a unit vector that points in the direction of the vector −4i+7j can be written as

The dot plot that would be a representative sample of the population is the third dot plot (option c).

A sample is a fraction of the population being studied; due to this, samples are expected to be representative, which means they should reflect the general trends or behaviors in the population. Due to this, it is expected a representative dot plot shows the most common number of books are 4 and 7 and there are no students who read 9 books per month.

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The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°.

A'(0, 0)

B'(-5, -2)

C'(-5, 5)

D'(0, 3)

From the graph we can write the coordinates of ABCD as

A(0, 0),

B( 5, 2)

C(5, -5)

D(0, -3)

Now, the rule for 180 degree rotation is

(x, y) -> (-x, -y)

So, the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°.

A(0, 0) -> A'(0, 0)

B( 5, 2) -> B'(-5, -2)

C(5, -5) -> C'(-5, 5)

D(0, -3) - >D'(0, 3)

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The measure of the angle of the circle is ∠STR = 224°

Given data ,

Let the measure of the central angle be ∠STR

Now , the measure of the arc angle = 112°

And , Central Angle = 2 x Angle in other segment

So , on simplifying , we get

m∠STR = 2 ( 112 )°

m∠STR = 224°

Hence , the measure of angle is 224°

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The average of the points A, B and C with weights 1, 1 and 1

respectively is: (-5/3, -2)

A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.

Thus:

Weighted average = [(w₁ × x₁) + (w₂ × x₂) + (w₃ × x₃)]/(w₁ + w₂ + w₃)

Where:

w_i is the weight of the ith point

x_i is the coordinate of the ith point.

Thus:

x-coordinate = [(1 × -4) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

x-coordinate = -5/3

y-coordinate = [(1 × -5) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

y-coordinate = -2

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The maximum number of taffy Nadia can buy is 11.

As per the question,

Nadia spends 7 x $0.55 = $3.85 on bags of chips.

She has $8.00 - $3.85 = $4.15 left to spend on taffy.

Now, divide the amount of money she has left by the cost of each taffy to find the maximum number of taffy Nadia can buy:

= $4.15 ÷ $0.35

= 11.857, which rounds down to 11.

Therefore, the maximum number of taffy she can buy is 11.

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Answer:

what’s the company’s profit if each sign sold is $20?

Answer:

Step-by-step explanation:

x+y=15

2x+3y=34

The total area of the playing area, including the minimum free zone of 2 meters around it, is 164 square meters.

To calculate the area of a square, we simply need to multiply the length of one side by the length of another side. In this case, we can use the formula:

Area of a square = length x width

Since all sides of a square are equal, we can also use the formula:

Area of a square = side x side

So, the area of the playing area would be:

Area of the playing area = 8 meters x 8 meters

Area of the playing area = 64 square meters

The strip of land around the playing area is also a square, but with sides that are 2 meters longer than the sides of the playing area square. This means that each side of the strip of land square is 10 meters long (8 meters + 2 meters). To calculate the area of the strip of land square, we can use the same formula as before:

Area of the strip of land square = 10 meters x 10 meters

Area of the strip of land square = 100 square meters

Now we can calculate the total area of the playing area by adding the area of the strip of land square to the area of the playing area square:

Total area of the playing area = Area of the playing area square + Area of the strip of land square

Total area of the playing area = 64 square meters + 100 square meters

Total area of the playing area = 164 square meters

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Complete Question

The playing area is a square measuring 8 meters by 8 meters with a two (2) meters minimum free zone around it.

Find the total area of the playing area.

Answer: y = -3x^2 + 24x - 45

Step-by-step explanation:

To find the equation of the parabola with a vertex of (4, 3) and passing through points (2, -9) and (5, 0), we can use the vertex form of a parabolic equation:

y = a(x - h)^2 + k

Here, (h, k) is the vertex of the parabola. So, we have:

y = a(x - 4)^2 + 3

Now, we need to find the value of 'a' using the two points (2, -9) and (5, 0).

First, let's plug in the point (2, -9):

-9 = a(2 - 4)^2 + 3

-9 = a(-2)^2 + 3

-9 = 4a + 3

Subtract 3 from both sides:

-12 = 4a

Now, divide both sides by 4:

a = -3

Now that we have the value of 'a', we can plug it back into the equation:

y = -3(x - 4)^2 + 3

This is the equation of the parabola in vertex form. To convert it to standard form, we can expand the equation:

y = -3(x^2 - 8x + 16) + 3

y = -3x^2 + 24x - 48 + 3

Now, combine the constants:

y = -3x^2 + 24x - 45

This is the equation of the parabola in standard form.

The area of the triangle JTR is 1/2x² + 7/2x + 5 square units

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

Base = x + 5

Height = x + 2

The area of the triangle is calculated as

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * (x + 5) * (x + 2)

So, we have

Area = 1/2 * (x² + 7x + 10)

This gives

Area = 1/2x² + 7/2x + 5

Hence, the area is 1/2x² + 7/2x + 5

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Answer:

The answer for Length is D

110m

Step-by-step explanation:

P=2L+2W

L=20+W

400=2(20+W)+2W

400=40+2W+2W

C.L.T

400-40=4W

360=4W

divide both sides by 4

4W/4=360/4

W=90m

L=20+W

L=20+90

L=110m

Answer:7,947 gallons

Step-by-step explanation:

Jim can alone finish painting fence in 6 hours, is the required answer of the word problem.

The given question is a word problem which can calculated as,

Tom and Huck paints a fence for four hours.

If Jim had not helped them to finish the work it would have taken Tom and Huck 5 more hours to finish.

That is, in (4+5)hours = 1 (total work)

⇒ in 9 hours = 1 (total) work is done

⇒ in 1 hour = 1/9 work is done

After Jim helped Tom and Huck after 4 hours they finished the work in 2 more hours.

That is, in 6 hours they did the total work.

Total work done by jim is = 1 - (4/9)

Since, Tom and Huck had already worked for 4 hours before Jim.

Thus. Work done by jim is 5/9 in two hours along with tom and Huck.

Work done by three of them in  1 hour is  = 5/9*2 = 5/18

Therefore, work done by Jim in 1 hour = Work done by three of them in 1 hour - Work done by Tom and Huck in one hour

= 5/18 - 1/9

= 1/6

Thus, Jim can alone finish the total work in 6 hours.

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To find the zeros of the equation:

2 = x^2 - 10x

we first need to rearrange the equation into standard quadratic form:

x^2 - 10x - 2 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -10, and c = -2.

Substituting these values, we get:

x = (-(-10) ± sqrt((-10)^2 - 4(1)(-2))) / 2(1)

Simplifying inside the square root:

x = (10 ± sqrt(100 + 8)) / 2

x = (10 ± sqrt(108)) / 2

x = (10 ± 6√3) / 2

x = 5 ± 3√3

Therefore, the zeros of the equation are:

x = 5 + 3√3 and x = 5 - 3√3

Answer:

A

Step-by-step explanation:

Which comparison is true?

A 2.919 > 2.94

B 0.99 <0.569

C 1.27> 1.189

D 3.861 < 3.75

Answer:

Step-by-step explanation:

Given a right triangle with an acute angle marked θ next to a side marked 7 and opposite a side marked 8, you want the primary trig function values for angle θ.

The hypotenuse of the triangle can be found using the Pythagorean theorem:

  c² = a² +b²

  c² = 7² +8² = 113

  c = √113 . . . . length of the hypotenuse

You are reminded of the side length ratios for the different trig functions by the mnemonic SOH CAH TOA.

  Sin = Opposite/Hypotenuse

  sin(θ) = 8/√113

  Cos = Adjacent/Hypotenuse

  cos(θ) = 7/√113

  Tan = Opposite/Adjacent

  tan(θ) = 8/7

__

Additional comment

If you are required to "rationalize the denominator", then you need to replace 1/√113 with (√113)/113.

<95141404393>

Answer:

  746.0 feet

Step-by-step explanation:

You want to know the horizontal distance to a lighthouse if the angle of elevation to the 145-ft high beacon is 11°.

The tangent ratio is useful for solving this problem. It tells you ...

  Tan = Opposite/Adjacent

  tan(11°) = (145 ft)/(distance)

Solving for distance, we get ...

  distance = (145 ft)/tan(11°) ≈ 746.0 ft

The ship's horizontal distance from the lighthouse is 746.0 feet.

<95141404393>

A graph of the function represented by [tex]y=\sqrt[3]{x-2}[/tex] for the domain -6 ≤ x ≤ 10 is shown in the image attached below.

In Mathematics, a cubic function is sometimes referred to as a cubic polynomial and it can be defined as a type of polynomial in which the degree of the highest term (coefficient or exponent) is equal to three (3).

In this context, we can reasonably infer and logically deduce that a graph that represents the parent cubic function was shifted by 2 units to the right in order to create or produce the transformed cubic function [tex]y=\sqrt[3]{x-2}[/tex].

In conclusion, we would use an online graphing calculator to plot the graph of the given cubic function [tex]y=\sqrt[3]{x-2}[/tex] over the interval -6 ≤ x ≤ 10 as shown below.

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I agree with Andre. There are only two unique bases, not seven different faces as Noah suggests.

Both bases are the same, so you only need to calculate their area once and double it.

The other five rectangles have the same height, meaning you can calculate their areas more efficiently.

Noah's approach of finding the area of seven different faces is unnecessary and overcomplicates the problem.

Thus, I agree with Andre because his process is correct and more straightforward.

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The distance from the midpoint of AB to the midpoint of AC is equal to: D. √37.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

For line segment AB, we have:

Midpoint of AB = [(-6 - 8)/2, (6 - 2)/2]

Midpoint of AB = [-14/2, 4/2]

Midpoint of AB = [-7, 2].

For line segment AC, we have:

Midpoint of AC = [(-6 + 4)/2, (-4 + 6)/2]

Midpoint of AC = [-2/2, 2/2]

Midpoint of AC = [-1, 1].

In Mathematics and Geometry, the distance between two (2) endpoints that are on a coordinate plane can be calculated by using the following mathematical equation (formula):

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-1 + 7)² + (1 - 2)²]

Distance = √[6² + 1²]

Distance = √[36 + 1]

Distance = √37 units.

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Based on the sample of three sharks measured, we do not have sufficient evidence to support the marine biologist's claim.

To test marine biologists' claims that great white sharks off the coast of Bermuda grow longer than the known average length of 21 feet, a one-sample t-test can be performed.

First, we need to set the null and alternative hypotheses. Let μ be the true average length of a great white shark off Bermuda.

H0:

μ = 21 (true mean length equals 21 feet)

teeth:

μ > 21 (true average length greater than 21 feet)

You can then compute the sample mean and sample standard deviation of the three measured sharks.

x = (24 + 20 + 23) / 3 = 22.33 feet

[tex]s = sqrt(((24-22.33)^2 + (20-22.33)^2 + (23-22.33)^2) / 2) = 1.53 feet[/tex]

You can use the t-test formula to calculate the t-statistic.

t = (x- μ) / (s / sqrt(n)) = (22.33 - 21) / (1.53 / sqrt(3)) = 2.21

This test has n-1 = 2 degrees of freedom.

Using the t-table or the 2 Degrees of Freedom Calculator, we can confirm that the critical value for the one-tailed test at the 5% significance level is 4.303.

The computed t-statistic (2.21) is less than the critical value (4.303), so the null hypothesis is not rejected.

Therefore, based on his three shark samples measured, there is not enough evidence to support a marine biologist's claim that great white sharks off Bermuda grow longer than the known average length of 21 feet at the 5% significance level.  

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Answer:

Option A:

A. Each side of 5√x = 10 should be squared.

(5√x)^2 = 10^2

25x = 100, so x = 4

B. x = -6 is an extraneous solution, so x = 2 is the only solution. When solving equations with radicals, you need to check for extraneous solutions.

Option B:

[tex] \sqrt{2x} + 5 = 1[/tex]

does not have any real solutions.

[tex] \sqrt[4]{m + 4} - \sqrt[4]{3m} = 0[/tex]

[tex] \sqrt[4]{m + 4} = \sqrt[4]{3m} [/tex]

[tex]m + 4 = 3m[/tex]

[tex]2m = 4[/tex]

[tex]m = 2[/tex]

Answer:

Step-by-step explanation:

a. To write the product a.sin(3x)cos(2x) as a sum, we can use the identity:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Using this identity, we can write:

a.sin(3x)cos(2x) = a.sin(3x)cos(x + x)

= a[sin(3x)cos(x) + cos(3x)sin(x)]

= a[sin(x)cos(3x) + sin(3x)cos(x)]

= a.sin(x)(cos(3x) + sin(3x))

Therefore, the product a.sin(3x)cos(2x) can be written as the sum a.sin(x)(cos(3x) + sin(3x)).

b. To write the product cos(7x)cos(2x) as a sum, we can use the identity:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Using this identity, we can write:

cos(7x)cos(2x) = cos(7x)cos(-x - (-x + 2x))

= cos(7x)cos(-x)cos(-(-x+2x)) - sin(7x)sin(-x)cos(-(-x+2x))

= cos(7x)cos(x)cos(x) + sin(7x)sin(x)sin(x)

= cos(7x)cos^2(x) + sin(7x)sin^2(x)

Therefore, the product cos(7x)cos(2x) can be written as the sum cos(7x)cos^2(x) + sin(7x)sin^2(x).

A skewed distribution is neither symmetrical nor normal as the data values trail off more sharply on one side than on the other. It occurs due to the lower or upper bounds on data. In symmetric distribution left and right sides mirror each other.

a. The given data distribution is skewed as the data is not even on either side.

b. The median is defined as the middle value of a data set. Here 20 is the median as it is the mid point.

c. The average of the given numbers is known as mean and it is obtained by dividing sum of numbers divided by total numbers.

Mean = 207 / 11 = 18.81

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Answer:

  25π yd²

Step-by-step explanation:

You want the exact area of a 40° sector of a circle of radius 15 yards.

The area of a sector is given by ...

  A = 1/2r²θ

where θ is the central angle in radians.

There are π radians in 180°, so there are (40/180)π = 2π/9 radians in 40°.

Then the area of the sector is ...

  A = 1/2(15 yd)²(2π/9) = 25π yd²

The area of sector GPH  is 25π square yards.

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An equation which represents this graph include the following: D. y = 2x/3 + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 0)/(0 + 3)

Slope (m) = 2/3

At data point (0, 2) and a slope of 2/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 2/3(x - 0)

y - 2 = 2x/3

y = 2x/3 + 2

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x=5

Step-by-step explanation:

Multiply 3 on both sides.

Add 8 to both sides.

Divide both sides by -2

The distance to the lightbulb is 28.22 meters.

The brightness of a light source decreases as distance from the source increases. This relationship is described by the inverse square law that says brightness of a light source is inversely proportional to the square of the distance from the source.

The formula for calculating brightness is: Brightness = Luminosity / (4π × Distance²)

Given:

Luminosity = 100 W

Brightness = 0.01

We will solve for distance:

Distance² = Luminosity / (4π × Brightness)

Distance² = 100 / (4π × 0.01)

Distance² = 100 / 0.1256

Distance² = 796.178343949

Distance = √796.178343949

Distance = 28.2166323992

Distance = 28.22.

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Paolo makes $2 per hour and his earnings is proportional to the hours worked

The graph is added as an attachment

Start by calculating the slope of the graph as follows

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (6 - 0)/(3 - 0)

Evaluate

Slope = 3

This mens that

Paolo makes $2 per hour

Because the graph is a proportional graph, then Paolo's earnings is directly proportional to the number of hours worked

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