PLEASE HELP!!



A sprinkler sprays water in a circle. The distance from the sprinkler to the outer edge of the circle is 2. 5 m.


What is the approximate area that is watered by the sprinkler? (Use 3. 14 as an estimate for It. )

The points (0,10) and (-8,4) are solutions of the system of inequalities.

A system of inequalities refers to a set of two or more inequalities that are graphed together on the same coordinate plane. Each inequality in the system represents a region in the plane where the solution to that inequality lies.

To determine if a point is a solution of the system of inequalities, we need to check if it satisfies both inequalities. Let's check each point given:

(4,6):

8(4) + 5(6) = 47 > 40 (true)

-6(4) + 2(6) = -14 ≥ 18 (false)

(9,8):

8(9) + 5(8) = 97 > 40 (true)

-6(9) + 2(8) = -40 ≥ 18 (false)

(0,10):

8(0) + 5(10) = 50 > 40 (true)

-6(0) + 2(10) = 20 ≥ 18 (true)

(5,-6):

8(5) + 5(-6) = 34 > 40 (false)

-6(5) + 2(-6) = -30 ≥ 18 (false)

(-1,-8):

8(-1) + 5(-8) = -44 ≤ 40 (false)

-6(-1) + 2(-8) = 10 ≥ 18 (false)

(-8,4):

8(-8) + 5(4) = -24 ≤ 40 (true)

-6(-8) + 2(4) = 52 ≥ 18 (true)

Therefore, the points (0,10) and (-8,4) are solutions of the system of inequalities.

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The distance between the points (1, 1) and (1, -4) is 5 units and the reflection of the coordinate points is (-4, 6.2).

(a) We need to find the length between the pair of points which are (1, 1) and (1, −4). It can be determined by using the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given as,

[tex]d = √(x2−x1)²+(y2−y1)²[/tex]

Given data:

The first points are = (1, 1)

second points are =(1, −4)

Substituting the first and second values into the distance formula, we get:

= √(1−1)²+(−4−1)²

= √0+(−5)²

= √25​

= 5

Therefore, The distance between the points (1, 1) and (1, -4) is 5 units.

(b )We need to find the reflection of the coordinate point. According to the reflection rule when a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. The reflected point will be,

= (x, y) = (-x, y).

Given Data:

Coordinate points = (4, 6.2)

According to the rule, it is given as:

= (4, 6.2)

= (-4, 6.2)

Therefore, the reflection of the coordinate points is (-4, 6.2)

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An equation shows the number of points available, p, in round n of the game show is p=20·5ⁿ. Therefore, option D is the correct answer.

The given geometric sequence is 20, 100, 500, 2500,...

Here, a=20

Common ratio (r) = 100/20 = 5

The formula to find nth term of the geometric sequence is [tex]a_n=ar^n[/tex]. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, aₙ=20·5ⁿ

Therefore, option D is the correct answer.

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a) The median of the dataset is: 11.5

b) The mean of the dataset is: 12.5

c) The mode of the dataset is: 9 and 14

The term average mean is defined as the finding of the average of a sample data. Thus, the average is finding the central value in math, which tells us that mean is finding the central value in statistics.

The numbers arranged in ascending order is:

5, 7, 9, 9, 14, 14, 19, 23

a) The median is defined as the middle term of the distribution when arranged in ascending or descending order. Thus, the median here is:

(9 + 14)/2 = 11.5

b) The mean of the data is expressed as:

(5 + 7 + 9 + 9 + 14 + 14 + 19 + 23)/8

= 12.5

c) The mode is the most frequently occurring term in the data.

In this case, the mode is 9 and 14

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Joey forgot to record approximately 9,412 views after the second month.

Using a regression calculator, we find that the equation that best models the data is:

y = 4298.76x + 809.72

The coefficient of determination (R-squared value) for this regression is 0.994, indicating a strong linear relationship between the number of months and the total number of views.

We need to find the value of y for x = 2, using the regression equation we found in part a:

y = 4298.76(2) + 809.72

y ≈ 9412.24

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Alleen's mom is not correct because if her friend reads 20 pages, she can read 30 pages in the same time period.

To answer this question, we need to use the terms "ratio" and "proportion". The given ratio of Alleen's reading speed to her friend's speed is 1.5:1. If Alleen's friend reads 20 pages, we can use proportion to find how many pages Alleen can read:

1.5 / 1 = x / 20

To solve for x (the number of pages Alleen reads), we can cross-multiply:

1.5 * 20 = 1 * x
30 = x

So, if Alleen's friend reads 20 pages, Alleen can read 30 pages in the same time period.

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The function can be expressed in terms of natural logarithms as f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).

The function is, f(x) = ln √(4x+5)/√(7x-4)

First, note that we can simplify the expression inside the natural logarithm by applying the rules of radicals:

√(4x+5)/√(7x-4) = (4x+5)^(1/2) / (7x-4)^(1/2)

Now, we can apply the rule for the logarithm of a quotient, which states that:

ln (a/b) = ln a - ln b

Using this rule, we can rewrite the given function as:

f(x) = ln [(4x+5)^(1/2) / (7x-4)^(1/2)]

= ln (4x+5)^(1/2) - ln (7x-4)^(1/2)

Next, we can apply the rule for the logarithm of a power, which states that:

ln a^n = n ln a

Using this rule, we can simplify the logarithms in the expression above:

f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).

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The mass of the lamina that occupies the region D is 31/2 units and the center of mass is located at (1/2, 2/e).

We can find the mass of the lamina by integrating the density function over the region D:

m = ∫∫D p(x,y) dA

where dA is the area element in polar coordinates, which is equal to r dr dθ. The region D can be described as 0 ≤ x ≤ 1 and 0 ≤ y ≤ e, so the integral becomes:

m = ∫0^1 ∫0^e 31y dy dx

Solving the integral, we get:

m = 31/2

To find the center of mass, we need to find the x-coordinate and y-coordinate separately:

x = (1/m) ∫∫D x p(x,y) dA

y = (1/m) ∫∫D y p(x,y) dA

For the x-coordinate, we have:

x = (1/m) ∫0^1 ∫0^e x(31y) dy dx

Simplifying, we get:

x = (1/m) ∫0^1 31/2 x dx

x = 1/2

For the y-coordinate, we have:

y = (1/m) ∫0^1 ∫0^e y(31y) dy dx

Simplifying, we get:

y = (1/m) ∫0^1 31/3 e^3 dx

y = (2/e)

Therefore, the center of mass is located at (1/2, 2/e).

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The fraction is 1/6. Option D

First, we need to know the conversion factor the parameters.

Then, we have that';

1 liter = 1000 milliliter

10 milliliters (ml) = 1 centiliter (cl)

10 centiliters =  1 deciliter (dl) = 100 milliliters

1 liter =  1000 milliliters

1 milliliter =  1 cubic centimeter

1 liter =  1000 cubic centimeters

Then, we can say that;

If 1 liter = 1000ml

Then 2 4/8 = 400ml

2.4 liters is equal to 2.4 x 1000= 2400 milliliters.

400/2400

Simplify the fraction;

4/24

Divide the values, we get;

1/6

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Using the composition of functions, if the two functions are inverses of each other, therefore, we cannot conclude if f(x) and g(x) are inverses of each other.

To check if the two functions f(x) and g(x) are inverses of each other, we need to verify if their composition f(g(x)) and g(f(x)) results in the identity function f(x) = x.

Let's first find the composition f(g(x)):

f(g(x)) = f(x^2 - 4)

= sqrt(x^2 - 4) + 4

Now, let's find the composition g(f(x)):

g(f(x)) = g(sqrt(x) + 4)

= (sqrt(x) + 4)^2 - 4

= x + 16 + 8sqrt(x)

To check if f(x) and g(x) are inverses of each other, we need to check if f(g(x)) = x and g(f(x)) = x for all x in the domain of the functions.

For f(g(x)):

f(g(x)) = sqrt(x^2 - 4) + 4

This function is only defined for x > 2, since the square root of a negative number is not real. Therefore, the domain of f(g(x)) is (2, infinity).

For g(f(x)):

g(f(x)) = x + 16 + 8sqrt(x)

This function is only defined for x >= 0, since the square root of a negative number is not real. Therefore, the domain of g(f(x)) is [0, infinity).

Since the domains of f(g(x)) and g(f(x)) do not overlap, we cannot check if they are inverses of each other. Therefore, we cannot conclude if f(x) and g(x) are inverses of each other.

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Answer:

1. [tex]9^{2} + 12^2 = 15^2\\81+144=225[/tex]

Janice's monthly payment for her 5-year, 4% APR car loan would be $626.38.

To calculate Janice's monthly payment, we first need to use the formula for calculating loan payments:

Loan Payment = Loan Amount / Discount Factor

The discount factor can be calculated using the following formula:

Discount Factor = [(1 + r)ⁿ] - 1 / [r(1 + r)ⁿ]

Where r is the monthly interest rate (4% divided by 12 months = 0.00333) and n is the total number of payments (5 years x 12 months = 60).

Plugging in the values, we get:

Discount Factor = [(1 + 0.00333)⁶⁰] - 1 / [0.00333(1 + 0.00333)⁶⁰] = 55.8389

Now, we can calculate Janice's monthly payment:

Loan Payment = $35,000 / 55.8389 = $626.38

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Answer: this is the answer

Step-by-step explanation:

the acme company manufactures widgets. the distribution of widget weights is bell-shaped. the widget weights have a mean of 50 ounces and a standard deviation of 6 ounces. use the standard deviation rule, also known as the empirical rule. suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between oz and oz b) what percentage of the widget weights lie between 32 and 56 ounces? % c) what percentage of the widget weights lie below 62

The density of the wooden cube is 0.638 g/cm³. The type of wood the cube is made of is ash.

The wooden cube has a edge length of 6 centimetres and a mass of 137.8 grams.

The density of the wood can be calculated as follows:

density = mass / volume

volume of the wood = l³

where

Therefore,

volume of the wood = 6³

volume of the wood = 216 cm³

density of the wood = 137.8 / 216

density of the wood = 0.63796296296

density of the wood = 0.638 g/cm³

Therefore, the cube wood is made of ash.

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The possible dimensions of the rectangular prism are (2x + 3) cm, (x + 4) cm, and 4 cm, or (2x + 3) cm, 4 cm, and (x + 4) cm, where x is a measure in centimeters.

The polynomial 8x² + 44x + 48 represents the volume of a rectangular prism in cubic centimeters, where x is a measure in centimeters.

To find the possible dimensions of the box, we need to factor the polynomial into three factors that represent the length, width, and height of the rectangular prism.

First, we can factor out the greatest common factor of the polynomial, which is 4:

8x² + 44x + 48 = 4(2x² + 11x + 12)

Next, we can factor the quadratic expression inside the parentheses:

2x² + 11x + 12 = (2x + 3)(x + 4)

Therefore, the polynomial can be factored as:

8x² + 44x + 48 = 4(2x + 3)(x + 4)

This means that the dimensions of the rectangular prism could be (2x + 3), (x + 4), and 4, where x is a measure in centimeters. Alternatively, the dimensions could be (2x + 3), 4, and (x + 4).

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The total area on which the dart may land is 530.93 square units

The dart is a circle and hence the calculations will be accomplished using formula pertaining to a circle.

The circumference of a circle (dart) is given by the formula below

C = 2 * π * r

where

C is the circumference

π = pi is a constant term and

r is the radius.

26π = 2πr

Dividing both sides by 2π, we get:

r = 13

Area of the dart (circle)

A = πr²

A = π * (13)²

A = 169π (in terms of pi)

A = 530.93 square units (to 2 decimal place)

Therefore, the total area on which the dart may land is 169π square units.

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The radius of the circle x^2 + (y - 3/4)^2 = 144 is 12 units

From the question, we have the following parameters that can be used in our computation:

x^2 + (y - 3/4)^2 = 144

As a general rule, the equation of a circle is represented as

(x - a)^2 + (y - b)^2 = r^2

Where

Radius = r

Using the above as a guide, we have the following:

r^2 = 144

SO, we have

r = 12

Hence , the calculated value of the radius is 12 units

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The amount of levels left at the end is 105.

There is a total of 840 levels in the game.

On the first day she completes 1/6 of the total, so she completes:

840/6 = 140

The remaining is 840 - 140 = 700

Then she completes 1/4 of that, which is:

(1/4)*700 = 175

So now she has left 700 - 175 = 525

Then she completes 4/5, so she does:

(4/5)*525 = 420

The amount left is: 525 - 420 = 105

The correct option is B.

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The AA Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. We can complete the figure by drawing a line segment of length 10.5 from point A to point H.

Using this theorem, we can write the following if-then statement to describe the given illustration:

If angle RH is congruent to angle A and angle NH is congruent to angle E, then triangle PHN is similar to triangle AHE.

This means that the corresponding sides of these triangles are proportional to each other. We can use this information to complete the figure by finding the length of side AH.

Since triangle PHN is similar to triangle AHE, we can set up the following proportion:

PH/AH = HN/HE

We know that PH = 6 and HN = 8, and we want to find AH. Let x represent the length of AH.

6/x = 8/14

Cross-multiplying gives us:

6 * 14 = 8 * x

Simplifying:

84 = 8x

Dividing both sides by 8:

x = 10.5

Therefore, we can complete the figure by drawing a line segment of length 10.5 from point A to point H.

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The amount of money that he will spend a year for car payment would be = $258,000

To calculate the amount of money that will be used for car payment the following is carried out.

The cost for purchasing 2022 Jeep Grand Wagoneer Series III = $109,000

The cost for purchasing a 2023 Cadillac Escalade V = $149,000

The total amount spent of car payments = 109000+149000

= $258,000

Therefore, the buyer will spend up to $258,000 a year for car payment when the price for both cars he bought is being summed up.

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The rate of change for the water level between Weeks 2 and 3 is: D. 3 7/8.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (1 5/8 + 2 1/4)/(3 - 2)

Rate of change (slope) = (13/8 + 9/4)/(1)

Rate of change (slope) = 3 7/8

Based on the table, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 3 7/8.

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Answer:

It’s an hour

Answer:

11:15 to 12:15 is 1 hour.

11:15 is 1 hour and 15 minutes after 10:00. 12:15 is 1 hour and 15 minutes after 11:00. Therefore, the time span between 11:15 and 12:15 is 1 hour.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

0.4 inches = 2 miles

x    inches = 8 miles

Cross multiplication:

0.4 * 8 = 2 * x

3.2 = 2x

x = 1.6''

Answer:

Its B because you find the number in the middle, if theres two numbers in the middle, you add them up and divide by 2

the answer is B

the answer is B because 21 and 23 both seem to be in the middle. when two numbers are in the middle, you add them, then divide by two as a result, you would get 22.

Based on the information provided, the one that is the correct graph is "On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2..." (option 2).

The graph of y = StartFraction 1 Over x + 2 EndFraction + 1 is the second option described: On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrants 1 and 4. It crosses the x-axis at (3, 0). The other curve opens down and to the left and it crosses the y-axis at (0, negative 1.5).

This graph has a vertical asymptote at x = 2 and a horizontal asymptote at y = 1. It is a hyperbola that opens up and to the right in quadrants 1 and 4. The curve crosses the x-axis at x = 3, which means that when y = 0, x = 3. The other curve opens down and to the left and it crosses the y-axis at y = -1.5, which means that when x = 0, y = -1.5.

Note: This question is incomplete; here is the complete question:

Which of the following is the graph of y = StartFraction 1 Over x + 2 EndFraction + 1?

On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrant 1. The other curve opens down and to the left and it crosses the x-axis at (1, 0).

On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrants 1 and 4. It crosses the x-axis at (3, 0). The other curve opens down and to the left and it crosses the y-axis at (0, negative 1.5).

On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1 and 2. It crosses the y-axis at (0, 1.5). The other curve opens down and to the left and it crosses the x-axis at (negative 3, 0).

On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1, 2, and 4. It crosses the x-axis at (negative 1, 0). The other curve opens down and to the left in quadrant 3.

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Answer:

6

Step-by-step explanation:

A=hbb/2=4·3/2=6

To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formula

or

The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm2, inches2, and so on.

The wavelength of the light is approximately 0.687 μm.

Using the single slit diffraction formula, we have:

sin θ = (mλ) / w

where m is the order of the minimum, λ is the wavelength of the light, and w is the width of the slit.

We can rearrange the formula to solve for the wavelength of the light:

λ = (w sin θ) / m

Plugging in the given values, we get:

λ = (1.2 μm)(sin 32.3°) / 1 = 0.687 μm

Therefore, the wavelength of the light is approximately 0.687 μm.

The wavelength is the distance between two consecutive peaks or troughs in a wave. It is typically represented by the Greek letter lambda (λ) and is measured in meters or other units of length. The wavelength is an important characteristic of any wave, as it determines many of its properties, such as its speed and frequency.

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

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

V = a³

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

a = ∛V

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

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The minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

To find the minimum and maximum measurements of Joshua's model airplane, we need to subtract and add 0.5 inches to the given length of 45 inches, respectively.

Minimum measurement:

45 - 0.5 = 44.5 inches

Maximum measurement:

45 + 0.5 = 45.5 inches

Therefore, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

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Lesli ganará $750 de interés si presta $5000 a pagar en 3 años al 5% de interés simple anual.

Para calcular el interés que ganará Leslie en diferentes escenarios, consideraremos los siguientes casos:

A) Tasa simple anual del 5%:

El interés simple se calcula multiplicando el capital prestado por la tasa de interés y el tiempo en años.

Interés = Capital x Tasa x Tiempo

Interés = 5000 x 0.05 x 3 = $750

B) Tasa simple anual del 10%:

De manera similar al caso anterior, el interés se calcula como:

Interés = 5000 x 0.10 x 3 = $1500

C) Tasa compuesta anual del 5%:

En el caso de la tasa de interés compuesta, los intereses se acumulan en cada período. La fórmula para calcular el monto total es:

Monto = Capital x (1 + Tasa)^Tiempo

Monto = 5000 x (1 + 0.05)^3 = $5788.75

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