Question 6 of 13, Step 1 of 1
A psychology professor assigns letter grades on a test according to the following scheme.
A: Top 6% of scores
B: Scores below the top 6 % and above the bottom 62 %
C: Scores below the top 38 % and above the bottom 24 %
D: Scores below the top 76 % and above the bottom 6%
F: Bottom 6% of scores
Scores on the test are normally distributed with a mean of 72.2 and a standard deviation of 8.6. Find the numerical limits for a D grade. Round your answers to the
nearest whole number, if necessary.
Answer
Correct
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The expression is,

So, according to BODMAS which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction, calculations are to be done in ths order.

So.

On solving the provided question, we can say that - Area enclosed by the square and the circle= 400 - 314 = 86 ft sq

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Side of the square =20feet

Therefore,

Radius of the inscribed circle= 20/2 = 10 feet

Area of square=20 X 20 = 400 feet sq.

Area of circle=\(\pi * r^{2} \\\pi * 10*10\\3.14*100\\314 ft sq\)

Area enclosed by the square and the circle= 400 - 314

                                                                           = 86 ft sq

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Answer:

The answer is 9.45

Step-by-step explanation:

2.7*3.5=9.45

The number of phones sold and the number of accessories sold if Luis earns a $14 commission for every phone he sells and a $2 commission for every accessory he sells and earn a total commission of $110 is 5 and 20 respectively.

Equation: a statement stating the equality of two expressions containing variables or numbers. Essentially, equations are questions, and attempt to methodically find the answers to these questions have been the inspiration for the development of mathematics.

Given:

The commission on phone = $14 each,

The commission on accessories = $2 each,

Total commission earned = $110,

Let x is the no of phone sold and y is the no of accessories sold, then,

y = 4x and 14x + 2y = 110,

Solve the above equation by substitution method we get

x = 5 and y = 20

Therefore, the number of phones sold and the number of accessories sold are 5 and 20 respectively.

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Answer:

see explanation

Step-by-step explanation:

Given

v < 7

Then the values which are solutions must be less than 7, thus

v = 7 ← No

v = 11 ← No

v = 1 ← Yes

v = 5 ← Yes

Answer:

Step-by-step explanation:

Hello,

the line passes through (-8,11) means than y = 11 for x  = -8

I believe that you wanted to write the first one as below

\(y=-\dfrac{5}{8}x+6\)

in that case for x = -8

y = - 5 * - 1 + 6 = 5 + 6 = 11

hope this helps

The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

First we need to find the slope

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

   = (7/2 -11)/(4--8)

   = (7/2 - 22/2)/(4+8)

   = (-15/2)/(12)

  = -15/24

Divide top and bottom by 3

  -5/8

Then we can use point slope form to write the equation

y-y1 = m (x-x1)

y- 11 =-5/8(x--8)

y- 11 =-5/8(x+8)

Distribute

y-11 =-5/8 x -5

Add 11 to each side

y-11 = -5/8x -5+11

y = -5/8x +6

Hence, The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

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Answer:

$115.20

Step-by-step explanation:

See attached image

Answer: c

Step-by-step explanation: a parrelagram has each side parrel

Answer:

B. - it has four right angles

The equation of the line is y+x+1=0.

It is required to find the equation of the line.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The given line is

y=-x-5.

Slope of line

y+x-5=0

We have to find the  equation of the line.

According to given question we have

Slope =-1

Thus the slope of the required line is

-1

The point (5, -6)

The equation of the line is

  y+6=-1​(x−5)

=>y+6=-x+5

=>y+x+1=0

Therefore, the equation of the line is y+x+1=0.

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3(4x + 2) = 12x + 6

- 5c(3c - 6) = - 15c^2 + 30c

\(hope \: it \: helps \\ ray4918 \: \: here\)

Answer:

3(4x+2)= 12x+6.

-5c(3c-6)= -15c^2+30c.

Answer:

number multiplied by itself

Step-by-step explanation:

Answer:

a = 12

Step-by-step explanation:

Given that a is inversely proportional to b then the equation relating them is

a = \(\frac{k}{b}\) ← k is the comstant of proportion

To find k use the condition when a = 4, b = 36, then

4 = \(\frac{k}{36}\) ( multiply both sides by 36 )

144 = k

a = \(\frac{144}{b}\) ← equation of proportion

When b = a , then

a = \(\frac{144}{a}\) ( multiply both sides by a )

a² = 144 ( take square root of both sides )

a = ± \(\sqrt{144}\) = ± 12

However a is a positive number, thus a = 12

The probability that there will be at least one pair among the four shoes selected is 38/115 (approx.).

Given that ten pair of shoes are in a closet and four shoes are selected at random, we need to find the probability that there will be at least one pair among the four shoes selected.

Possible cases are i) selecting all four shoes of different pairs and

ii) selecting at least one pair of shoes.i

i) Selecting at least one pair of shoes:

This can be done in two ways, either by selecting a pair of shoes and then selecting two shoes from the remaining pairs, or by selecting two pairs of shoes and then selecting one shoe from each pair.

The number of ways of selecting one pair from ten pairs of shoes is 10C1 = 10

The number of ways of selecting 2 shoes from the remaining 18 shoes (one shoe from each of the remaining 9 pairs) is 18C2 = (18 × 17)/(2 × 1) = 153

The number of ways of selecting 2 pairs from ten pairs of shoes is 10C2 = (10 × 9)/(2 × 1)

= 45

The number of ways of selecting one shoe from each of the two pairs of shoes selected is 2 × 2 = 4

Total number of ways of selecting at least one pair of shoes = 10 × 153 + 45 × 4

= 1530 + 180

= 1710

The number of ways of selecting 4 shoes from 20 shoes is 20C4 = (20 × 19 × 18 × 17)/(4 × 3 × 2 × 1) = 4845

Probability of selecting at least one pair of shoes= 1710/4845= 38/115 (approx.)

Therefore, the probability that there will be at least one pair among the four shoes selected is 38/115 (approx.).

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Answer:

The circumference of the firepit is 6π or approximately 18.84 feet.

Step-by-step explanation:

The circumference of a circle is 2πr.

Substitute the variable r with 3 and then solve the rest; 2π(3) = 6π or ≅18.84

Approximately 7 singers have joined the initial singer to increase the level from 74 dB to 83 dB.

To calculate the number of singers that have joined the initial singer, we can use the logarithmic nature of the decibel scale. The decibel scale is logarithmic, meaning that an increase of 10 dB represents a tenfold increase in sound intensity.

In this case, we have an increase from 74 dB to 83 dB, which is an increase of 9 dB. Since each singer is equally loud, we can assume that each additional singer adds the same amount of sound intensity.

To find out how many singers have joined, we need to determine how many times 9 dB represents a tenfold increase. We can use the formula:

\(10^{\\increase} ^{\\in dB/10)}\\\) = number of singers

Let's calculate it:

\(10^{(9/10)\) ≈ 7.94

Therefore, approximately 7 singers have joined the initial singer to increase the level from 74 dB to 83 dB.

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Answer:

-2/3 + 0

= 2

– — + 0

3 2

Add — 2/3 and 0 to get – —

3

2

= – —

3

= (–1).2/3 = –0.666666667

the answer is = –0.666666667

Step-by-step explanation:

#Carry on learning

Answer:

Start at postive 1 on the y axis put a dot there. From the dot go down 6 and go left 5.

Step-by-step explanation:

6/5=rise over run

1=y-axis

y=mx+b

m=slope

b=y-intersept

Step-by-step explanation:

Hey, there!!

To graph a equation, we must find the coordinates of x and y.

So, as the equation is,

\(y = \frac{6}{5} x + 1\)

Here, the equation is for finding the coordinates of y and x should be supposed. Remember, always suppose the value in equal interval.

Now,

x = 0 1 2 3

y= 1 2.2 3.4 4.6

Here, if you are confused how do i get 1, 2.2,3.4,4.6 as y value, put the value of x such as,

\(y = \frac{6}{5} \times 0 + 1\)

which is equal to 1.

so,in this we got values.

Now,

List coordinates,

(0,1),(1,2.2),(2,3.4),(3,4.6)

Then plot on graph!!!

Hope it helps.....

The simplified expression is 4.

To simplify the expression (-3)(-2) -2), we need to follow the order of operations, which are parentheses first, then multiplication and division from left to right, and finally addition and subtraction from left to right.

First, we need to simplify (-3)(-2) to get:

(-3)(-2) = 6

Now we can substitute this value into the expression to get:

6 - 2) = 4

Therefore, the simplified expression is 4.

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Total cost in dollars of the meal, tax and tips is $18.75

Tips are bonus or extra payment that a customer wants to pay to the counter of restaurant or to certain workers to express the gratitude toward their hospitality. How much money will be paid is determined by the customer himself.

given, cost of meal = $15 before tax and tip

After that $7% tax and $18% tip are included upon the cost of meal

Now, cost for tax = $ (7/100 × 15) = $1.05

cost for tip = $ (18/100 × 15) =$2.7

Total cost for meal, tax and tips = cost for meal + cost for tax + cost for tip

 Total cost = $18.75

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Answer:

The answer is 36

Step-by-step explanation:

12+6=18

18/3=6

6 squared is 36

36 simplified is still 36

To find the arc length, we use the formula L = rθ, where r is the radius of the circle, θ is the central angle of the arc in radians, and L is the arc length.

Arc length refers to the distance covered along the curved portion of a circle or any other curved shape. It is an important concept in geometry and trigonometry and is used to measure the size of circular arcs, the size of angles, and in many other mathematical applications.

To find the arc length, we need to use the formula for the circumference of a circle and the central angle of the arc.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.

The central angle of the arc is given in radians and is defined as the angle between two radii that meet at the endpoints of the arc.

To find the arc length, we use the formula

=> L = rθ,

where L is the arc length, r is the radius of the circle, and θ is the central angle of the arc in radians.

To convert the central angle from degrees to radians, we use the formula θ = (π/180) x degrees, where degrees are the central angle in degrees.

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The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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If two matrices a and b have exactly the same eigenvalues (with the same algebraic multiplicity) and eigenvectors (with the same eigenspace for each distinct eigenvalue), then we can conclude that a and b are similar matrices.

This means that there exists an invertible matrix P such that a = PBP^-1, where B is a diagonal matrix with the same eigenvalues as a and b on the diagonal entries.

This can be proved using the fact that if a matrix A has a complete set of eigenvectors, then A can be diagonalized as A = PDP^-1, where D is a diagonal matrix whose entries are the eigenvalues of A, and P is the matrix whose columns are the eigenvectors of A. If two matrices have the same eigenvectors, then they can be diagonalized by the same matrix P.

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By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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Answer:

210

Step-by-step explanation:

Answer:

the first one (25x + 30y is less than or equal to 100)

Step-by-step explanation:

money for clothing set x amount of sets plus pairs of shoes has to be less than or equal to 100 dollars.

During the year, Poch Co. incurred cost of goods sold of $59,823 million on net sales of $76,643 million. To find Poch's return on sales ratio, we need to divide the cost of goods sold by the net sales and multiply by 100.

The calculation would be:
Return on Sales Ratio = (Cost of Goods Sold / Net Sales) * 100
Plugging in the given values:
Return on Sales Ratio = ($59,823 million / $76,643 million) * 100
Now, let's solve the calculation:
Return on Sales Ratio = (0.7807) * 100
Return on Sales Ratio ≈ 78.07%
Since none of the provided answer options match with the calculated ratio, we cannot determine the exact return on sales ratio.

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Hey!!

Solution,

3x^2+6x

take the common,

3x(X+2)

hope it helps

Good luck on your assignment

It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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