Complete the Proof Correctly.

Answer: To find the height of the ramp, we need to use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ramp, porch, and ground form a right triangle, with the height of the ramp being the missing side.

We know that the ramp begins 96 centimeters from the porch and is 100 centimeters long. Let's represent the height of the ramp with the variable "h". Then, we can write the Pythagorean theorem equation:

h^2 + 96^2 = 100^2

Simplifying this equation, we get:

h^2 + 9216 = 10000

Subtracting 9216 from both sides, we get:

h^2 = 784

Taking the square root of both sides, we get:

h = 28

Therefore, the height of the ramp is 28 centimeters.

Step-by-step explanation:

The required perimeter of the rectangle is 42 cm.

A quadrilateral with four right edges is a rectangle. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equally long edges.

Let's assume that the width of the rectangle is w cm.

The length of the rectangle is twice the width, which means that the length is 2w cm.

The area of the rectangle is given as 98 square cm, so we have:

[tex]$$A = lw = (2w)w = 2w^2 = 98$$[/tex]

Solving for w, we get:

[tex]$$w^2 = 49$$[/tex]

[tex]$$w = \pm 7$$[/tex]

Since the width of the rectangle cannot be negative, we take w = 7 cm.

Then, the length of the rectangle is 2w = 14 cm.

The perimeter of the rectangle is given by:

[tex]$$P = 2l + 2w = 2(14) + 2(7) = 28 + 14 = 42 \text{ cm}$$[/tex]

Therefore, the perimeter of the rectangle is 42 cm.

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Answer:

Step-by-step explanation:

The equation would be

f(x) = (x - 1)^2 + 1

Answer:

7.111 per pound of seed.

Step-by-step explanation:

64/9 = 7.111

Step-by-step explanation:

The parent square root function is given by f(x) = √x. The function g(x) is obtained by applying the following transformations to the parent function:

Shift the graph 3 units to the left: f(x+3)

Shift the graph 4 units down: f(x+3)-4

Add a constant 3: f(x+3)-4+3 = f(x+3)-1

Take the square root: g(x) = √(f(x+3)-1) = √(√(x+3)-1)

Therefore, the graph of f is translated 3 units to the left and 1 unit down to obtain the graph of g. None of the given options accurately describe the transformation, so the correct answer is option E: None of the above.

Answer: true

Step-by-step explanation:

6:8 = 12:16

12:16 less than 14:16

The probability of the ball landing on a number that is less than six is:

5/38.

The word "probability" derives from the Latin word "probitatem," which means "credibility, probability," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

American roulette has five numbers that are less than six, namely 1, 2, 3, 4, and 5.

The odds of the ball landing on a number less than six are 5 to 1 out of a total of 38 outcomes (the 36 digits plus 0 and 00).

Hence, the likelihood that the ball will land on a number smaller than six is:

5/38.

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Answer:

3

Step-by-step explanation:

the coordinates are the answers for X and Y.

x+3y=20

n+3n=20

n=5

y=ax-10

5=5a-10

a=3

Answer:

x = 45

Step-by-step explanation:

since the lines are congruent, then the opposite angles will be the same.

2x+90=180

Hope this helps

Answer:

[tex]y=-\frac{2}{3}x+2[/tex]

Step-by-step explanation:

The formula for equation of a line is [tex]y=mx+b[/tex] where m is the slope, b is the y-intercept, and (x,y) can represent any point on the line. We calculate the slope using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. We are subtracting the y-coordinates in the numerator and the x-coordinates in the denominator.

[tex]\frac{0-2}{3-0} = -\frac{2}{3}[/tex]

You can subtract the coordinates of your second point from your first point and you will get the same slope. Just be sure not to mix up the order.

Now that we have our slope, we can either pull the y-intercept off the graph; the line crosses the y-axis as y = 2, or we can solve our equation for the value of b.

We can pick any point on the line to solve for b. It is recommended to use one of the intercepts because either the x or y component will be zeroed out. I will use the point (0,2)

[tex]y = mx + b\\y = -\frac{2}{3}x +b\\2 = (-\frac{2}{3})(0) + b\\b = 2[/tex]

Now we have all the parts of our equation in slope-intercept form.

[tex]y = -\frac{2}{3}x +2[/tex]

The Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

What is length ?

Length is a physical quantity that describes the size or distance of an object in one dimension. It is typically measured in units such as meters, feet, inches, or centimeters, and can refer to the distance between two points or the size of an object in one direction. In geometry, length is a fundamental concept that is used to define other geometrical properties such as area, volume, and perimeter. In general, length can be defined as the extent of something along its longest dimension, and it is a crucial parameter in many fields, including physics, engineering, architecture, and mathematics.

According to the question:

The combined length of two Alphabet Cone seashells is:

1(3/4) inches + 1(3/4) inches = 3(1/2) inches

The length of the Scotch Bonnet seashell is:

2(1/8) inches

To find the difference in length, we can subtract the length of the Scotch Bonnet seashell from the combined length of the two Alphabet Cone seashells:

3(1/2) inches - 2(1/8) inches = 3(4/8) inches - 2(1/8) inches

Simplifying the expression, we get:

3(4/8) inches - 2(1/8) inches = 3(2/8) inches = 3/4 inches

Therefore, the Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

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Answer: 87

Step-by-step explanation:

(74+85+x)/3  = 82

3(82)=74+85+x

246 = 74+85 + x

246-74-85=x

x= 87

The mean of the data-set represented by the frequency table is given as follows:

d) 13.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

We have a frequency distribution, hence each observation is considered to be the midpoint of each interval, and thus the sum of the observations is given as follows:

5 x 4 + 10 x 7 + 15 x 9 + 20 x 5 = 325.

The number of observations is given as follows:

4 + 7 + 9 + 5 = 25.

Hence the mean is given as follows:

325/25 = 13.

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Answer:

To solve the problem, we need to determine the number of ways to choose 2 girls out of 8 and 2 boys out of 4, and then multiply those numbers together to get the total number of arrangements.

The number of ways to choose 2 girls out of 8 is given by the combination formula:

C(8,2) = 8! / (2! * 6!) = 28

Similarly, the number of ways to choose 2 boys out of 4 is:

C(4,2) = 4! / (2! * 2!) = 6

Therefore, the total number of different arrangements of 2 girls and 2 boys that can be chosen from the 12 students is:

28 x 6 = 168

So there are 168 different arrangements possible.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number of different arrangements, we can use combinations.

The number of ways to choose 2 girls out of 8 is C(8,2) = 28.

The number of ways to choose 2 boys out of 4 is C(4,2) = 6.

So, the total number of ways to choose 2 girls and 2 boys from 8 girls and 4 boys is:

C(8,2) * C(4,2) = 28 * 6 = 168

Therefore, there are 168 different arrangements for the piano teacher to take 4 of her 12 students to the concert.

Answer: 5 Miles and 1,241 Yards and 2 Feet

Step-by-step explanation: There are 5,280 ft in a mile. To convert to miles, you can do 30,125/5,280. This will give you 5 miles with a remainder of 3,725 ft.

Next, we convert to yards. There are 3 yards in a foot. For this you can do 3,725/3. This will give you 1,241 yd. with a remainder of 2 feet.

Combine these and it will give you 5 miles and 1,241 yd. and 2 ft.

To check your work, you can do (5*5,280)+(3,725*3)+2=30,125.

Please reply back if you have any question.

-Your Brainly Helper!

Answer:

As per the given information, Paul's profit from selling b bottles of water is given by the formula:

P(b) = 1.05b - 279

Here, b represents the number of bottles sold, and P(b) represents the profit made by Paul in dollars.

We can find the profit made by Paul by substituting the given value of b in the above equation. For example, if Paul sells 100 bottles of water, then his profit can be calculated as follows:

P(100) = 1.05(100) - 279

= 105 - 279

= -174

So, if Paul sells 100 bottles of water, he will make a profit of $174.

Note that the profit is negative in the above example, which means that Paul will incur a loss if he sells only 100 bottles of water. To make a profit, he needs to sell more than 265 bottles of water. We can find this by setting P(b) equal to zero and solving for b as follows:

P(b) = 1.05b - 279 = 0

1.05b = 279

b = 265.71

Therefore, Paul needs to sell more than 265 bottles of water to make a profit.

Paul's profit from selling bottled water is described by the formula P(b)=1.05b-279. This suggests he makes $1.05 per bottle minus an initial cost of $279. To break even, Paul must sell approximately 266 bottles.

The question involves understanding of linear functions in the context of a real-world problem. Paul is planning to sell bottled water at the local carnival. His profit function, P(b), represented by the formula P(b)=1.05b-279, describes how his profit changes based on the number of bottles, b, he sells. This formula suggests that for every bottle Paul sells, he makes a profit of $1.05 with the subtraction of $279, which probably represents his initial costs. To break even, Paul has to sell enough water such that his profit, P(b), is zero. Solving the equation P(b)=0 gives b=279/1.05. This means Paul needs to sell approximately 266 bottles of water to break even. Any sales beyond this would generate profit.

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Answer:

Step-by-step explanation:

SA=2r^{2}+2rh=175.84

Answer:

Step-by-step explanation:1.) Each person receives 5/6 of a cake.

To see why, we can think of dividing the 5 cakes into 6 equal parts. This would give us 30 equal parts, and each person would receive 5 of these parts. So, the fraction of a cake each person receives is:

5/30 = 1/6

2.) Each person receives 3/8 of a pizza.

To see why, we can think of dividing the 3 pizzas into 8 equal parts. This would give us 24 equal parts, and each person would receive 3 of these parts. So, the fraction of a pizza each person receives is:

3/24 = 1/8

3.) Each person receives 1/2 of a granola bar.

To see why, we can think of dividing the 4 granola bars into 8 equal parts. This would give us 32 equal parts, and each person would receive 4 of these parts. So, the fraction of a granola bar each person receives is:

4/32 = 1/8

1/8 ÷ 2 = 1/16

So, each person receives 1/2 of a granola bar, which is equal to 1/8 ÷ 2 = 1/16.

4.) Each pie has 2.4 pounds of blueberries.

To see why, we can divide the 12 pounds of blueberries by the 5 pies:

12 ÷ 5 = 2.4

So, each pie has 2.4 pounds of blueberries.

5.)

4 ÷ 5 = 4/5

5 ÷ 4 = 1 1/4

12 ÷ 30 = 2/5

30 ÷ 12 = 2 1/2

Answer: 1) 5/6

              2) 3/8

              3) 4/8 OR 1/2

              4) 12/5lb OR 2 2/5lb OR 2.4lb

              5) 4/5

                  5/4 OR 1 1/4

                  12/30 OR 2/5

                  30/12 OR 5/2 OR 2 1/2

Step-by-step explanation:

Answer:

p=10m.

Step-by-step explanation:

For every painting Sydney sells, $10 is saved.

Marlo can draw two different isosceles right triangles and third vertices are (-0.5, 5) and (-0.5, 7)

An isosceles triangle is a type of triangle in which two sides of the triangle have the same length.

Since the triangle is isosceles, its third vertex must lie on the line that is perpendicular to the line passing through the two given vertices and passes through the midpoint of that line.

The midpoint of the two points (-3,6) and (2,6) connecting the line segment is

((-3+2)/2,    (6+6)/2) = (-0.5, 6)

The line passing through (-3,6) and (2,6) has equation y = 6. The line perpendicular to it passing through (-0.5,6) has equation x = -0.5.

Therefore, the third vertex of the isosceles right triangle must have coordinates (-0.5, y), where y is an integer.

To find how many different isosceles right triangles can be drawn, we need to find how many different integer values of y satisfy the condition that the distance between (-3, 6) and (-0.5, y) is the same as the distance between (2, 6) and (-0.5, y).

We know that the distance formula, So,

[tex]\sqrt{((2 - (-0.5))^2 + (6 - y)^2)}[/tex] = [tex]\sqrt{((-3 - (-0.5))^2 + (6 - y)^2)}[/tex]

Simplifying this equation gives:

(2.5)² = (3.5)²

y = 6 ± 1

Therefore, there are two possible values of y, 5 and 7, which correspond to the two possible third vertices of the isosceles right triangle: (-0.5, 5) and (-0.5, 7). So, Marlo can draw two different isosceles right triangles with two vertices at (-3, 6) and (2, 6) such that the coordinates of the third vertex are both integers.

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Therefore , the solution of the given problem of volume comes out to be  1.5 centimetres is the appropriate height measurement option A.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are the numbers cm3 and in3. However, an object's bulk can be used to determine its dimensions. Typically, an object's weight is transformed into mass units like kilogrammes and kilos.

Here,

The technique used by the classmate made a mistake by rearranging the measurements in the formula. The right equation to use to determine a rectangle prism's volume is:

=> V = lwh

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

The colleague in this instance applied the formula:

=>  h = 1.5(1.2)(2.5)

which, rather than the height, is the method for calculating the volume.

We must rewrite the volume formula to determine the height:

=>  V = lwh

=>  h = V/lw

Now that we know the numbers to substitute, we can determine the height:

=>  h = 1.5(1.2)(2.5) / (1.2)(2.5)

=>  h = 1.5 cm

Consequently, 1.5 centimetres is the appropriate height measurement (option A).

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The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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We expect the cube to show a two 8 times out of 48 rolls.

Six faces, numbered from 1 to 6, make up a typical number cube. When the cube is rolled, there is an equal chance that every face will show up. As a result, there is a 1/6 chance that the cube will roll a two on any given roll.

We can use the calculation for the anticipated value of a discrete random variable to get the expected number of times the cube will reveal a two in 48 rolls:

E(X) = np

where n is the number of trials (in this example, 48 rolls), p is the probability of success on each trial (in this case, 1/6), and X is the random variable (in this case, the number of times the cube reveals a two).

When we change the values, we obtain:

E(X) = 48 * (1/6) = 8

Hence, we anticipate that the cube will display a two 8 times out of every 48 rolls.

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Answer:

Step-by-step explanation:

a, YES,  x is a solution as 4 + 2 = 6.

b. looks like there's a missing symbol here.

When 1. 384 is divided by 0. 4, the quotient would be 3. 46.

One way to divide 1. 384 by 0. 4 is to use the fact that division is the same as multiplying by the reciprocal of the divisor. The reciprocal of 0. 4 is 1 / 0. 4 or 2. 5. Therefore, we can rewrite the division as:

1. 384 / 0. 4 = 1. 384 x 2.5

We can then use multiplication to get the result:

1. 384 × 2. 5 = 3. 46

Therefore, 1. 384 divided by 0. 4 equals 3. 46.

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A) the annual rate of change between 1991 and 2000 is -$3,000.

B)  the correct answer to part A in percentage form is -6.67%.
C) where n is the number of years from 2000 to 2003, which is 3, $8,450. approximately.

A) The total change in value between 1991 and 2000 is $45,000 - $12,000 = $33,000. The number of years between 1991 and 2000 is 9. Therefore, the annual rate of change is:

r = (final value - initial value) / (number of years)

r = ($12,000 - $45,000) / 9

r = -$3,000 per year

Thus, the annual rate of change between 1991 and 2000 is -$3,000.

B) To convert the rate of change to percentage form, we need to divide it by the initial value and multiply by 100:

r = (-$3,000 / $45,000) * 100%

r = -6.67%

Therefore, the correct answer to part A in percentage form is -6.67%.

C) If the value continues to drop by the same percentage, we can use the following formula to find the value in 2003:

value = initial value * (1 + r)^n

where n is the number of years from 2000 to 2003, which is 3. Plugging in the values, we get:

value = $12,000 * (1 - 0.0667)^3

value = $8,454.58

Rounding to the nearest $50, we get the value in 2003 to be $8,450.

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The volume of the Cylinder formed  approximately 16.37 cubic units.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two parallel circular bases, connected by a curved lateral surface. It is similar to a prism, but instead of having polygons as its bases, it has circles. The lateral surface of a cylinder is formed by the set of all straight lines connecting the points on the edge of one base to the corresponding points on the edge of the other base.

Now,

To find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸about the y-axis, we can use the method of cylindrical shells.

First, we need to express the equation y=5+x⁸ in terms of x, so we can integrate with respect to x:

y = 5 + x⁸

y - 5 = x⁸

x = (y - 5)¹/⁸

Next, we need to determine the limits of integration. The region is bounded by x=0 and x=1, so we integrate from x=0 to x=1.

Volume of a cylindrical shell is

V = 2πrhΔx

In this case, the radius r is simply x, the height h is y, and Δx is dx. So, we have:

V = 2πxy dx

V = 2πx(5+x^8) dx

V = 10πx dx + 2πx⁸ dx

Integrating with respect to x from x=0 to x=1, we get:

V = [5π + 2π/10] - [0 + 0]

V = 5.2π

Therefore, the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸ about the y-axis is approximately 16.37 cubic units.

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Answer:

1.49 minutes

Step-by-step explanation:

Let the number of minutes be x.

Deandre paid $17.43 for $7 to start  and 7 cents per minute.

Mathematically,

7x+7=17.43

7x= 17.43-7

7x = 10.43

∴ x = 10.43/7

x = 1.49 minutes.

Hope this helps! :)