A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The upper half of the ball can be formed by revolving the region bounded by the curves y.

The question is solved by carefully analyzing the given figures and working step by step to avoid double counting of items. Adding numbers to find total whales and then subtracting or combining them as required gives the specific group numbers.

This question requires calculations around the given number of whales and their specific dislikes. Let's address each part of the question step by step:

A. To find out the total number of whales surveyed, we add all the mentioned whales together, including those with no dislikes.
B. To find out the number of whales disliking at least one thing, we subtract the whales with no dislikes from the total number of whales.
C. To find out the number of whales that dislike Captain Ahab but not giant squids, we need to remove the whales that dislike both these things.
D. To determine the number of whales that dislike either giant squids or pollution, we need to avoid counting the whales that dislike both twice.

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Answer:

2/3 of the track

Step-by-step explanation:

5/7 • 4/5 is 2/3 so Sarah ran 2/3 around the track.

Answer:

The answer to your question is: 1 bag of apples cost $6.

Step-by-step explanation:

We need to write an equation:

1 bag of apples + 3 cartons of strawberries = $18

but 1 bag of apples = 1.5 cartons of strawberries

So

1.5 cartons of strawberries + 3 cartons of strawberries = $18

simplify   4.5 cartons of strawberries = 18

                1 carton of strawberries = 18/ 4.5 = 4

finally         1 bag of apples = 1.5 (4) = 6

Answer:

$6.00

Step-by-step explanation:

Explanation:

Given Statement: Gerald bought his first car after saving up $5,000.

The conditional conjunction after identifies the dependent clause, the one corresponding to the "if" statement in a conditional.

Conditional Statement:

If Gerald saved $5000, then he bought his first car.

__

Converse Statement:

If Gerald bought his first car, then he saved $5000.

__

Inverse Statement:

If Gerald did not save $5000, then he did not buy his first car.

__

Contrapositive Statement: (converse of the inverse)

If Gerald did not buy his first car, then he did not save $5000.

__

Biconditional Statement:

If and only if Gerald saved $5000, then he bought his first car.

Answer with Step-by-step explanation:

We are given that Events [tex]A_1,A_2 \;and\;A_3[/tex] form a partition of the sample space S .

[tex]P(A_1)=0.3,P(A_2)=0.5,P(A_3)=0.2[/tex]

If E is an event in S

[tex]P(E/A_1)=0.1,P(E/A_2)=0.6,P(E/A_3)=0.8[/tex]

[tex]P(E)=P(A_1)\cdot P(E/A_1)+P(A_2)\cdot P(E/A_2)+P(A_3)\cdot P(E/A_3)[/tex]

Substitute the values then we get

[tex]P(E)=(0.3)(0.1)+(0.5)(0.6)+(0.2)(0.8)=0.03+0.30+0.16=0.49[/tex]

[tex]P(E)=0.49[/tex]

Bayes theorem

[tex]P(E_i/A)=\frac{P(E_i)P(A/E_i)}{\sum_{i=1}^{n}P(E_i)P(A/E_i)}[/tex]

Now, using Bayes theorem

[tex]P(A_1/E)=\frac{P(A_1)\cdot P(E/A_1}{P(A_1)P(E/A_1)+P(A_2)P(E/A_2)+P(A_3)P(E/A_3)}[/tex]

Substitute the values then we get

[tex]P(A_1/E)=\frac{0.3\times 0.1}{(0.1)(0.3)+(0.5)(0.6)+(0.2)(0.8)}=\frac{0.03}{0.49}=\frac{3}{49}[/tex]

[tex]P(A_1/E)=\frac{3}{49}[/tex]

Similarly

[tex]P(A_2/E)=\frac{(0.5)(0.6)}{0.49}=\frac{0.30}{0.49}=\frac{30}{49}[/tex]

[tex]P(A_2/E)=\frac{30}{49}[/tex]

[tex]P(A_3/E)=\frac{(0.2)(0.8)}{0.49}=\frac{0.16}{0.49}=\frac{16}{49}[/tex]

[tex]P(A_3/E)=\frac{16}{49}[/tex]

You can use the Bayes' theorem and the law of total probability with chain rule to find the needed probabilities.

The needed probabilities are:

Suppose that there are two events A and B. Then suppose the conditional probability are:

P(A|B) = probability of occurrence of A given B has already occurred.

P(B|A) = probability of occurrence of B given A has already occurred.

Then, according to Bayes' theorem, we have:

[tex]\rm P(A|B) = \dfrac{P(B|A)P(A)}{P(B)}[/tex]

(assuming the P(B) is not 0)

For two events A and B, by chain rule, we have:

[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)[/tex]

Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as [tex]B_i \: ; i \in \{1,2,3.., n\}[/tex]

Then, suppose there is event A in sample space.

Then probability of A's occurrence can be given as

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i)[/tex]

Using the chain rule, we get

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)[/tex]

Using the above, rules, as we're already given that

[tex]A_1, A_2, A_3[/tex] are forming partition of the sample space (thus they're mutually exclusive and exhaustive events)

Also, its given that

[tex]P(A_1) = 0.3\\P(A_2) = 0.5\\P(A_3) = 0.2[/tex]

[tex]P(E|A_1) = 0.1\\P(E|A_2) = 0.6\\P(E|A_3) = 0.8[/tex]

Thus, by using the chain rule, we get:

[tex]P(E) = \sum_{i=1}^3P(A_i)P(E|A_i) = 0.3 \times 0.1 + 0.5 \times 0.6 + 0.2 \times 0.8 = 0.49\\\\P(E) = 0.49[/tex]

We have:

[tex]P(A_i \cap E) = P(A_i|E)P(E) = P(E|A_i)P(A_i)\\\\\rm P(A_i|E) = \dfrac{P(E|A_i)P(A_i)}{P(E)}[/tex]

Evaluating for i = 1, ,2, 3, we get:

[tex]\rm P(A_i|E) = \dfrac{P(E|A_i)P(A_i)}{P(E)}\\P(A_1|E) = \dfrac{0.1 \times 0.3}{0.49} \approx 0.0612[/tex]

[tex]\rm P(A_i|E) = \dfrac{P(E|A_i)P(A_i)}{P(E)}\\\\P(A_2|E) = \dfrac{0.6 \times 0.5}{0.49} \approx 0.612[/tex]

[tex]\rm P(A_i|E) = \dfrac{P(E|A_i)P(A_i)}{P(E)}\\P(A_3|E) = \dfrac{0.8 \times 0.2}{0.49} \approx 0.327[/tex]

Thus,

The needed probabilities are:

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Answer:

You must wait 60 minutes for all three lines to arrive at Union Station at the same time again.

Step-by-step explanation:

The complete question in the attached figure

Step 1

Find the least common multiple (LCM) of the three numbers

List the prime factors of each number

[tex]10=(2)(5)\\12=(2^2)(3)\\15=(3)(5)[/tex]

Multiply each factor the greatest number of times it occurs in any of the numbers to find out the LCM

The LCM is equal to

[tex](2^2)(3)(5)=60[/tex]

therefore

You must wait 60 minutes for all three lines to arrive at Union Station at the same time again.

Answer:

  see below

Step-by-step explanation:

If (x+5) is a factor of p(x), then the value x=-5 will make that factor be zero. The product p(x) of which it is a part will also be zero, so p(-5) = 0.

Since p(-5) = 0 at x=-5, there will be an x-intercept at x=-5.

Dividing something by a factor of that thing will always give a remainder of zero. So, p(x)/(x+5) has a remainder of 0.

Answer:

[tex]8.53\°[/tex]

Step-by-step explanation:

we know that

The grade of a road can be thought of as rise/run, and you usually see it as a percentage.

So, a 15% grade is the same as a grade of 15/100; for every 15 units the road goes up vertically, it goes 100 units horizontally

see the attached figure to better understand the problem

Let

[tex]\theta[/tex] -----> angle does the road come up from the ground

The tangent of angle theta is equal to the ratio of the opposite side by the adjacent side

[tex]tan(\theta)=\frac{15}{100}[/tex]

[tex]\theta=tan^{-1}(\frac{15}{100})=8.53\°[/tex]

Answer:

Step-by-step explanation:

When I am dealing with fractions I put them in money wise so 2 1/4 would be like 2.25 and 3/8 would be like 0.75.

So that means you divide 2.25 by 0.75 and that will give you three.

Therefore Kia can make 3 small bags of candies.

have a nice day

please follow

Answer:

The answer to your question is: AC = 20

Step-by-step explanation:

Data

   AB = 2x - 4

   BC = 4x

   AC = 2x + 12

   AC = ?

            AB + BC = AC

        2x - 4 + 4x = 2x + 12

       6x - 4 = 2x + 12

       6x - 2x = 12 + 4

       4x = 16

       x = 16/4

       x = 4

AB = 2(4) - 4 = 8 - 4 = 4

BC = 4(4) = 16

AC = 2(4) + 12 = 8 + 12 = 20

         4 + 16 = 20

         20 = 20

Answer:

Memory Locations assigned

a) 58 b) 60 c) 52 d) 3  

Step-by-step explanation:

We are given that:

h(k) = k mod 101

To find the memory location, we need to evaluate the modulus value abbreviated as mod, k modulo n, which returns the value of remainder when k is divided by 101.

a) 104578690

104578690 mod 101 = 58

b) 432222187

432222187 mod 101 = 60

c) 372201919

372201919 mod 101 = 52

d) 501338753

501338753 mod 101 = 3

The memory locations assigned by the hashing function h(k) = k mod 101 to the Social Security numbers are: a) 81, b) 14, c) 15, and d) 38.

The hashing function h(k) = k mod 101 assigns memory locations to records based on the modulus operation. To find the memory locations assigned to the Social Security numbers given, we need to calculate the result of k mod 101 for each number.

Therefore, the memory locations assigned to the records are:

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By using sample space we can say that complement of 4 heads in the toss of 4 coins is at least one tail .

set of all possible outcomes experiment is called sample space .

To find compliment of 4 heads we will first find sample space Sample space= S

= { HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT TTHH, TTHT, TTTH, TTTT }

Given case is 4 heads Say A= { HHHH}

Now we can calculate A complement as

A' = S-A

= { HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT TTHH, TTHT, TTTH,TTTT }- { HHHH}A'={ HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT TTHH, TTHT, TTTH,TTTT }

By using sample space we can say that complement of 4 heads in the toss of 4 coins is at least one tail .

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The complement of 4 heads in the toss of 4 coins is 'at least one tail', which includes any outcome where at least one coin lands on tails, encompassing all possibilities except for the exact outcome of 4 heads.

The student is asking about the concept of the complement in probability when flipping coins. Specifically, the complement of getting four heads in the flip of four coins. In probability, the complement of an event is all the possible outcomes that are not part of the event itself. In the case of flipping four coins, the event of getting four heads (HHHH) has a complement that consists of any outcome that does not have four heads. That includes outcomes with at least one tail.

Therefore, the complement of getting four heads is at least one tail, meaning any outcome where at least one coin lands on tails. All the outcomes with 0 heads and 4 tails, 1 head and 3 tails, 2 heads and 2 tails, or 3 heads and 1 tail would be part of this complement.

Since the question refers to the flip of four coins, only the following outcomes (macrostates) are possible: 0 heads (all tails), 1 head, 2 heads, 3 heads, or 4 heads (all heads). The complement of '4 heads' would comprise all outcomes except for '4 heads', reaffirming that the correct answer is at least one tail.

Answer: Our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]

Step-by-step explanation:

Since we have given that

Total amount he spent on flowers = $40

Let the number of small flowers be 'X'.

Let the number of large flowers be 'Y'.

cost of small flowers = $2

cost of large flowers = $3

According to question, it becomes,

[tex]2X+3Y=40[/tex]

Hence, our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]

The equation that describes this situation is.

2X + 3Y = 40

Let's define:

X = number of small flowers

Y = number of large flowers.

We know that Jane spent $40 on the flowers, and each small flower costs $2 and each large flower costs $3, then the total cost of the X and Y flowers is:

2*X + 3*Y

And that must be equal to 40, which is the amount she spent.

2X + 3Y = 40

That is the equation.

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Answer:

9 cats were fed that evening.

Step-by-step explanation:

6 divided by 2/3 equals 9, so 9 cats were fed that evening.

Hope this helps! ☺

Answer:

There are 9 cats in total

Step-by-step explanation:

Let x be the no. of cats

Each cat received cup of food = [tex]\frac{2}{3}[/tex]

Caps received by x cats = [tex]\frac{2}{3}x[/tex]

We are given that 6 cups of cat food were shared

So, [tex]\frac{2}{3}x=6[/tex]

[tex]x=\frac{3}{2} \times 6 [/tex]

[tex]x=9 [/tex]

Hence there are 9 cats in total .

Answer:

Just find the distance of the vertices of the quadrilateral ( such as : AB, BC, CD DA )by using distance formula...

Then if opposite sides of quadrilateral is equal then it is rectangle .....

hope you understand...

Answer: 25%

Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. If we want to write 1/4 as a percent, we need to find a fraction equivalent to 1/4 with a 100 in the denominator. We can do this by setting up a proportion.

[tex]\frac{1}{4}[/tex] = [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

4n = 100

÷4     ÷4    ← divide by 4 on both sides

  n = 25

Therefore, 1/4 is equivalent to 25%.

The coefficient of determination R2 calculated by Microsoft Excel is:

R2=0,974024991

To plot the given data in Excel, follow these steps: Create a scatter plot with temperature on the x-axis and pressure on the y-axis. To calculate R2 in Excel, add a trendline and check the 'Display R-squared value on chart' option.

To plot the given data in Excel, follow these steps:

To calculate the coefficient of determination (R2) in Excel, follow these steps:

The calculated coefficient of determination (R2) will be displayed on the chart.

Answer:

y''=-1.26

Step-by-step explanation:

We are given that [tex]2x^2+y^2=17[/tex]

We have evaluate the second order derivative of y w.r.t. x when x=2 and y=3.

Differentiate w.r.t x

Then , we get

[tex]4x+2yy'=0[/tex]

[tex]2x+yy'=0[/tex]

[tex]yy'=-2x[/tex]

[tex]y'=-\frac{2x}{y}[/tex]

Again differentiate w.r.t.x

Then , we get

[tex]2+(y')^2+yy''=0[/tex] [tex](u\cdot v)'=u'v+v'u)[/tex]

[tex]2+(y')^2+yy''=0[/tex]

Using value of y'

[tex]yy''=-2-(-\frac{2x}{y})^2[/tex]

[tex]y''=-\frac{2+(-\frac{2x}{y})^2}{y}[/tex]

Substitute x=2 and y=3

Then, we get [tex]y''=-\frac{2+(\frac{4}{3})^2}{3}[/tex]

[tex]y''=-\frac{18+16}{9\times 3}=-\frac{34}{27}[/tex]

Hence,y''=-1.26

Answer:

B. Changes in the fair value of the investors ownership shares of the investee

Step-by-step explanation:

The fair value option is defined as the alternative for any business that helps them to record its financial instruments at their fair values.

The answer is : Changes in the fair-value of the investor's ownership in shares of the investee.

Answer:

The answer to your question is 900 black and white copies

Step-by-step explanation:

Data

9 black and white copies for every 2 colored

printed 200 color copies

black and white copies = ?

Process

                 This is a proportion exercise

                         BW : C ::  bw : c

                          9 : 2 ::  bw : 200

                         bw = 200(9) / 2

                         bw = 1800 / 2

                         bw = 900 copies

We find that the telephone pole is 1.8 meters tall.

To figure out the height of the telephone pole, we can use similar triangles. Picture a right triangle formed by the telephone pole, the ground, and the wire, and another smaller triangle formed by Leah standing 2.5 meters from the pole, reaching the point where her head touches the wire 1.5 meters above the ground. Because these two triangles are similar, we can set up a proportion.

The large triangle's height is the height of the pole (H), and its base is 3 meters. The smaller triangle's height is Leah's height (1.5 meters), and its base is 2.5 meters. Using the similar triangles:

H (height of the pole) / 3 meters (distance from pole to cable ground attachment) = 1.5 meters (Leah's height) / 2.5 meters (Leah's distance from the pole)

H / 3 = 1.5 / 2.5

H = (1.5 / 2.5) * 3

H = 1.8 meters

Therefore, the telephone pole is 1.8 meters tall.

Answer:

C

Step-by-step explanation:

For this problem, the point where the line changes its slope is the focus point. The trick for this is to find the x point for the point. You have to look at he absolute value parenthesis, for this just put the opposite negative value of the number being added or subtracted inside the parenthesis. The "b" (y=mx+b) for the equation, isn't changed at all, so -2 would be the y value.

Answer:

1) His total commission is $1,234.3

2) The purchase of the car is $24,790.

Step-by-step explanation:

1) 21640*0.02= 432.8+ 250= 682.8

15075*0.02= 301.5+ 250= 551.5

682.8+ 551.5= 1,234.3

2) 745.8- 250= 495.8/ 0.02= 24,790

Jack's total commission for selling two cars is $1234.3, and if

c(p) = 745.80, the purchase price of the car is $24,790.

We have,

Let's first find Jack's total commission for selling two cars, one for $15,075 and the other for $21,640.

For the car sold for $15,075:

c(p) = 250 + 0.02p

c(15075) = 250 + 0.02 * 15075

c(15075) = 250 + 301.5

c(15075) = 551.5

So, the commission for the car sold for $15,075 is $551.5.

For the car sold for $21,640:

c(p) = 250 + 0.02p

c(21640) = 250 + 0.02 * 21640

c(21640) = 250 + 432.8

c(21640) = 682.8

So, the commission for the car sold for $21,640 is $682.8.

Now, to find Jack's total commission, simply add the commissions for both cars:

Total Commission = Commission for first car + Commission for second car

Total Commission = $551.5 + $682.8

Total Commission = $1234.3

Jack's total commission for selling two cars is $1234.3.

Next, if c(p) = 745.80, we need to find the purchase price of the car (p). We can use the equation:

c(p) = 250 + 0.02p

Now, set c(p) equal to 745.80 and solve for p:

745.80 = 250 + 0.02p

Subtract 250 from both sides:

745.80 - 250 = 0.02p

495.80 = 0.02p

Now, divide both sides by 0.02 to isolate p:

p = 495.80 / 0.02

p = 24,790

Thus,

Jack's total commission for selling two cars is $1234.3, and if

c(p) = 745.80, the purchase price of the car is $24,790.

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Answer:

L= z z -$13

Step-by-step explanation:

We will write "L" for Linda and" z z" for Juan.

As linda spent $13 less than Juan, It is that Linda spent $13 less than zz.

We must substract $13 to what zz spent to obtain what Linda spent. That is,

L = zz - $13

The algebraic expression for how much Linda spent is z - 13, where z represents how much Juan spent.

To represent how much Linda spent, we can use the algebraic expression z - 13.

We will write "L" for Linda and" z z" for Juan.

Since Linda spent $13 less than Juan,

we subtract 13 from the amount Juan spent to get the amount Linda spent.

As linda spent $13 less than Juan, It is that Linda spent $13 less than zz.

We must substract $13 to what zz spent to obtain what Linda spent. That is,

L = zz - $13

So the expression for how much Linda spent is z - 13.

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Answer:

x = 20

y = 110

Step-by-step explanation:

5x + 45 + 3x - 25 = 180

those angles are supplementary (they make a straight angle in segment CD)

Solving that you get:

8x + 20 = 180

8x = 160

x = 20

Evaluating:

5(20) + 45 = 145

3(20) - 25 = 35

2(20) - 5 = 35

Now in segment AB:

y + (2x - 5) + (3x - 25) also sum 180, because they form a straight angle

y + 35 + 35 = 180

y = 110

Answer:

97

Step-by-step explanation:

We are asked to find the size of sample to be 95% confident that the error in psychologist estimate of mean reaction time will not exceed 0.01 seconds.

We will use following formula to solve our given problem.

[tex]n\geq (\frac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex], where,

[tex]\sigma=\text{Standard deviation}=0.05[/tex],

[tex]\alpha=\text{Significance level}=1-0.95=0.05[/tex],

[tex]z_{\alpha/2}=\text{Critical value}=z_{0.025}=1.96[/tex].

[tex]E=\text{Margin of error}[/tex]

[tex]n=\text{Sample size}[/tex]

Substitute given values:

[tex]n\geq (\frac{z_{0.025}\cdot\sigma}{E})^2[/tex]

[tex]n\geq (\frac{1.96\cdot0.05}{0.01})^2[/tex]

[tex]n\geq (\frac{0.098}{0.01})^2[/tex]

[tex]n\geq (9.8)^2[/tex]

[tex]n\geq 96.04[/tex]

Therefore, the sample size must be 97 in order to be 95% confident that the error in his estimate of mean reaction time will not exceed 0.01 seconds.

Answer:

  x^3 +x +2 +3/(x -1)

Step-by-step explanation:

Synthetic division can be done using a divisor with a power of the variable other than one, but the most straightforward application of it uses a binomial divisor with a variable coefficient of 1. Fortunately the divisor in this problem is the difference of squares, so can be factored into two divisors. We can make use of synthetic division to divide by one of them, then we can use it again with the other divisor.

  = ((x^5 +2x^2 +2x +1)/(x +1)) / (x -1)

  = (x^4 -x^3 +x^2 +x +1)/(x -1)

  = x^3 +x +2 + 3/(x -1)

The remainder from the second division is simplified by the fact that there is no remainder from the first division. If desired, the final remainder can be expressed over the original divisor as (3x +3)/(x^2 -1) by multiplying numerator and denominator by the first divisor, (x+1).

_____

The synthetic division tableaux are attached. First, we divide by (x+1), then that result is divided by (x-1).

We assume you've been shown how this works. If not, there are numerous web sites and videos that can explain better than is possible in this space.

Answer:

10 in each with 5 left over

Step-by-step explanation:

Answer:

YXZ= 56 degrees

Step-by-step explanation:

Add the angles and set them equal to 180. Then solve for x. then Pug it in 2x+28.

Answer: [tex]\angle{YXZ}=56^{\circ}[/tex]

Step-by-step explanation:

Given : ∠WXY and ∠YXZ are supplementary angles.

∠WXY= 8x+12   and   ∠YXZ = 2x+28

We know that the pair of supplementary angles are added up to 180°.

According to the question, we have

[tex]\angle{WXY}+\angle{YXZ}=180^{\circ}\\\\\Rightarrow\ 8x+12+2x+28=180\\\\\Rightarrow\ 10x+40=180\\\\\Rightarrow\ 10x=180-40\\\\\Rightarrow\ 10x=140\\\\\Rightarrow\ x=\dfrac{140}{10}=14[/tex]

Now, [tex]\angle{YXZ}=2(14)+28=56^{\circ}[/tex]

Hence, the measure of  [tex]\angle{YXZ}=56^{\circ}[/tex].

The function that represents the number of likes each day is[tex]\(c(n) = 143(3)^{n-1}\)[/tex]. Therefore, the correct answer is option D.

The function [tex]\(c(n) = (3)n - 1\)[/tex] models the number of likes each day, where [tex]\(n\)[/tex] is the number of days since the video was posted.

On the first day, there were 143 likes.

To find the function that shows the number of likes each day, we need to substitute [tex]\(n = 1\)[/tex] into the given function and solve for the number of likes.

Substituting [tex]\(n = 1\) into \(c(n) = (3)n - 1\)[/tex], we get:

[tex]\[c(1) = (3)(1) - 1\][/tex]

[tex]\[c(1) = 3 - 1\][/tex]

[tex]\[c(1) = 2\][/tex]

So, on the first day[tex](\(n = 1\)),[/tex] there were 2 likes. Since the problem states that there were actually 143 likes on the first day, the correct function should take this into account. Therefore, the correct function is:

[tex]\[c(n) = 143(3)^{n - 1}\][/tex]

Thus, the correct option is:

[tex]D. \(143(3)^{n-1}\)[/tex]

The correct function modeling the number of likes each day with 143 initial likes and tripling daily is:  [tex]\[ c(n) = 143 \times 3^{n-1} \][/tex]

This aligns with the given exponential growth pattern.

To determine which function models the number of likes each day, let's consider the following:

- The initial number of likes is 143. This is the base case.

- The function is described as having 3 times more likes each day. This suggests an exponential growth pattern.

To derive the correct function, we need to incorporate this growth rate into the initial likes:

Given the base case (the first day) has 143 likes, and the number of likes triples each day, the correct function should start with the initial likes (143) and then account for the exponential increase by multiplying by the growth factor raised to the appropriate power.

This can be represented mathematically as:

[tex]\[ c(n) = 143 \times 3^{n-1}. \][/tex]

Let's break it down:

- Exponential Growth: Multiplying by 3 every day suggests exponential growth with a base of 3.

- Initial Value : The function starts with 143 likes.

- Days Since Posting : The exponent  n-1 accounts for the base case.

If  n = 1 , then [tex]\( 3^{n-1} = 3^{0} = 1,[/tex] which preserves the initial value of 143.

This leads us to option D , which correctly models the number of likes each day:

[tex]\[ c(n) = 143 \times 3^{n-1}.[/tex]  

Question :

Every day, there are 3 times more likes on an internet video of a cat which is modeled by the function c(n) = (3)n − 1, where n is the number of days since the video posted. On the first day, there were 143 likes. What is the function that shows the number of likes each day?

A. c(n) = (3)(143)^{n-1}

B. c(n) = 143^{n-1}

C. c(n) = (3)143 − n

D.143(3)^{n-1}