Question 4 (3 mark) : Write a program called Powers to calculate the first 4 powers of a given number. For example, if 3 were entered, the powers would be \( 3,9,27 \) and \( 81\left(3^{1}, 3^{2}, 3^{

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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Answer:

It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

Step-by-step explanation:

The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.

In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

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The length of one side of the square room of Rhett for his movie and music collection is (2x+7) feet.

Area of square is the square of its sides length. It can be given as,

\(A=a^2\)

Here, \(a\) is the length of the side of the square

Rhett decides to build a square room for his movie and music collection. The area of the room is given by the polynomial equation as,

\(A=(4x^2 +28x +49)\rm ft^2\)

Find the factors of the above equation using the split the middle term method as,

\(A=4x^2 +28x +49\\A=4x^2 +14x+14x +49A=x(2x+7)+7(2x+7)\\A=(2x+7)(2x+7)\\A=(2x+7)^2\rm ft^2\)

Compare it with the area of the square we get,

\(a=(2x+7)\rm ft\)

Hence, the length of the square room of Rhett for his movie and music collection is (2x+7) feet.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:

21x+4

Step-by-step explanation:

X’s: 21x

#’s: 4

So it will be 21x+4

Answer :

D

Step-by-step explanation:

Because when you put it in the calculator it will show if the solution is right. For example,

f(x) = a(x-h)^2 +k

Vertex is (2,-4)

Plug in the vertex and Pick a coordinate to test

I pick (0,-3)

f(x) = a(0-2)^2 -4= -3

Plug in each a to shows that the equation is true . In this case, 0.25 worked!

Test

0.25(0-2)^2-4= -3

-3 = -3

Hope this helped!

Pls make me the Brainliest if the answer is right it would meant a lot. Thanks

Answer:

D. 1/4 and \(f(x)=-2(x-8)^{2}+6\)

Step-by-step explanation:

I did the test.

Step-by-step explanation:

5k-12k-1+k

= 5k-12k+k-1

= -6k-1

Answer:

4: 32a^5 5: 2a / bc^2

Step-by-step explanation:

4. (2a)^3 / (2a)^-2

  = (2a)^3 * (2a)^2

     = 8a^3 * 4a^2

         = 32a^5

5. 10a^7 b^9 c^6 / 5a^6 b^10 c^8

    = 2a^7 b^9 c^6 / a^6 b^10 c^8

      = 2a / bc^2

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

$36

Step-by-step explanation:

22+14=36

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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Answer:

-10

Step-by-step explanation:

expand: 3x-12>5x+2

subtract 3x and subtract 2 to both sides

-14>2x

which is just

2x<-14

so x<-7.

the only value is -10. :D

Answer:

-10

Step-by-step explanation:

3(x – 4) > 5x + 2

Distribute

3x -12 > 5x+2

Subtract 3x from each side

3x-12-3x > 5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12 -2 > 2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

X must be less than -7

-10 is less than -7

Step-by-step explanation:

I hope this answer is helpful ):

The value of x will be 34°

Given that

(x+12)°+100°+x° are forming linear pair

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.

(x+12)°+100°+x°= 180°

⇒ x+ 12+ 100+x = 180°

⇒ 2x+112 = 180°

⇒ 2x = 180- 112

⇒ 2x = 68

⇒ x= 68/2

⇒ x= 34

For verification we will put value of x

(34+12)°+100°+34°

⇒ 46°+100°+34°

⇒146°+34°

⇒ 180°

So here we can see that by putting value of x we are getting the sum of 180°

Therefore value of x is 34

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Answer:

D

Step-by-step explanation:

i took the test

The equivalent expressions of \((x^{6} )^{-3}\) will be \((x )^{-18}\).

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive the equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The given expression is;

\((x^{6} )^{-3}\)

Required to Determine the equivalent expression.

First, we need to evaluate the expression in the bracket:

Apply the following law of indices:

\((x^a)^b = x ^{ab}\)

So:

\((x^{6} )^{-3}\)

becomes

\((x )^{6 \times -3}\\\\\)

\((x )^{-18}\)

Hence: the equivalent expressions of \((x^{6} )^{-3}\) will be \((x )^{-18}\).

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Answer:

AZ = 12.80

Step-by-step explanation:

There are 2 triangles in the square XARS. Squares are always congruent, all sides are the same. Given that WT is 6, we can assume that RS is also 6 (because of congruency). RA is is the hypotenuse of the triangle ARS. To find AS, we can plug in the pythagorean theorem 6^2+x=^2=10^2. We end up getting square root of 64 which simplifies to 8. AS is now 8. We also know that ST is 6 since the square WRST has all congruent sides. 8+6=14 gives us line AT. TZ is 8 due to triangle XAR and the congruency theorem. Now we plug in pythagorean theorem to find AZ and we get 8^2+10^2=x^2. After simplifying the square root of 164, we see that AZ is equal to 12.80

Answer:

12.80

Step-by-step explanation:

SO IT IS 12.80 BECAUSE IT IS 12.80. SIMLIFY TO 12.8 SO YEAH!!

HOPE YOU UNDERSTAND.

Answer:

9

Step-by-step explanation:

Common ratio = Second term ÷ First term

                        = 171 ÷ 19  = 9

Answer:

It will take 5.68 seconds to cover a distance of 100 meters.

Step-by-step explanation:

Given that:

A greyhound dog runs with a top speed of 17.6 m/s

Distance to cover = 100 meters

We know that:

Distance = Speed * Time

Putting the values in formula

100 = 17.6 * Time

Time = \(\frac{100}{17.6}\)

Time = 5.68 seconds

Hence,

It will take 5.68 seconds to cover a distance of 100 meters.

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Answer:

I would use equation d

Step-by-step explanation:

because need to find out X which is the second section so you would do 60 subtract 35 which gives 25 so X would be 25 .

I hope this helped . if you need any more help pls ask :)

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The two mathematical expressions 5(3t - 6) and 15t - 30 are equivalent.

Mathematical expressions are equivalent or equal when they have the same value.

Equivalent expressions work the same way despite their different looks.

We determine that two or more mathematical expressions are equivalent when simplified or yield the same value after substituting the variables.

Equivalent mathematical expressions are usually indicated using the equation symbol (=).

5(3t - 6) = 15t - 30

If t = 3

5(3t - 6) = 15

15t - 30 = 15

Thus, if two algebraic expressions are equivalent, then the two expressions have the same value.

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The variable X has a binomial distribution when the cards are drawn with replacement.

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. In the given scenario, we have 10 cards with numbers from 1 to 10, and we are interested in the variable X, which represents the number of successes (or the number of times a specific number appears) in a fixed number of trials.

To have a binomial distribution, two conditions must be met:

1. The trials must be independent: Each card drawn is independent of the others, meaning that drawing one card does not affect the probability of drawing another card.

2. The probability of success must be the same for each trial: In this case, the probability of drawing a specific number from the 10 cards is 1/10 since each card has a different number.

In the given scenario, if the cards are drawn with replacement (i.e., after drawing a card, it is put back into the set before the next draw), both conditions are satisfied. Each draw is independent, and the probability of drawing a specific number remains the same for each trial.

Therefore, when the cards are drawn with replacement, the variable X, representing the number of times a specific number appears, follows a binomial distribution.

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here is your formula then

Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - \(\frac{4}{52}\)

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

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The value of x the function when x = -7.5 is 34.5

Functions are written in terms of variables

Given the expression  –3.8x + 6, when the value of x is -7.5, hence;

f(x) =  –3.8x + 6

f(-7.5) = -3.8(-7.5) + 6

f(-7.5) = 28.5 + 6

f(-7.5) = 34.5

Hence the value of x the function when x = -7.5 is 34.5

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