What does b= and c= and d=

Answer:

(a) The probability that the average of the draws will be in the range 80 to 120 is 1.

(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.

Compute the mean and standard deviation of sample mean as follows:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1[/tex]

So, [tex]\bar X\sim N(100, 1)[/tex]

(a)

Compute the probability that the average of the draws will be in the range 80 to 120 as follows:

[tex]P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})[/tex]

                            [tex]=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1[/tex]

Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.

(b)

Compute the probability that the average of the draws will be in the range 99 to 101 as follows:

[tex]P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})[/tex]

                            [tex]=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827[/tex]

Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Answer:

Option A.

Step-by-step explanation:

See attachment.

Basically, the reason why I left it at cm(3) was because that's the standard unit for volume, any length of measurement to the third power.

Answer: 6 - 5

Step-by-step explanation:

|z - 6| - |z - 5|    ; z < 5

Since z < 5, then

|z - 6| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:

-(z - 6) =  -z + 6

|z - 5| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:  

-(z - 5) = -z + 5

Now subtract them without the absolute value signs:

-z + 6 - (-z + 5)

Distribute the negative sign:

-z + 6 + z - 5

-z + z = 0 which leaves:

6 - 5

Answer: 1

Step-by-step explanation: first you need to pretend that the absolute value bars are parentheses. Then substitute a with any number less that five, for example z=3

Now we can write our new equation: (3-6)-(3-5)

now we have to determine if the final answer inside the parentheses is positive or negative. In the first parentheses 3-6=-3 with is negative. In our second parentheses we have 3-5=-2 which is a also negative.

Knowing that both parentheses are negative results we can set up an equation using z instead of 3:

-(z-6)-(-(z-5)) is our new equation. If we simplify this equation we get 1 for an answer

Answer:

The possible number of goats is 6 and the possible number of chicken is 24

Step-by-step explanation:

Let

chicken=c

Goat=g

the number of chickens could be four times the number of goats

c=4g

Total number of animals=30

c+g=30

Recall, c=4g

So,

c+g=30

4g+g=30

5g=30

Divide both sides by 5

5g/5=30/5

g=6

Recall,

c+g=30

c+6=30

c=30-6

=24

c=24

The possible number of goats is 6 and the possible number of chicken is 24 making a total of 30 animals

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

The answer would be clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

THE DIRECTION OF THE ROTATION WAS CLOCKWISE.

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

Step-by-step explanation:

Answer: A. 82

Step-by-step explanation:

The measure of <BAD can be found by simply adding 25(<BAC)+57(<CAD) = 82.

[tex]\mathrm{BAD}=\mathrm{BAC}+\mathrm{CAD}=25^{\circ}+57^{\circ}=82^{\circ}[/tex].

Hope this helps.

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Well to find n you gotta separate it.

3 1/5 + n = 9

-3 1/5

n = 5.8

Thus,

to seperate it you subtract 3 1/5 from both sides.

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Answer:

The correct answer is option:

D) ΔABC and ΔA″B″C″ are congruent triangles.

Step-by-step explanation:

Given

To find: The true statement among the given options.

Solution:

Let the triangle be situated in 1st quadrant.

It is rotated about the origin by [tex]270^\circ[/tex].

Now, it moves towards quadrant 2 if it is rotated clockwise. It is termed as

[tex]\triangle A'B'C'[/tex].

It is given that now it is translated 10 units upwards. i.e. 10 units added to x coordinate of each vertex to form [tex]\triangle A''B''C''[/tex].

Now, we can see that there is no change in the dimensions of the triangle. We are just changing the location of the triangle.

So, all its angles will be equal to each other and all the sides will be equal to each other.

i.e.

[tex]\angle A = \angle A''\\\angle B = \angle B''\\\angle C = \angle C''\\Side\ AB = Side\ A''B''\\Side\ BC = Side\ B''C''\\Side\ AC = Side\ A''C''[/tex]

Hence, the correct option is:

D)ΔABC and ΔA″B″C″ are congruent triangles.

Answer:A-B

Step-by-step explanation:

Answer:

The expected amount to be paid by the carnival committee for prices would be $366.80

Step-by-step explanation:

Hello!

Here, we want to calculate the amount of money the carnival committee is expected to pay for the prizes for that booth

From the question, we have 3 categories of prices to be won

To calculate for people that won’t win anything , we simply subtract the percentages of all from 100

That would be 100-32-10-8 = 100-50 = 50%

So now let’s calculate the number of people out of 200 that will win each category based on the percentages

For stuffed toy

32/100 * 200 = 64

Jump rope

10/100 * 200 = 20

For t-shirt

8/100 * 200 = 16

So total price paid for stuffed toy= 3.25 * 64 = $208

For jump rope, we have 1.7 * 20 = $34

For t-shirt , we hav 16 * 7.8 = $124.8

So the total value spent on prices by the committee would be;

124.8 + 34 + 208 = $366.80

The correct answer is A. T = 0.25k + 0.97t

Explanation:

For an equation to be correct it needs to include all important values and use the appropriate mathematical symbols to show how the values relate. In the case presented, it is known the total bill (T) is the result of both the electricity (k) and gas (t) consumed. According to this, the two values need to be added to find the total (T). This means T = k + t.

Besides this, it is specified a kilowatt or unit of electricity costs $0.25, this means the correct expression for finding the total paid for electricity is 0.25k as the number of kilowatts consumed need to be multiplied by the cost of a kilowatt. Similarly, the cost of the gas requires multiplying the number of therms by the cost of one therm, which is $097. According to this, the correct equation is T = 0.25k + 0.97t

Step-by-step explanation:

cross multiply to get 3x:= 10( -5/2)

3x=-25

x=25/3

x=8 rem 1

8.33

Answer:

- 204

Step-by-step explanation:

2x = 60

x = 30

6 - 7(30) = -204

Answer:

-204

Step-by-step explanation:

Step 1- Solve for the value of x

2x = 60

Divide 60 by 2 so x is by its self

x = 30

Step 2- Plug in 30 for x in the second equation

6 - 7(30)

6 - 210

-204 is the answer

Answer:

option three!!!!!

Step-by-step explanation:

its closed circle

on 6

and pointing  left

Answer:

I believe its 40

Step-by-step explanation:

Answer:

Hey there!

The perimeter can be expressed as 10+7+2+2+6+2+2+7, or  38.

Hope this helps :)

Answer:

-5-2c

Step-by-step explanation:

The additive inverse of a term must be the opposite of it.

●-(5+2c)

●-5-2c

Answer:

Step-by-step explanation:

The additive inverse is just the opposite of the binomial in terms of the signs. The additive inverse of 5 + 2C is -(5 + 2C) which is, without parenthesis,        -5 - 2C.

Answer:

b^8

Step-by-step explanation:

When multiplying exponents with the same base, we can add the exponents

b^2 * b^6

b^ (2+6)

b^8

Answer:b8 x

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "b6"   was replaced by   "b^6".  1 more similar replacement(s).

STEP

1

:

Multiplying exponential expressions

1.1    b2 multiplied by b6 = b(2 + 6) = b8

Final result :

 b8x

The pyramid consists of 4 congruent triangular faces, and 1 square base.

Area of 1 triangular face:

1/2 * (5 in)/2 * (5.6 in) = 7 in^2

Area of base:

(5 in)^2 = 25 in^2

Then the total surface area is

4 * (7 in^2) + 25 in^2 = (28 + 25) in^2 = 53 in^2

Answer:

720 seating arrangments

Step-by-step explanation:

There are eight people but driver is always the same so we only have to deal with combinations of the other 7 seats.

the combination of the five seats has 5! times 2 combinations for each of the 3 passengers willing to ride in the two boat seats thus the total number of different seating arrangements is 5! times 3! or 720

hope this helps :)

Using the Fundamental Counting Theorem, it is found that there are 5760 possible seating arrangements.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

Hence:

[tex]N = 8 \times 6 \times 5! = 5760[/tex]

There are 5760 possible seating arrangements.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

Answer:

The expression for the shaded region is 10x² + 12x .

Step-by-step explanation:

First, you have to find the area of both rectangles using the formula :

[tex]area = length \times height[/tex]

Small rectangle,

[tex]area = x \times (5x - 2)[/tex]

[tex]area = 5 {x}^{2} - 2x[/tex]

Large rectangle,

[tex]area = (3x + 2) \times 5x[/tex]

[tex]area = 15 {x}^{2} + 10x[/tex]

In order to find the shaded region, you have to subtract the smaller from the larger one :

[tex]area \: of \: shaded = large - small[/tex]

[tex]area = 15 {x}^{2} + 10x - 5 {x}^{2} + 2x [/tex]

[tex]area = 10 {x}^{2} + 12x[/tex]

Answer:

Just multiply 2 by (36*15) which equals 1080

Than divide 1080 by 100

1080/100

Which would give us 10.8 10.8 * 70 = $756.00

So, the answer is $756.00

Step-by-step explanation:

Answer:

The amount of CD's she could buy would be 3.

Step-by-step explanation:

80-20=60

60÷18 = 3 CD's

Answer:

1,2,3

Step-by-step explanation:

Answer:

1290000

Step-by-step explanation: Given that

The volume of the Sun is about = 1.41 x 10^18 cubic kilometers.

The volume of Earth is about 1.09 x 10^12 cubic kilometers.

The number of Earths that can fit inside the Sun can be found by dividing the Sun's volume by Earth's volume.

= Volume of Sun ÷ Volume of the Earth

= 1.41 x 10^18 cubic km/1.09 x 10^12 cubic km

= 1.41 x 10^18/1.09 x 10^12

=(1.42/1.09)× 10^18-12

= 1.29×10^6

n is 1.29×10^6.

Hence the number of Earth that can be fitted in the Sun is 1290000

Answer:

x = - 1, x = 1

Step-by-step explanation:

Given

f(x) = [tex]\frac{2x^2+3x+6}{x^2-1}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

x² - 1 = 0 ← difference of squares

(x - 1)(x + 1) = 0

x - 1 = 0 ⇒ x = 1

x + 1 = 0 ⇒ x = - 1

x = - 1 and x = 1 are vertical asymptotes

Answer: x = 137°

Step-by-step explanation:

When a quadrilateral is inscribed in a circle, the opposite angles are supplementary.

x + 43° = 180°

      x   =  137°

The value of x is 137°.

The quadrilateral whose all 4 vertices lie on the circumference of the circle is called an inscribed quadrilateral.

In inscribed quadrilateral opposite angles are supplementary i.e. sum of those opposite angles is 180°.

Here given in the picture that the measurements of the two opposite angles in the inscribed quadrilateral in the circle are 43° and x°.

So as we know in the inscribed quadrilateral opposite angles are supplementary.

So sum of those opposite angles in the quadrilateral is 180°.

so we can write x+43°= 180°

⇒ x = 180°- 43°

⇒ x = 137°

Therefore the value of x is 137°.

Learn more about inscribed quadrilateral

here: https://brainly.com/question/26690979

#SPJ2

Answer:

  3.5 times as large

Step-by-step explanation:

The ratio can be written using a colon or a fraction bar. In the latter case, simplifying the fraction gives you your answer:

  a : b = 7 : 2 = 7/2

'a' is 7/2 = 3.5 times as large as 'b'

Answer:

X ^3 (4x+1) (4x-1)

Step-by-step explanation:

Factor x3 out of  16x5−x3

Rewrite 16x2 as  (4x)2

Rewrite 1 as 1^2

Factor

x^3 (4x+1) (4x-1)

I hope I helped

Diagram related to the question can be found in the attached picture below :

Answer: 6 units

Step-by-step explanation:

From the diagram attached to the question:

Length AB = 17

Length DC = 8

height (h) = x

Area of trapezium = 75sq units

The Area (A) of a trapezium is given by:

(1/2) × (a + b) × h

Where ;

a and b are the upper and base lengths of the trapezium

h = height of trapezium

A = (1/2) × (a + b) × h

75 = (1/2) * (17 + 8) * x

75 = 0.5*25*x

75 = 12.5x

x = 75 / 12.5

x = 6 units