write in expanded form
(2g+7)(3g^2−5g+2)

The functions g(x) and h(x) for the composition of functions f(x) = g(h(x)) are given as follows:

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

Then the functions for this problem are given as follows:

The composition of these two functions is given as follows:

\(g(h(x)) = \sqrt[3}{4x - 2} + 2\)

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The square feet of paper that will cover the model is 56 ft squared.

The model above is a square base pyramid. Therefore, the square feet of papers he will need to cover the model is the surface area of the model.

Therefore,

surface area of the square base pyramid = A + 1 / 2 ps

where

Therefore,

p = 4 × 4 = 16 ft

s = 5 ft

A = 4² = 16 ft²

Therefore,

surface area of the square base pyramid = 16 + 1 / 2 × 16 × 5

surface area of the square base pyramid = 16 + 40

surface area of the square base pyramid = 56 ft²

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Answer:

Step-by-step explanation:

The correct equation that shows a step in the process of completing the square on the given quadratic y = x^2 + 8x – 3 is y = x^2 + 8x + 16 – 3 – 16. Completing the square involves adding and subtracting a constant term in order to create a perfect square trinomial. In this case, the constant term added is (8/2)^2 = 16, which is half the coefficient of the x-term squared. This step transforms the quadratic into the form (x + a)^2 + b, where a represents half of the x-term coefficient and b represents the constant term.

By adding 16 to the equation to create a perfect square trinomial, we need to subtract 16 afterward to maintain the equation’s balance. Thus, the equation becomes:

y = x^2 + 8x + 16 - 3 - 16

Simplifying further:

y = (x + 4)^2 - 19

Therefore, the correct equation is:

y = (x + 4)^2 - 19

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

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f + g =

x/3 - 2 + 3x² + 2x - 6 =

3x² + 7/3 x - 8

Answer:D

Step-by-step explanation:

It’s a permutation

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Answer:

A and B are true

Step-by-step explanation:

It mean X will be a better choice for all inputs except small inputs when we say that an algorithm X is asymptotically more efficient than Y. So the option B is correct.

Asymptotic analysis takes algorithm growth in terms of input size into account. If an algorithm X runs faster than Y for all input sizes n greater than or equal to n₀, then X is said to be asymptotically better than Y.

When we claim that a method X is asymptotically more efficient than Y, we indicate that X will be a better option for all inputs except small inputs. The better choice would depend on the specific problem and algorithm.

Generally, if X is asymptotically more efficient than Y, then X should be the preferred choice for larger inputs, while Y may be better suited for small inputs. So the option B is correct.

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The complete question is:

What does it mean when we say that an algorithm X is asymptotically more efficient than Y?

a) X will be a better choice for all inputs

b) X will be a better choice for all inputs except small inputs

c) X will be a better choice for all inputs except large inputs

d) Y will be a better choice for small inputs

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

12.25

Step-by-step explanation:

3.5*3.5=12.25

Answer:

12.25m^2

Step-by-step explanation:

3 1/2 × 3 1/2

3 1/2 is equivalent to 7/2

7/2 × 7/2= 49/4

this simplifies to 12.25

answer: 12.25 m^2

Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

Given that the time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle.

Here we will use the concept of proportionality.

Since the rate is constant while the distance varies, we can establish a ratio:

100 meters / 47.52 seconds = 25 meters / x seconds

Where x is the unknown time for one lap in the 25-meter pool.

To solve for x, we can cross-multiply:

100 meters × x seconds = 47.52 seconds × 25 meters

100x = 1188

Dividing both sides by 100, we get:

x = 11.88 seconds

Hence Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

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Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

\( {(x + 5)}^{2} - {x}^{2} \\ {x }^{2} + 10x + 25 - {x}^{2} \\ 10x + 25 \\ 5(2x + 5)\)

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Answer: 30%

Step-by-step explanation: 21/70 = 21 divide 70 = 0.3 = 30%

The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term  \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.

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Answer:

x=35

Step-by-step explanation:

Add 56 to both sides of the equation

2x-56+56=14+56

Simplify

2x=70

Divide both sides of the equation by the same term

2x/2=70/2

Simplify

x=35

Solve, 2x - 56 = 14

=> 2x - 56 = 14

=> 2x = 14 + 56

=> 2x = 70

\( = > x = \frac{70}{2} \)

( 2 × 35 = 70 )

=> 35

Answer/Step-by-step explanation:

✔️Reference angle = 50°

Opposite side length = y

Hypotenuse = 8 cm

Adjacent = x

Thus, applying CAH we can find x as shown below:

Cos 50 = adj/hyp

Cos 50 = x/8

8 × cos 50 = x

x = 5.1 (to 1 decimal point)

Thus, applying SOH, we can find y as shown below:

Sin 50 = opp/hyp

Sin 50 = y/8

8 × Sin 50 = y

y = 6.1 (to 1 decimal point)

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Plug each ordered pair into the equation

A: 4 = 3(-1)-1

4=-3-1

This is false

B: 2= 3(-1)-1

2=-3-1

This is false

C: -4 = 3(-1)-1

-4=-3-1

This is true

Answer:

w=5000+0.7s

Step-by-step explanation:

please give 5 star I need it

Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportion p in a sample of size n, we have that \(\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}\)

In this question:

\(p = 0.8, n = 100\)

So

\(\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04\)

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.85 - 0.8}{0.04}\)

\(Z = 1.25\)

\(Z = 1.25\) has a pvalue of 0.8944.

X = 0.75

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.75 - 0.8}{0.04}\)

\(Z = -1.25\)

\(Z = -1.25\) has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

9514 1404 393

Answer:

  x = 20

  y = 70

Step-by-step explanation:

The exterior angle marked 40° is the sum of the remote interior angles in the isosceles triangle at lower right, both of which are x°.

  40° = 2x°

  x = 20 . . . . . divide by 2°

The angle marked y° is the complement of the one marked x°.

  y = 90 -x = 90 -20

  y = 70

Answer:

D: 1,130 cm³

Step-by-step explanation:

You need the volume of  a cylinder.

V = πr²h

V = 3.14159 * (6 cm)² * 10 cm

V = 3.14159 * 36 cm² * 10 cm

V = 1130.97 cm³

Answer: D: 1,130 cm³

Answer:

The choose D. 1130 cm³

v = r² pi/ h

v = (6)² × 3.14 × 10

v = 1130.4

v = 1130