I need help completing this problem ASAP

Answer:

[tex]|F'H'| = 2 * |FH|[/tex]

Step-by-step explanation:

Given

[tex]E = (0,1)[/tex]             [tex]E' = (-1,2)[/tex]

[tex]F = (1,1)[/tex]             [tex]F' = (1,2)[/tex]

[tex]G = (2,0)[/tex]             [tex]G' =(3,0)[/tex]

[tex]H = (0,0)[/tex]            [tex]H' = (-1,0)[/tex]

[tex](x,y) = (1,0)[/tex] -- center

[tex]k = 2[/tex] --- scale factor

See comment for proper format of question

Required

Compare FH to F'H'

From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;

Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.

i.e.

[tex]|F'H'| = k * |FH|[/tex]

[tex]|F'H'| = 2 * |FH|[/tex]

To prove this;

Calculate distance of segments FH and F'H' using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Given that:

[tex]F = (1,1)[/tex]             [tex]F' = (1,2)[/tex]

[tex]H = (0,0)[/tex]            [tex]H' = (-1,0)[/tex]

We have:

[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]

[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]

[tex]FH = \sqrt{1 + 1}[/tex]

[tex]FH = \sqrt{2}[/tex]

Similarly;

[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]

[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]

Distribute

[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]

[tex]F'H' = \sqrt{(2)^2*2}[/tex]

Split

[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]

[tex]F'H' = 2 *\sqrt{2}[/tex]

[tex]F'H' = 2\sqrt{2}[/tex]

Recall that:

[tex]|F'H'| = 2 * |FH|[/tex]

So, we have:

[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]

[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true

Hence, the dilation relationship between FH and F'H' is::

[tex]|F'H'| = 2 * |FH|[/tex]

Answer:NOTT !!  A segment in the image has the same length as its corresponding segment in the pre-image.

Step-by-step explanation:

Answer:

x^2+y^2=1

Step-by-step explanation:

Since cos^2(x)+sin^2(x)=1, x^2+y^2=1

Answer:

17 : 27

Step-by-step explanation:

x=3

y=5

4(3)+5 : 6(5)-3

= 12+5 : 30-3

= 17 : 27

Answer:

The correct answer is "76.98%".

Step-by-step explanation:

According to the question,

⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]

                                       [tex]=P(-1.2<z<1.2)[/tex]

                                       [tex]=P(z<1.2)-P(z<-1.2)[/tex]

                                       [tex]=0.8849-0.1151[/tex]

                                       [tex]=0.7698[/tex]

or,

                                       [tex]=76.98[/tex]%

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

Muhammad lives 8 km away from the school.

Hita lives 4 km away from the school.

Step-by-step explanation:

First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.

Answer:

AC = 377.19

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 5 = 33/AC

AC tan 5 = 33

AC = 33/ tan 5

AC = 377.19

Answer:

the answer could be B i think cause that makes total sense

14. largest 9510

15. smallest 1000000

16. n+6=22 —> n=22-6 —>n = 16

17. Add : 204 + 38429= 38633

Answer:

Sample space = 36

P(sum of 6) = 5/36

Step-by-step explanation:

Number of faces on a dice = 6

The sample space, for a toss of 2 dice ; (Number of faces)^number of dice

Sample space = 6^2 = 6*6 = 36

Sum of numbers appearing on the dice = 6

The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5

Total possible outcomes = sample space = 36

Probability, P = required outcome / Total possible outcomes

P = 5 / 36

Probabilities are used to determine the chances of events

The given parameters are:

[tex]n=6[/tex] --- the faces of a six-sided die

[tex]r = 2[/tex] -- the number of dice

(a) The number of sample points

This is calculated as:

[tex]Sample = n^r[/tex]

So, we have:

[tex]Sample = 6^2[/tex]

Evaluate the exponent

[tex]Sample = 36[/tex]

Hence, the number of sample points is 36

(b) The probability that the sum of 6

See attachment for the sample space of the sum of two dice.

From the sample space, there are 5 outcomes where the sum is 6.

So, the probability is:

[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points

Divide 5 by 36

[tex]Pr = 0.1389[/tex]

Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389

Read more about probabilities at:

https://brainly.com/question/10707698

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).

If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).

If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).

Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).

If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)

This question is incomplete, the complete question is;

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ      { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥  ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850

Answer:

i think its 2 1

Step-by-step explanation:

Answer:

y =2/3x-1

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( 3-1)/ (6-3)

   = 2/3

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using a point

3 = 2/3(6)+b

3 = 4+b

3-4 =b

-1=b

y =2/3x-1

Answer:

0.5665 = 56.65% probability of less than four twos.

Step-by-step explanation:

For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A die is rolled 20 times

This means that [tex]n = 20[/tex]

One out of six sides is 2:

This means that [tex]p = \frac{1}{6} = 0.1667[/tex]

Probability of less than four twos:

This is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]

[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]

[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]

[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]

So

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]

0.5665 = 56.65% probability of less than four twos.

Answer:

15

Step-by-step explanation:

By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.

21*6 = 126

126/7 = 18

18 + 12 = 30

30 - 15 = 15

Answer:

15

Step-by-step explanation:

21 × 6 ÷ 7 + 12 - 15​

= 126 ÷ 7 + 12 - 15

= 18 + 12 - 15

= 30 - 15

= 15

Answer:

4s-9t-7

Step-by-step explanation:

multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same

Answer:

1st degree

Step-by-step explanation:

You look at the largest exponet, right here, there are none so it would be 1st degree.

Answer:

1

Step-by-step explanation:

The degree of an expression with multiple exponents is the highest exponent in it. In this expression, there is no expression, so the answer will be 1 because there is no exponent and every variable and number has an invisible 1 as its exponent.

Hope this helps.

Answer:

15. 52

16. 6

17. 59

18. 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

684 dollars

Answer:

Step-by-step explanation:

Answer:

3/8 x 5/8= 15/64

Step-by-step explanation:

Answer:

His least score for him in the fourth paper has to be 76.

Step-by-step explanation:

Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:

(70 x 4) - (68 x 3) = X

280 - 204 = X

76 = X

Therefore, his least score for him in the fourth paper has to be 76.

Answer:

B

Step-by-step explanation:

they have the same intercepts

Answer:

[tex]Given:[/tex] Δ ABC ≈ ΔDEF

[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²

⇒ 34/A(ΔDEF)=9²/(13.5)²

⇒34/A(ΔDEF)=81/182.25

⇒A(ΔDEF)=34×182.25/81

⇒Area of ΔDEF=76.5 cm²

----------------------------------

Hope it helps...

Have a great day!!!

9514 1404 393

Answer:

  below

Step-by-step explanation:

When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.

Answer:

4

Step-by-step explanation:

We want the cubed root of 64  

(64)^(1/3)  

(4*4*4) ^ (1/3)  

4  

Unless this is 3 * sqrt(64)  

then it would be  

3 sqrt(8*8)  

3 (8)  

24

Answer:

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n instances of a normal variable:

For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

Sum of normal variables:

When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.

Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.

This means that:

[tex]\mu_A = 10000*50 = 500000[/tex]

[tex]s_A = 1000\sqrt{50} = 7071[/tex]

Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.

This means that:

[tex]\mu_B = 20000*50 = 1000000[/tex]

[tex]s_B = 2000\sqrt{50} = 14142[/tex]

Distribution of the total of the 100 claims:

[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]

[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]

Find the probability the total of the 100 claims exceeds 1,530,000.

This is 1 subtracted by the p-value of Z when X = 1530000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]

[tex]Z = 1.9[/tex]

[tex]Z = 1.9[/tex] has a p-value of 0.9713

1 - 0.9713 = 0.0287

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

AS IN THE PICTURE...........