P(x) = 3x³+ 2x²-x what is the value of P(2)​

Answer:

To find the surface area of a pyramid, we need to use the formula:

Surface Area = Base Area + [ (Perimeter of Base) x (Slant Height) ] / 2

Assuming the base of the pyramid is a square with sides of length 9in, the Base Area = 9in x 9in = 81in²

To find the slant height, we need to use the Pythagorean theorem:

( Slant Height )² = ( Height )² + ( 1/2 Base )²

( Slant Height )² = ( 9/2 )² + ( 9/2 )²

( Slant Height )² = 81/4 + 81/4

( Slant Height )² = 162/4

( Slant Height )² = 40.5

Slant Height = sqrt( 40.5 ) = 6.36in (rounded to two decimal places)

Perimeter of Base = 4 x Base = 4 x 9in = 36in

Now we can plug these values into the formula:

Surface Area = 81in² + [ ( 36in ) x ( 6.36in ) ] / 2

Surface Area = 81in² + ( 228.96in² ) / 2

Surface Area = 81in² + 114.48in²

Surface Area = 195.48in²

Rounding to the nearest tenth gives us answer A. O 187.1 in²

Answer:

yes it is rotated

Step-by-step explanation:

since it was already dilated (widened), it was the rotated to create the way that it is now

Answer:

B

Step-by-step explanation:

Hope this help

a) If the contribution to the profit of a model A satellite radio is $10.00/radio,

the optimal profit is P = $1,232.00, achieved at (x, y) = (194, 10(194-16)).

Substitute y = 10 and solve for x by setting the derivative of (1) with respect to x to zero and solve for x. The first-order condition is:dy/dx = -0.016x + 3.2 = 0 → x = 200.

Substitute x = 200 in the function (1) to obtain the optimal profit:P = -0.008(200)^2 + 3.2(200) = $1,600.00

Since the production of model A satellite radios has been limited to no more than 80/day, the optimal production level of x = 80 is less than the optimal production level of x = 200.

x = 80 is the production level that should be used. Since the optimal production level of x = 80 does not correspond to the optimal profit, the company should not sell the model A satellite radio at $10.00/radio.

b) If the contribution to the profit of a model A satellite radio is $12.50/radio,

the optimal profit is P = $1,800.00, achieved at (x, y) = (150, 12.5(150-12)).

Substitute y = 12.5 and solve for x by setting the derivative of (1) with respect to x to zero and solve for x.

The first-order condition is:dy/dx = -0.016x + 3.2 = 0 → x = 200.

Substitute x = 150 in the function (1) to obtain the optimal profit:P = -0.008(150)^2 + 3.2(150) = $1,800.00

The company should sell the model A satellite radio at $12.50/radio in order to achieve the optimal profit of $1,800.00.

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Given that a card is drawn at random from a standard deck of cards. We are asked to find the probabilities of

1) A queen or a spade.

2) A black or a face card.

3) A red queen.

This can be seen below;

Explanation

The formula for the probability of an event is given as;

For a given deck of cards, the number of total possible outcomes is 52 different cards. Next, we find the number of events for each case

Therefore we can find the probability in each case. Recall that "or" in probability implies we will add the values of the probabilities we are comparing.

1) A queen or a spade

Answer

2) A black or a face card

Answer:

3) A red queen

Answer

Total marbles = 13

Number of yellow = 2

probability of getting yellow = 2/13

The research hypothesis posits that the more caffeine consumed by a subject, the longer a subject will stay awake (H1: rxy > 0). In this case, we are given the correlation coefficient r(10) = 0.653 and p < 0.05.

To interpret these results, we need to understand the correlation coefficient (r) and the p-value. The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the relationship between caffeine consumption and staying awake.

The correlation coefficient ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase. A negative value indicates a negative relationship, where as one variable increases, the other tends to decrease. The closer the value is to 1 or -1, the stronger the relationship.

In this case, the correlation coefficient is 0.653, which is positive. This suggests a moderate positive relationship between caffeine consumption and staying awake.

The p-value, on the other hand, measures the probability of obtaining the observed correlation coefficient (or a more extreme one) if the null hypothesis were true. The null hypothesis (H0) states that there is no relationship between caffeine consumption and staying awake.

In this case, we are given that p < 0.05. This means that the probability of obtaining a correlation coefficient as extreme as 0.653, or more extreme, under the assumption that there is no relationship, is less than 0.05. This is considered statistically significant.

Based on these results, we can conclude that there is a statistically significant positive relationship between caffeine consumption and staying awake. However, it's important to note that correlation does not imply causation. Other factors could be influencing the relationship, and further research would be needed to establish a causal relationship.

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Inferential statistics is one of the three basic ways of explaining the results of a research investigation. Group of answer choices Comparing variable quantities Graphing relationships between variables Comparing group percentages Making precise statements about data by correlating the scores of individuals on two variables.

Making precise statements about data by correlating the scores of individuals on two variables is one of the three basic ways of explaining the results of a research investigation.

This is also known as inferential statistics, which involves making predictions or generalizations about a larger population based on sample data.

The other two basic ways of explaining research results are descriptive statistics, which involves summarizing and describing the characteristics of a sample, and graphical representation, which involves using visual aids to display data and relationships between variables.

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The cost of four and three-fourths pounds of beef is $18.95.

Given,

Amount of beef purchased = 4 and 3/4th  pounds.

Cost of beef per pound = $3.99

We need to find how much four and three-fourths pounds of beef cost.

Find the cost of 1 pound of beef.

1 pound = $3.99

We can write four and three-fourths as:

= 4 3/4

= 19/4

Find the cost of 19/4 pounds of beef.

1 pound = $3.99

Multiplying by 19/4 on both sides.

19/4  x 1 pound = 19/4 x $3.99

19/4 pounds =$18.95

Thus the cost of four and three-fourths pounds of beef is $18.95.

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Answer:

Principal is $1000

Step-by-step explanation:

• From the formular of simple interest:

\(s.i = principal \times rate \times time\)

• substitute and find the principal:

\(100 = p \times \frac{2}{100} \times 5 \\ \\ 0.1p = 100 \\ \\ = { \underline{ \: \:1000 \: \: dollars \: \: }}\)

Answer:

50

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

2/4 = 1/2

1/2 = 0.5

0.5 = 50%

(Could explain slightly more but this should get the point across!)

The sum of the measures of the interior angles is (n-2) * 180 where n are the sides.

This is a hexagon so it has 6 sides. If we plug it into the equation, we get:

(6-2) * 180

4 * 180

720

Now that we know the sum, we divide 720/6 and get 120.

Each interior angle is 120.

The function of the town's population is an exponential growth

From the question, we have the following parameters that can be used in our computation:

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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The center of the circle is (-2, -4) and the radius of the circle is sqrt(75).

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

\((x-h)^2 + (y-k)^2 = r^2\)

We are given that;

The equation; x² + y² + 4x+8y-55= 0

We can rewrite the given equation in the standard form for the equation of a circle:

(x² + 4x) + (y² + 8y) = 55

Completing the square for both x and y, we can rewrite this as:

(x² + 4x + 4) + (y² + 8y + 16) = 55 + 4 + 16

Simplifying, we get:

(x + 2)² + (y + 4)² = 75

Now we can identify the center and radius of the circle. The center of the circle is given by (-2, -4), which is the opposite of the coefficients of x and y in the completed square form of the equation. The radius of the circle is given by the square root of the constant term on the right-hand side of the equation, which is sqrt(75).

Therefore, by the given equation of circle answers will be (-2, -4) and sqrt(75).

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Answer: w+x=90

z=y+90

Step-by-step explanation: because the sum of the inner angles of triangle is 180. given that one angle is 90 degrees the sun of x and w has to be 180-90=90

for the second part, you have to use the triangle exterior angle theorem: an exterior angle of a triangle is equal to the sum of the opposite interior angles. The opposite interior angles in this case is 90 degrees and y

The probability that player B entered the tournament is 3/14.

Given that player, A, who enters a golf tournament, is not certain whether player B will enter. The probability that player B enters is 1/3. Player A has a probability of 1/6 of winning the tournament if player B enters and a probability of 3/4 of winning if player B does not enter the tournament. The question asks to find the probability that player B entered the tournament. To find this probability, we can use Bayes' Theorem which is as follows: P(B|A) = P(A|B) * P(B) / P(A)

Where P(B|A) is the probability that player B entered the tournament given that player A won the tournament P(A|B) is the probability that player A won the tournament given that player B entered the tournament P(B) is the probability that player B entered the tournament P(A) is the probability that player A won the tournament

By substituting the given values in Bayes' theorem, we get: P(B|A) = P(A|B) * P(B) / P(A)P(B|A) = (1/6) * (1/3) / [ (1/6) * (1/3) + (3/4) * (2/3) ]P(B|A) = 3/14Therefore, the probability that player B entered the tournament is 3/14.

The probability that player B entered the tournament is 3/14.

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The given formula f(x) = 440(2)^x/12 is used to determine the frequency of any pitch relative to the A above middle C (A440), where x represents the number of half-steps above or below A440.The correct answer is d) 440•(x square root) 2^12.

The given formula f(x) = 440(2)^x/12 is used to determine the frequency of any pitch relative to the A above middle C (A440), where x represents the number of half-steps above or below A440. To determine the equivalent expression of f(x), we need to simplify the given formula.
First, we can simplify 2^x/12 by using the property of exponents, which states that (a^m)^n = a^(mn). So, we can rewrite 2^x/12 as (2^1/12)^x.
Substituting this value in the given formula, we get f(x) = 440 * (2^1/12)^x.
Now, we can rewrite (2^1/12) as a square root of 2 raised to the power of 1/6. So, the equivalent expression of f(x) is:
f(x) = 440 * (2^1/6)^x = 440 * (x square root) 2^12
Therefore, the correct answer is d) 440•(x square root) 2^12.
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Answer: Compression.

Step-by-step explanation: Shrink means to get smaller. Compression is a synonym of shrink. Compression means the action of being compressed.

The fourth quintile based on the given sample observations is approximately 15.5.

To find the fourth quintile, we first need to arrange the sample observations in ascending order:

-31, 9, 13, 18, 24

The fourth quintile represents the value below which 80% of the data falls. Since we have 5 data points, the fourth quintile is located at the 80th percentile, which can be calculated as:

80th percentile = (80/100) * (n + 1) = (80/100) * (5 + 1) = 4.8

Since the 80th percentile falls between the fourth and fifth observations, we can estimate the fourth quintile by taking the average of these two values:

Fourth quintile ≈ (13 + 18) / 2 = 15.5

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The limit doesn't exist for lim(x,y)→(0,0) [(x² + 3y²)/(2x² + 23y²)]² because the limit along the x-axis and the limit along the y-axis give different values.

To find the limit of lim(x,y)→(0,0) [(x² + 3y²)/(2x² + 23y²)]², we can first simplify the expression inside the parentheses by dividing both the numerator and denominator by y²:

[(x²/y² + 3)/(2(x/y)² + 23)]²

As (x,y) approaches (0,0), both x and y approach 0, so x²/y² approaches 0/0, which is an indeterminate form. To resolve this, we can use L'Hôpital's rule, taking the partial derivative with respect to x and y:

lim(x,y)→(0,0) [(x²/y² + 3)/(2(x/y)² + 23)]²

= [lim(x,y)→(0,0) 2(x/y)² / 4(x²/y²) ]² (using L'Hôpital's rule)

= [lim(x,y)→(0,0) x² / 2y² ]²

= [lim(x,y)→(0,0) (x/y)² / 2 ]²

Since (x,y) approaches (0,0), we have (x/y)² approaching 0/0, another indeterminate form. Using L'Hôpital's rule again, we get:

lim(x,y)→(0,0) (x/y)² / 2

= lim(x,y)→(0,0) 2x / (2y)

= lim(x,y)→(0,0) x / y

Now, we have two paths to consider: approaching along the x-axis (y = 0) and approaching along the y-axis (x = 0). Along the x-axis, the limit is:

lim(x,0)→(0,0) x / 0

which does not exist, since the expression approaches infinity as x approaches 0 from either direction. Similarly, along the y-axis, the limit is lim(0,y)→(0,0) 0 / y which is 0.

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Answer:

I hope it's good enough

Step-by-step explanation:

Talia bought 4 watermelons for her annual watermelon summer party. She also spent an additional 9 dollars on the party supplies. The total amount she spent was less than 30 dollars. Write an equation to represent this word problem in which the amount of money each watermelon was is represented by x.

Answer:

so

box1 = x

box2= 9

Step-by-step explanation:

5(x+9)  

distribute

5(x) + 5(9)

5x + 45

Answer:  360,000

Reason:

Think of 360 as 360.0

We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.

The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.

Answer:

8xy

Step-by-step explanation:

(5xy)-(-3xy)= 5xy+3xy=8xy

Why:

Well if you have 5 of that something and get 3 more of that something you have 8 of that something.

Answer:

8xy

Step-by-step explanation:

5xy--3xy

a - and a - equal a +, so it's 5xy+3xy, which equels 8xy.

The coordinate rule for each point is;

R'(x, y) → (x + 2, y + 1)

S'(x, y) → (x + 2, y - 1)

T'(x, y) → (x + 4, y - 2)

Coordinate plane rules is simply (x, y) → (x ± h, y ± k)

where h and k are the horizontal and vertical shifts.

Thus, the coordinate rule for each point is;

R'(x, y) → (x + 2, y + 1)

S'(x, y) → (x + 2, y - 1)

T'(x, y) → (x + 4, y - 2)

The transformation is (x, y) = (x, y) for Point R

The transformation is (x, -y) = (x, -y) for Points S and T

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Given:

\(f(x)=2x\)

\(g(x)=f(x)+4\)

To find:

The y-intercept of g(x).

Solution:

We have,

\(g(x)=f(x)+4\)

Putting \(f(x)=2x\), we get

\(g(x)=2x+4\)

Substitute x=0 to find the y-intercept of g(x).

\(g(0)=2(0)+4\)

\(g(0)=0+4\)

\(g(0)=4\)

Therefore, the y-intercept of g(x) is at point (0,4). So, the y-intercept of g(x) is 4.