find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common​

Answers

Answer 1

Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]


Related Questions

3 x 10³ - 7000
(8 × (-5)) + (4² + 22)

please help!
solve as simplest answer!​

Answers

Answer:

283038 or 2.83038×10⁵

Step-by-step explanation:

3×10³-7000(-40)+(16+22)3×10³+280000+383×1000+2800383000+280038283038

PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?

Answers

Answer:

$46.272

Step-by-step explanation:

A light bulb consumes 1440 watt-hours per day. How long does it take to consume 6480 watt-hours?

Answers

The number of days it will take to consume the given power = 4.5 days

Calculation of energy consumption

The amount of power consumed per day = 1440watt-hours

Therefore X days = 6480 watt-hours?

Make X the subject formula;

X = 1 × 6480/1440

X = 4.5 days

Therefore, The number of days it will take to consume the given power = 4.5 days.

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Tim needs 18 pens. He can buy them in packages containing 6,9, or 12 pens each. He will buy only one type of package. Which packages could Tim buy? Write two different ways of how Tim can buy exactly 18 pens. (Goodluck)

Answers

Answer:

9 and 6

Step-by-step explanation:

You see, 9x2=18 and 6x3=18

a sticker shaped like a rectangle has an area of 56 square centimeters. it has a width of 7 centimeters.

Answers

Step-by-step explanation:

Soln:-

Given,

Area of sticker=56 cm^2

Width of sticker=7 cm

Length of sticker=?

We know that,

Area of rectangle=l×b

or,56=l×7

or,l=56÷7

•°•l=8

Hence,the required length of the sticker is 8 cm.

Let f(x) = -3x³ + 4 and g(x) = -8x² + 2x. What is f(x) g(x)?
·

Answers

Answer:

[tex]{ \tt{f(x).g(x) = ( - 3 {x}^{2} + 4)( { - 8x }^{2} + 2x) }} \\ = { \tt{( - 3 \times - 8) {x}^{(2 + 2)} + (2 \times - 3) {x}^{(2 + 1)} + ( - 8 \times 4) {x}^{2} + (4 \times 2)x }} \\ = { \tt{24 {x}^{4} - 6 {x}^{3} - 32 {x}^{2} + 8x}}[/tex]

The probability distribution for a
random variable x is given in the table.
X
-10 -5 0
5
10 15 20
Probability ,20 15.05 .1
25 .1 .15
Find the probability that -5 ≤x≤5

Answers

The correct answer is 0.3

Given as:

                X :  -10     -5      0        5     10       15       20          

     P(X)=f(x): 0.20   0.15   0.05   0.1  0.25     0.1   0.15

To find:

  probability of -5≤x≤5

Solution: ∑f(x)= f(-5)+f(0)+f(5)

              ⇒ P(-5≤x≤5) = 0.15 +0.05+0.1 = 0.3

Hence, the answer of the given question is 0.3.

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What type of function is represented by the table of values below?
y
4
8
12
16
20
A. exponential
B. cubic
C. linear
D. quadratic
X12345
X

Answers

Answer

The type of function that is represented by the table of values below is C. linear

The formula for the nth term of an arithmetic sequence can be found using the formula a Subscript n Baseline = a Subscript 1 Baseline + (n minus 1) d. Which of the following is equivalent to this equation?

Answers

The equation of nth term will be written as for n as will be ([tex]\rm a_n[/tex] - a₁ + d) / d. Then the correct option is D.

The missing options are attached to the picture given below.

What is a sequence?

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The formula for the nth term of an arithmetic sequence can be found using the formula given below.

[tex]\rm a_n = a_1 + (n-1)d[/tex]

Then arrange the equation for n, we have

[tex]\begin{aligned} \rm a_n - a_1 & \rm = nd - d\\\\\rm a_n - a_1 + d & \rm =nd\\\\\rm n & \rm = \dfrac{a_n - a_1 + d}{d} \end{aligned}[/tex]

Then the correct option is D.

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Answer: The answer is D

Step-by-step explanation:

took the test

At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4. If the
graph of f goes through the point (2, 3), then f(x) =
A)
2x² - 4x - 4
B)
2x² - 4x
C)
2x² - 1
D)
2x² - 4x + 3
E)
16x - 12

Answers

Answer:

f(x)= 2x² - 4x + 3

Step-by-step explanation:

dy/dx = 4x - 4

y = integrate dy/dx

y = 4x²/2 - 4x + c

y = 2x² - 4x + c

at (2,3)

3 = 2(2)² - 4(2) + c

3 = 8 -8 + c

c = 3

therefore f(x)= y = 2x² - 4x + 3

The graph of the function is given by f ( x ) = 2x² - 4x + 3

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4

So , dy/dx = 4x - 4

On integrating , we get

f ( x ) = 2x² - 4x + c

where the function passes through P ( 2 , 3 )

So , 3 = 2 ( 2 )² - 4 ( 2 ) + c

c = 3

Hence , the function is f ( x ) = 2x² - 4x + 3

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A box 10 centimeters high, 5 centimeters long, and 5 centimeters wide.Find the volume of a box with a length of 5 cm, a width of 5 cm, and a height of 10 cm.

Answers

Answer:

250 [tex]cm^{3}[/tex]

Step-by-step explanation:

First, start with the formula for the volume of a rectangular prism (aka a box):

V=length*width*height

Then, plug in your values:

V=5*5*10

V=25*10

V=250

Don't forget your units!

250 [tex]cm^{3}[/tex]

what is 14 divided bye 3

Answers

Answer:

4.66

14÷ 3 = 4 r 2

add 0 to 2 ( this attracts a decimal point in your answer)

20 ÷ 3 = 6r 2

and = 4.66

Answer: 4.66666667

Yea, no need to explain for that.




How many solutions does this linear system have
y =
x+2
6x - 4y = -10

Answers

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

Slope-intercept form

y = mx + b

m ... slope

b ... y-intercept

[tex]6x - 4y = -10[/tex]

[tex]6x + 10 = 4y[/tex]

[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]

[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]

If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.

If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.

If two lines have different slopes then they intersect in one point - system has one solution.

We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

.
A grab-bag contains 20 packages worth $.70 each, 15 packages $.60 cents each, and 5 packages worth $.30 each. What is the expected value if you have to pay $.50 to pick one package at random?
about $0.53
about $0.00
about $0.60
about $0.11

Answers

The expected value if I have to pick one package given the price I would have to pay is $0.11.

What is the expected value?

The expected value is the cost you would have to pay subtracted from the total value of one package.

Total value of one package  =[ (15 x 0.60) + (5 x 0.3) + (20 x 0.7)]/ (20 + 15 + 5) = $0.61

Expected value = $0.61 - $0.50 = $0.11

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Question 1 of 10
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = x² +12?

Answers

The answer is b
Solution f(x) = x^2First compress vertically by a factor of . f(x) = x ^ 3; y(x) = 1/5 * x ^ x Then I'm going move up q(x)= 1 xi x^ * Rightarrow hex)= 1/5 x^2+1

Would the answer for c be 21 square root of 3?

Answers

Answer:

c = 14√3 km

Step-by-step explanation:

[tex]x\sqrt{3} =42\Longrightarrow x=\frac{42}{\sqrt{3} } = \frac{42 \times \sqrt{3} }{\sqrt{3}\times \sqrt{3} }=\frac{42 \times \sqrt{3} }{3 }=14 \sqrt{3}[/tex]

Since c = x

Then

c = 14√3

Devaughn earns $7.25 per hour working as a waiter at TGI Fridays. He typically pays a total of $89.76 towards deduction. If he works 37 hours, what will Devaughn net?

Answers

Hello, the answer should be $178.49.

If Devaughn earns $7.25 an hour at his job, we need to find out how much money he will make if he works for 37 hours.

[tex]37.(7.25)=268.25[/tex]

Next, we need to subtract the deduction amount from the total amount.

Net Equation will be defined as;

[tex]N=T-D[/tex]

[tex]N=(268.25)-(89.76)=178.49[/tex]

Good luck! If you have any questions, then feel free to ask in comments!

Julia made a model of a square pyramid. She used cardboard to construct the model with the dimensions shown. It has an open bottom.

A square pyramid has a square base with side lengths of 8 centimeters, and 4 triangular sides with a height of 5 centimeters.

What is the surface area of the model?
A. 80 cm2
B. 144 cm2
C. 224 cm2
D. 320 cm2

Answers

Answer:

A.  80 cm²

Step-by-step explanation:

If a square pyramid has an open base, then the surface area is made up of the 4 congruent triangular sides only.

Area of a triangle = 1/2 × base × height

Given:

Base = 8 cmHeight = 5 cm

⇒ Area of one triangular face = 1/2 × 8 × 5

                                                 = 20 cm²

⇒ Total surface area = 4 triangular faces

                                   = 4 × 20

                                   = 80 cm²

Answer:

80 cm²

Step-by-step explanation:

I did it and I got it right

Evaluate each function at the given value using the remainder theorem.

F(x)=x^4+5x^3-18x+1 at x=-4

Please show work , I give brainliest. :)

Answers

Answer:

9

Step-by-step explanation:

[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]

HELLPPP!!! ASAPPP WHAT IS THE EQUATION FOR THE RED GRAPH?!?!

Answers

Answer: The correct answer is D.

Step-by-step explanation: A and B is incorrect because the x value is 0. C is incorrect because the y-intercept is 3, not -3. Hence, it is D.

. Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible? Use the table to help you try different shapes and sizes to make your selection (You can show your work on a separate piece of paper.):

Answers

The volume-to-surface-area ratio would be better for an ice cube is the highest possible one.

How to explain the volume?

When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slowly melt and cool the drink for as long as you can.

You would want to have the highest possible volume to surface area ratio in an ice cube. If your ice cube is mostly surface area with less volume, it will melt quickly and water down your drink. If your ice cube has a higher ratio of volume to the surface area, it will stay solid longer and chill your drink longer.

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Does this graph represent a function? Why or why not?
10-
8-
6-
2
--8-
-10-
O A. No, because it fails the vertical line test.
OB. Yes, because it passes the vertical line test.
OC. Yes, because it is a curved line.
OD. No, because it is not a straight line.
-1080

Answers

The answer is 100 percent B

184 is 130% more than what number?

Answers

Answer:

  80

Step-by-step explanation:

The wording "130% more" suggests that we have the result of adding 130% of the original number to the original number.* This can be expressed as an equation to be solved for the original number.

__

Let x represent the original number. The given relation is ...

  184 = x + 130% × x

  184 = 2.30x . . . . . . . . . collect terms (130% = 1.3)

  80 = x . . . . . . . divide by 2.3

184 is 130% more than 80.

_____

* One needs to be a little careful here. You will often see the wording ...

"<some number> times more".

Usually the intention there is that the result is <some number> times the original amount. That is, percentages are often treated differently from other number expressions in problems like this.

if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day in how many days can 12 men, 18 women and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women and boys proportion 3:2:1 respectively? ​

Answers

Answer:

144 days

Step-by-step explanation:

Let's put the efficiency in terms of   b

m = 3b      w = 2b       b=b

starting with    6 m  = 18 b

                        8w =   16 b

                        16b = 16 b           total 50 b

then increase   12m = 36b

                         18w = 36b

                         28b = 28 b    total = 100 b

You doubled 'b'  workers  so work time will be halved     to  144 days


An 80-centimeter ramp connects the sidewalk to the bed of a truck. If the ramp
forms a 30-degree angle with the ground, the truck bed is centimeters off the ground.

Answers

The truck bed is 40cm .

What is a right-angled triangle?

A right-angled triangle is a triangle with one of its angle 90°.

Analysis:

The ramp, the height of the truck bed from ground and the distance of truck bed to the point the ramp makes contact with the ground form a right angle triangle.

So that sin 30 = height of truck bed above ground/length of ramp

sin 30 = height/80

height of the truck = 0.5 x 80 = 40cm

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Anyone know the answer

Answers

Step-by-step explanation:

-2g(1+g)

-2g - 2g²

(-2)g - (2)g²


In a class there are two girls for every three boys. The ratio 2 : 3 compares the
number of girls to the number of boys.
a) What is the ratio of boys to the whole class? - 3:5
b) If this class has eight girls, determine how many boys there are using the ratio that there are two girls for every three boys

Answers

Answer:

a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class

B. 12 boys

how many minutes does the white vacuum need to clean 86.25 square feet?
black vacuum cleans 8 square feet per min

white vacuum cleans 60 square feet for 8 min

red vacuum cleans 150 square feet for 25 min

Answers

Answer:

1.5 hours

As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.

can someone do this for me please?! Just the answer pls

Answers

The time taken that the aliens on Vormir will be waiting is 6 days.

How to calculate the distance?

From the information given, the speed ia given as 0.7 and the time taken is given as 8.5. It should be noted that the formula for calculating distance will be:

Time = Speed × Distance

Time = 0.7 × 8.5

Time = 6 days approximately.

Therefore, the correct option is D.

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This histogram represents a sampling of recent visitors to the mall on a Friday night, grouped by their ages.



Which of the following describes the overall shape of the distribution?

The distribution is nearly symmetrical.
The distribution is skewed left.
The distribution is skewed right.
The distribution is symmetrical.

Answers

Answer:

skewed to the right

Step-by-step explanation:

Other Questions
Read the excerpt from The Riddle of the Rosetta Stone, by James Cross Giblin.There being assembled the Chief Priests and Prophets and those who enter the inner shrine for the robing of the gods, and the Fan-bearers and the Sacred Scribes and all the other priests from the temples throughout the land who have come to meet the king at Memphis, for the feast of the assumption by PTOLEMY, THE EVER-LIVING, THE BELOVED OF PTAH, THE GOD EPIPHANES EUCHARISTOS, of the kingship in which he succeeded his father, they being assembled in the temple in Memphis on this day declared:What is the central idea of the excerpt?Chief Priests and Prophets were permitted to enter the inner shrine.The Sacred Scribes joined the assembly to record the events at the temple.Ptolemy became the king of Egypt when he succeeded his father.Many important people gathered in the temple in Memphis to honor Ptolemy. Euler's formula, V E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 5 vertices and 8 edges have? 60 . 25 ,20 15 . ? Solve the following equation:1. 5-3x = -6(x+2) Describe what happens when blood glucose levels are not kept stable. Help pls, I dont know Why is special about dialysis tubing being that it is good to be used in this experiment about osmosis? Sample Response: Forces are either positive or negative vectors, depending on the direction in which the force is acting. The net force is the sum of all of the forces acting on an object. If the children pull on the toy with the same force in opposite directions, the forces will be perfectly balanced and cancel out, leaving a net force of zero.What did you include in your response? Check all that apply.Forces are vectors. 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A teacher was quoted as saying the little boy could also pronounce the names of the foreign cities correctly."What's the capital of Finland? my mother asked me, looking at the magazine story.What evidence supports the conclusion that the narrators mother wants her to excel? Select three options.Every night after dinner, my mother and I would sit at the Formica kitchen table.She would present new tests, taking her examples from stories of amazing children she had read in Ripley's Believe It or Not, or Good Housekeeping, Reader's Digest, and a dozen other magazines she kept in a pile in our bathroom.My mother got these magazines from people whose houses she cleaned. And since she cleaned many houses each week, we had a great assortment.She would look through them all, searching for stories about remarkable children.The first night she brought out a story about a three-year-old boy who knew the capitals of all the states and even most of the European countries. . . . 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