Which of the following is the differnce of two squares

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.

9514 1404 393

Answer:

  23°

Step-by-step explanation:

The angle a vector makes relative to the +x axis is found as ...

  α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°

The angle is about 23°.

__

Additional comment

This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)

Answer:

The proportion of products that exhibit edge roughness is 0.029 = 2.9%.

Step-by-step explanation:

Proportion of products that exhibit edge roughness:

2% of 25%(new blades).

3% of 60%(average sharpness).

4% of 15%(worn). So

[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]

The proportion of products that exhibit edge roughness is 0.029 = 2.9%.

Answer: 9

Step-by-step explanation:

[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]

Answer:

x=8

Step-by-step explanation:

Answer:

431.2

Step-by-step explanation:

Area of a regular polygon = # of sides * side length of 1 side * apothem

We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters

So # of sides = 7

apothem = 8

side length = 7.7

so the area would equal 7 * 8 * 7.7 = 431.2

It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth

Answer:

That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2

15.6

Step-by-step explanation:

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:

[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:

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:

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:

Step-by-step explanation:

Answer:

3/8 x 5/8= 15/64

Step-by-step explanation:

Answer:

y+10=2

y=-8

Step-by-step explanation:

y=2-10

y=-8

Answer:

According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.

Step-by-step explanation:

To evaluate such, a comprehension of linear Cartesian data is required:

Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.

Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.

X-intercept: The peculiar point in which the linear data observed intersects the x-axis.

Since this is a negative linear, all negative slopes apply.

The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.

A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.

B. Contains a negative slope, thus is disclosed as a correct answer.

C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

2x + y = 4

Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.

D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

X - y = 9

-y = -x + 9

Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).

Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.

*I hope this helps.

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:

17 : 27

Step-by-step explanation:

x=3

y=5

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

= 12+5 : 30-3

= 17 : 27

Answer:

6 11/12

Step-by-step explanation:

4 1/6 + 2 3/4

Get a common denominator of 12

4 1/6 *2/2  + 2 3/4 *3/3

4 2/12 + 2 9/12

6 11/12

Answer:

B

Step-by-step explanation:

they have the same intercepts

Answer:

-2

-1

-2

Step-by-step explanation:

really ? this is a problem ? why ?

f(0) means the functional value for x = 0.

is x = 2 ? no.

so, automatically the other case applies, and f(0) = -2

f(2) means x=2

is x = 2 ? yes.

so that case applies, and f(2) = -1

f(5) means x=5

is x = 2 ? no.

so again, the case for x <> 2 applies, f(5) = -2

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

...

Calculate Energy Cost by Appliance

Answer:

Step-by-step explanation:

You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):

y = 0.5x + 0.5

It takes 0.5 hour to clean up.

Answer:

Step-by-step explanation:

g(5) = 2 > 0

:::::

g(x) = 0 for x = -2, 2, 4

:::::

g(x) < 0 for  -3 ≤ x < -2

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:

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

9514 1404 393

Answer:

  (-3, 3)

Step-by-step explanation:

The blanks are trying to lead you through the process of finding the point of interest.

__

The horizontal distance from T to S is 9 . (or -9, if you prefer)

The ratio you're trying to divide the line into is the ratio that goes in this blank:

Multiply the horizontal distance by 2/3 . (9×2/3 = 6)

Move 6 units left from point T.

The vertical distance from T to S is 6 .

Multiply the vertical distance by 2/3 . (6×2/3 = 4)

Move 4 units up from point T.

__

Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).

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:

Step-by-step explanation:

Are you trying to find a variable expression? the product of 86 means multiplication so 86*n or 86n. Other than that I dont understand the question.

Answer:

[tex]P(x=3)=0.2269[/tex]

Mean=2.1

Standard deviation=1.21

Step-by-step explanation:

We are given that

n=7

Probability of success, p=0.3

q=1-p=1-0.3=0.7

We have to find the probability of 3 success for the binomial experiment  and find the mean and standard deviation.

Binomial distribution formula

[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]

Using the formula

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]

Using the formula

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

[tex]P(x=3)=0.2269[/tex]

Now,

Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]

Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]

Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]

Standard deviation, [tex]\sigma=1.21[/tex]