a simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside of the 99% confidence interval for the population mean?

Answer:

The complex number z = -5 into its rectangular form

Step-by-step explanation:

* Lets revise the complex numbers

- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the

 imaginary part in the polar form

- The value of i = √(-1) ⇒ imaginary number

- Then z = a + bi , where a is the real part and bi is the imaginary part

  in the rectangular form

∴ a = r cos Ф and b = r sin Ф

* Lets solve the problem

∵ z = r (cos Ф ± i sin Ф)

∵ z = 5 (cos π + i sin π)

∴ The real part is 5 cos π

∴ The imaginary part is 5 sin π

- Lets find the values of cos π and sin π

∵ The angle of measure π is on the negative part of x axis at the

  point (-1 , 0)

∵ x = cos π and y = sin π

∴ cos π = -1  

∴ sin π = 0

∴ a = 5(-1) = -5

∴ b = 5(0) = 0

∴ z = -5 + i (0)

* The complex number z = -5 into its rectangular form

Answer:

(-5,0)

Step-by-step explanation:

just cuz

ANSWER

The correct factorization is

[tex]p^{3} - 343q^{3} = (p - 7q)( {p}^{2} + 7pq + {49q}^{2} )[/tex]

EXPLANATION

The given expression is

[tex] {p}^{3} - 343 {q}^{3} [/tex]

We can write this as difference of cubes.

[tex]{p}^{3} - {7}^{3} {q}^{3} [/tex]

[tex]{p}^{3} - ( {7} {q})^{3} [/tex]

We can now factor using the difference of cube identity:

[tex] {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )[/tex]

We substitute x=p and y=7p to get:

[tex]{p}^{3} - ( {7} {q})^{3} = (p - 7q)( {p}^{2} + p \times 7q + ({7q})^{2} )[/tex]

[tex]{p}^{3} - ( {7} {q})^{3} = (p - 7q)( {p}^{2} + 7pq + {49q}^{2} )[/tex]

Final answer:

The polynomial p^3 - 343q^3 is factorized as (p - 7q)(p^2 + 7pq + 49q^2) using the difference of cubes formula.

Explanation:

The correct factorization of the polynomial p3 - 343q3 can be done using the difference of cubes formula, which is a3 - b3 = (a - b)(a2 + ab + b2). Comparing the given polynomial to the formula, we see that a corresponds to p and b corresponds to 7q since 343 is 7 to the power of 3. Therefore, the factorization would be (p - 7q)(p2 + 7pq + 49q2). Always check for the correct signs and coefficients when factoring polynomials, especially when dealing with differences and sums of cubes.

Answer:

2.10.

Step-by-step explanation:

100 costs 7.00

1 costs  7.00 / 100 = 0.07

30 costs 0.07 *30

=  2.10.

Answer:

Step-by-step explanation:

7.00 / 100 = .07

so that makes each pencil worth .07 cent

.07 * 30 = $2.10

so 30 pencils will cost $2.10

Can you someone please help me with this question?

Tyler is building a fish tank in the shape of a sphere that has a diameter of 18 inches. Based on Tyler's research, it is recommended to have no more than 1 goldfish for every 693 cubic inches of water. How many goldfish should Tyler buy for his fish tank?

The unclear query may pertain to post-high school plans or high school curriculum. The majority of high school graduates in the US tend to pursue higher education immediately after graduating. Similarly, the number of English courses taken by male and female high school students is typically equivalent.

The question is somewhat ambiguous as it does not specify a clear query related to students from grade 11 and 12. However, deriving from the provided information, perhaps the student is seeking to understand statistics related to post-high school plans, or is interested in curriculum reviews, or the number of English courses taken by students.

For instance, focusing on life after high school, we know that a significant majority of high school graduates in the US (~69%) begin their college journey immediately following their graduation. This indicates that the orientation towards pursuing higher education is prevalent among recent high school graduates.

On the other hand, if interest lies in the English curriculum, an analysis reveals that the mean number of English courses taken by both male and female high school students over two years generally align with each other.

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Answer:

The ratio for the surface areas is equal to 4

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z -----> the scale factor

In this problem

The scale factor is equal to

[tex]z=\frac{2}{1}[/tex] ----> the ratio of its corresponding radii or its corresponding altitudes

step 2

Find the ratio for the surface areas of the cones

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the larger cone

y ----> the surface area of the smaller cone

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=\frac{2}{1}[/tex]

substitute

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

[tex]4=\frac{x}{y}[/tex]

The ratio for the surface areas is equal to 4

That means-----> The surface area of the larger cone is 4 times the surface area of the smaller cone

Answer:

Its a four sided polygon

Answer:

1. P(A|B) - option 2

2. does not affect - option 2

3. P(A) - option 1

Step-by-step explanation:

By the definition, the notation P(A|B) reads the probability of event A given that event B has occured. So, for the first gap correct choice is 2 - P(A|B).

If events A and B are independent, then the probability of event B occuring does not affect the probability of event A occuring. So, for the second gap correct choice is 2 - does not affect.

Events A and B are independent, then

[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

Use formula for the conditional probability:

[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]

Since events A and B are independent, we get

[tex]P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)[/tex]

So, for the third gap correct answer is 1 - P(A)

For (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

From the basic definitions of the events of probability.

P(A|B) = The probability of Event A given that Event B has occurred

In the independent events, the probability of Event B occurring does not affect the probability of Event A occurring.

P(A|B) = P(A) if events A and B are independent.

Thus, for (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.

Learn more about the probability here:

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Answer:

[tex]f(x) = 2 \times 2 + 3 \\ f(3) = 4 + 3 \\ 3f = 7 \\ f = \frac{7}{3} [/tex]

Answer:

The  answer is 15

Step-by-step explanation:

If ƒ (x ) = 2x 2 + 3, find ƒ (3).

2(3)^2 +3

6^2+3

= 15

Answer:

31.96

Step-by-step explanation:

The product of 2 numbers is simply one number multiplied by another

6.8 x 4.7 = 31.96

As a sanity check, just round the numbers off to a whole numbers and take a product of those two:

i.e 6.8 rounded off to the nearest whole number is 7 and 4.7 rounded off to the nearest whole number is 5.

7 x 5 = 35

If you look at the possible answers, only 31.96 is anywhere close to 35, hence you can be be more confident that your answer of 31.96 is correct.

Answer:

31.96 is your answer

Step-by-step explanation:

its just like a normal multiplication problem multiply 6.8 and 4.7 and you'll get your answer :))

Answer:

A = 3/5

Step-by-step explanation:

At the outset, the question doesn't give us a figure to refer to nor does it tell us if this is a right angled triangle. However we observe that both sin A and tan A have the numbers 3, 4 and 5. We recognize this to be consistent with  3-4-5 standard right angled triangle.

Hence we can guess that it is probably a right angled triangle, but we should do the following to confirm:

Knowning that for a right angled triangle,

sin A = opposite / hypotenuse = 4/5

tan A = opposite / adjacent = 4/3

From this we can surmise that

Opposite = 4

hypotenuse = 5

adjacent = 3

Assemble the triangle to see if this works (see attached). We can futher verify that 3-4-5 works using the Pythagorean theorem.

Now that we have determined that the triangle is a 3-4-5 right angled triangle,

cos A = adjacent / hypotenuse = 3/5

Answer:

A

Step-by-step explanation:

Answer:

q = ± 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

q² - 125 = 0 ( add 125 to both sides )

q² = 125 ( take the square root of both sides )

q = ± [tex]\sqrt{125}[/tex]

  = ± [tex]\sqrt{25(5)}[/tex]

  = ± [tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex]

  = ± 5[tex]\sqrt{5}[/tex]

Answer:

Roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Step-by-step explanation:

Given : Function [tex]f(q)=q^2-125[/tex]

To find : Which are the roots of the quadratic function ?

Solution :

To find the roots equate the function to zero.

[tex]q^2-125=0[/tex]

Add 125 both side,

[tex]q^2=125[/tex]

Taking root both side,

[tex]q=\pm \sqrt{125}[/tex]

[tex]q=\pm \sqrt{5\times 5\times 5}[/tex]

[tex]q=\pm 5\sqrt{5}[/tex]

Therefore, roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Answer:

y = - 4x + 3

Step-by-step explanation:

The perpendicular bisector is positioned at the midpoint of AB at right angles.

We require to find the midpoint and slope m of AB

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)

m = [tex]\frac{6-8}{-5-3}[/tex] = [tex]\frac{-2}{-8}[/tex] = [tex]\frac{1}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{4} }[/tex] = - 4

mid point  = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the coordinates of A and B, then

midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )

Equation of perpendicular in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

with m = - 4

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 7) into the partial equation

Using (- 1, 7), then

7 = 4 + c ⇒ c = 7 - 4 = 3

y = - 4x + 3 ← equation of perpendicular bisector

Answer:

he perpendicular bisector is positioned at the midpoint of AB at right angles.

We require to find the midpoint and slope m of AB

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)

m =  =  =

Given a line with slope m then the slope of a line perpendicular to it is

= -  = -  = - 4

mid point  = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the coordinates of A and B, then

midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )

Equation of perpendicular in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

with m = - 4

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 7) into the partial equation

Using (- 1, 7), then

7 = 4 + c ⇒ c = 7 - 4 = 3

y = - 4x + 3 ← equation of perpendicular bisector

Answer:

2x + 1.

Step-by-step explanation:

y=x^2 + x + 1

Using the algebraic derivative rule, if y = ax^n then y' =  anx^(n-1) :

The derivative is 2x^(2 - 1) +  1x^(1-1)

= 2x^1 + x^0

= 2x + 1.

Answer:

y'(x) = 1 + 2 x

Step-by-step explanation:

Find the derivative of the following via implicit differentiation:

d/dx(y) = d/dx(1 + x + x^2)

Using the chain rule, d/dx(y) = ( dy(u))/( du) ( du)/( dx), where u = x and d/( du)(y(u)) = y'(u):

d/dx(x) y'(x) = d/dx(1 + x + x^2)

The derivative of x is 1:

1 y'(x) = d/dx(1 + x + x^2)

Differentiate the sum term by term:

y'(x) = d/dx(1) + d/dx(x) + d/dx(x^2)

The derivative of 1 is zero:

y'(x) = d/dx(x) + d/dx(x^2) + 0

Simplify the expression:

y'(x) = d/dx(x) + d/dx(x^2)

The derivative of x is 1:

y'(x) = d/dx(x^2) + 1

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

Answer:  y'(x) = 1 + 2 x

Answer:

5 ft

Step-by-step explanation:

Let the height of the previous jump be represented by j.  Then 1.1j = 5.5 ft.

Dividing both sides by 1.1, we get j = 5 ft.  This was the height of the previous jump.

Answer:

5 ft

Step-by-step explanation:

The previous jumper jumped p

The new jumper jumped p*1.1 and that was 5.5 ft

1.1p = 5

Divide each side by 1.1

1.1p/1.1 = 5.5/1.1

p = 5

The previous jumper jumped 5 ft

Answer:

1/16

Step-by-step explanation:

1/2*1/2=1/4*1/2=1/8*1/2=1/16

Answer:1/16

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c : a ≠ 0, then

the discriminant Δ = b² - 4ac

Given

3x² - 10x = - 2 ( add 2 to both sides )

3x² - 10x + 2 = 0 ← in standard form

with a = 3, b = - 10 and c = 2

b² - 4ac = (- 10)² - (4 × 3 × 2) = 100 - 24 = 76

Answer:

Discriminant : 74 .

Step-by-step explanation:

Given : 3x² - 10x = -2.

To find : Find the discriminant .

Solution : We have given  3x² - 10x = -2.

On compare with standard form ax² +bx +c = 0.

Where, a =3 ,b = -10 , c = 2.

Discriminant : [tex]b^{2} - 4ac[/tex].

Plug the values of a , b , c .

Discriminant : [tex](-10)^{2} - 4(3)(2)[/tex].

Discriminant : 100 - 24 .

Discriminant : 74 .

Therefore, Discriminant : 74 .

To determine how many pounds of tomatoes can fit into one crate, calculate 2/3 of a pound for 1/4 of the crate, and then multiply by 4. The answer is 2 1/10 pounds.

A vegetable farmer fills 3/4 of a wooden crate with 2/3 of a pound of tomatoes.

Answer:

$0.25/lb

Step-by-step explanation:

Convert 1 lb to 16 oz mentally.  Then the unit cost of the berries is

$4.00

------------ = $0.25/lb

16 oz

The answer would be: A. 31,275

to solve this you would take the population (18,922) and multiply it as shown below:

18,922(1+0.03)^17

This would equal 31,275 which would be your answer.

Hope this helps! :3

Answer:

an = 8-3(n-1)

an = 11 - 3n

Step-by-step explanation:

This is an arithmetic sequence which is defined by

an = a1 + d(n-1)

where a1 is the first term of the sequence and d is the common difference

a1 = 8

d = a2-a1

d = 5-8 = -3

an = 8 + -3(n-1)

an = 8-3(n-1)

We can simplify this by distributing the -3

an = 8 -3n +3

an = 11 - 3n

Answer:

Step-by-step explanation:its the first one 3 5ths ,1

i just took the assignment

Answer:

the answer A

Step-by-step explanation:

Answer: They are parallel so there is no solution.

Step-by-step explanation:

Brayden- y=5x-1 or y-5x= -1

Howard- y=5x+1 or y-5x= 1

Vincent- y=4x+5 or y-4x= 5

In summary, they are all parallel so there is no solution.

Answer:

    5y - 1 = 5y + 1

(Braydon = Howard)

Answer:

1 square meter = 10000 square centimeters.

Step-by-step explanation:

We know that 1 meter = 100 centimeters.

Then 1 square meter = ( 100 cm)(100 cm) = 10000 square centimeters.

Then:

1 square meter = 10000 square centimeters.

Answer: Second Option

x < 22.5; Sam has fewer than 22.5 minutes left to finish running

Step-by-step explanation:

We have the following inequality

[tex]10.5 + x < 33[/tex]

Notice that 10.5 is the amount of time in minutes that Samuel has run.

x represents the amount of additional time it will take to finish the race

33 represents the time limit in which you want to finish the race

The we solve the inequality

[tex]10.5 + x < 33[/tex]

Subtract 10.5 on both sides of the inequality

[tex]10.5 -10.5 + x < 33-10.5[/tex]

[tex]x < 33-10.5[/tex]

[tex]x < 22.5[/tex]

This result means that Samuel must finish the race before 22.5 minutes have elapsed

The answer is the second option

Answer:

X<22.5;sam has fewer than 22.5 left to finish running

Step-by-step explanation:

edgen.

That's a difference of three standard deviations or 3(1.9) = 5.7 minutes.

Answer: 5.7 min, third choice

Answer:

How many hours per week do you watch television?

Step-by-step explanation:

In order to conduct a proper survey about a specific topic, it is necessary to be direct and clear. In the case of time spent by students watching TV, asking this question would be effective enought to collect necessary data so as to provide useful and good quality information, which will result in a sucessful survey.

Answer:

B is your answer :D

Step-by-step explanation:

Answer:

Nope, not every ordered pair in the plane is a solution to a system of linear equations.

Answer:

Answer is 0.80%

Step-by-step explanation:

Because if you divide the numerator by the denominator, you'll get your answer.

Hope my answer has helped you!

Answer:

80%

Step-by-step explanation:

Divide 4 by 5 to get 0.8

0.8 is the percentage written as a decimal. To write it as a percentage, multiply the decimal by 100.

0.8 x 100 = 80.

So your answer is 80%