The sum of the first 7 terms of an arithmetic
sequence 2.5, 7.5, 12.5, 17.5, ... would be:

Answer:

1310720

Step-by-step explanation:

Find out the frist part "4 to the square root of 81"  262144

then times it by 5

to get 1310720

Answer:9%

U already provided the answer. Anyways have a good day!!

The probability of choosing a captain that is a girl two days in a row is 9%

The given parameters are:

Boys = 21

Girls = 9

The total number of students is

Total = 21 + 9

Total = 30

This means that the probability of selecting a girl is:

P(Girl) = 9/30

For two days, the required probability is

P = 9/30 * 9/30

Evaluate

P = 9%

Hence, the probability of choosing a captain that is a girl two days in a row is 9%

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Answer: x= 5

Step-by-step explanation: Lets solve by completing the square.

You first need to get -15 by itself.

x^2-8x=15   Now you need to complete the square my finding a perfect constant that will go with x^2-8x, then add it to the other side containing -15 to balance the equation out.

-8x/2= -4^2=16 This will be the perfect square.

x^2-8x+16 = -15 + 16

(x-4)^2 = 1 factor into a binomial, then use the square root on both sides.

√ x-4 ^ 2 = √ 1

x-4 = 1

x=5

Answer:

0.28

Step-by-step explanation:

The sum of the geometric value progression is S = 0.28

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sequence be A = { 1 - 0.99 + 0.99² - 0.99³... - 0.99⁷⁹ }

So , A = 1 - { 0.99 - 0.99² + 0.99³... + 0.99⁷⁹ }

Let the first term of the GP be a₁ = 0.99

Now , the common ratio of GP , r = 0.99

And , the number of terms in GP = 80

And , Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

S₈₀ = 0.99 ( 1 - 0.99⁸⁰ ) ( 1 - 0.99 )

On further simplification , we get

S₈₀ = 0.7224

So , the sum of the GP is S = 1 - S₈₀ = 0.28

Hence , the sum of GP is 0.28

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Answer:

  36.644 mL . . . . depending on your value of π (see below)

Step-by-step explanation:

The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...

  45² = 36² +h²

  h = √(45² -36²) = 27 . . . . . mm

The volume is given by the formula ...

  V = (1/3)πr²h

  V = (1/3)π(36 mm)²(27 mm) = 11664π mm³

For π = 3.14

  11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL

For π = 3.14159265

  11665π mm³ = 36,644 mm³ = 36.644 mL

_____

Comment on units

A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.

Answer:

The answer is 11664pimm^3

Step-by-step explanation:

Answer:

(z-6)(z+3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

z^2-6z + 3z -18

z(z-6)+3(z-6)

(z+3)(z-6)

Answer:

-4x^2+7x

Step-by-step explanation:

Multiply -4x+7 and x.

You get -4x^2+7x.

Answer:

His economics grade had a higher z-score, so you performed better relative to the class average in economics.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In which class did you perform better relative to the class average?

In whichever class you had the higher z-score.

Statistics:

Scored 65, mean 60, standard deviation 6. So [tex]X = 65, \mu = 60, \sigma = 6[/tex]

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

[tex]Z = \frac{65 - 60}{6}[/tex]

[tex]Z = 0.83[/tex]

Economics:

Scored 78, Mean 75, Standard deviation 2.5. So [tex]X = 78, \mu = 75, \sigma = 2.5[/tex]

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

[tex]Z = \frac{78 - 75}{2.5}[/tex]

[tex]Z = 1.2[/tex]

His economics grade had a higher z-score, so you performed better relative to the class average in economics.

Answer:

(6,4)

Step-by-step explanation:

I just did quick math in my head.

Answer: 2r(0)/3.

Step-by-step explanation:

So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);

S(r) = (r0 - r) ar^2 -----------------------------(1).

We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:

dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).

dS/dr = 2ar(r0) - 2ar^2 - ar^2.

dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).

Note that dS/dr = 0.

Hence, - 3ar^2 + 2ar(r0) = 0.

Making ra the subject of the formula we have;

ra[ - 3r + 2r(0) ] = 0. -------------------------(4).

Hence, r = 0 and r = 2r(0) / 3.

If we take the second derivative of S(r) too, we will have;

d^2S/dr = -6ar + 2ar(0). -------------------(5).

+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.

Answer:

[tex]r =\frac{2r_{0}}{3}[/tex]

Step-by-step explanation:

We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.

Let's take the derivative:

[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]

[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]

[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]

[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]

Let's equal it to zero, to maximize S.

[tex]0=ar(2r_{0}-3r)[/tex]

We will have two solutions:

[tex]r = 0[/tex]

[tex]r =\frac{2r_{0}}{3}[/tex]

Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].

I hope it helps you!

Answer:

Rectangular prism          

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

The figures are made out of squares.

[tex]\text {Formula for area of a square: } A =s^2\\s-\text {Length of side.}[/tex]

Square 1 (the gray square):

The side measure is 4 cm.

[tex]A = 4^2 = 16cm^2[/tex]

Square 2 (white square):

The side measure is 2 cm.

[tex]A=2^2=4cm^2[/tex]

Subtract the area of the white square from the gray square to get the area of the shaded region:

[tex]16 - 4 =12[/tex]

The shaded region is [tex]12cm^2[/tex].

Option B should be the correct answer.

Brainilest Appreciated!

Answer:113 cubic meter

Step-by-step explanation:

Diameter=6

Radius=r=6/2

Radius=r=3

π=3.14

Volume of sphere=4/3 x π x r x r x r

Volume of sphere=4/3 x 3.14 x 3 x 3 x 3

Volume of sphere=(4x3.14x3x3x3) ➗ 3

Volume of sphere=339.12 ➗ 3

Volume of sphere=113.04

Volume of sphere =113 cubic meter

Answer:

a) 4 hours

b) 11 am

Step-by-step explanation:

So say the number of hours is x

a) 72 + 6x = 96

6x = 24

x = 4

b) 7am + 4 hours = 11am

Answer:40.25

Step-by-step explanation:

23% of 175

23/100 x 175

(23 x 175)/100

4025/100=40.25

Answer:

255.50

Step-by-step explanation:

If each day the number is doubled, then all you must do is keep on doubling to the ninth day and then add it all together

A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.

In other words, prime numbers are the numbers

divisible by 1 and the number itself.

For example, let us take 2.

2 has only two factors and those are 1 and 2 so it's prime.

Similarly, 7 is also a prime number because it has only two factors

and these are 1 and the number itself which is 7.

Answer:

A number that is only divisible by itself and 1

Step-by-step explanation:

Answer:

r = 5.97 cm

Step-by-step explanation:

The area of the sector is given by the following equation:

[tex]A = r*S = 2\pi*r^{2}*\frac{58}{360}[/tex]

Where:

r: is the radius

A: is the area

The radius is:

[tex]r = \sqrt{\frac{A}{2*\pi*58/360}} = \sqrt{\frac{36.07 cm^{2}}{2*\pi*58/360}} = 5.97 cm[/tex]

Therefore, the radius of Circle M is 5.97 cm.

I hope it helps you!

Answer:

9π or 28.27 cm

Step-by-step explanation:

The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.

The value of the circumference of the given circle is 9π cm OR 28.278 cm

From the question, we are to determine the circumference of the circle.

The circumference of a circle can be calculated by using the formula,

C = πd

Where C is the circumference of the circle

and d is the diameter

From the diagram,

d = 9 cm

Therefore,

Circumference of the circle = π × 9

Take π = 3.142

Then,

Circumference of the circle = 28.278 cm

Hence, the value of the circumference of the given circle is 9π cm OR 28.278 cm

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Answer:

60

Step-by-step explanation:

Answer:

it is 60

Step-by-step explanation:

Answer:volume=125 cm^3

Surface area=150 cm^2

Step-by-step explanation:

Part A:

volume=length x width x height

volume=5 x 5 x 5

Volume=125 cm^3

Part B:

Surface area=6x5x5

Surface area=150 cm^2

Answer:

The overview of the problem is listed in the segment below on the explanation.

Step-by-step explanation:

The given values are:

Sample mean, [tex]\bar{Z}=0.017[/tex]

The hypothesized mean value, [tex]\mu_{0}=0.02[/tex]

Population standard deviation, [tex]\sigma=0.036[/tex]

As we know, the status of the test is as follows:

⇒  [tex]z^* = \frac{\bar X - \mu_0}{\frac{\sigma}{\sqrt{n}}}[/tex]

On putting the values, we get

⇒       [tex]= \frac{0.017 - 0.02}{\frac{0.036}{\sqrt{40}}}[/tex]

⇒       [tex]=-0.5357[/tex]

Now, even though this is a one-sided check, here so the p-value is measured as:

[tex]p=P(Z<-0.5357)[/tex]

  [tex]=0.2[/tex]

Consequently p-value > 0.05 the check isn't relevant so there is no data to suggest that perhaps the concentration of mercury fallen from 1980 until 2012.  

Answer:

To find the volume of the pipe, we need to subtract the inside cylinder volume from the outside cylinder volume.

Remember that the volume of a circular cylinder is

[tex]V=\pi r^{2} h[/tex]

Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height.

[tex]V_{outside}=\pi r^{2}h= \pi (6in)^{2} (48in)=1,728 \pi in^{3}[/tex]

[tex]V_{inside}=\pi r^{2}h= \pi (5.75in)^{2} (48in)=1,587 \pi in^{3}[/tex]

Notice that we used the height 4 feet in inches units, that's why the height in the formulas is 48 inches, because each feet is equivalent to 12 inches.

[tex]V_{pipe}=V_{outside} -V_{inside} =1,728 \pi in^{3}-1,587 \pi in^{3} =141 \pi in^{3}[/tex]

(A) Therefore, the volume of metal used to build the pipe is 141π cubic inches.

Now, to know the amount of powder-coat we must use, we need to find the surface area of the pipe, which is basically the sum of the surface area of both cylinders.

[tex]S_{inside}=2\pi r^{2}+2\pi rh=2 \pi (5.75in)^{2}+ 2 \pi (5.75in) (48in)= 66.13 \pi in^{2} +552 \pi in^{2} =618.13 \pi in^{2}[/tex]

[tex]S_{powder}=648 \pi in^{2} + 618.13 \pi in^{2} =1,266.13 \pi in^{2}[/tex]

(B) Therefore, we need 1,266.13π sqaure inches of powder to cover the whole pipe.

Answer:

A. volume of the metal used to build the pipe is 141[tex]\pi[/tex] cubic inches.

B. The total surface area to be powder coated is 1122.125 square inches.

Step-by-step explanation:

The length of the cylinder = 4 feet = 48 inches.

Radius of the outside of the pipe = 6 inches.

Radius of the inside of the pipe = 5.75 inches

A. volume of the metal used to build the pipe = volume of the outside pipe - volume of the inside pipe

volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

volume of the outside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h

                                             = [tex]\pi[/tex] × [tex]6^{2}[/tex] × 48

                                             = 1728[tex]\pi[/tex] cubic inches

volume of the inside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h

                                          = [tex]\pi[/tex] × [tex]5.75^{2}[/tex] × 48

                                          = 1587[tex]\pi[/tex] cubic inches

volume of the metal used to build the pipe = 1728[tex]\pi[/tex] - 1587[tex]\pi[/tex]

                                                                       = 141[tex]\pi[/tex] cubic inches

B. Total surface area of a hollow cylinder = 2[tex]\pi[/tex] ( [tex]r_{1}[/tex] +  [tex]r_{2}[/tex]) ( [tex]r_{2}[/tex] - [tex]r_{1}[/tex] + h)

where [tex]r_{1}[/tex] is the inner radius and [tex]r_{2}[/tex] is the outer radius.

            =  2[tex]\pi[/tex] (6 + 5.75)(5.75 - 6 + 48)

            =  2[tex]\pi[/tex] (11.75 × 47.75)

           = 1122.125[tex]\pi[/tex] square inches

The total surface area to be powder coated is 1122.125 square inches.

Answer:

Step-by-step explanation:

In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y. Since a function is defined on its entire domain, its domain coincides with its domain of definition, the subset of the domain for which the function associates an image. However this coincidence is no longer true for a partial function since the domain of definition of a partial function can be a proper subset of the domain.

Question:

Given the equation (2x + 2)/y = 4w + 2.

What is the value of x?

Answer:

x = 2wy + y - 1

Step-by-step explanation:

Given

(2x + 2)/y = 4w + 2

Required

Find x

To find the value of x; the following steps will be used.

First, Multiply both sides by y

y * (2x + 2)/y = (4w + 2) * y

2x + 2 = 4wy + 2y

Subtract 2 from both sides

2x + 2 - 2 = 4wy + 2y - 2

2x = 4wy + 2y - 2

Multiply both sides by ½

½ * 2x = ½(4wy + 2y - 2)

x = ½(4wy + 2y - 2)

Open bracket

x = ½ * 4wy + ½ * 2y - ½ * 2

x = 2wy + y - 1

Hence, the value of x is 2wy + y - 1

Answer:

B

Step-by-step explanation:

I took the test

Answer:

English Plz

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

Let the sailboats be s and the dinghies be d.

We have that:

s : d = 5 : 7

In other words:

s / d = 5 / 7

If there are 70 sailboats, this implies that s = 70

=> 70 / d = 5 / 7

=> d = (70 * 7) / 5 = 490 / 5 = 98

There will be 98 dinghies.