The $23 rd term in a certain geometric sequence is 16 and the $28th term in the sequence is 24. What is the $43 rd term?

Answers

Answer 1

Answer:

81

Step-by-step explanation:

Geometric sequence formula:  [tex]a_n=ar^{n-1}[/tex]

Given:

[tex]a_{23}=ar^{22}=16[/tex][tex]a_{28}=ar^{27}=24[/tex]

Find common ratio (r):

[tex]\begin{aligned}\implies \dfrac{a_{28}}{a_{23}} =\dfrac{ar^{27}}{ar^{22}} & =\dfrac{24}{16}\\ \implies r^5 & =\dfrac32\\ \implies r & = \sqrt[5]{\frac32} \end{aligned}[/tex]

Find initial term (a):

[tex]\implies ar^{22}=16[/tex]

[tex]\implies a(\sqrt[5]{\frac32} )^{22}=16[/tex]

[tex]\implies a(\frac32} )^{\frac{22}{5}}=16[/tex]

[tex]\implies a=\dfrac{16}{(\frac32)^{\frac{22}{5}}}[/tex]

Find the 43rd term:

[tex]\implies a_{43}=ar^{42}[/tex]

[tex]\implies a_{43}= \left(\dfrac{16}{(\frac32)^{\frac{22}{5}}}\right)(\sqrt[5]{\frac32} )^{42}[/tex]

[tex]\implies a_{43}=16 \cdot (\frac32)^{-\frac{22}{5}} \cdot (\frac32)^{\frac{42}{5}}[/tex]

[tex]\implies a_{43}=16 \cdot (\frac32)^4[/tex]

[tex]\implies a_{43}=16 \cdot \left(\dfrac{3^4}{2^4}\right)[/tex]

[tex]\implies a_{43}=16 \cdot \left(\dfrac{81}{16}\right)[/tex]

[tex]\implies a_{43}=81[/tex]


Related Questions

HURRYYY PLEASEEE
The diagram shows a cone of a height of 5 cm and a base radius of 12 cm.
What is its volume?

Answers

Answer:

volume V = 314.159265 cm³

Step-by-step explanation:

By formula, Volume is = (1/3)πr²h

0.33×3.14×12×12×5

is = 314.159265 m3

Other info

radius r = 5 m

height h = 12 m

slant height s = 13 m

volume V = 314.159265 m3

lateral surface area L = 204.203522 m2

base surface area B = 78.5398163 m2

total surface area A = 282.743339 m2

Roman art differed slightly from the Greek style because it included __________ on sculpted and painted faces. A. Beards B. Eyebrows C. Expressions D. Imperfections Please select the best answer from the choices provided A B C D

Answers

Answer:

D imperfections

Step-by-step explanation:

i did the practice test:)

Answer:

The asnwer is D!^^

Step-by-step explanation:

Multiply and combine like terms to determine the product of these polynomials.
(3x – 4)(2x + 5)

Answers

Answer: Find attached the workings in the picture.

Step-by-step explanation:

A car rental company charges $28 per day for a rented car and $0.50 for every mile driven. A second car rental
company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both
companies charge the same amount for a one-day rental?

Answers

Answer:

56 miles

Step-by-step explanation:

According to the question, lets say the miles at x they charge the same rental

       34 + 0.50x = 20 + 0.75x (Solve equation)

       0.75x - 0.50x = 34 - 20

       0.25x = 14

       x = [tex]\frac{14}{0.25}[/tex]

       x = 56

So at 56 miles, they charge the same rental.

How do you work out the intersection?

Answers

Answer:

Get the two equations for the lines into slope-intercept form. ... Set the two equations for y equal to each other.Solve for x. ... Use this x-coordinate and substitute it into either of the original equations for the lines and solve for y.

Step-by-step explanation:

Shane and Damien are racing. Shane ran 8 miles in 4 hours. Damien ran 8 miles in 2 hours. How much faster did Damien run than Shane?
Damien ran 4 mph faster than Shane
Damien ran 2 mph faster than Shane
Damien ran 6 mph faster than Shane

Answers

The answer is 6 and 7 and 8
Damien ran 2 miles faster than Shane

You throw three number cubes that are numbers 1-6 all at the same time. What is the probability that you would get a triple 3 on the first throw?

Answers

Answer:

3/18 but if you have to simplify it, it would be 1/6

Answer:

1/27

Step-by-step explanation:

For each cube the probabilty of number 3 is 1/6 since it is one option out of 6 possible numbers.

The probability of same number on all three cubes is:

P(3,3,3) = 1/3*1/3*1/3 = 1/27

1/9 divided by 1/8 in fraction form

Answers

Answer: 8/9

Step-by-step explanation: Math in the image

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 102 < 122 acute, because 6 10 > 12 obtuse, because 62 102 < 122 obtuse, because 6 10 > 12

Answers

If the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle. Then the correct option is C.

What is a Pythagoras theorem?

The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. And it is given as

P² + B² = H²

A triangle with side lengths of 6 cm, 10 cm, and 12 cm.

We know that if the square sum of the perpendicular and base is greater than the square of hypotenuse then the angle will be an acute angle.

Ans if the square sum of the perpendicular and base is less than the square of hypotenuse then the angle will be an obtuse angle.

Then we have

6² + 10² < 12²

Then the angle will be an obtuse angle.

More about the Pythagoras theorem link is given below.

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Answer: C

Explanation: Obtuse, because 6^2+10^2<12^2

PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!

Answers

Answer:

angle HCG- 45/c

angle DF- 105/b

Step-by-step explanation:

m<HCG and m<ECD are opposite angles hence they are equal

m<HCG=45°

Now

mDF=

M<ECD+m<ECF45+60105°

Mark plants 9 red rose bushes and 4 yellow rose bushes.What is the ratio of yellow rose bushes planted to the total number of roes bushes planted?

Answers

Answer:

4:13

Step-by-step explanation:

First as stated in the problem, mark is looking to find the ratio of Yellow rose bushes planted the Total amount of rose bushes planted; so therefor we must find the total amount of rose bushes planted first.

9+4 = 13.

13 will be our second number, since it is Yellow : total.

Then, we understand that mark plants 4 yellow rose bushes, so 4 is our first number.

Now; we can put our numbers together.

4 to 13 ; [tex]\frac{4}{13}[/tex] , or 4:13.

I really hope this helps! Have an amazing day!

Answer: There are a total of thirteen (13) rose bushes planted but specifically there are six (6) white, five (5) red, and two (2) yellow rose bushes.

Step-by-step explanation: I done it in my head to figure it out so, i hope this helps you have a good day love.


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- 6
- 2
6
6
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6
8
What is the range of the function graphed above?

Answers

Answer:

From the graph   range = (-inf, + inf)

Step-by-step explanation:

range is the y values that the graph can have

need help asap please​

Answers

Step-by-step explanation:

first of all, your teacher wrote nonsense in the answer options : an area is always given in squared units. never in cubed units (which would be volume).

the area is : 1/2 × perimeter × apothem

the perimeter is simply 12 × 5 = 60 meters.

apothem = (a/2)×cot(pi/12) = 5/2 × cot(pi/12) =

= 9.330127019... meters

so the area is

1/2 × 60 × 9.330127019... = 279.9038106... m²

therefore, the third answer option is correct (although it is m², and not m³).

by the way, you have question 3 wrong. I answered this with the correct apothem calculation in the explanation for question 4.

Write the equation of the line that passes through the points (-1, 3) and (-5, -3)

Answers

Answer:

[tex]y= \frac{3}{2}x+\frac{9}{2}[/tex]

Step-by-step explanation:

First find the slope: [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{-3 - (3)}{-5-(-1)} = \frac{-6}{-4} = \frac{3}{2}[/tex]

Next use the point-slope fomula and one of the points to find the line:

[tex]y-y_{1} =m(x-x_{1} )[/tex] and the ordered pair (-1,3)

[tex]y-3=\frac{3}{2}(x-(-1))\\ y-3 = \frac{3}{2}(x+1)\\y-3=\frac{3}{2}x + \frac{3}{2}\\y=\frac{3}{2}x +\frac{3}{2}+3\\y = \frac{3}{2}x + \frac{9}{2}[/tex]

1. 7h + 2h - 5h
Α 4h
Β. 14h​

Answers

Answer:

A 4h

Step-by-step explanation:

[tex]7 + 2 - 5 = 9 - 5 = 4[/tex]

Find all possible values of x. The triangles are NOT drawn to scale.

Answers

Answer:

0 < x < 28

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of the triangle should be greater than the third side.

Therefore,

0 < x < 28

All the possible values of x are 26 < x < 28.

What is Triangle?

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

So a triangle has three sides.

We have the triangle inequality theorem which states that,

The length of any side of the triangle is always less than the sum of the other two sides.

And the range of the possible measure of the third side is the sum and the difference of the other two sides.

So x < 27 + 1 = 28

and,

x > 27 - 1 = 26

So 26 < x < 28

Hence the measures of third side is 26 < x < 28.

Learn more about Triangles here :

https://brainly.com/question/11680381

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Solve for s. You must write your answer in fully simplified form.
-5s = -13

Answers

Hey there!

-5s = -13


DIVIDE -5 to BOTH SIDES

-5s/-5 = -13/-5

CANCEL out: -5/-5 because it give you 1

KEEP: -13/-5 because it help solve for the s-value

NEW EQUATION: s = -13/-5

SIMPLIFY IT!
s = 13/5


Therefore, your answer is: s = 13/5


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Answer:

[tex]\boxed{\sf{s=\dfrac{13}{5} }}[/tex]

Step-by-step explanation:

Isolate the term of s from one side of the equation.

-5s=-13

First, you have to divide by -5 from both sides.

→ -5s/-5=-13/-5

Solve.

Divide the numbers from left to right.

→ -13/-5=13/5

[tex]\Longrightarrow: \boxed{\sf{s=\dfrac{13}{5} }}[/tex]

Therefore, the correct answer is s=13/5.

I hope this helps! Let me know if you have any questions.

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.? acute, because 102 122>152 acute, because 122 152>102 obtuse, because 102 122>152 obtuse, because 122 152>102

Answers

The triangle with side lengths of 10 in., 12 in., and 15 in. is acute because 10^2 + 12^2 > 15^2

What is the acute angle?

An acute angle is defined as the measure of an angle that is less than 90 degrees.

The side lengths of the triangles are 10, 12 and 15

The smallest side lengths are: 10 and 12

The sum of the squares of these side lengths is

[tex]10^2 + 12^2[/tex]

For the triangle to be acute, then the following must be true

[tex]10^2 + 12^2 > 15^2[/tex]

Evaluate the exponents

[tex]244 < 255[/tex]

The above inequality is true.

Hence, the triangle is acute because 10^2 + 12^2 > 15^2

Read more about triangles here;

brainly.com/question/17972372

What is the sum? startfraction 3 y over y squared 7 y 10 endfraction startfraction 2 over y 2 endfraction startfraction 5 over y minus 5 endfraction startfraction 5 (y 2) over (y minus 2) (y 5) endfraction startfraction 5 over y 5 endfraction startfraction 5 (y minus 2) over (y minus 5) (y 2) endfraction

Answers

The sum of the fraction expression is equal to 5/(y+5) then the correct option is C.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given as

[tex]\rm \dfrac{3y}{y^2+7y+10} + \dfrac{2}{y+2}[/tex]

Then the sum of the expression is given as

[tex]\rm \rightarrow \dfrac{3y}{y^2+7y+10} + \dfrac{2}{y+2}\\\\\\\rightarrow \dfrac{3y}{(y+2)(y+5)} + \dfrac{2}{y+2}\\\\\\\rightarrow \dfrac{3y + 2(y+5)}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5y+10}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5(y+2)}{(y+2)(y+5)}\\\\\\\rightarrow \dfrac{5}{(y+5)}[/tex]

More about the fraction number link is given below.

https://brainly.com/question/78672

Answer:

C on edge 2022

Step-by-step explanation:

5/y+5

34-w=6 is the question I need answered.

Answers

w = 28

solving stepwise:

[tex]\dashrightarrow \sf \ \ 34-w=6[/tex]

[tex]\dashrightarrow \sf \ \ -w=6-34[/tex]

[tex]\dashrightarrow \sf \ \ -w=-28[/tex]

[tex]\dashrightarrow \sf \ \ w=28[/tex]

Answer:

w = 28

Step-by-step explanation:

Given equation:

34 - w = 6

Substact 6 both sides:

⇒ 34 - w = 6⇒ 34 - w - 6 = 6 - 6⇒ 28 - w = 0

Subtract 28 both sides:

⇒ 28 - w = 0⇒ 28 - 28 - w = 0 - 28⇒ 0 - w = -28⇒ -w = -28

Multiply -1 both sides:

⇒ -w = -28⇒ -w × -1 = -28 × -1⇒ w = 28

Which expression is equivalent to (2^0 / 2^3) ^2
A 1/8
B 1/16
C 1/32
D 1/64

Answers

Answer:

D

Step-by-step explanation:[tex](\frac{2^0}{2^3})^2[/tex]

__________________________________

Calculate the power

[tex](\frac{1}{2^3})^2[/tex]

[tex](\frac{1}{8})^2[/tex]

[tex]\frac{1}{64}[/tex]

__________________________________

Determine true/false

[tex]Determine\ whether\ (\frac{2^0}{2^3})^2\ and\ \frac{1}{64}\ are\\ equivalent:[/tex]

[tex]True[/tex]

I hope this helps you

:)

How do i solve this pls help

Answers

Answer:

7.07106781

simplified

7.07

Step-by-step explanation:

HELP ME PLEASE THERES A PICTURE I WILL GIVE BRAINLIEST TO BEST ANSWER

Answers

Answer:

we need to know how many students are in the class

if there are more boys, than the probability of picking a boy is higher, and if there is more girls, the probability of picking a girl is higher and if the amount of boys and girls are the same, then the probability of picking a girl or a boy is the same.

Step-by-step explanation:

Please mark my answer as brainliest

is 6 and 9 like terms or unlike terms

Answers

Answer:

i think they are unlike terms

Step-by-step explanation:

Which of the following graphs represent a function?
4 graphs. Graph A is a curved line, graph b is horizontal, vertical, and then horizontal, graph C is a line with positive slope, graph D is a circle.
a.
Graph A and Graph C
b.
Graph A
c.
Graph D
d.
Graph B and Graph D

Answers

A I think sorry if wrong

A screening test for a newly discovered disease is being evaluated. In order to determine the effectiveness of the new test, it was administered to 900 workers. 150 of the individuals diagnosed with the disease tested positive. A negative test finding occurred in 60 people who had the disease. A total of 50 persons not diseased tested positive for it. Assume the prior probability is not known. What is the overall accuracy of the test

Answers

The overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.

What is the accuracy of a test?

Accuracy of a test is the ratio of the correct results to the total results the test gives.

Thus, we have:

[tex]\rm Accuracy =\dfrac{\text{Total number of correct results}}{\text{Total number of results}} = \dfrac{TP + TN}{TP + FP + TN + FN}[/tex]

where T represents True, F represents False, N represents Negative, and P represents Positive. The negativity and positivity are the results of the test.

For this case, we're specified that:

The test is happening for diagnosis of a newly discovered disease.Total number of tests done = total number of workers administered = 900True positive (TP)= test result positive (ie test saying that the person has disease) when disease is actually present (that actual presense is known by some other method, and here we're evaluating the quality of 'disease testing procedure' in consideration) = 150 in count.False Negative (FP)= test result negative (no disease detected by the test) when person is diseased in reality = 60False positive (FN) = test result positive when person has no disease in reality = 50As total 900 tests were done, so we get: True negative(TN) = 900 - TP - FP - FN = 640

(as each test result would be one of the TP, TN, FP, FN and these four no test result can lie in more than one of these categories).

Now, we have:

true results = TP + TN = 640 + 150 = 790

total results = 900

Thus, we get:

[tex]\text{Test accuracy} = \dfrac{TP + TN}{TP + FP + TN + FN} = \dfrac{790}{900} \approx 0.8778 = 87.78%[/tex]

Thus, the overall accuracy of the screening test for a newly discovered disease is being evaluated for this case is 87.78% approximately.

Learn more about accuracy of a test here:

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A ring-toss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely fill with water. The dimensions of the rectangular prism are shown in the diagram.

a) 90cm3
b) 208cm3
c) 29cm3
d) 480cm3​

Answers

Answer:

answer = C) 3 x 10 x 16 = 480 cm³

what is the area of a prism

Answers

Answer:

The area of prism is calculated by:(a+b)h/2

6.

The cost of 5. 5 pounds of apples is $40. 81

What is the constant of proportionality that relates

the cost in dollars, y

to the number of pounds of apples, X?

A) 5. 5

B) 5. 94

C) 6. 37

D) 7. 42

F)8. 16

G) Not listed

Answers

Answer:

D 7.42

Step-by-step explanation:

y = k x

40.81 = k ( 5.5)

k = 40.81/5.5 =

Find the measure of the missing angle of

Answers

73° + a = 180°

a = 180° - 73°
a = 107°
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