A team of scientists estimate the current number of butterflies in a park to be 20 thousand. The butterfly population is expected to increase at a rate of 4% per year. Which equation models the number of butterflies, in thousands, in the park after n years? A. 0.04(20)n B. 20(1.04)n C. 1.04(20)n D. 20(0.04)n

That would be choice C.

The graph of  4|x| is shaped like a V whose vertex is at the origin.

Every y value will be positive for y = 4|x|  as |x| is always positive  and a reflection in the x axis will make every y value negative.

Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let [tex]\bold{ h(x) = f(x) - c}[/tex]. Shifting downward c units yields this graph of h from the graph of f.

Given:

[tex]\bold{f(x)=4|x|}[/tex]

Calculation:

           [tex]\bold{g(x)=-(4|x|)}\\\\\bold{g(x)=-4|x|}\\\\[/tex]

So, the equation [tex]g(x)=-4|x|[/tex] describes [tex]g(x)[/tex].

Therefore, the final choice is "Option C".

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Answer:

14. The correct option is 2.

13. The correct option is 4.

Step-by-step explanation:

14.

The given function is

[tex]f(x)=4|x|[/tex]

The function is non-negative for all values of x. So, the function opens in upward direction.

The function uis in the form of

[tex]f(x)=k|x|[/tex]

Where, a is vertical stretch factor or compress factor.

If k>1, then it represent vertical stretch and if 0<k<1, then it represent vertical compression.

Since the value of k is 4, therefore it represents vertical stretch and option 2 is correct.

13.

The given function is

[tex]y=x^3[/tex]

The traslate form of given function is

[tex]y=(x+a)^3+b[/tex]

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then the graph shifts left side by a units and if a<0, then the graph shifts right side by a units.

If b>0, then the graph shifts upward by b units and if b<0, then the graph shifts downward by b units.

Since the graph shifts vertically 5 units down and horizontally 4 units left, therefore the value of a is 4 and value of b is -5. The required equation is

[tex]y=(x+4)^3-5[/tex]

Therefore option 4 is correct.

That would be FALSE

They have the same angles, so they're similar triangles.  For them to be congruent, the corresponding sides must have equal length.  Here we have two sides of length 7, but they're not corresponding sides.  If on the second triangle the 7 was the length of the side between the 60 and 62 degree vertices then we'd have equal corresponding sides and congruent triangles.

Answer: no

Step-by-step explanation: this answer would be FALSEEE

Only point U.

Therefore your answer is ONE.

Answer:

B) One

Step-by-step explanation:

If the points are collinear, then they lie on the same line.

Here U is lie on the same line where C and D points lie.

Therefore, answer is B) One.

Hope this will helpful.

Thank you.

96 square yards would complete the room

Now for this you would have to think what two numbers multiplied to get 6x^2. Let's say for example 3x and 2x=6x^2

And now what two numbers multiplied together make -15, For example it can be 5 and -3

Now your ANSWER: (3x+5)(2x-3)

662.46 is your answer

The required Kendall's monthly mortgage payment is $662.14.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

Here,
Kendall's down payment is 12% of $119,000, which is:

0.12 * $119,000 = $14,280

So the amount she is financing is:

$119,000 - $14,280 = $104,720

To calculate her monthly mortgage payment, we can use the formula for a fixed-payment loan:

[tex]M = P * (r / (1 - (1 + r)^{-n}))[/tex]

First, we need to calculate the monthly interest rate. The annual interest rate is 4.5%, so the monthly interest rate is:

4.5% / 12 = 0.375%

Next, we need to calculate the total number of monthly payments. Kendall has a 20-year loan, which is:

20 years * 12 months/year = 240 months

Now we can plug in the values and solve for M:

[tex]M = $104,720 * (0.00375 / (1 - (1 + 0.00375)^{-240}))[/tex]

M = $662.14

So Kendall's monthly mortgage payment is $662.14.

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Answer:

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Step-by-step explanation:

Given : A card is chosen from a standard deck of cards.

To find : What is the probability that the card is a queen, given that the card is a club?

Solution : It is the conditional probability

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

Let A is probability that card is queen.

Let B is the probability that card is a club.

Probability that card is queen given card is club [tex]P(A\cap B)=\frac{4}{52}=\frac{1}{13}[/tex]

Probability that card is club from deck of 52 cards [tex]P(B)=\frac{13}{52}=\frac{1}{4}[/tex]

To find probability that card is queen given that card is club [tex]P(A|B)[/tex]

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

[tex]P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}[/tex]

[tex]P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}[/tex]

Therefore, Option A is correct.

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Answer:

the correct answer was 1/13

Step-by-step explanation:

i took my test and put 4/13 which was wrong and said that 1/13 is the right answer

Answer:

Total time taken for doing home work = 3.6 hours.

Explanation:

Time taken for English home work = 1.15 hours.

Time taken for Mathematics home work = 1.75 hours.

 Time taken for Science home work = Time taken for Mathematics home work - 1.05 hours = 1.75 - 1.05 = 0.7 hours

 Total time taken for doing home work = 1.15 + 1.75 + 0.7 = 3.6 hours.

So the answer is not 4 hours, it is 3.6 hours, that is why it is showing it as wrong.

The answer is A=D apex

Answer:

It's the first one, I just literally got done taking the test it was my last question anyways.

Set up the proportion.  Then cross multiply and isolate the variable to solve.

[tex]\frac{8(trash bags)}{30 (days)} = \frac{x (trash bags)}{180 (days)}[/tex]

8(180)= 30(x)

[tex]\frac{8(180)}{30} = \frac{30x}{30}[/tex]

8(6) = x

48 = x

Answer: 48 trash bags

Two Angles are Supplementary when they add up to 180°.

m∠2 + m∠1 = 180° (*)

If ∠1 ≅ ∠3, then m∠1 = m∠3.

Substitute to the (*)

m∠2 + m∠3 = 180°

Therefore ∠2 and ∠3 are supplementary.

[tex]x^3-4^3 = (x-4)(x^2+4x+16)=(x-4)(x+4)(x+4)[/tex]

The GCF is 1.

Explanation:

1 has: 1 (LOL)

12 has: 1,2,3,4,6,12

16 has: 1,2,4,8,16

21 has: 1,3,7,21

24 has: 1, 2, 3, 4, 6, 8, 12, 24

30 has:  1, 2, 3, 5, 6, 10, 15, 30

44 has:  1, 2, 4, 11, 22, 44

70 has: 1, 2, 5, 7, 10, 14, 35, 70

So therefore, The GCF is 1

Hope this helps!

-Queenb369

P.S Could you possible give me the brainlist if i get it right.

Answer : C

[tex]f(x)= \sqrt{x}[/tex]

[tex]g(x)= \sqrt{x-5}[/tex]

Parent function is f(x). In g(x) 5 is subtracted from x

If any number is added or subtracted from x, then we move left or right

When a number 'a' is added with x  then we shift 'a' units to the left

When a number 'a' is subtracted from x  then we shift 'a' units to the right

f(x) is our parent function. Here 5 is subtracted from x to get g(x)

For -5, the graph of g(x) is the graph of f(x) shifted right 5 units

the first answer would be C

the next 3 questions are ACB

B

Assuming you mean the value of f(5)

If so then substitute x = 5 into f(x)

f(5) = (3 × 5) - 2 = 15 - 2 = 13 → B

The unemployment rate is calculated as the number of unemployed divided by the labor force, resulting in approximately 9.6%, which is the closest to 9.3% as listed. It is higher than the historical average and the February 2015 rate.

The unemployment rate of an economy is calculated by taking the number of unemployed persons and dividing it by the total labor force, and then multiplying the result by 100 to get a percentage.

In this case, using the given figures, the unemployment rate is calculated as follows: 14.8 (unemployed) / 153.9 (labor force) = approximately 9.6%.

This indicates that the correct answer is not explicitly listed, but the closest answer given is 9.3%, which seems to be a typo.

Furthermore, this current unemployment rate is significantly higher than the February 2015 rate of 5.5% and above the historical average unemployment rate, which tends to range between 4% to 6% over time, according to Federal Reserve Economic Data.

The dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

To solve this problem, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:

vf² = vi² + 2ad

The positive value of d indicates that the dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

The dolphin's friend is 5.3 meters below the surface of the water.

Let's reassess the problem with the given constraints more carefully.

We need to find the position of the dolphin's friend relative to the surface of the water.

1. Dolphin's height above the water:

[tex]\[ 4.5 \text{ meters above the surface} \][/tex]

2. Distance between the dolphin and her friend:

[tex]\[ 9.8 \text{ meters below the dolphin} \][/tex]

Since the friend is swimming below the dolphin, we need to subtract this distance from the height of the dolphin above the surface to find the position of the friend relative to the water surface.

3. Calculate the position of the dolphin's friend:

[tex]\[ \text{Position of friend} = 4.5 \text{ meters} - 9.8 \text{ meters} \][/tex]

[tex]\[ \text{Position of friend} = -5.3 \text{ meters} \][/tex]

This means the dolphin's friend is 5.3 meters below the surface of the water.

Perimeter = 2*14 + 2x   where x is length of the adjacent side

46 = 28 + 2x

2x =  18

x = 9 inches Answer

Answer:

  (3±√147, 0) ≈ (-9.124, 0) and (15.124, 0)

Step-by-step explanation:

The points (x, 0) satisfy the distance formula:

  d = 14 = √((x -3)² +(0+7)²)

  196 = (x -3)² +49 . . . . . square both sides

  147 = (x -3)² . . . . . . . . . subtract 49

  3 ±√147 = x . . . . . . . . . take the square root and add 3

The points at distance 14 from (3, -7) on the x-axis are (3±√147, 0).

Using the distance formula, it equals sqrt(1)

We have been given the dimensions of the rectangular prism.

Lets say that the length, width, and height of the rectangular prism are:

Length [tex]= x+1[/tex]

Width [tex]=x-1[/tex]

Height[tex]=x[/tex]

Volume of a rectangular prism is given by:

[tex]length \times width\times height[/tex]

Plugging the values of length, width, and height, we get:

Total volume of the prism [tex]= (x+1)\times(x-1)\times x[/tex]

[tex]=(x^2-1)x=x^3-x[/tex]   (we have used [tex](a+b)\times (a-b)=a^2-b^2[/tex])

So, the expression for the total volume of the prism is:

[tex](x^3-x)[/tex]