tbh this question confusing the **** outta me​

The average value of function f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

To find the average value of a function f(x) over an interval [a,b], you need to follow these steps:

Calculate the definite integral of the function f(x) over the interval [a,b]. The definite integral will give you the total area under the curve of the function over the interval.

Find the length of the interval [a,b] by subtracting the lower bound a from the upper bound b. The length of the interval will be (b-a).

Divide the value of the definite integral by the length of the interval to get the average value of the function over the interval [a,b]. That is:

Average value of f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

So, the average value of a function over an interval is simply the total area under the curve of the function over that interval divided by the length of the interval.

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y=x+1

or,0=x-y+1 ........... {1}

now...

slope of line..(m1)

= -(coe of x/Coe of y)

=-(1/-1)

=1

hence the slope of line , perpendicular to line y=x+1...

is m1*m2=-1

1*m2=-1

m2 =-1

hence the slope of line perpendicular to liney=x+1... is .. -1

Answer:

m = −1

Step-by-step explanation:

Simplify \(-\frac{1}{-1}\) to find the slope of the perpendicular line.

*My answer has been deleted for no reason.

Answer:

-2(7) + -2(5g)

Step-by-step explanation:

Using the distributive property we can confirm that:

-2(7) + -2(5g) = -2(7+5g)

Answer:

−14−10g

Step-by-step explanation:

First, solve the product:

-2 ⋅ 7 - 2 ⋅ 5g

Multiply -2 times 7 to -14.

So, the equivalent expression would be:

-14 - 2 ⋅ 5g = -14 - 10g

-14 - 10g

To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.

Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100

Count of values = 31

Mean = (Sum of the data set) / (Count of values)

Now we can substitute the values and calculate:

Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31

After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).

Therefore, the mean of the data set is 71.29.

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Answer:

0

Step-by-step explanation:

15-12= 3

3^2 is 9

9-9= 0

To find out how much Kim spent in total with the 8% sales tax included, we first need to add up the cost of all 4 items: $32.45 + $46.78 + $12.91 + $52.38 = $144.52

Next, we'll multiply that total cost by the sales tax rate as a decimal (8% expressed as 0.08) to find out how much tax Kim had to pay: $144.52 x 0.08 = $11.56

Finally, we'll add the total cost of the items and the tax to find out how much Kim spent in total: $144.52 + $11.56 = $156.08

Answer:

5.98°

Step-by-step explanation:

Given

with reference angle 50.1°

perpendicular (p) = x

base (b) = 5

Now

tan 50.1° = p / b

1.195 = x / 5

x = 1.195 * 5

x = 5.98

Hope it will help :)

An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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Answer:

Solving it would turn into these:

(20x+37)/ x- 5

20+ (137/x-5)

Population in 20 years is 2654 .So option(2) is correct

A percentage is a percentage of something expressed as a number between 0 and 100 rather than as a fraction. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

Given that a population of 1000 people were to increase by 5% every year

We have to determine the population be in 20 years

P = 1000

R = 5

T = 20

Population in 20  years = P[(1+(r/100)]t

= 1000[1 + 5/20]20

= 1000(21/20)20

= 1000 x 2.6538

= 2653

Therefore population in 20 years is 2654

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Answer:

B

Step-by-step explanation:

Look at the chart you can find out by looking at 20 then your answers

The new volume of the inflatable ball after the radius becomes half of the original one is 16π.

The original volume of the ball is given as 96π

The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.

The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³

With this the original volume of the ball is

(4/3)π X r³

and the new volume of the ball after it's halved is

V₂ = (4/3)π X (r/2)³

After simplification

V₂ = (4/3)π X (r³/8)

The new volume of the ball is:

V₂ = (1/6) X πr³

So the new volume is (1/6) of the original volume. We can calculate this as

V₂ = (1/6) X 96π

= 16π

Therefore, the new volume of the inflatable ball is 16π.

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Answer:

y=4x-3

Step-by-step explanation:

We're given that the equation is linear (a line), so it must be in the form y=mx+b. We're also given that it contains the points (0,-3) and (1,1).

Plugging the values of the x and y coordinates in that first point, we get the equation -3=m*0+b, simplifying to -3=b. Therefore, the b-value is -3.

Next, we can plug in the values from the second point to get the equation 1=m*1-3, which simplifies to 1=m-3. Adding 3 to both sides, we get m=4. Therefore, the equation of the line is y=4x-3.

Note that -3 is the value where the line intercepts the y-axis, which means -3 is known as the y-intercept. The value of b is always the y-intercept.

The required volume of the sphere is approximately 904.32 cm³

To find the volume of a sphere with a diameter of 12 cm, we need to use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, and r is the radius of the sphere.

Since the diameter is 12 cm, the radius (r) is half of that, which is 6 cm. Now we can plug in the radius value into the formula:

V = (4/3)π(6³)

V = (4/3)π(216)

V = 288π

Now, since π (pi) is approximately equal to 3.14, we can calculate the volume:

V = 288 × 3.14

V ≈ 904.32 cm³

So, the volume of the sphere is approximately 904.32 cm³. None of the provided options match this answer, so it is possible there was an error in the question or answer choices.

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

If f does not attain a maximum value on [a,b], then the function does not attain a maximum value. The option "f does not attain a minimum value on [a,b]" must be true.

A maximum value is the highest value of a function, that is, the largest y-value of a graph. For example, f(x) = x² has a maximum value of infinity because the parabola opens upwards, and its value keeps increasing infinitely. Therefore, the highest value it attains is infinite.

If f does not attain a maximum value, then there is no highest value, meaning that the value of the function increases indefinitely. In that case, there must not exist a minimum value, since the function keeps rising indefinitely without any upper bound. Hence, f does not attain a minimum value on [a,b].

Option C must be true, which is: O f does not attain a minimum value on [a,b].

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Answer:

51/200

Step-by-step explanation:

To write a decimal as a fraction, you have to make the decimal the numerator, and put a multiple of ten with that number of zeroes in the denominator:

0.255 = 255/1000

Then we simplify

51/200

Answer:

I'm pretty sure it's an open circle on 22 pointing to the right

Answer:

It would be h>22. So graph it at 22.

Step-by-step explanation:

Was it correct?? Hope this helps!!

Answer:

its A

Step-by-step explanation:

asymptotes:=-1 and hole:x=4

Answer:

When g(x) = 0, x = -3.

Step-by-step explanation:

g(x) is being represented on the y axis. Paraphrasing, what is the value of x when the line cuts the line y = 0? The intersection of your line and the bold vertical line is at -3.

The statement that a yo-yo has an outer radius of 8cm and an inner radius of 2cm is true.

A yo-yo typically has a circular body with an outer radius and an inner radius where the string attaches. The inner radius is the distance from the center of the yo-yo to where the string is tied, while the outer radius is the distance from the center to the outer edge of the yo-yo. In the case of the yo-yo in question, the inner radius is given as 2cm and the outer radius is given as 8cm.

It is important to note that the difference between the outer and inner radii affects the way the yo-yo behaves during play. The larger the difference between the two radii, the more stable the yo-yo will be during tricks. Additionally, the thickness of the yo-yo body and the weight distribution also play a role in how the yo-yo performs. Overall, the geometry of the yo-yo is an important factor to consider when choosing and using a yo-yo for different types of tricks and styles of play.

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The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

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It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.

The surface integral of a vector field F⃗ over a surface S is given by the formula:

∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)

where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.

In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:

r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗

To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:

n⃗ = ∂r/∂x × ∂r/∂z

= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)

= -2xz i⃗ + 2zj⃗ + 2xk⃗

Now, we can calculate the flux:

∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS

= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS

= ∬S (-6x^2z + 2xz + 6xz^2) dS

To evaluate this integral, we need to determine the limits of integration for x, y, and z.

Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:

0 ≤ y = x^2 + z^2 ≤ 16

Simplifying the inequality, we get:

0 ≤ x^2 + z^2 ≤ 16

From this, we can see that x and z both range from 0 to 4.

Now, we can evaluate the flux:

∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA

where dA is the differential area.

Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.

However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

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Answer:

Division!

Step-by-step explanation:

(1/6) ÷ (3/7)

(1/6)(7/3)

= 7 / 18