The function f is defined as follows
h(x)=-4x^2+6
if the graph of h is translated vertically downward by 5 units, it becomes the graph of function g
FIND THE EXPRESSION FOR G(X)

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side c

Using Pythagoras theorem we have

c² = b² + a²

where

c is the hypotenuse

So we have

\( {c}^{2} = {5}^{2} + {3}^{2} \\ c = \sqrt{ {5}^{2} + {3}^{2} } \\ c = \sqrt{ 25 + 9} \\ c = \sqrt{34} \: \: \: \: \: \: \: \: \\ = 5.83095189...\)

We have the final answer as

Hope this helps you

50%

since 98/2 = 49

Thats it

Answer:

440cm³

Step-by-step explanation:

Area of trapezium base=

\( \frac{1}{2} \times (a + b) \times h\)

\( \frac{1}{2} \times (8 + 14) \times 4\)

\( \frac{1}{2} \times 22 \times 4 \\ = \frac{88}{2} \\ = 44 {cm}^{3} \)

Volume=Area or trapezium x Height between trapezium ends

\( = 44 \times 10 \\ = 440 {cm}^{3} \)

The greatest common divisor of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

To find the greatest common divisor (GCD) of 6, 14, and 21 and write it in the form 6r 14s 21t, we can use the Euclidean algorithm.

Step 1: Find the GCD of 6 and 14.
- Divide 14 by 6: 14 ÷ 6 = 2 remainder 2
- Replace 14 with 6 and 6 with 2: Now we have 6 and 2.
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Since the remainder is 0, the GCD of 6 and 14 is 2.

Step 2: Find the GCD of the result from step 1 (2) and 21.
- Divide 21 by 2: 21 ÷ 2 = 10 remainder 1
- Replace 21 with 2 and 2 with 1: Now we have 2 and 1.
- Divide 2 by 1: 2 ÷ 1 = 2 remainder 0
- Since the remainder is 0, the GCD of 2 and 21 is 1.

Therefore, the GCD of 6, 14, and 21 is 1. In the given form 6r 14s 21t, r would be 0, s would be 0, and t would be 1.

So, the GCD of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

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Answer:

point slope form---> y-2=1/4(x- -8)

slope intercept form---> y=1/4x+4

Step-by-step explanation:

i didnt know which equation you were asking for

Answer:

  f(x) = -x^2 +8x -16

Step-by-step explanation:

With the given data, we can write the factored function as ...

  f(x) = -1(x -4)^2 . . . . . -1 is the leading coefficient; exponent of 2 gives root multiplicity

  f(x) = -x^2 +8x -16

The population variance is approximately 16.41 and the population standard deviation is approximately 4.05. These values indicate the spread or dispersion of the children's ages around the mean age of 7.71 in the given family.

To find the population variance and standard deviation for the ages of children in a family, follow these steps:

Calculate the mean (average) of the ages by adding all the ages and dividing by the total number of children, which is 7 in this case.

Mean = (1 + 3 + 5 + 7 + 8 + 11 + 14) / 7 = 7.71 (approximately)

Calculate the squared difference of each age from the mean.

Find the sum of the squared differences.

Divide the sum by the number of data points (7) to calculate the population variance.

Finally, take the square root of the variance to get the population standard deviation (σ).

After performing the calculations, the population variance is approximately 16.41 and the population standard deviation is approximately 4.05.

These values indicate the spread or dispersion of the children's ages around the mean age of 7.71 in the given family.

The standard deviation measures the average amount by which each age deviates from the mean, providing a useful metric to understand the variability within the age distribution.

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The radius of the circle is 29 cm.  Let's denote the radius of the circle we want to find as r (in cm).

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

The area of the first circle with a radius of 21 cm is A1 = π(21)² = 441π cm².

The area of the second circle with a radius of 20 cm is A2 = π(20)² = 400π cm².

According to the problem, the area of the circle we want to find is equal to the sum of the areas of these two circles:

A = A1 + A2

A = 441π + 400π

A = 841π cm²

Now, we can set up an equation using the formula for the area of a circle:

πr² = 841π

Dividing both sides of the equation by π:

r² = 841

Taking the square root of both sides:

r = √841

Simplifying:

r = 29 cm

Therefore, the radius of the circle is 29 cm.

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Answer: 10 times

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, but I would show how to solve.

Transformation is the movement of a point from its initial location to a new location. Types of transformation is reflection, translation, rotation and dilation.

Dilation is the enlargement or reduction of the size of an object by a factor.

If a point A(x, y) is dilated by a factor k with a center of dilation at (a, b), then the new point is:

A'(x, y) = [k(x - a) + a, k(y - b) + b]

Let us assume that point A(2, 0) dilation with a scale factor of 2 centered at (1, 2). Hence the new point is:

A'(x, y) = [2(2 - 1) + 1, 2(0 - 2) + 2]  = (3, -2)

The initial value problems (a), (b), and (c) have unique solutions defined for all x ≥ 0 based on the Picard-Lindelöf theorem.

a) For the initial value problem y' = sin(x + y + √|y|), y(0) = 0, the existence and uniqueness of solutions can be established using the Picard-Lindelöf theorem.

Since sin(x + y + √|y|) is a continuous function in both variables x and y, and the initial condition y(0) = 0 is well-defined, the theorem guarantees the existence of a unique solution defined for a certain interval around x = 0.

b) For the initial value problem y' = sin(x² + y²), y(0) = 1, the existence and uniqueness of solutions can also be established using the Picard-Lindelöf theorem.

Since sin(x² + y²) is a continuous function in both variables x and y, and the initial condition y(0) = 1 is well-defined, the theorem guarantees the existence of a unique solution defined for a certain interval around x = 0.

c) For the initial value problem y' = 1 + y³/(1 + y²), y(0) = π, the existence and uniqueness of solutions can be established using the Picard-Lindelöf theorem.

Since 1 + y³/(1 + y²) is a continuous function in both variables x and y, and the initial condition y(0) = π is well-defined, the theorem guarantees the existence of a unique solution defined for a certain interval around x = 0.

In all three cases, the solutions are defined for all x ≥ 0 as long as the interval of existence obtained from the Picard-Lindelöf theorem extends to x = 0.

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Answer:

Solution given;

length(L) =6+12=18yd

again

b=√(15²-12²)=9yd

so

breadth (B)=8+9=17yd

since it is a rectangular shape so

perimeter of rectangle=2(L+B)=2(18+17)=70yd

70 yards of fencing materials do they need for the fence

The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8

The solution to the equation is given as

x = 12

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.

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

Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.

Hence, the solution to each of these equations is x = 12.

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Therefore, the probabilities P(X = 1) and P(X = 2) are given by: P(X = 1) = c/4 P(X = 2) \(= (2 - 16c^2)/(64c + 8)\).

To determine the probabilities P(X = 1) and P(X = 2) based on the given cumulative distribution function (CDF) F(x), we need to calculate the difference in probabilities at those specific points.

P(X = 1):

P(X = 1) is the probability that the random variable X takes the value 1. We can calculate this probability by subtracting the CDF values at x = 0 and x = 1:

P(X = 1) = F(1) - F(0)

Substituting the given CDF function:

\(P(X = 1) = (c(1)^2)/(3(1)^2 + 1) - (c(0)^2)/(3(0)^2 + 0)\)

= c/4

P(X = 2):

P(X = 2) is the probability that the random variable X takes the value 2. We can calculate this probability by subtracting the CDF values at x = 1 and x = 2:

P(X = 2) = F(2) - F(1)

Substituting the given CDF function:

\(P(X = 2) = (c(2)^2)/(3(2)^2 + 2) - (c(1)^2)/(3(1)^2 + 1)\)

= (4c)/(16c + 2) - c/4

= (4c - c(16c + 2))/(16c + 2)(4)

\(= (4c - 16c^2 - 2c)/(64c + 8)\)

\(= (2 - 16c^2)/(64c + 8)\)

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Answer:

1 and 3

Step-by-step explanation:

where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.

x = oz of 100% acid

y = oz of 4% acid

the first solution is 100% acid, if the amount of ounces in it is "x", how much only acid is there?  well, (100/100) * x = 1.0x.

likewise, how much only acid is there in the 4% solution?  well, (4/100) * y = 0.04y.

\(\begin{array}{lcccl} &\stackrel{\stackrel{oz}{solution}}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of acid }}{amount}\\ \cline{2-4}&\\ \textit{first solution}&x&1.00&1.0x\\ \textit{second solution}&y&0.04&0.04y\\ \cline{2-4}&\\ mixture&480&0.08&38.4 \end{array}~\hfill \begin{cases} x+y=480\\\\ x+0.04y=38.4 \end{cases}\)

\(x+y=480\implies y=480-x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{x+0.04(480-x)=38.4} \\\\\\ x+19.2-0.04x=38.4\implies 0.96x+19.2=38.4\implies 0.96x=19.2 \\\\\\ x=\cfrac{19.2}{0.96}\implies \boxed{x=20}~\hfill \boxed{\stackrel{480-20}{y=460}}\)

Answer:

\(( - 2) ^{4} \times ( - 3) ^{7} \\ = 16 \times 27 \\ = positive\)

Answer:

Step-by-step explanation:

Use Pythagorean to find the missing side x of the triangle.

It is a hypotenuse with other sides 18 in and half of 15 in:

The perimeter is:

The Solution of -x +y = 84, x + 3y = 12, x - 7y + z = 15 be \(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right]\)

The correct option is (C)

The inverse of matrix is another matrix, which on multiplying with the given matrix gives the multiplicative identity.

Given equation are:

-x +y = 8

4x + 3y = 12

x - 7y + z = 15

So,

\(\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right] \;*\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right]\)

then,

\(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right]\)

Now, Calculating the inverse of Matrix we have,

\(\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \;\) =      \(\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\)

so, \(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \;\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\; \left[\begin{array}{ccc}8\\12\\15\end{array}\right]\)

\(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-12/7\\44/7\\425/7\end{array}\right]\)

 \(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right]\)

Hence ,\(\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right]\)

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To calculate the total number of samples in the sample space when randomly sampling 3 objects in order from among 42 objects, we need to consider the concept of permutations.

A permutation is an arrangement of objects in a specific order. In this case, we are interested in the number of permutations when selecting 3 objects from a pool of 42 objects.

The formula to calculate permutations is given by nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being selected.

In our case, n = 42 (total objects) and r = 3 (objects being selected). Therefore, the total number of samples in the sample space can be calculated as 42P3.

By substituting the values into the formula, we have 42P3 = 42! / (42 - 3)!

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The percentage of U.S. adults with a high school education has risen from 8 percent in 1960 to 35 percent in 2018.

In the early 20th century, education wasn't given much importance, only a few Americans completed high school education. However, after the mid-1900s, things began to change, more and more people started taking an interest in education and slowly, the percentage of U.S. adults with a high school education began to increase. As per data, the percentage of Americans with a high school education rose from 8% in 1960 to 35% in 2018.

This rise was witnessed because of the changes made in education policies, providing free education to everyone, and most importantly, increasing the focus on the importance of education in society. Today, a high school diploma is an essential requirement to acquire good jobs, and it helps a person to become a responsible citizen of the country. Therefore, the U.S. government has made it possible for everyone to attain a good education.

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Work Shown:

n(A only) = number of items inside set A only

n(A only) = 12

n(A and B) = 16

n(B only) = 20

n(A or B) = n(A only) + n(A and B) + n(B only)

n(A or B) = 12 + 16 + 20

n(A or B) = 48

n(Total) = n(A only) + n(A and B) + n(B only) + n(Not A, not B)

n(Total) = 12+16+20+24

n(Total) = 72

P(A or B) = n(A or B)/n(Total)

P(A or B) = 48/72

P(A or B) = 0.67 approximately

The correct statement true about the two points of intersection in Step 3 is,

⇒ They are the same distance from AB.

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

Steps are,

Step 1: Place a compass at A. Use a compass setting that is greater than half the length of AB and draw an arc.

Step 2: Keep the same compass setting. Place the compass at B. Draw an arc.

Step 3: Draw a line through the two points of intersection of the arcs.

Now, Cleary this method is used to divide a line in two equal parts.

Hence, The correct statement true about the two points of intersection in Step 3 is,

⇒ They are the same distance from AB.

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Answer: Can you add a picture

Step-by-step explanation:

The series converges because the limit used in the Ratio Test is satisfied.

To determine whether the series ∑(n=1 to infinity) (n!/(n+4)(n+7)) converges or diverges, we can use the Ratio Test. The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Let's apply the Ratio Test to the given series:

lim(n→∞) |((n+1)!/((n+1)+4)((n+1)+7)) * ((n+4)(n+7))/(n!)|

Simplifying this expression:

lim(n→∞) |(n+1)(n+4)(n+7)/(n+8)(n+11)|

As n approaches infinity, the highest order terms dominate, and we are left with:

lim(n→∞) |n^3 / n^2| = lim(n→∞) |n|

The absolute value of n goes to infinity as n approaches infinity. Since this limit is not less than 1, we cannot conclude that the series converges using the Ratio Test.

Therefore, the correct answer is C. The series converges because the limit used in the Ratio Test is satisfied.

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We have that the equation of the volume of a rectangular prism is:

in this case, we have the following information:

then, using the formula we have:

therefore, the volume of the prism is 60 cm^3

Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).

The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.

To calculate the X-coordinate of the center of gravity, we use the formula:

Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)

Similarly, for the Y-coordinate:

Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)

Substituting the given values:

Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92

Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08

Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.

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The net sales in the department during the month of april is $15960.

Sell-thru perecentage rate = Units sold / Units recieved

In our case:

Net sales = (Sell-thru rate)*(opening inventory)

Net sales = (0.28)*($57000)

= $15960

Net sales refer to the total amount of revenue generated by a company from its primary business operations, minus any returns, allowances, and discounts. This figure reflects the actual revenue earned by a company after accounting for any deductions and is a critical metric for evaluating the financial performance of a business.

Net sales are reported on a company's income statement and are a key component of the top line, which also includes other sources of revenue, such as interest income or gains from the sale of assets. Understanding a company's net sales is essential for assessing its growth potential, profitability, and overall financial health. Investors, creditors, and other stakeholders use net sales as a metric to evaluate a company's ability to generate revenue from its core operations, as well as its ability to compete effectively in its industry.

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