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

Answers

Answer 1

Answer:

just google it i am not able to put the link to a website which ahs the answer to this sorry :(

Step-by-step explanation:

Answer 2

Answer:

2.5 7.5 12.5 17.5 22.5 27.5 32.5

Step-by-step explanation:

Just add 5 to the previous sum considering it is arithmetic sequence is always addition.


Related Questions

On the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00. on day 3, $2.00, etc. How much do students earn on the 9th day

Answers

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

day 1 each student is given $0.50
day 2- $1.00
day 3- $2.00
this means every day the amount each student is given doubles from the day before.
day 4- $4.00
day 5- $8.00
day 6- $16.00
day 7- $32.00
day 8- $64.00
day 9- $128.00
so on the 9th day the students would earn $128.00

day 9- $128.00

Find the sum of the geometric series 1−0.99+0.99^2−0.99 ^3 +...−0.99

Answers

Answer:

0.28

Step-by-step explanation:

The sum of the geometric value progression is S = 0.28

What is Geometric Progression?

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

To learn more about geometric progression click :

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x^2 = 8x - 15
.......................

Answers

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

What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?

Answers

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

Given the equation StartFraction 2 x + 2 Over y EndFraction = 4 w + 2 what is the value of x?

Answers

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

what is (4 to the square root of 81)5?

Answers

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

Given f(x) = -4x + 7 and g(x) = x, choose
the expression for (fºg)(x).

Answers

Answer:

-4x^2+7x

Step-by-step explanation:

Multiply -4x+7 and x.

You get -4x^2+7x.

A G.P has a common ratio of 2 find the value of 'n' for which the sum 2n terms is 33 times the sum of n?

Answers

The above formulas do not hold for r = 1. For r = 1, the sum of n terms of the Geometric Progression is Sn
n
= na.

(ii)When the numerical value of r is less than 1 (i.e., - 1 < r < 1), then the formula Sn
n
= a(1−rn)(1−r)
(
1

r
n
)
(
1

r
)
is used.

(iii) When the numerical value of r is greater than 1 (i.e., r > 1 or, r < -1) then the formula Sn
n
= a(rn−1)(r−1)
(
r
n

1
)
(
r

1
)
is used.

(iv) When r = 1, then Sn
n
= a + a + a + a + a + .................... to n terms = na.

(v) If l is the last term of the Geometric Progression, then l = arn−1
n

1
.

Therefore, Sn
n
= a(1−rn1−r
1

r
n
1

r
) = (a−arn1−r
a

a
r
n
1

r
) = a−(arn−1)r(1−r)
a

(
a
r
n

1
)
r
(
1

r
)
= a−lr1−r
a

l
r
1

r

Thus, Sn
n
= a−lr1−r
a

l
r
1

r

Or, Sn
n
= lr−ar−1
l
r

a
r

1
, r ≠ 1.

A 4-foot long steel pipe consists of two concentric cylinders, with the inner cylinder hollowed
out. The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe
is 5.75 inches.
HINT: The units of measure must be the same! Convert to inches and keep your answer in
terms of π.
A. Determine the volume of metal used to build the pipe.
B. If the pipe is to be powder-coated on the inside and outside surfaces, what is the total
surface area to be powder-coated?

Answers

Answer:

The pipe is formed by two concentric cylinders.The outside cylinder has 6 inches of radius.The inside cylinder has 5.75 inches of radius.

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.

Outside cylinder volume.

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

Inside cylinder volume.

[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.

Volume of the pipe.

[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.

Surface area of outside cylinder.[tex]S_{outside}=2\pi r^{2}+2\pi rh=2 \pi (6in)^{2}+2 \pi (6in)(48in)= 72 \pi in^{2} +576 \pi in^{2} =648 \pi in^{2}[/tex]Surface area of the inside cylinder.

[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]

The total surface is

[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.

When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form

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

where a is positive constant. Find the radius r for which the speed of the air is greatest.

Answers

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!

The ratio of sailboats to dinghies in the bay was 5 to 7 If there were 70

sailboats in the bay, how many dinghies were there?

Answers

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.

Find the volume of a block of woods

Answers

Multiply all the numbers together. Once you have that you have to make every face of the cube and put that as the number you got. Then you add all the numbers together

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

You score a 65% on your AP Statistics Exam and a 78% on your Economics Exam. The AP Statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. The Economics scores were also normally distributed with an average of 75% and standard deviation of 2.5%. In which class did you perform better relative to the class average? Be sure to justify your answer.

Answers

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.

Calcula el 23 % de 175

Answers

Answer:40.25

Step-by-step explanation:

23% of 175

23/100 x 175

(23 x 175)/100

4025/100=40.25

What are prime number​

Answers

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:

Which goes with which

Answers

T is perpendicular, cookie crumb is a point, rows of seats are parallel lines, a sun ray is a ray, line is the horizon

Find the radius of Circle M, if the area of a sector is 36.07 cm^2 and the central angle of that sector is 58º. Round your answers to the hundredths place if necessary

Answers

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!

Find the area of the shaded region and choose the appropriate result?

Answers

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!

Mercury is a heavy metal that can cause severe health problems in even small concentrations. Fish and shellfish efficiently concentrate mercury into their flesh, so it is important to monitor seafood for its mercury content. An extensive study conducted in 1980 concluded that the mean mercury level in oysters from the White Bear estuary was 0.020 parts per million (ppm) with a standard deviation ppm. In 2012, a sample of 40 oysters from the same estuary exhibited a mean mercury concentration of . Can you conclude that the 2012 mercury concentration is lower than in 1980? Use the level of significance.

Answers

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.  

GIVING BRANLIEST Which prism has a greater surface area?

2 prisms. A rectangular prism has a length of 12 inches, height of 8 inches, and width of 6 inches. A triangular prism has a rectangular base with a length of 6 inches and height of 12 inches. 2 rectangular sides are 12 inches by 10 inches. The triangular sides have a base of 6 inches an height of 8 inches.
The rectangular prism has a greater surface area by 72 square inches.
The rectangular prism has a greater surface area by 88 square inches.
The triangular prism has a greater surface area by 72 square inches.
The triangular prism has a greater surface area by 88 square inches.

Answers

Answer:

Rectangular prism          

Step-by-step explanation:

1. To measure the resting heart rate of an animal biologist use the function h(m) = 530m-C), where h
is resting heart rate in beats per minute, given the mass m in pounds.
Part A: What is a feasible domain for the function him?

Answers

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.

Complete A and B for 5-8 points.

Answers

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

B(4,8) and C(8,0) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.

Answers

Answer:

(6,4)

Step-by-step explanation:

I just did quick math in my head.


How many unique ways are there to arrange the letters in the word PRIOR?

Answers

Answer:

60

Step-by-step explanation:

Answer:

it is 60

Step-by-step explanation:

Factor.

Z^2- 3z – 18

Answers

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)

faz um bom tempo que não faço expressões numéricas,vcs podem me ajudar!

Answers

Answer:

English Plz

Step-by-step explanation:

Question 11 of 15

Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45

millimeters. How much water can Micah fill in his cup?

Answers

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:

A physical education class has 21 boys and 9 girls. Each day, the teacher randomly selects a team captain. Assume that no student is absent. What is the probability that the team captain is a girl two days in a row?

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

Answers

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%

How to determine the probability?

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%

Read more about probability at:

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Need help. not in college

Answers

The length of ab is 24

What is the circumference of the following circle?
9 cm

Answers

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

Calculating circumference of a circle

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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