If f(x) = x^2 + 10 and g(x) = x + 9, find (g•f)(-3).

Answer:

The lowest score was 80, because no student had gotten that grade.

7 students scored higher than 85.

The highest score there was, was 70, cause 4 student got that for a grade.

The range is 3, because the highest amount of studnets was 4 and the lowest was 1.

4 - 1 = 3

Step-by-step explanation:

Hope this helps! =D

An even number of data values will always have two middle numbers, and an odd number of data values will always have one middle value. Therefore, the true statements are:

An even number of data values will always have two middle numbers.

An odd number of data values will always have one middle value.

What is even number?

An even number is an integer that is divisible by 2, i.e., when divided by 2, the remainder is 0. Examples of even numbers are 2, 4, 6, 8, 10, 12, etc.

The statement "an even number of data values will always have two middle numbers" is true. When there is an even number of data values, there is no single middle number because there are two values in the center.

For example, in the set {1, 2, 3, 4}, the middle numbers are 2 and 3. In general, if there are an even number of data values, the middle two values are found by taking the average of the two values in the center of the set. This is different from the case when there is an odd number of data values, where there is a single middle value.

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Answer:

B. Decreasing

Step-by-step explanation:

From the table, we can see that as variable x increases, variable y decreases relatively.

If the data points are plotted on a scatter plot, the trend line would be sloping downwards from our left to our right. This shows that the trend line is decreasing because the sloping downwards from the left to the right shows implies a decrease.

Answer:

this answer is attached to the picture

Radical function or values are values inside the square root. This shows that the cube root of the given value is 3

Radical function or values are values inside the square root. For instance;

√a is a radical function.

According to the law of indices

a^1/3 = ∛a

Given the expression

27^1/3 = ∛27

∛27 = 3

This shows that the cube root of the given value is 3

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Answer:

72.00 =105.6

Step-by-step explanation:

i searched it up

Answer:

If she bought 2lbs of almonds, she bought 0.4lbs of raisins. If she bought  1lb of almonds, she can buy up to 2.36lbs of raisins. If she bought 0.64lbs of almonds, she can buy up to 1.9lbs of almonds.

Step-by-step explanation:

The total pounds of raisins bought  is 0.47 pounds.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Priya bought 0.47 pounds of raisins, Almonds cost is $5.20 per pound and Raisins cost $2.75 per pound.

The Total cost of almonds purchased = $5.20a

The Total cost of raisins purchased = $2.75r

Where:

a = total pounds of almonds bought

r = total pounds of raisins bought

The Total amount spent on raisins and almonds;  

5.20a +2.75r = 11.70

If 2 pounds of almonds are bought;

5.20(2) +2.75r = 11.70.

10.40 + 2.75r = 11.70

Combine similar terms;

2.75r = 11.70 - 10.40

2.75r = 1.30

Now Divide both sides of the equation by 2.75

r = 0.47 pounds

Hence, the total pounds of raisins bought  is 0.47 pounds.

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Answer:

A. (-7,-3)

D.(-3,-7) If clockwise

Answer:

No b/c the hypotenuse is too long

Step-by-step explanation:

17² + 25² = 36²

289 + 625 = 1296

914 ≠ 1296

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

X-intercept: (-0.2,0)

Step-by-step explanation:

y=15x+3

I don't know how to show a graph but what you do is start by plotting (0,3) and go up 15 and over 1 to form a line (because the slope is 15).

To find the x-intercept, replace y with 0 and solve for x.

0=15x+3

-3=15x

-3/15

-1/5 (or -0.2)

(-0.2,0)

Substituting a cumulative area of 0.2420, a mean of 0, and a standard deviation of 1 into the inverse normal distribution, the z-score is -0.71 to two decimal places.

Given that the cumulative area of 0.2420, a mean of 0, and a standard deviation of 1, the required z-score has to be determined.We know that the standard normal distribution with mean 0 and standard deviation 1 is denoted as N(0, 1). The inverse normal distribution with a cumulative area of x is the inverse of the normal distribution with cumulative area x. Let z be the z-score corresponding to a cumulative area of x, then we can say that P(Z ≤ z) = x, where P is the cumulative distribution function of the standard normal distribution.

Substituting the given values in the formula, we get:0.2420 = P(Z ≤ z)We need to find the corresponding z-value using inverse normal distribution. Therefore, we take the inverse of the cumulative distribution function, as follows:z = invNorm(0.2420)z = -0.71 (rounded to two decimal places)Thus, the required z-score is -0.71.

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Let's calculate the probability of winning a single game first. The die has 8 faces, and the game is won if a seven or an eight is rolled. Out of the 8 possible outcomes, 2 are favorable (seven and eight), so the probability of winning a single game is 2/8 or 1/4.

Now, we need to calculate the probability of winning exactly two or four times out of five games. We can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

For winning exactly two times:

P(X = 2) = C(5, 2) * (1/4)^2 * (3/4)^(5-2)

For winning exactly four times:

P(X = 4) = C(5, 4) * (1/4)^4 * (3/4)^(5-4)

Finally, we can sum up the probabilities of winning exactly two times and exactly four times to get the overall probability:

P(Two or Four Wins) = P(X = 2) + P(X = 4)

By calculating these probabilities, we can determine the probability that someone wins two or four times out of five games in the given party game.

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Answer:

Answer B is correct

Step-by-step explanation:

This is a trapezium.

The formula to find the area of a trapezium is,

1/2 ( Sum of the parallel sides ) × height

Let us find it now.

\(\sf \frac{1}{2}*(38+18)*16 \\\\\sf \frac{1}{2}*56*16 \\\\\sf \frac{1}{2}*896\\\\448cm^2\)

The area of the smaller sector or minor sector is  125.66 yd².

The area of the larger sector or major sector is  326.73 yd².

The areas of the minor and major sectors is calculated by applying the following formulas follow;

Area of sector is given as;

A = (θ/360) x πr²

where;

The area of the smaller sector or minor sector is calculated as follows;

A = ( 100 / 360 ) x π ( 12 yd)²

A = 125.66 yd²

The area of the larger sector or major sector is calculated as follows;

θ = 360 - 100

θ = 260⁰

A =  ( 260 / 360 ) x π ( 12 yd)²

A = 326.73 yd²

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The given initial-value problem x^2(dy/dx) = y - xy, y(-1) = -5 can be solved using separation of variables. After integrating both sides and using the initial condition, the explicit solution is y(x) = -5e^(-1/2)e^(-1/x - 1/2).

To find an explicit solution of the given initial-value problem x^2(dy/dx) = y - xy, y(-1) = -5, we can use separation of variables.

First, we can rewrite the equation as:

dy/dx = (y/x) - (1/x^2)y

Next, we can separate the variables by bringing all the y terms to one side and all the x terms to the other:

dy/(y/x - (1/x^2)y) = dx/x

Now, we can integrate both sides:

ln|y/x - (1/x^2)y| = ln|x| + C

where C is the constant of integration.

We can simplify the left side by using the logarithmic property of subtraction:

ln|xy^(-1) - x^(-2)y| = ln|x| + C

Taking the exponential of both sides gives:

|xy^(-1) - x^(-2)y| = e^(ln|x|+C) = Ce^ln|x| = C|x|

where C is now just a positive constant.

Since we are given the initial condition y(-1) = -5, we can plug in x = -1 and y = -5 to find the value of C:

|-1(-5)^(-1) - (-1)^(-2)(-5)| = C|-1|

C = 20/3

So, the explicit solution of the given initial-value problem is:

|xy^(-1) - x^(-2)y| = (20/3)|x|

Note that since we took the absolute value of both sides, the solution actually consists of two functions:

xy^(-1) - x^(-2)y = 20/3x or xy^(-1) - x^(-2)y = -20/3x
To find the explicit solution for the given initial-value problem, x² dy/dx = y - xy, y(-1) = -5, we need to first solve the differential equation and then use the initial condition to find the specific solution.

1. Rewrite the given equation in the form of a separable equation:
x² dy/dx + xy = y
dy/y = (1 - x) dx/x²

2. Integrate both sides of the equation:
∫(1/y) dy = ∫(1 - x) dx/x²

3. Perform the integration:
ln|y| = -1/x - 1/2 + C (using the property of logarithms)

4. Solve for y:
y = Ae^(-1/x - 1/2) (where A = e^C)

5. Apply the initial condition y(-1) = -5:
-5 = Ae^(1 - 1/2)
-5 = Ae^(1/2)

6. Solve for A:
A = -5e^(-1/2)

7. Plug A back into the equation to get the explicit solution:
y(x) = -5e^(-1/2)e^(-1/x - 1/2)

This is the explicit solution for the given initial-value problem.

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Answer: i think it is either A B C or D

Step-by-step explanation: So i know that there are 4 answers so that means one of the four answers are correct........ well i hope that one is correct

The description of the transformation of z on the complex plane that gives the product of and is to scale by a factor of 4, then rotate counterclockwise by /6 radians.

To understand this transformation, let's break it down into its components. Scaling by a factor of 4 means multiplying by 4. This scales the magnitude of by a factor of 4 but does not change its direction. Next, rotating counterclockwise by /6 radians means rotating around the origin by an angle of /6 in the counterclockwise direction. By performing these two transformations in succession, we first scale by a factor of 4, which stretches or compresses it depending on whether it is inside or outside the unit circle, respectively. Then, we rotate counterclockwise by /6 radians, which changes its angle in the counterclockwise direction by /6 radians.

The resulting transformation gives the product of and because scaling and rotation are commutative operations when applied to complex numbers. The order in which the transformations are performed does not affect the result. Therefore, scaling by a factor of 4, then rotating it counterclockwise by /6 radians, will yield the same result as scaling by a factor of 4, then rotating it counterclockwise by /6 radians.

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Answer:

This is so cool.

Step-by-step explanation:

Oh my god.

A

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

Answer:

The fraction 3/10 is a rational number. All fractions are rational numbers.

The result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

To calculate log4 57 to the nearest thousandth, we can use a scientific calculator or a logarithmic table.

Using a calculator, we can find the logarithm of 57 to the base 4 directly:

log4 57 ≈ 3.682

Therefore, the correct answer is option C: 3.682.

If you prefer to verify the result using logarithmic properties, you can do so as follows:

Let's assume log4 57 = x. This means \(4^x\) = 57.

Taking the logarithm of both sides with base 10:

log (\(4^x\)) = log 57

Using the logarithmic property log (\(a^b\)) = b \(\times\) log a:

x \(\times\) log 4 = log 57

Dividing both sides by log 4:

x = log 57 / log 4

Using a calculator to evaluate the logarithms:

x ≈ 3.682

Thus, the result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

width = 40 feet, length = 90 feet

Step-by-step explanation:

length = 2w + 10

width = w

Perimeter = 260

Perimeter of rectangle = 2length + 2width

Sub the values into that equation:

260 = 2(2w + 10) + 2(w)

260 = 4w + 20 + 2w

260 = 6w + 20

260 - 20 = 6w

240 = 6w

w = 240/6

w = 40

So now we know the width of the garden is 40 feet.

To find the length, substitute the width into the length equation:

length = 2w + 10

length = 2(40) + 10

length = 90 feet

length = 90 feet, width = 40 feet

Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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Answer:

bedroom is 12ft which is equal to 6ft on left of bathroom if we add 6 +6=12 because it is rectangle and bathroom is square and square have 4 equal sides so both sides are 12ft

============================================

Explanation:

These are state abbreviations

Since the given sequence is "AL, AK, AZ, AR, CA", and the states are listed alphabetically so far (in terms of the two letter abbreviations), then the next two would be CO and CT in that order.

The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.

The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.

The distance of the ship from the lighthouse = 50 miles

Bearing of the lighthouse from the ship = N 30° W

The direction in which the ship travels = due east

The new bearing to the lighthouse = N 40° W

In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;

m∠A = 30° + 90° = 120°

m∠B = 90° - 40° = 50°

Therefore; m∠C = 180° - (120° + 50°) = 10°

Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°

The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°

The law of sines indicate that we have;

\(\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}\)

50 × sin(120°) = The new distance of the lighthouse × sin(50°)

The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53

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Answer:

Step-by-step explanation:

A. C. np

Answer:

I think 10

Step-by-step explanation:

Answer:

John is 9

Step-by-step explanation:

(9*3)-5=22+9=31

Answer:

sandwiches n[S]=4

drinksn[D]=3

desserts[d]=2

total n[T]=9

number of possible choices for:

4 sandwiches=n[S]/n[T]=4/9

For

3 drinks=n[D]/n[T]=3/9=1/3

and

For 2 desserts=n[d]/n[T]=2/9