x and g(x) = -4√3x is 6√3x and the value of (f-g)(12) is 36.

A **function **is simply a relationship that maps one input to one output.

Given that;

f(x) = 2√3xg(x) = -4√3x(f-g)(x) = ?(f-g)(12) = ?First, set up the **function**;

(f - g)(x) = f(x) - g(x)

Replace the function designators with the actual function.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 2√3x - (-4√3x)

(f - g)(x) = 2√3x + 4√3x

(f - g)(x) = 6√3x

Now, we evaluate when x = 12.

(f - g)(x) = 6√3x

Replace x with 12

(f - g)( 12 ) = 6√3(12)

(f - g)( 12 ) = 6√36

(f - g)( 12 ) = 6 × 6

(f - g)( 12 ) = 36

Therefore, the **function operation **(f-g)(x) is 6√3x and (f-g)(12) is 36.

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Sorry for the grease LOL was eating a big mac also this is urgent

Jada's grandparents started a savings account for her in 2010. The table shows the

amount in the account each year.

If this relationship is graphed with the year on the horizontal axis and the amount in

dollars on the vertical axis, what is the vertical intercept? What does it mean in this

context?

2

year

2010

2012

2014

2016

1gnibasi

Seadsh

amount in dollars

The** vertical intercept** for the table showing the relationship for **Jada's grandparents **starting a savings account for her is starting savings amount in the account of $ 600.

The** vertical intercept** in a **graph **is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The vertical intercept would therefore be first amount in the **savings **account by** Jada's grandparents** which is the $ 600. This is the amount when x = 0 or rather when x was the starting year of 2006.

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the same type of machines are used in two factories, a and b. with statistical data on 1000 machines operated in factory a, the reliability of the machine is estimated to be 0.99. statistics from factory b show that 5 machines failed out of 600 machines operated in factory b. based on the statistics from both factories, what is the reliability of the machine?

The **reliability** of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600. we can take the **average** of the two reliability estimates, giving us a reliability of 0.9833.

The reliability of a **machine** can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the **reliability** of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the **average** of the two reliability **estimates**, giving us a reliability of 0.9833.

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the base of the rectangle is 7 more than its height x. if the perimeter of the rectangle is greater than 30in find the height

The **height **of the **rectangle **must be **greater **than **4 inches** if the perimeter of the rectangle is greater than 30 inches.

In geometry, a rectangle is a **quadrilateral **with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the **total distance** around it.

Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.

Now, we can calculate the perimeter of the **rectangle **using the formula:

Perimeter = 2(length + **width**)

In a rectangle, the **length **and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:

**Perimeter **= 2(x + (x + 7)) = 4x + 14

As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the **inequality**:

4x + 14 > 30

Solving for x, we get:

4x > 16

x > 4

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Please answer it’s for school

Using the vertices given, the** area **of** triangle** PQR is 18 squared units

The **area of triangle** PQR can be found using the Shoelace Theorem. This theorem states that the area of a polygon can be calculated by taking the sum of the products of the coordinates of its vertices and subtracting the sum of the products of the coordinates of its vertices in reverse order.

In this case, the** vertices** of triangle PQR are P(-8, 2), Q(-2, 4), and R(-6, 8), so the area can be calculated as follows:

A = 1/2 * |(-8 * 4) + (-2 * 8) + (-6 * 2) - (2 * -2) - (4 * -6) - (8 * -8)| = 1/2 * |-32 + 16 + -12 - 4 + 24 + 64| = 1/2 * |36| = 18 square units

So the area of triangle PQR is 18 square units.

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Question 9 Multiple Choice Worth 2 points) (09.06 MC) Sara's kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How m 00.16 meters 016 meters O106 centimeters 1,060 centimeters

The** difference **in** height **between Sarah and Tayjen kite is 1060 cm (10.6 m)

An equation is an expression that shows how** numbers and variable**s are linked together using **mathematical operations** such as addition, subtraction, multiplication and division.

1 m = 100 cm

Sara's kite flew 48 meters in the air. Hence:

Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm

Tayjen's kite flew 5,860 centimeters in the air. Therefore:

Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m

The** difference **in** height **is 1060 cm (10.6 m)

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Megan dilates ∆JKL about point J by a scale factor of 3/5 to create ∆JNO.

What is the length of segment NO?

Show all work solving for segment NO.

The **measure **of the **length **NO after dilation will be 15.

The **scale factor **is the ratio of the **actual size **of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

Given that to make JNO, Megan enlarges JKL by a scale factor of 3/5 around point J.

The measure of side NO will be calculated as:-

NO = 3 / 5 x 25

NO = 3 x 5

NO = 15

Therefore, the length of the side NO is 15.

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Problem: Solve the equation AB = BC for A, assuming that A, B, and C are square and B is invertible.

I do know how to solve for A to show that it's invertible which is by finding a matrix C such that AC = CA = i, then C = A^-1

Theorem: If A and B are invertible then AB is invertible

(AB)^-1 = B^-1A^-1

Please help in finding B

Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is **invertible**. We can conclude that B is invertible.

To do this, we will use the fact that if A is **invertible**, then we can multiply both sides of the equation by its inverse to isolate B:

AB = BC

[tex]A^-1 AB = A^-1 BC[/tex]

B = A^-1 BC

Here, A^-1 is the **inverse** of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.

Now, let's consider the **invertibility** of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.

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Two sides of a triangle are

shown. Find the range of

values of the third side.

8, 5

< X <

The **range **of values for the third side must be 5 < C < 13 this means that the third side must be a value **greater than** 5 and less than 13.

**What is triangle?**

A **triangle **is a two-dimensional geometric shape with three sides and three angles. It is a basic polygon and one of the simplest shapes in **geometry**. Triangles come in different types based on the length of their sides or the measure of their angles, such as equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), **scalene triangles** (no sides are equal), right triangles (one angle measures 90 degrees), and obtuse triangles (one angle measures greater than 90 degrees).

The third side of a triangle must satisfy the **triangle inequality theorem**, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides A, B, and C, we have:

A + B > C

B + C > A

A + C > B

For the given sides of 8 and 5, the range of values for the third side can be found by considering the two **inequalities**:

5 + C > 8

8 + C > 5

Adding the two inequalities, we get:

13 > C

So the range of values for the third side must be:

5 < C < 13

This means that the third side must be a value **greater than **5 and less than 13.

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A, B, C and D are points on the circumference of a circle, centre O. ED is a tangent to the circle. Angle ODB= 25degrees. Work out angle BAD. You must give a reason for each stage of your working.

Can someone please help!

Thank you

the angle BAD is 75 degrees and we used the properties of angles in a circle and the** tangent-secant theorem **to find angle BAD .

To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:

Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the **circumference**, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:

Angle AOB = 2x (angle at the center is twice the angle at the circumference)

Angle BCD = x (angles in the same segment are equal)

Angle OBD = 90 degrees (tangent and radius are perpendicular)

Angle OED = 90 degrees (tangent and radius are** perpendicular**)

Angle ABD = y (we need to find this angle)

Angle BAD = z (we need to find this angle)

Use the sum of angles in a triangle

We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem

We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the **intercepted arcs**. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.

Solve for x

To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.

Find angle ABD and angle BAD

Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.

Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.

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Problem

Aurelia has a coin that she suspects is unfair. She wants to test

H

0

:

p

=

0.5

H

0

:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus

H

a

:

p

≠

0.5

H

a

:p

=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where

p

pp is the proportion of flips that this coin lands showing heads.

She flipped the coin

100

100100 times and it landed showing heads

43

4343 of those times.

Which of the following represents the P-value for Aurelia's test?

The correct option is C,** P - value ** is **0.0718.**

A sample proportion in **statistics **is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the **sample's **overall **population **by the proportion of participants who exhibit the characteristic.

For instance, if a sample of **100 individuals **is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the **sample proportion **would be 0.3 or 30%, as 30 out of 100 individuals state that they do.

We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical **normal distribution **when the null **hypothesis **is true.

The **sample proportion **of heads is:

**p' = 43/100 = 0.43**

The test statistic is:

[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]

where p is the **hypothesized proportion **under the null hypothesis, and n is the sample size.

Substituting the given **values**, we get:

[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]

Since this is a two-sided test, we need to find the area under the **standard normal** **distribution **curve in both tails of the distribution that is more extreme than the observed test **statistic**.

Using a **standard** **normal distribution** table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:

P-value = 2 × 0.0359 = **0.0718**

So, the correct answer is:

**c) 0.0718**

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Answer:C

Step-by-step explanation: Kahn Academy

Find the mode of each group of numbers:

62,63,67,66,66,63,62,68,69,65,67,63,64,68,65,62,69,63,61,60,63,65

The **mode **of the data set given is 63.

Statistics uses the terms **mean**, **median**, and **mode **to describe central tendency. They each provide information about what value in a **data set **is conventional or representative of the data set in their own unique ways.

The number that appears the most frequently in a piece of data is the **mode**. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one **mode **is acceptable. Additionally, there is no **mode **if all numbers appear exactly once.

Given that:

62,63,67,66,66,63,62,68,69,65,67,63,64,

By rearrangement, we have:

62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69

Therefore, the highest occurring number(mode) is 63.

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plss help!

An ice cream shop sold a combined total of 367 ice cream cones in the flavors of chocolate or vanilla. They sold 95 more vanilla cones than chocolate. How many chocolate ice cream cones did they sell?

Related Concepts**Systems of Equations****Word problems**Solving the Question**vanilla cones **be *x* and the number of **chocolate cones** be *y.*

**Let's first assign variables to the numbers given. **

**We're given:**

**Plug the second equation into the first one and solve for y:**

[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]

Therefore, they sold 136 chocolate cones.

AnswerThey sold 136 chocolate ice cream cones.

X=Vanilla

Y=Chocolate

X+Y=367

95+Y=X

(95+Y)+Y=367

2Y+95=367

-95. -95

2Y=272

Y=136

Chocolate=136

Vanilla=231

Y=Chocolate

X+Y=367

95+Y=X

(95+Y)+Y=367

2Y+95=367

-95. -95

2Y=272

Y=136

Chocolate=136

Vanilla=231

At soccer practice last night, Leroy made 4 times as many penalty kicks as he missed.

Pick the diagram that models the ratio in the story.

If Leroy made 9 more penalty kicks than he missed, how many penalty kicks did he make?

Penalty kicks:

The model that would model the ratio is 4 : 1

the **penalties** made is given as 12

To get the **penalty kicks** that he made given that he made 9 more penalty kicks than he missed

let the penalty kicks be

= x

if he made more than 9 than missed we would have

x + 9 = 4

x = 1

cross multiply

1 (x + 9) = 4 * X

x + 9 = 4x

9 = 3x

x = 3

since x + 9 **penalties **made

3 + 9 = 12

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GUITAR CLASS, HELP ASAP, WILL GIVE BRAINLIEST,

Five horizontal, parallel, equidistant lines with black oval with stem in 3rd space.

What is the name of the note shown above?

A

B

C

G

The above-shown note is **labeled **B based on the information provided.

A point is considered to really be equidistant from both of two other points when they are equally distanced from one another. The **distance **between any two given points may be calculated using the distance formula utilizing the coordinates of the two points.

Example: Given that points A and B have the coordinates (1, -2) and (5, 6), respectively, determine the midpoint of line **segment **AB. Find the midpoint's distance between points A and B to confirm it. The midpoint is confirmed to be equally far from points A and B because both of those places are from it.

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The sum of two numbers is 14. The difference of twice the first and the second is -5. What are the two numbers?

The **two numbers **are 3 and 11 respectively

From the information given, we have that

The** first** number is x

The **second number** is y

Also,

2x - y = -5

x + y = 14

Make 'x' the subject from equation 2

x = 14 - y

Make 'x' the subject

2(14-y) - y = -5

28 - 2y - y= -5

collect like terms

-3y = -33

y = 11

Substitute the values

x = 3

Hence, the **values **are 3 and 11

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out of the 10,000 people who took their driving test for the first time, it was found that 6500 passed the test on the first attempt. estimate the probability that a randomly selected person would pass the driving test on the first attempt.

To estimate the **probability** that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).

Probability = Number of favorable **outcomes** / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.

Probability = 6500 / 10000= 0.65

Therefore, the estimated probability that a** randomly** selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly **selected **person from the group of 10,000 would pass the driving test on their first try.

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what distance does the tip of the minute hand on a clock travel in 11 minutes if the minute hand is 23 cm long?

The tip of the **minute **hand on a clock travels **approximately **26.4 cm in 11 minutes if the minute hand is 23 cm long.

**What is Circle?**

A **circle **is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a **fixed distance** away from a given point, called the center of the circle. This distance is known as the **radius **of the circle.

A circle can also be defined as the locus of a point that moves in a **plane **in such a way that its distance from a fixed point is **constant**. The constant distance is the **radius **of the circle.

The minute hand on a **clock** makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the **circumference **of a circle is C = 2πr, where r is the radius of the circle, and π is a **mathematical **constant approximately equal to 3.14.

Therefore, the **circumference of the circle** traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the **circumference **it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the **circle **in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a **clock** travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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What is the measure of the smallest angle?

one line has 2x #2 had 3x - 11 #3 had 2x + 9

67°

69°

52°

61°

In the preceding **equation** the measure of the smallest angle is 52° in length.

Internal angles 2 and 3 are alternate options. Two **angles** that share a vertex and a side but no interior points in common. two angles that don't have any shared interior points but do have a common vertex and side.

We know that a triangle has 180 angles altogether.

So, 2x + 3x - 11 + 2x + 9 = 180

7x - 2 = 180

7x = 180 + 2

x = 182 / 7

x = 26

Now, magnitude of angles = 2x = 2(26) = 52 [ Smallest ]

3x - 11 = 3(26) - 11 = 78 - 11 = 67 [ Largest ]

2x +9 = 2(26) + 9 = 52 + 9 = 61

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The image of a trapezoid is shown.

An isosceles trapezoid with a short base of 3 meters and a height of 5.8 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.

What is the area of the trapezoid?

The **area** of the **trapezoid** would be 42.5 m².

**What is the area of a trapezoid?**

The **area** of a **trapezoid** is given by the formula:

**Area = (1/2) × (sum of the bases) × height**

where the **bases** are the two **parallel sides** of the **trapezoid** and the **height** is the **perpendicular** distance between the **bases**.

The parameters of the trapezoid are;

Short base length = 3 m

Height = 5

Large base length = 4 + 3 + 7 = 14 m

Thus;

Area of a trapezoid = 1/2 * (Short base + Large base) * h

Area = 1/2 * (3 + 14) * 5

= 1/2 * 17 * 5

= 42.5 m²

Hence, the **area** of the **trapezoid** would be 42.5 m².

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PLEASE HELP ASAP??!!!

Andrew factored the polynomial 3x²y 6xy² as 3xy(x – 2y). Determine

if he is correct. If he is incorrect, help him fix his error. If he is correct, explain what

he did to get his answer.

**Answer:**

He is correct.

**Step-by-step explanation:**

Shown in picture.

Hope its clear.

Mr. Taylor has been looking at buying a house, and he is even thinking about having a pool put into his backyard!

Your Task: Design a pool that will fit inside Mr. Taylor's backyard and find out how much water it will take to fill the pool.

Rules!

1. Your pool design must include at least two different solids that are connected

2. Your pool must fit inside Mr. Taylor's backyard and leave at least 3 feet of space on each side of it for construction purposes

3. Your pool must be accessible and realistic

*Look at the photo for the blueprint of the house.

*You must clearly describe the pool design. Write this in a word-written response

To design a pool that would fit inside Mr. Taylor's backyard, you would need to know the **dimensions** of the available space.

You would also need to take into account any landscaping, **slopes**, and other features of the backyard that could impact the design and construction of the pool.

Once you have the necessary information about the backyard, you can start designing a pool that would be accessible and realistic. Here are some tips and guidelines for designing a pool.

Choose a shape and **size** that fits the available space and is functional. Rectangular or oval shapes are typically the most common and practical, but other shapes can be used as well.

Consider the depth of the pool. For safety reasons, the depth should be at least 4 feet at the **shallow** end and 8 feet at the deep end. You may also want to consider adding a gradual slope in the pool to make it easier for people to enter and exit.

Choose the material for the pool. Concrete, fiberglass, and vinyl are common materials used for pools. Each material has its own advantages and disadvantages, so research the options and choose the one that is best for your design and **budget**.

Consider adding features such as a diving board, slide, or waterfall to make the pool more enjoyable and attractive.

Calculate the amount of water it will take to fill the pool. This will depend on the size and depth of the pool. To get an **estimate**, you can use online pool volume calculators or consult with a pool contractor.

Once you have a design for the pool and know how much water it will take to fill, you can determine if it is feasible and within Mr. Taylor's budget.

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find the volume of the cylinder 9in and 5in

706.5 in³

The volume of a shape describes the **amount of space** a shape takes up.

**Volume Formula**

For a cylinder, the volume formula is** V = πr²h**. In this formula, V represents the total **volume**. Additionally, π represents the constant **pi**, which is approximately 3.14. The variable r represents the **radius**. Remember that radius is the distance from the center of the circle to the edge. Finally, h is the **height** of the cylinder.

**Solving for Volume**

The diagram shows that the** radius is 5in**. We know this because the distance from the center to the edge of the circle is 5in. Additionally, the **height is 9in**. Now, we can plug these values into the formula.

For this calculation, I used 3.14 for π. The unrounded volume in terms of pi is **225π**.

The volume of the cylinder is **706.5 in³**.

Daniel was given a large box of 36 chocolates for his birthday. If he eats exactly 3

chocolates each day, how many chocolates would Daniel have remaining 8 days after

his birthday?

Answer:12

Step-by-step explanation:

8 times 3 equals 24.24 subtract36 get 12

3. Find the height of the tree below to the nearest foot.

The** height **of the** tree **to the nearest foot is 27 feet.

The height of the tree can be found as follows:

The height of the tree can be found using **trigonometric ratios**. Therefore,

let

tan ∅ = opposite / adjacent

Therefore,

opposite side = adjacent tan ∅

Hence,

height of the tree = 20 + x tan 45° = x tan 75°

20 + x tan 45° = x tan 75°

20 tan 45 + x tan 45° = x tan 75°

20 tan 45 = x tan 75° - x tan 45°

20 tan 45 = x(tan 75 - tan 45)

20 tan 45 = x(3.73205080757 - 1)

2.73205x = 20

x = 20 / 2.73

x = 7.32600732601

x = 7.34

Therefore,

**height **of the tree = x tan 75°

height of the tree = 7.34 × tan 75°

height of the tree = 27.3186119114

height of the tree = 27 ft

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a plane ticket to beacelona is £175 the price decreased by 6%

how much is the plane ticket now?

100%-6%=94%

94/100x175

=£164.5

94/100x175

=£164.5

Chandra just spends 15 minutes away or math problems she spends the same amount of time on each problem how many minutes does she spend on each problem

Chandra spends 3 minutes on each math problem if she spends a total of 15 **minutes** on math problems and spends the same amount of time on each problem

Chandra spends the same amount of time on each math problem. Let's call the amount of time she spends on each problem "t".

We know that Chandra spends a total of 15 minutes on math problems. If she spends the same** amount of time** on each problem, then the total time spent on all the problems is equal to the number of problems multiplied by the time spent on each problem.

So, we can write the following equation:

total time spent on all problems = number of problems * time spent on each problem

We know that the total time spent on all problems is 15 minutes, so we can substitute this into the **equation**:

15 = number of problems * t

We don't know the number of problems, but we can solve for t by rearranging the equation:

t = 15 / number of problems

So, the amount of time Chandra spends on each math problem is equal to 15 divided by the number of problems.

For example, if Chandra works on 5 **math problems**, then the amount of time she spends on each problem is:

t = 15 / 5 = 3

So, Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem.

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