Using the graph, determine the coordinates of the y-intercept of the parabola.

Answer:

Step-by-step explanation:

b^7. b^5 ⇒ b^12

Product Rule says that to multiply two exponents with the same base, you keep the base and add the powers.

b^7 + 5

b^12

-------------------------------------------------------------------------

14x^8/7x^4 ⇒ 2x^4

2 times 7 goes into 14.

Answer:

B

Step-by-step explanation:

Answer:

B) is not a function

Step-by-step explanation:

For an table to be a function the y axis all have to be different from each other but on B it is not, it is only 1, therefore B is not a function

Answer:

Part A is not a rt triangle

Part B is not a rt triangle

Part C is a rt triangle

Step-by-step explanation:

Part A:

290^2 + 696^2 = 750^2

84,100 + 484,416 = 562,500

Add the numbers on the left to see if the 2 sides are equal.

568,516 ≠ 562,500

Part B:

514^2 + 684^2 = 855^2

264,196 + 467,856 = 731,025

Add the numbers on the left to see if the 2 sides are equal.

732,052 ≠ 731,025

Part C:

450^2 + 1080^2 = 1170^2

202,500 + 1,166,400 = 1,368,900

1,368,900 = 1,368,900

The probability that the second ball you draw is gold is 0.619.

What is the probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Here, we have

Given: a room contains several urns 13 urns contain two gold balls, 6 urns contain one gold ball and one silver ball, 20 urns contain two silver balls.

Conditional probability is a measure of the probability of an event occurring given that another event has occurred.

Here given event is that first ball is gold. Hence sample space will have 13+8 = 21 urns.

For second ball to be gold, urn should have 2 gold balls hence it has 13 urns under above condition.

Probability = 13/21 = 0.619

Hence, the probability that the second ball you draw is gold is 0.619.

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To calculate the total number of points for the ride based on the number of favorite votes (x), second favorite votes (y), and third favorite votes (z), we can assign point values to each category and sum them up.

Let's assume the point values are as follows:

Favorite vote: 3 points

Second favorite vote: 2 points

Third favorite vote: 1 point

To calculate the total points, we can use the following expression:

Total points = (3 * x) + (2 * y) + (1 * z)

This expression represents the sum of the points awarded for each category based on the number of votes received.

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Answer:

25.907= 9 terceira casa a direita ( centena), 900.

a. The probability that the time to arrive is more than 22 minutes is 0.0918.

b. The probability that the time to arrive is between 13 and 21 minutes is 0.8164.

Given that, µ = 17 minutes and σ = 3 minutes.

Arrival time is a normal random variable and hence it follows normal distribution.

P(X) ~ N(17, 3)

a. To find the probability that the time to arrive is more than 22 minutes:

z = (X - µ) / σ

z = (22 - 17) / 3

z = 5 / 3

P(Z > 5/3) = 1 - P(Z < 5/3) = 1 - 0.9082 = 0.0918

b. To find the probability that the time to arrive is between 13 and 21 minutes:

z1 = (X1 - µ) / σ

z1 = (13 - 17) / 3

z1 = -4 / 3

z2 = (X2 - µ) / σ

z2 = (21 - 17) / 3

z2 = 4 / 3

P(13 < X < 21) = P(-4/3 < Z < 4/3)

P(-4/3 < Z < 4/3) = P(Z < 4/3) - P(Z < -4/3)

P(Z < 4/3) = 0.9082

P(Z < -4/3) = 1 - P(Z < 4/3) = 1 - 0.9082 = 0.0918

P(-4/3 < Z < 4/3) = P(Z < 4/3) - P(Z < -4/3)

P(-4/3 < Z < 4/3) = 0.9082 - 0.0918 = 0.8164

Note: The question is incomplete. The complete question probably is: The time for an emergency medical squad to arrive at the sports center at the edge of town is distributed as a normal variable with µ = 17 minutes and σ = 3 minutes. Determine the probability that the time to arrive is (a) more than 22 minutes and (b) between 13 and 21 minutes.

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As mining representative, the actions which can be taken to address citizen's concerns are through:

The primary concerns of the people would be the potential environmental impact of the mining activity, so, it is important to engage in open communication with them to address these concerns and inform them about steps being taken to minimize environmental impacts.

This can involve providing regular updates on environmental monitoring and management plans as well as holding public meetings to address concerns and answer questions.

The company will also implement measures to mitigate environmental impacts like using best available technologies to reduce emissions and waste, reclaiming and restoring mined land and minimizing water usage.

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Answer:

392in²

Step-by-step explanation:

Bottom = 6x10=60

Back = 10x6=60

Front = 10x6 + 4x4=76

Back = 76

6x4=24

6x4=24

6x6=36

6x6=36

392 Total

a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools The U.S. Population Census is an example of a census

Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.

Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.

The primary objective of population census is to know the total size of the population of a country.

Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.

In conclusion, the U.S. population census is the only example of census.

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Answer:

The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.

Step-by-step explanation:

It's possible because they cut cakes into different number of slices.

You know that Luke, Kira and Ali each served \(\frac{2}{3}\) of their own cake and Luke served 4 slices, Kira served 6 slices and Ali served 8 slices.

Being x the whole slices of cake, and if Luke served \(\frac{2}{3}\) of his cake, which are 4 slices, the whole slices of cake of Luke is:

\(\frac{2}{3}*x=4 slices\)

Solving:

x= 4 ÷\(\frac{2}{3}\)

x= 6

Then, whole slices of Luke's cake is 6.

Performing the same approach for Kira you get:

\(\frac{2}{3}*x=6 slices\)

x= 6 ÷\(\frac{2}{3}\)

x= 9

Then, whole slices of Kira's cake is 9.

Finally, performing the same approach for Ali you get:

\(\frac{2}{3}*x=8 slices\)

x= 8 ÷\(\frac{2}{3}\)

x= 12

Then, whole slices of Ali's cake is 12.

The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.

Answer: A

Step-by-step explanation

2.167x10^4 = 21,670

                   = 9,978

1.1x10^6      = 1100,000

                   = 56,344,000

2.468x10^5 =  246,800

Answer: A. 9,978

Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)

2.167 × 10^4 = 21670

1.1 × 10^6 = 1100000

2.468 × 10^5 = 246800

Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.

a. The equation representing the water level L(x) (in ft), x days after January 1 is L(x) = 2.5 - 0.015x.

b. The inverse function for \(L^{-1}\) (x) is x = (2.5 - L)/0.015.

a. The function representing the water level L(x) (in ft), x days after January 1 can be written as:

L(x) = 2.5 - 0.015x

where x is the number of days after January 1.

b. To write an equation for \(L^{-1}\)(x), we need to find an expression for x in terms of L.

L(x) = 2.5 - 0.015x

0.015x = 2.5 - L

x = (2.5 - L)/0.015

Therefore, the equation for \(L^{-1}\)(x) is:

\(L^{-1}\)(x) = (2.5 - x)/0.015

This equation gives the number of days (x) required for the water level to reach a certain level (L).

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The question is -

Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day.

a. Write a function representing the water level L(x) (in ft), x days after January 1.

b. Write an equation for L^{-1} (x).

The additive identity property, we know that for any vector v, v + 0 = v. Applying this property, we get:

0 = 0u

To prove theorem 6.1(a), which states that 0u = 0, where 0 represents the zero vector and u is any vector, we will use the axioms and properties of vector addition and scalar multiplication.

Proof:

Let 0 be the zero vector and u be any vector.

By definition of scalar multiplication, we have:

0u = (0 + 0)u

Using the distributive property of scalar multiplication over vector addition, we can write:

0u = 0u + 0u

Now, we can add the additive inverse of 0u to both sides of the equation:

0u + (-0u) = (0u + 0u) + (-0u)

By the additive inverse property, we know that for any vector v, v + (-v) = 0. Applying this property, we get:

0 = 0u + 0

Now, let's subtract 0 from both sides of the equation:

0 - 0 = (0u + 0) - 0

By the additive identity property, we know that for any vector v, v + 0 = v. Applying this property, we get:

0 = 0u

Hence, we have proved that 0u = 0.

Therefore, theorem 6.1(a) holds true.

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Answer:

proportional

Step-by-step explanation:

as x increases y increases

Answer:

The solution to the system is (1.8, 7.6)

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.

Plot the lines:

y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.

y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.

Find the intersection point:

To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.

Substitute x from y = 2/3x + 4 into y = -x + 1:

-x + 1 = 2/3x + 4

Multiplying both sides by -3, we get:

3x - 3 = -2x - 12

Adding 2x to both sides, we get:

5x - 3 = -12

Adding 12 to both sides, we get:

5x = 9

Dividing both sides by 5, we get:

x = 1.8

Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:

y = 2/3x + 4

y = 2/3 * 1.8 + 4

y = 3.6 + 4

y = 7.6

So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.

Answer:

(D) 6yr

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

Two angles are complimentary angles when their sum is 90°.

Let the complement of 60° be x.

→ 60° + x = 90°

→ x = 90° – 60°

→ x = 30°

Therefore, the complement of 60° is 30°.

The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

What is sampling distribution ?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.            

                         It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given,

Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.

Simulation A will consist of 1500 trials with a sample size of 100.

Simulation B will consist of 2000 trials with a sample size of 50.

Center for Simulation A and Simulation B will be roughly equal.  

Overall Sample size of Simulation A will be

  = 1500 * 100  = 150000

Overall Sample size of Simulation B will be

 = 2000 *  50  =  100000

Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

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The complete question is -

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

A power series representation for the function f(x) =\(x/36 + x^2\) is  Σ((1/36) * \(x^n\)) from n=1 to infinity + Σ\((x^{(2n)})\) from n=0 to infinity and its interval of convergence is -1 < x < 1.

To find a power series representation for f(x), we'll rewrite it as a sum of power series:

f(x) = \(x/36 + x^2\)
f(x) = (1/36) * \(x + x^2\)
f(x) = Σ((1/36) * \(x^n\)) from n=1 to infinity + Σ\((x^{(2n)})\) from n=0 to infinity

Now let's find the interval of convergence for the given power series. We'll use the Ratio Test:

For the first power series, let a_n = (1/36) * \(x^n\):
lim (n→∞) (|a_(n+1)/a_n|) = lim (n→∞) (|\((x^{(n+1)\))/(36 * \(x^n\))|) = |x|/36

For the second power series, let b_n = \(x^{2n\):
lim (n→∞) (|b_(n+1)/b_n|) = lim (n→∞) \((|(x^{(2(n+1)}))/(x^{(2n)})|) = |x|^2\)

The interval of convergence is where both series converge. The first series converges when |x|/36 < 1, or -36 < x < 36. The second series converges when \(|x|^2\) < 1, or -1 < x < 1. Therefore, the interval of convergence for f(x) is:

-1 < x < 1

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Answer: I THINK it’s A

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The minimum surface area of the container is approximately 275.52 cm².

Let's suppose that the length, width, and height of the rectangular container are l, w, and h, respectively. We know that the container has a square base, so l = w. Also, we know that the volume of the container is 864 cm³, so we have:

l × w × h = 864

Since l = w, we can write this as:

l² × h = 864

We want to minimize the surface area of the container, which consists of the area of the base (l²) and the area of the four sides (2lh + 2wh). We can express the surface area in terms of l and h:

Surface Area = l² + 2lh + 2wh

Using the equation l² × h = 864, we can solve for h in terms of l:

h = 864 / (l²)

Substituting this into the equation for the surface area, we get:

Surface Area = l² + 2l(864 / l²) + 2w(864 / (lw))

Simplifying and using l = w, we get:

Surface Area = 2l² + 1728/l

To find the minimum surface area, we can take the derivative of this expression with respect to l, set it equal to zero, and solve for l:

d/dl (2l² + 1728/l) = 4l - 1728/l² = 0

4l = 1728/l²

l³ = 432

l = ∛432 ≈ 8.77 cm

Since the container has a square base, the length and width are both 8.77 cm. Using the equation l² × h = 864, we can solve for h:

h = 864 / (8.77)² ≈ 10.85 cm

Therefore, the minimum surface area of the container is:

Surface Area = 2(8.77)² + 2(8.77)(10.85) ≈ 275.52 cm²

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If they work together, they will take 14.3 min to shovel the parking lot.

Provided to us :

time taken by Sebastian to shovel the parking lot = 50 min

time taken by Clair to shovel the parking lot = 20 min

both are doing the same work , so we take work as 1

Now , rate of doing work = work / time

Sebastian's rate of doing work = 1 /50

Clair's rate of doing work =  1/20

If they work together , the rate of doing work will

become = 1/50 + 1/20 = 7/100

So, the time for both to do the same work together will be

time = work / rate

time = 1 / (7/100)

time = 100/7

time = 14.3 minutes

So the time taken by both to work together and clear the parking lot will be 14.3 minutes.

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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The steps of finding mean and standard deviation of a simple random sample are given below.

What is standard deviation and mean?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.

The steps of finding mean and standard deviation of a simple random sample are:

Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX):  = σ/n.

How to determine sample means

Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...

Sum divided by the quantity of samples.

The outcome is the mean.

To determine the variance, use the mean.

To determine the standard deviation, use the variance.

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Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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By solving the given equation f(x) = \(x^{2} +3x-40\), the zeroes are -3 and 5.

To solve the given equation we have to do the factorization.

What is factorization: Factorization is the method of writing numbers as the product of their factors or divisors.  In other words, we can say finding what to multiply together to get an expression.

To do the factorization, we have to follow the steps as shown below:

 \(x^{2} +3x-40\) \(= 0\)

\(-40 = 8 * -5\\\)                        [ multiplication of 8 and -5 is -40]

\(x^{2}+8x-5x -40\) \(= 0\)

\(x(x+8) -5(x+8)\) \(= 0\)

\((x-5)(x+8)\) \(= 0\)

\(x = 5\)   and  \(x = -8\)              [ The roots or zeroes]

From the above solution, we can conclude that the zeros of the given function \(x^{2} +3x-40\) are 5 and -8.

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By taking the quotient between the area and the width, we conclude that the height is 16 inches.

Remember that for a rectangle of height H and width W, the area is given by the simple formula:

A = H*W

Here we know that:

A = 144 in^2

W = 9 in

Now, we can replace these in the area equation, and then solve it for H, so we can get the height of our rectangle.

We will get:

A = H*W

H = A/W

H = (144 in^2)/(9 in) = 16in

In this way, we can conclude that the height of our rectangle is equal to 16 inches.

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The mass of a lamina with a mass density function p(x, y) = |x - yl|, where l is a constant, occupying the unit disc D, is determined. The unit disc is defined as D = {(x, y) | x² + y² ≤ 1}.

To determine the mass of the lamina, we need to integrate the mass density function p(x, y) over the unit disc D. The unit disc is defined as D = {(x, y) | x² + y² ≤ 1}.

Using polar coordinates, we can express the integral as follows:

M = ∫∫D p(x, y) dA

Converting to polar coordinates, x = rcos(θ) and y = rsin(θ), and the Jacobian determinant is r. Therefore, the integral becomes:

M = ∫∫D |rcos(θ) - rsin(θ)*l| * r dr dθ

We evaluate this double integral over the region D using appropriate limits for r and θ. The result will give us the mass of the lamina.

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