Ingrid is putting in a circular pool with a diameter of 20 feet. How much yard space will the new pool take up?​

The missing portions of the proof are:

2) ∠4 ≅ ∠1 ; ∠3≅∠2 - Corresponding Angles Theorem

3) CDB ≅CEA           -     AA Similarity

The other information that could have been stated to proof that Angle - Angle similarity is: Angle C ≅ angle C

Reflexive Property

The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If an is a positive integer, then a = a.

When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding angles with the transversal.

So in the above proof, ∠4 ≅ ∠1 ; ∠3≅∠2 because they are a pair of corresponding angels because they are created in matching corners.

Looking at the shape, we can see that CDB  and CEA   are triangles since we have established that their angles are similar, hence, the Angle Angle Similarity postulate.

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The sample size for estimate the proportion of families in a certain area that are living below the poverty level is equals to the 318.75.

The standard error is a statistic term that is the standard deviation of its sampling distribution or an estimate of that standard deviation. In case of sample mean, it is called the standard error of the mean. Formula of standard mean is

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

where, n--> sample size

We have a simple random sample for estimate the proportion of families,

Sample proportion = 0.15

Standard error = 0.02

We have to determine the sample size for the standard error of the estimate is .02.

Here, SE = 0.02, \hat p = 0.15

Using the standard score formula,

[tex] 0.02 =\sqrt{ \frac{0.15 (1 - 0.15)}{n}} [/tex]

Squaring both sides

[tex] 0.02² = \frac{0.15 ×0.85 }{n} [/tex]

[tex] 0.0004 = \frac{0.1275 }{n} [/tex]

=> n = 318.75

Hence, required value is 318.75.

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The two afternoon buses were 5 minutes late.

In Mathematics, a median is the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

Since the mode is equal to 0, the frequency of 0 shall be greater than 2 of the given times in minutes and less than or equal to 4 given times in minutes.

Therefore, the frequency of 0 is equal to 3. Consequently, the number of time in minutes late for each bus after arranging them in ascending order is given by:

0, 0, 0, 2, 2, x, 6, 8, 8, 9

Median = (2 + x)/2

3.5 = (2 + x)/2

2 + x = 7

x = 7 - 2

x = 5

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Answer:

A. 3x−1=3x+1 and D. 2x+2=2(x+1) have infinitely many solutions.

The mean of the heart rates is 9.20

Given that, the heart rates of 36 whales, we need to find the mean of the population,

Mean μ = ∑x / N

N = sample size

x = observed population

Mean μ = 11+10+12+12+8+10+13+11+13+9+11+8+12+6+8+13+5+8+9+8+12+6+9+7+6+8+7+9+9+5+12+9+11+7+8+9 / 36

= 331 / 36

= 9.20

Hence, the mean of the heart rates is 9.20

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Answer: The slop is 1

Step-by-step explanation: The coordinates points:

(-2,-8), and (-3,-9)

x1 = -2  y1= -8

x2 = -3  y2= -9

m = y2 - y1/ x2 - x1

put the value

m= -9 - (-8) / -3 - (-2)

   = -9 + 8 / -3 + 2

   = -1/-1

   = 1

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Answer: If the question is asking how many teaspoons of red paint does it take to have 15 teaspoons of yellow paint, then your answer would be 9 I believe, hope this helps:)

Step-by-step explanation:

Answer:

The answer to you question is 9 teaspoons of red paint.

Step-by-step explanation:

3 teaspoons of red paint = 5 teaspoons of yellow paint

6 teaspoons of red paint = 10 teaspoons of yellow paint

9 teaspoons of red paint = 15 teaspoons of yellow paint

I hope this helps and have a wonderful day!

The expression that can be used to find the value of x is ∘23sin85∘​/sin55∘, the correct option is A

We are given that;

In triangle DEF, EF=23, DE=x, angleD=85degree, angleF=55degree

Now,

To find the value of x, we can use the law of sines with the given information:

sin85∘x​=sin55∘23​

Solving for x, we get:

x=sin55∘23sin85∘​

Using a calculator, we can approximate x as:

x≈26.6

Therefore, by the given angles the answer will be ∘23sin85∘​/sin55∘

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Answer:

x= 4 and y= 2

Step-by-step explanation:

3x+3y= 18 (1)

2y= x (2)

from (1):

x+y= 6

y= 6-x (3)

sub (3) into (2):

2(6-x)= x

12-2x= x

-3x= -12

x= 4 (4)

sub (4) into (3):

y= 6-4

= 2

Answer:

7 you would times 6 by 7 to get 42

Answer:

Step-by-step explanation:

Product is 42 after you multiply by

Here you do the reverse:

42 ÷ 6 =

7 is greater than 6 therefore your answer is

Answer:

To find the equation for d, the distance in meters that Martin covers per second, we need to use the formula:

distance = speed × time

Here, the distance covered by Martin is 100 meters, and the time taken is 15 seconds. Therefore, we can write:

distance = speed × time

100 meters = speed × 15 seconds

To find the speed, we can rearrange the equation as:

speed = distance / time

speed = 100 meters / 15 seconds

So the speed of Martin is:

speed = 6.67 meters per second

Therefore, the correct equation for d, the distance in meters that Martin covers per second, is:

d = speed

d = 6.67 meters per second

Answer: There is no option that matches the correct equation for d, which is simply d = 6.67 meters per second.

Step-by-step explanation:

The center and the radius of the circle of equation 3x² + 3y² + 12x + 18y - 36 = 0 are given as follows:

A. (-2, -3), r = 5.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation of the circle in this problem is given as follows:

3x² + 3y² + 12x + 18y - 36 = 0

Simplifying by 3, we have that:

x² + y² + 4x + 6y - 12 = 0.

Completing the squares, we have that:

x² + 4x + y² + 6y = 12

(x + 2)² + (y + 3)² = 12 + 2² + 3²

(x + 2)² + (y + 3)² = 25.

Hence the correct option is given by option A.

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Answer:

If the origin is the only point with 0 for both coordinates, then it must be the point of intersection of the x-axis and the y-axis. In other words, the origin is the point (0,0), where the x-coordinate and y-coordinate are both zero. It is the unique point in the Cartesian plane that satisfies this condition.

Step-by-step explanation:

Eliza took home 35/24 pans of fruit bars.

The problem involves finding the number of fruit bars left after a certain fraction has been consumed and then calculating how much of the remaining fruit bars were taken home using another fraction.

Here we have

Eliza brought 6 pans of homemade fruit bars to school.

Her classmates ate 5/12 of each pan.

The total amount of fruit bars they consumed is:

=>  6 pans x 5/12 = 2.5 pans

So Eliza had 6 - 2.5 = 3.5 pans of fruit bars left.

Eliza gave 1 whole pan of the leftover fruit bars to the school's secretaries and took the rest home.

Leftover bars = 3.5 pans - 1 pan = 2.5 pans

To find the number of the fruit bars she took home, multiply the number of pans by the amount that wasn't eaten, which is:

=> 2.5 pans x 7/12 = 35/24 pans

Therefore,

Eliza took home 35/24 pans of fruit bars.

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The equivalent expression by distributing the sign outside the parentheses: [tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex] will be [tex]18.8\text{q} - 6[/tex].

It should be noted that based on the information given, the expression is illustrated as:

[tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex]

The signs should be taken into consideration. This will be:

[tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex]

[tex]= 9.4\text{q} - 3 + 9.4\text{q} -3[/tex]

[tex]\boxed{=\bold{18.8\text{q} - 6}}[/tex]

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The ideal way to organize electronically the raw data for a study is to use a spreadsheet or database management system.

A spreadsheet or database management system allows you to input, store, and manage large amounts of data in a structured and organized manner. This makes it easier to analyze and process the data, as well as share it with others working on the study. Using these tools, you can sort, filter, and manipulate the data to find patterns, trends, and insights, making it easier to draw conclusions from the raw data.

Utilizing a spreadsheet or database management system is the most effective and efficient way to organize raw data electronically for a study, as it provides structure, organization, and ease of data manipulation.

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The probability of not throwing the ball to a receiver on either throw is 0.66, or 66%. 

Consider two conceivable scenarios for quarterback tosses.

1. He tosses the ball to the recipient on his to begin the endeavor.

2. He misses the collector on his to begin with endeavor and once more on his moment endeavor.

The likelihood of situation 1 is 1 – 0.4 = 0.6. Usually since the quarterback on the primary attempt he misses the collector 40% of the time.

The likelihood for Situation 2 can be calculated as

P(1st Endeavor Fizzled + 2nd Endeavor Fizzled) = P(1st Endeavor Fizzled) * P(2nd Endeavor Fizzled | 1st Endeavor Fizzled)

= 0.4 * 0.15 = 0.06

Subsequently, the likelihood of not tossing the ball to the recipient on any toss is the entirety of the probabilities of Scenarios 1 and 2.

P(Don't toss to recipient) = P(Scenario 1) + P(Scenario 2)

= 0.6 + 0.06

= 0.66

Hence, the likelihood of not tossing the ball to the collector on any toss is 0.66, or 66%. 

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The ratio of the length of a side of a square to its perimeter is **1:4**. Therefore, any ratio that is not equivalent to 1:4 is a wrong answer. For example, 2:8 is equivalent to 1:4, but 3:8 is not.

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| 2 cm        | 8 cm      | 2:8   |

| 3 cm        | 12 cm     | 3:12  |

| 4 cm        | 16 cm     | 4:16  |

| 5 cm        | 20 cm     | 5:20  |

Part A: Click the wrong answers.

The wrong answers are **3:12** and **5:20**, because they are not equivalent to 1:4.

Part B: Drag numbers into each box to produce the correct answers. Place the smaller number in the box on the left.

To produce the correct answers, we need to find two numbers that have a ratio of 1:4. For example, we can use 1 and 4, or 2 and 8, or 3 and 12, etc.

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [ ] cm      | [ ] cm    | [ ]:[ ]|

| [ ] cm      | [ ] cm    | [ ]:[ ]|

One possible way to fill in the blanks is:

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [1] cm      | [4] cm    | [1]:[4]|

| [2] cm      | [8] cm    | [2]:[8]|

Another possible way is:

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [3] cm      | [12] cm   | [3]:[12]|

| [4] cm      | [16] cm   | [4]:[16]|

There are other possible ways as well, as long as the ratio is equivalent to 1:4.

In order to develop an interval estimate of a population mean, the margin of error must be computed using: either population standard deviation, σ or the sample standard deviation, s.

In Mathematics, the margin of error (MOE) can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.

This ultimately implies that, the margin of error (MOE) can be used to determine the confidence interval.

In Mathematics and Statistics, a sample size that would result in a specific standard deviation can be calculated by using the following mathematical equation (formula):

Sample size, n = (zσ/ME)²

Where:

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The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

We have,

Sin = Perpendicular / Hypotenuse

Cos = Base / Hypotenuse

Tan = Perpendicular / Base

Now,

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

And,

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

Thus,

The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

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the percentage reduction in cost is 0%, which means there was no reduction in cost for adults.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

we know that the cost for an adult was not changed in May. Therefore, we can set the original cost equal to the new cost:

x = $22.10

Substituting this value in the equation above, we get:

$22.10 = 22.10 * (100/ (100-p))

Simplifying the equation, we get:

1 = 100 / (100-p)

Multiplying both sides by (100-p), we get:

100-p = 100

Therefore, p = 0.

So, the percentage reduction in cost is 0%, which means there was no reduction in cost for adults.

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106.8 is the population variance.

To calculate the population variance, we use the formula:

[tex]s^{2}[/tex] = Σ [[tex](xi-u)^{2}[/tex]] / N,

where xi is the ith observation, u is the population mean, and N is the population size.

First, we need to calculate the population mean:

u = (38 + 26 + 13 + 41 + 22) / 5 = 28.

Next, we calculate the sum of squares:

Σ [[tex](xi-u)^{2}[/tex]] = [tex](38-28)^{2}+ (26-28)^{2}+(13-28)^{2}+(41-28)^{2}+(22-28)^{2}[/tex]

= 100 + 4 + 225 + 169 + 36

= 534.

Finally, we divide by the population size:

[tex]s^{2}[/tex] = Σ [[tex](xi-u)^{2}[/tex]] / N = 534 / 5 = 106.8.

Therefore, the population variance is 106.8.

The closest choice to this answer is 106.8, which is the first option. So the answer is 106.8.

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The solution of the given system of equations are 1) (2, 1) and 2) (4, 3)

Given are two system of linear equation, we need to solve it,

1) y = 6x-11......(i)

-2x-3y = -7.........(ii)

Solution -

Put eq(i) in eq(ii),

-2x-3(6x-11) = -7

2x + 18x - 33 = 7

20x = 40

x = 2

Put x = 2, in eq(i)

y = 6(2)-11

y = 12-11

y = 1

The solution is (2, 1)

2) 2x-3y = -1......(i)

y = x-1.........(ii)

Solution -

Put eq(ii) in eq(i),

2x-3(x-1) = -1

2x-3x+3 = -1

-x = -4

x = 4

Put x = 4, in eq(ii)

y = 4-1

y = 3

The solution is (4, 3)

Hence, the solution of the given system of equations are 1) (2, 1) and 2) (4, 3)

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The required situation that can be represented by the equation 18x = 19 + 12x is:

"J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?"

Let Krystal and Jondo work for x hours. Then Krystal would make 18x dollars, and Jondo would make 12x + 19 dollars (Jondo already has 19 dollars).

The equation 18x = 12x + 19 represents the situation where Krystal and Jondo make the same amount of money. Solving this equation gives:

18x - 12x = 19

6x = 19

x = 19/6

So Krystal and Jondo would need to work for approximately 3.17 hours (or 3 hours and 10 minutes) to make the same amount of money.

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The value of x in the model expression is x = 10/8

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

The model

When represented as an equation, we have

4x - 4 = -4x + 6

Collect the like terms

So, we have

4x + 4x - 4 + 6

Evaluate the like terms

8x = 10

Divide by 8

x = 10/8

Hence, the solution is x = 10/8

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The measure of the altitude NE in the triangle CNE for the given similarity  is equal to 4 units.

Here In the attached figure,

B is the unknown vertex where ray AM and DE intersects.

In the triangles,

Triangle ABE ~ Triangle CDE

⇒measure of ∠A = measure of ∠C  __(1)

AE = 15

CE = 5

ME = 12

Let 'x' be the measure of altitude NE.

In ΔAME and ΔCNE,

Measure of ∠A = Measure of ∠C  (from 1)

Measure of ∠AME = Measure of ∠CNE  ( each 90° )

Measure of ∠AEM = Measure of ∠CEN ( vertically opposite angles)

By AAA corollary we have,

ΔAME ~ ΔCNE

In similar triangles corresponding sides are in proportion .

AE / CE = ME / NE

Substitute the values we have,

⇒ 15 /5 = 12/ x

⇒x =12/3

⇒x = 4

⇒NE = 4 units.

Therefore , the length of the altitude NE is equal to 4 units.

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The above question is incomplete, the complete question is:

Use similar triangles to find the length of the altitude.

Triangle ABE ~ Triangle CDE. Find the length of altitude for NE.

Attached figure.

The height of the clock tower in Sara's drawing is 16.5 centimeters.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

The scale factor is 12 feet per 2 centimeters, which simplifies to 6 feet per 1 centimeter.

First, we need to figure out how many centimeters on Sara's drawing represent one foot:

2 cm : 12 ft

We can simplify this ratio by dividing both sides by 2:

1 cm : 6 ft

Now we can use this ratio to find the height of the clock tower in centimeters:

99 ft × (1 cm/6 ft) = 16.5 cm

Therefore, the height of the clock tower in Sara's drawing is 16.5 centimeters.

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Answer:

2nd choice:  144.53 ft²

Step-by-step explanation:

Area of base = 6 x 7 = 42

Area of 2 sides with 8 ft height = 2 · (1/2)(6)(8) = 48

Area of 2 sides with 7/79 ft height = 2 · (1/2)(7)(7.79) = 54.53

Total SA = 42 + 48 + 54.53 = 144.53 ft²

If point is plotted at (3, 5) and (3, -6), then the distance between the two points plotted is (b) 11 units.

The two points plotted are (3, 5) and (3, -6). We see that both the points have the same x-coordinate, which means that both points lie on the same "vertical-line" which is parallel to the y-axis.

The distance between these two points is the vertical distance between their y-coordinates, which is:

The "y-coordinate" of the points are 5 and -6,

So, the distance will be = |5 - (-6)| = 11 units,

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10.

A point is plotted at (3, 5) and at (3, -6).

What is the distance between the two points plotted?

(a) 1 unit

(b) 11 units

(c) -11 units

(d) -1 unit