A ramp is elevated to a height of 7 inches from the base. The horizontal distance between the lower end of the ramp and the base is 19 inches, as shown in the figure. What is the length of the ramp?

x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6 or in interval notation [-9,6]

To find out what are the steps in solving the below inequality:

Given equation is 2x - 3 > 15

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

−15≤2x-3≤15

First, subtract 3  from each segment of the system of equations to isolate the x term while keeping the system balanced:

−15−3≤2x-3−3≤15−3

−18≤2x-6≤12

−18≤2x-6≤12

Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:

[tex]-\frac{18}{2}\leq \frac{2x}{2} \leq \frac{12}{2}[/tex]

-9 [tex]\leq[/tex] x [tex]\leq[/tex] 6

or

x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6

or in interval notation [-9,6]

on the horizontal axis.

The lines will be a solid line because the inequality operators contain "or equal to" clauses.

We will shade between the lines to show the interval:

Hence the steps to solve an inequality has been show

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The two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).

In the given question we have to find the two x intercept of the equation.

The give equation is [tex]y=\frac{1}{2}(x+2)^2-4[/tex].

We can find the x intercept by putting y=0. Then solving the equation for x.

Now putting y=0 in the given equation.

0= [tex]\frac{1}{2}(x+2)^2-4[/tex]

Add 4 on both side, we get

[tex]\frac{1}{2}(x+2)^2[/tex] = 4

Multiply by 2 on both side, we get

[tex](x+2)^2[/tex] = 8

Taking square root on both side, we get

x+2 = √8

x+2 = ±2√2

Subtract 2 on both side we get

x=±2√2-2

Taking 2 common

x=2(±√2-1)

Now the values of x

x={2(-√2-1), 2(√2-1)}

x={-2(√2+1), 2(√2-1)}

Hence, the two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).

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Answer:

A

Step-by-step explanation:

The decimal place should be after only 1 digit so the answer is e

The solution of the equation is -3, 5+2i, 5-2i

What is solution of equation?

The solution of an equation is the array of all values that, when replaced for unknowns, make an equation true. For equations requiring one unknown, raised to a power one, two basic algebra rules involving the additive property and the multiplicative property are used to decide its solutions.

given equation is [tex]x^3+87=7x^2+x[/tex]

we can write it as

[tex]x^3+7x^2+x+87=0[/tex]

solving this cubic equation, we get

(x+3)(x2-10x+29)=0

x = -3 is the first root of the equation.

x2-10x+29 = 0

x =(-b±√b2-4ac)/2

x =(10±√-16)/2

x =5±2i

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Check the picture below.

Answer:

AM=M-A

-3 -1. -2

2 -. -3. = 5

-3. -2. -5

2. +. 5. =. 7

The goal of a confidence interval is to provide a range of values that are reasonable for the parameter of interest. So the correct option is (A).

The goal of a confidence interval is to provide a range of values that is reasonable for the parameter of interest. The confidence interval is based on the sample data and the level of confidence. The level of confidence is the probability that the confidence interval contains the true value of the parameter.

The confidence interval is calculated using the sample mean, the sample standard deviation, and the level of confidence. The confidence interval is calculated by adding and subtracting the margin of error from the sample mean. The margin of error is the product of the critical value and the standard error. The critical value is based on the level of confidence. The standard error is the standard deviation of the sampling distribution.

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Based on the data the correct interpretation of the interval is that we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. (Option B)

In statistics, a confidence interval indicates the probability that a population parameter will lie between a set of values around the population mean. It measures the degree of certainty or uncertainty in a sampling method. It is a range of values which are bounded above and below the statistic's mean that likely would contain an unknown population parameter. Confidence level is the percentage of certainty or probability of the confidence interval would include the true population parameter when a random sample is repeatedly drawn. Hence, in the given case based on the information we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches.

Note: The question is missing options which are A. We are 94% confident that the population mean height of college basketball players is 66.35 inches. B. We are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. C. A 94% of college basketball players have heights between 65.6 and 67.1 inches. D. There is a 94% chance that the population mean height of college basketball players is between 65.6 and 67.1 inches.

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1. The measure of angle H is 79 degrees

2. The measure of angle G is 54 degrees

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

1. Given is isosceles triangle

∠H=∠O = x

sum of all interior angles of a triangle= 180 degrees

22+x+x=180

2x+22=180

2x=158

x=158/2=79

So, ∠H=79

2. Given is isosceles triangle

∠D=∠O = 63

Let ∠G=x

sum of all interior angles of a triangle= 180 degrees

63+63+x=180

x+126=180

x=180-126=54

So, ∠G=54

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1. The patterns regarding the polygons are given as follows:

2. The relationship between the number of sides of the polygon, and the number of non-overlapping triangles in the polygon is:

The number of non-overlapping triangles in the polygon is two less than the number of sides.

3. The relationship between the number of sides of the polygon and the sum of the interior angles is:

The sum of the interval angles of a triangle is given by the multiplication of 180º and the number of non-overlapping triangles in the polygon.

The patterns in the context of this problem are all obtained from the last row of the table, and they are all axioms for polynomial relations.

For item 2, the relationship is given by the third column of the last row, and for item 3, by the fourth column.

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Answer:

Step 3 is wrong. If 3x+28=15, then 3x= 15-28

Answer:

43446

Step-by-step explanation:

52 weeks in an year

835.5*52

= 43446

The equation of the line in point slope form is (c) y - 6 = -2(x + 2)

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (2, -2) and (-2, 6)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2, -2) and (-2, 6)

Substitute the known values in the above equation

So, we have the following equation

m = (6 + 2)/(-2 - 2)

Evaluate

m = -2

The equation of a line can be represented as

y  - Y = m(x - X)

Where

Slope = m = -2

(X, Y) = (-2, 6)

So, we have

y - 6 = -2(x + 2)

Hence, the line has an equation of y - 6 = -2(x + 2)

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Answer:

<3, < 6, <7 are all 102,

<1, <4, <5 and <8 are all 78

Step-by-step explanation:

If you slide angles 1, 102, 3 qnd 4 down along p, they will fit perfectly over 5,6,7 and 8.  So if you find the top four angles, you have found the bottom 4 angles.

<3 is a vertical angle to 102 and vertical angles always have the same measurement.

Angles 1 and 4 are supplemental to 102.  That means that the two angles will add to 180.  180 - 102 = 78

Using cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.

The given equation is -

[tex]\frac{z}{-12}=-5[/tex]

We have to solve this equation.

Now,

[tex]\frac{z}{-12}=-5\\[/tex]

We have to use cross multiplication method to solve the given equation.

[tex]\frac{z}{-12}=-5\\\\= > z= (-5) (-12)\\= > z = 60[/tex]

Thus, by solving through cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.

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Question:

4 unit squares each have 5/7 of their area shaded. What is the total area that is shaded?

The total area that is shaded=20/7  unit squares

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

The total area= 4*(5/7)=20/7

This cannot be simplified any more than it is

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Answer:

105

Step-by-step explanation:

627-102=525

525 divided by 5 is 105

The pounds of berries that Gabrielle put in each container, given the pounds of berries she picked, are  5/6 pounds

Gabrielle was able to pick 5 ⁵/₆ pounds of berries. First convert this to an improper fraction for easier calculations:

= 5 ⁵/₆

= ((6 x 5) + 5) / 6

= 35 / 6

The pounds of berries that went into each container is:

= Pounds of berries / Number of containers

= 35 / 6 ÷ 7

= 35 /6 x 1/7

= 35/42

= 5/6 pounds

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Answer:

W

Step-by-step explanation:

It intercepts the y at 2 and x at -3

Answer:

W.

Step-by-step explanation:

The y-intercept of 2 can be found on the vertical line ( up and down ) and the x-intercept of -3 can be found on the horizontal line ( left to right )

Therefore the answer would be graph W.

Answer: [tex]4\frac{2}{3} in;[/tex]  [tex]5\frac{2}{3} in;[/tex]  [tex]6\frac{2}{3} in[/tex]

Answer:

600 miles

Step-by-step explanation:

1 Inch = 100 Miles

6 Inches = 600 Miles

The population of white tailed deer was increased by 40 times .

What are white tailed deer?

The medium-sized white-tailed deer is a native of North America, Central America, and South America as far south as Peru and Bolivia. It is often referred to as the white tail or Virginia deer.

Main body:

population of white tailed deer in 1905 = 5*10^5

population of white tailed deer in 2000 = 2*10^7

Population increase can be calculated by using simple division ,

calculating :

⇒ 2*10⁷/5*10⁵

⇒ 2*10⁽⁷⁻⁵⁾/ 5

⇒ 2*10²/ 5

⇒ 200/5

⇒ 40

Hence population increased by 40 times from 1905 to 2000 for white tailed deer.

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Using the triangle proportionality theorem, the missing lengths that are indicated are:

1. 35

2. 14

3. 28

4. 18

The triangle proportionality theorem states that when a line is drawn to be parallel to any side of a triangle that it intersects two of the side of the triangle at two different points, then the two sides are divided proportionally or in the same ratio.

Apply the triangle proportionality theorem to find all the missing length that are indicated. Let the missing side be represented as x.

Problem 1:

x/28 = 15/12

x = (28)(15)/12

x = 35

Problem 2:

x/28 = 6/(18 - 6)

x/28 = 6/12

x/28 = 1/2

x = 28/2

x = 14

Problem 3:

x/35 = 12/(12 + 3)

x/35 = 12/15

x/35 = 4/5

x = (35)(4)/5

x = 28

Problem 4:

x/54 = 8/24

x/54 = 1/3

x = 54/3

x = 18

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Answer:

x= 0.41

Step-by-step explanation:

tan 9° =[tex]\frac{x}{2.6}[/tex]

x= 2.6 tan9°  (cross multiply)

x= 0.41          (solve trignomatic function)

Answer:

Incomplete question.

Step-by-step explanation:

4 cm = 50 km

1 cm = 50/4 = 12.5 km

Use above ratio or

50 km = 4 cm

1 km = 4/50 = 0.08 cm

Answer are

a) The Excepted value (p-hat) of p is 0.57

b) The Standard error of p is 0.05

c) Sampling distribution of p is Normal distribution

d) E(p-hat) = 0.57 , σ(p-hat) = 0.05

Excepted value or "p-hat" is defined as the ratio of number of succes in any sample or event to the total the size of sample . It is also known as sample proportion.

P-hat = X/ N

we have given that,

Sample size (N) = 100

Probability of an event occuring (p) or population proportion = 0.57

The Excepted value of sample proportion i.e p-hat is equal to population proportion i.e p

a) so, excepted value of p = 0.57

b) Standard error of p-hat is equal to square roots of product of p and (1-p) divided by sample size .

Standard error of p- hat = √p(1-p)/n

= √0.57 × 0.43/100= 0.05

c) Sampling distribution of sample mean is normal distribution using central limit theorem.

d) Sampling distribution of p shows

E(p-hat) = 0.57

σ(p-hat) = 0.05

Hence, we get all the required values of excepted value of p , standard error of p , distribution of p.

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