A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 23 is 0.6784. Find the probability that a value in the distribution is less than 23.

Answer:

Below

Step-by-step explanation:

All of the angles labeled sum up to a right angle = 90 °

x+4     +      x+4        +  x+4      = 90

3x + 12 = 90

3x = 78

x = 26°

Answer:

x = 26

Step-by-step explanation:

from the diagram

∠ BFC + ∠ CFD + ∠ DFE = ∠ BFE , that is

x + 4 + x + 4 + x + 4 = 90

3x + 12 = 90 ( subtract 12 from both sides )

3x = 78 ( divide both sides by 3 )

x = 26

Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

The amount his account will have after 3 months be $ 759.38.

Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.

we have to find the amount in the account after 3 months,

So, the amount he made is,

Amount = 750(1 + 5/100)^0.25

Amount = 759.38

So, the amount his account will have after 3 months be $ 759.38.

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The percent increase in the median monthly rent prices is 14.3%

From the information, the median monthly rent in 2005 was $694 and $810 in 2010.

The increase in the amount will be:

= $810 - $694.

= $116

The percent increase in the median monthly rent prices from 2005 to 2010 will be:

= Increase in amount / Old rent × 100

= 116/810 × 100

= 14.3%

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The area of each of the following shaded regions in parts (a)-(d) is 2

There is a space in the shaded area. Because we are given two circles inside one larger circle, the size of the darkened zone is equal to the area of the circle less the area of the circle.

The answer is 2, and square meters are not the appropriate unit.

The area of each of the following shaded regions in parts (a)-(d) is 2

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The center of gravity of the distribution center is located at (14.84, 12.84)

The center of gravity is a point at which the total weight of a body can be thought to be located for calculation purposes.

The coordinates of the five distribution centers using the x and y coordinates are;

A(20, 15) 75, B(10, 12) 50, C(15, 10) 60, D(15, 20) 80, E(12, 12) 50

The center of gravity is found using the formula;

[tex]x = \dfrac{m_1\cdot g\cdot x_1+ m_2\cdot g\cdot x_2 + m_3\cdot g\cdot x_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]

[tex]y = \dfrac{m_1\cdot g\cdot y_1+ m_2\cdot g\cdot y_2 + m_3\cdot g\cdot y_3}{m_1\cdot g+ m_2\cdot g + m_3\cdot g}[/tex]

Coordinates of the center of gravity of the distribution center is therefore;

[tex]x = \dfrac{75\times 20+ 50\times 10+ 60\times 15+80\times 15+50\times 12}{75+50+60+80+50} \approx 14.92[/tex]

[tex]y = \dfrac{75\times 15+ 50\times 12+ 60\times 10+80\times 20+50\times 12}{75+50+60+80+50} \approx 12.84[/tex]

The coordinates of the center of gravity of the distribution center is; (14.92, 12.840

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Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

There are 4 different pairs of lines given to us.

We have to find out the pair of lines that are perpendicular to each other.

We know that the general equation of a line in slope-intercept form is represented as -

y = mx + c --- (1)

where

(x, y) = coordinates of the lines

m = slope of the line

c = y-intercept

It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.

A. y = -8 and y = 2

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

B. x = 4 and y = -1

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

C. x - y = 7 and y = x + 3

Now, x - y = 7

=> -y = 7 - x

=> y = x - 7

Comparing this to the equation (1), we have slope of the line, m = 1.

Also, y = x + 3

Comparing this to the equation (1), we have slope of the line, m = 1.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

D. y = -4x + 1 and 8x + 2y = -10

Now, y = -4x +1

Comparing this to the equation (1), we have slope of the line, m = -4.

Also, 8x + 2y = -10

=> 2y = -8x - 10

=> y = -4x - 10

Comparing this to the equation (1), we have slope of the line, m = -4.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

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The earnings of Rayan per hour is $5 per hour

The first point = (1, 5)

The second point = (2, 10)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = (10-5) / (2-1)

Subtract the terms

= 5 / 1

= $5 per hour

Hence, the earnings of Rayan per hour is $5 per hour

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The model’s distances isn't proportional to the actual dimensions of the solar system as B. No, because the ratios of model length to actual distance are different for the two planets.

Ratio demonstrates how many times one number can fit into another number. It is used to show the comparison between two or more things

In this case, in model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. This can be illustrated as:

= 7/19

= 0.368

If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, the ratio is:

= 91.549 / 2780.5

= 0.0329

Therefore, since they're different numbers, the information doesn't illustrate a proportional ratio.

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The sum of angles at a point is equal 360 degrees and using that, the value of x is 261 degrees.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360°.

In this question, when we sum all angles up, it will give us the sum of 360 degrees.

20 + 40 + 39 + x = 360

x + 99 = 360

x = 360 - 99

x = 261

x has a value of 261 degrees.

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The expression that represents the quotient of the given model is x + 5. The correct option is C. x + 5

From the question, we are to determine the expression that represent the quotient of the given model

From the given model, we can write that

x | x² + x + x + x + x + x

Dividing by using the long division

  x + 1 + 1 + 1 + 1 + 1      

x | x² + x + x + x + x + x

Thus, the quotient of the expression is

x + 1 + 1 + 1 + 1 + 1

Further simplification,

NOTE: 1 + 1 + 1 + 1 + 1 = 5

Then,

The expression x + 1 + 1 + 1 + 1 + 1  becomes

x + 5

Hence, the expression is x + 5

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Vertical angles are opposite of each othe. Attached is a picture of how it looks:

I hope this helps!

Answer: 6 dollars

Step-by-step explanation:

Freida would have earned at the end of the year an interest of $6 for the $200  investment at 3% interest for 1 year.

The principle amount is $200

The saving account earns a interest of 3%

We need to calculate that Frieda have earned at the end of the year.

Interest = PRT/100

where p is principle

r is rate of interest

and t is the time period

= 200 x 3 x 1 / 100

= 6

Therefore, Freida would have earned an interest of $6 for the $200  investment at 3% interest for 1 year.

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Answer:

NOT CONGRUENT

Step-by-step explanation:

There are several types of congruence:

ASA - Angle Side Angle

AAS - Angle Angle Side

HL - Hypotenuse Leg

This image shows two triangles which have 2 congruent sides and one congruent angle.

Is it ASA?

There is only one congruent angle, so this cannot be congruent by ASA

Is it AAS?

By the same reasoning, it cannot be congruent by AAS.

Is it HL?

Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.

There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT

15 kilograms of the first type should be mixed with 25 kilograms of the other kind

If the blend costs  $5.50/kg, then:

on each kg at $5.00/kg, gain = $0.50  ($5.50 - $5.00)

on each kg at $5.80/kg, loss = $0.30  ($5.50 - $5.80)

Hence 3kg of the first kind must be mixed with 5kg of the second so that the gain on the first (3 x $0.50) is exactly the same as the loss on the second (5 x $0.30)

The required proportion is 3:5

In order to find how many kilograms of each type are needed to make 40kg, we will use the proportion obtained:

We have 3:5, total share = 3+5 = 8

First kind share = 3/8 x 40 kg = 15 kg

Second kind share = 5/8 x 40 kg = 25kg

Therefore, 15  kilograms of the first type is needed and 25 kilograms of the other kind is needed

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a) Examining the data, the outlier in the data are

b) The measure I would use to describe the central tendency of the data is median

Outlier as used in data  analysis refers to a data that is abnormally away from other data. Outliers show high variability

In the given problem, $80 000 is the data that is farther away than any other data and hence the only outlier

The mean is usually a better measure of central tendency how ever the presence of outliers affects the result projected by mean.

The better choice to use here is the median

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For give expression Ben's work is correct.

In this question, Ben and Jerry both simplified the expression √24x⁵y³

where x > 0, y > 0

We need to determine which student is correct.

First we simplify given expression.

√24x⁵y³

= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)

= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)

= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y)    ...(seperate the radical symbol)

= 2 * √(2) * √(3) * x * x * √(x) * y * √(y)            ...........exponent rule

= 2x²y√(2)(3)(x)(y)                     ........(combine terms with same powers)

= 2x²y √6xy

So, Ben's work is correct.

We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.

Therefore, Ben's work is correct.

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The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted that the fraction given is 5/7.

The equivalent fraction will be:

= 5/7 × 5/5

= 25/35

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Complete question

Write the equvalent fraction of 2/5 using 35 as a common denominater

On the coordinate (0,7) the value of P is maximum 280.

What is a Linear Inequality?

In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.

Solution:

First of all to solve the Linear Inequality we need to plot the graph of the given equations.

Kindly find the attached graph

To maximise the equation P = 30x + 40y

we need to find the corner values of x and y.

According to the graph, the corner values of (x,y) are

(5,0), (3,4) and (0,7)

putting the values in the equation P = 30x + 40y

at x = 5 and y = 0

P = 150

at x = 3 and y = 4

P = 250

at x = 0 and y = 7

P = 280

So, on the cordinate (0,7) the value of P is maximum i.e. 280.

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Answer: 7/10

Step-by-step explanation:

This is the lowest term because you add the numbers.

The value of f(x+h)-f(x)  = h.

Given function:

f(x) = x + 7

difference quotient = f(x+h) - f(x)

= (x+h) - 7 - (x - 7)

= x + h - 7 - x + 7

= x - x + 7 - 7 + h

= 0 + 0 + h

= h

Therefore the value of f(x+h)-f(x)  = h.

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3. The amount of retained earnings transferred to the paid-in capital accounts (capitalized) for the stock dividend is $72,000.

4. The per-share cost of the treasury stock purchased is $10.

5. The net income earned by the Atticus Group this year was $217,500.

Stock dividends do not affect the cash account, unlike cash dividends.

Instead, the deduction is made from the retained earnings.

When the stock dividends are distributed, they are capitalized to the paid-in capital accounts (common stock and additional paid-in capital).

January 5 Dividend $17,500 Dividends Payable $17,500 (35,000 x $0.50)

Retained Earnings $17,500 Dividend $17,500

March 20 Treasury Stock $20,000 Paid-in Capital in Excess $30,000 Cash $50,000 ($50,000/5,000)

April 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)

Retained Earnings $15,000 Dividend $15,000

July 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)

Retained Earnings $15,000 Dividend $15,000

July 31 Stock Dividend $72,000 Dividends Issuable $72,000 (30,000 x 20% x $12)

Retained Earnings $72,000 Stock Dividend $72,000

August 14 Dividends Issuable $72,000 Common Stock $24,000 Paid-in Capital in excess of par value $48,000

October 5 Dividend $18,000 Dividends Payable $18,000 (36,000 x $0.50)

Retained Earnings $18,000 Dividend $18,000

Ending balance  $440,000

Add:

Dividend $17,500

Dividends $15,000

Dividends $15,000

Dividends $72,000

Dividends $18,000 $137,500

Less Beginning balance $360,000

Net income = $217,500

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Considering the sine function in this problem, we have that:

The general sine function has the definition presented as follows:

f(x) = asin(b(x+c))+d.

The coefficients are given as follows:

For this problem, the function is:

h(θ ) = 8.5 sin (θ + 180°) + 40

The amplitude is of:

a = 8.5.

The function should oscillate between:

-8.5 and 8.5.

However, with the vertical shift of 40, the minimum and maximum values are given as follows:

The measure of each cycle of the cosine function is of:

2π = 360º.

The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.

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Answer:

A. (10x^2) / (5x + 4y)

B. (8xy) / (4y + 5x)

Step-by-step explanation:

A. Factor the numerator and denominator, then cancel out like terms

(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))

(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))

(10x^2) / (5x + 4y)

B. Factor the numerator and denominator, then cancel out like terms.

(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))

(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))

(8xy) / (4y + 5x)

Answer:

Step-by-step explanation:

Point- slope form:

Given:

Substitute into equation to get the line:

Answer:

46.9

Step-by-step explanation:

sin54=x/58

58sin54=46.922

Refer to the attachment for the required table:

What is the unit rate?

A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

From the table,

For 0 hours, distance = 15 miles

For 1 hour, distance = 80 miles

Difference between distances= 80-15=65 miles

Since it is given that, it is at a constant rate,  for every hour there is an increase of 65 miles in distance.

The completed table is shown in the attachment.

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Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest

Step-by-step explanation:

5 blocks north, then 4 east, then 5 north is a total of 10 blocks north.  The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.

Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there: