Please help!!! If the first 4 terms of a geometric sequence are...

Answer:

  p(t) = 5*2^t

Step-by-step explanation:

We can solve for 'a' and 'b' using the point coordinates shown on the graph.

Substituting for (t, p(t)), the two equations we can make from the given points are ...

  p(t) = a*b^t

  5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)

  10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)

The first equation tells you ...

  5 = a

The second equation tells you ...

  10 = 5*b

  2 = b

The function is ...

  p(t) = a*b^t

  p(t) = 5*2^t

Answer:

15.2 in

Step-by-step explanation:

The surface area of a sphere is given by the formula below:

Surface area of sphere= 4πr², where r is the radius

Given that the surface area is 2903.33 in²,

2903.33= 4πr²

Divide both sides by 4π:

[tex] {r}^{2} = \frac{2903.33}{4\pi} [/tex]

Square root both sides:

[tex]r = \sqrt{ \frac{2903.33}{4\pi} } [/tex]

r= 15.2 in (3 s.f.)

For a similar question on surface area of sphere, do check out the following!

Answer:

Move all the points on the graph two points to the right

Step-by-step explanation:

f(x-2) is just a translation to the right by 2. The whole formula is typically y = a f(b(x + c)) + d. In this case, the C value is the one being changed and that indicates a translation left or right. -2 indicates 2 to the right.

Answer:

The Slope: 0

The y-intercept: (0,0_

x y

0 0

1 0 (there is supposed to be a line between the x and y that goes down all the way down the numbers but i cannot type that)

Step-by-step explanation:

Answer:

He needs to score 28 points.

Step-by-step explanation:

[tex]1^{st}\,\,score: 30\,\,points;\\\\2^{nd}\,\,score: 18\,\,points;\\\\3^{rd}\,\,score: 28\,\,points;\\\\4^{th}\,\,score: \,\,?[/tex]

Let's calculate Dante's 4th score, given that the average is 26 points:

[tex]\frac{S1 + S2 + S3 + S4}{4} = 26\\\\\frac{30 + 18 + 28 + S4}{4} = 26\\\\76 + S4 = 104\\\\S4 = 28\,\,points.[/tex]

Answer:

[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]

Step-by-step explanation:

[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].

This gives you the equation: [tex]u^2+3u+2=0[/tex].

Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:

[tex]u+2=0\\u=-2[/tex]

Now substitute x^2 back in as u

[tex]x^2=-2[/tex]

Take the square root of both sides

[tex]x=\pm \sqrt{-2}[/tex]

Separate the radical into sqrt(-1) * sqrt(2)

[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]

Rewrite using i

[tex]x=\pm i\sqrt{2}[/tex]

Now set the other factor equal to 0

[tex]u+1=0\\u=-1[/tex]

substitute x^2 back in as u

[tex]x^2=-1[/tex]

Take the square root of both sides

[tex]x=\pm\sqrt{-1}[/tex]

rewrite using i

[tex]x=\pm i[/tex]

the simplified value of the exponential expression is 1/9

Answer:

Number 4

Standard form - Not sure if right

y = − 0.2734375x^2 − 1.09375x +11.40625

Factored form - Not sure if right

y= 0.0390625 (−7x^2 −28x+292)

Number 5

Either form of the equation other than standard form

Vertex form : y = −(x +3)^2 + 25

Vertex of the parabola

(-3,25)

X and Y intercepts

x-intercept(s): (2,0) ,(−8,0)

y-intercept(s): (0,16)

1) 8

2) [tex]-\frac{3}{4}=-\frac{6}{8}[/tex], so it is equal to [tex]-\frac{6}{8}+\frac{5}{8}[/tex]

3) 1/8

It would take approximately 11 years for this population to reach 7300.

Based on the information provided, the future size of the population can be modelled by using an exponential function:

F = Pe^rt

Substituting the given parameters into the formula, we have;

7300 = 5000e^{0.035 × t}

7300/5000 = e^{0.035t}

1.46 = e^{0.035t}

Taking the ln of both sides, we have:

ln(1.46) = ln(e^{0.035t})

0.378 = 0.035t

t = 0.378/0.035

Time, t = 10.8 ≈ 11 years.

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The money spent on lottery tickets is 15.6% of the money spent to buy food.

The given parameters are:

Food = $122

Lottery = $19

The proportion of the lottery tickets is:

Proportion = Lottery/Food * 100%

This gives

Proportion = 19/122* 100%

Evaluate

Proportion = 15.6%

Hence, the money spent on lottery tickets is 15.6% of the money spent to buy food.

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324 divided into 6.846 is 47.33

The statement is given as:

324 divided into 6.846

This is represented as:

324/6.846

Using a calculator, we have:

47.3269062226

Approximate

47.33

Hence, 324 divided into 6.846 is 47.33

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Answer: B and D

Step-by-step explanation:

A is not, it's an arithmetic sequence where each term is +5 greater than the previous

B is because each term is 1/2 the previous term (common ratio of 1/2) thus making it a geometric sequence

C is not, it's the Fibonnaci sequence which is neither an arithmetic or geometric sequence

D is because each term is 1/3 the previous term (common ratio of 1/3) thus making it a geometric sequence

Answer:

B

Step-by-step explanation:

The values of m and n from the given equation are 1/4 and -2

Given the polynomial function below

f(x) = mx^4+2x^3-3x^2+nx-4

If the zeros are 2 and -2, hence;

0 = 16m+16-12+2n-4
0 = 16m-16+12-2n-4

_______________
16m+2n = 0
16m - 2n = 8

Subtract

2n+2n = -8
4n = -8

n = -2

Substitute for "m'

16m + 2(-2) = 0
16m = 4

m = 1/4

Hence the values of m and n from the given equation are 1/4 and -2

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Answer: L

Step-by-step explanation:

The two segments that form L meet at a 90 degree angle.

The frequency which is to filled in the table is 3,1,2,4.

Given  shopping time of ten shopkeeper: 36,20,32,18,20,33,28,34,37,23.

We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.

Shopping time is given as 36,20,32,18,20,33,28,34,37,23.

Intervals for which frequency is given is 18 to 22, 23 to 27, 28 to 32, 33 to 37.

Numbers in the range 18 to 22=18,20,23 therefore 3

Numbers in the range 23 to 27=23 therefore 1

Numbers in the range 28 to 32=32 , 28  therefore 2

Numbers in the range 33 to 37=36, 33, 37, 34 therefore 4.

Hence the frequency which is to filled are 3,1,2,4.

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Answer:

d i did the thing

Step-by-step explanation:

Answer:

[tex]g(s)=s^{2} +4s-3[/tex]

Step-by-step explanation:

So for our Question , we have  [tex]g(x)=x^{2} +4x-3[/tex]

and we want to find g(s) , so just substitute by x = s in the Equation of g(x)

[tex]g(s)=s^{2} +4s-3[/tex]

Answer:

$11,000

Step-by-step explanation:

Let amount invested for 12% yield be p . Amount for 4% yield is therefore (18000-p)

Interest for 12%: 12% of p=0.12p

Interest for 4%: 4% of (18000-p)=0.04(18000-p)=720-0.04p

Total interest:

=0.12p + (720-0.04p)

=0.12p-0.04p+720

=0.08p+720

But we already know the total interest is 1280

Therefore: 0.08p+720=1280

0.08p=1280-720

0.08p=560

p=560÷0.08

p=7000

Therefore at 4% the person invested:

(18000-p)

18000-7000

$11,000

Step-by-step explanation:

a number used multiplier variable

example 6z menas 6 times z and z is a variable so sixes coefficient variable with no number have a question of one example X is a really 1x

Step-by-step explanation:

hope it helps!!

Answer:

x = 75°

Step-by-step explanation:

∠ p = 40°     [alternate interior angles]

∠ q = 35°    [alternate interior angles]

x = ∠ p + ∠ q

x = 40° + 35°

x = 75°  

Answer:

For this one the parallel slope is going to be 2/5

Step-by-step explanation:

The amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90

From the equation given, we have that

$3 = I gallon

Let's take it that the farmer sells one gallon by per day

We know that the month of April has 30 days

So if he makes $3 in 1 day

He would make x in 30 days

Collect like terms

$30 × 30 days = amount

Multiply through

Amount = $90

Thus, the amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90

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a. The probability of winning the prize by the resident who purchased 10 tickets is 1% (10/1,000).

b. The expected profit (winnings - cost) for the resident who purchased 10 raffle tickets is $1,900 ($2,000 - $100).

c. The amount raised by the fire department after paying out the $2,000 prize (ignoring other raffle costs) is $8,000 ($10,000 - $2,000).

A raffle is a gambling competition or lottery organized to raise money for a purpose.

A raffle involves the sale of tickets which are drawn randomly to select some winners.

Price of a raffle ticket = $10

Prize = $2,000

Cost of purchasing 10 tickets = $100 ($10 x 10)

Number of raffle tickets sold = 1,000

Total revenue realized = $10,000 ($10 x 1,000)

Thus, if a resident purchases 10 tickets, the chance of winning the raffle is 1%.

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Answer:

31465

Step-by-step explanation:

n!/((n-r)! r!)

= 31!/(31-4)! 4!

= 31!/ 27! 4!

= 31465

Answer:

x<3

Step-by-step explanation:

There isn't a question that I can see for the first image, and I cannot see the yellow part, so I am not 100% sure if this is an accurate answer to the question you were asking.

The logarithmic form of √x = y is ㏒ₓy = 1/2

We have, logarithmic form as;

Given √x = y

Convert the square root to power of 1/2 as that is what it represents, we get

x^1/2 = y

Then compare with the universal logarithmic form, we have

㏒ₓy = 1/2

Thus, the logarithmic form of √x = y is ㏒ₓy = 1/2

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