50 Points!!

Select the reason that best supports statement 3 in the given proof

Answer: [tex]4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

Step-by-step explanation:

We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.

[tex]4(x^2-8)[/tex]

From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.

For review, a difference of two squares [tex]a^2-b^2[/tex] can be factored into [tex](a+b)(a-b)[/tex].

[tex]4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

Answer:

TS=QV

Step-by-step explanation:

To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.

In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

For triangles to be congruent by SAS congruency criteria, one angle and the two adjacent sides to the angle should be equal to corresponding angle and it's adjacent aides of another triangle.

And we have already been given the angle and one of the side. so the third side that need to be equal in both side to pe proved congruent are :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: The guy wire  = 393.4 ft

Step-by-step explanation:

Given images:

Refer to the attachment below (I apologize for the bad writing on the computer)

Given information:

Height of the tower = 175 ft

Height of the wire = 15 ft from the top (Opposite)

Angle with the ground = 24°

Length of wire = Unknown (Hypotenuse)

Determine the trigonometric function:

The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.

Determine the equation:

sin θ = (Opposite) / (Hypotenuse)

sin (24°) = (175 - 15) / (Length)

Simplify value in parenthesis

sin (24°) = (160) / (Length)

Multiply the Length of wire on both sides

sin (24°) * (Length) = (160) / (Length) * (Length)

sin (24°) * (Length) = (160)

Divide sin (24°) on both sides

sin (24°) * (Length) / sin (24°) = (160) / sin (24°)

Length = 160 / sin (24°)

[tex]\Large\boxed{Length~=~393.4~ft}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C

Let's the point that divides the line segment as point S.

We have that,

Point S divides the line segment into ratio 2:3

The ratio 2:3 means that we are to divide the line segment into;

= 2+3

= 5 equal parts.

We then have that the horizontal distance between the two coordinates is 5

The vertical distance between the two coordinates is 10

Now, let's divide both vertical and horizontal distance into five equal parts,

Horizontal distance = 5/5 = 1

Vertical distance = 10/ 5 = 2

The horizontal distance is 1

The vertical distance is 2

For every one unit move to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point S that divides the line segment into 2 parts and 3 parts is (-5,5)

Thus, the y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C

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Answer:

x = 4

Step-by-step explanation:

Hello!

We can solve for x by expanding the parentheses and isolating x.

The value of x is 4.

Answer:

there are 8 million different phone numbers whose phone numbers whose digits aren't 0 or 1

The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

What is an equation?

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

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

One grain =  60mg, hence:

1/4 gr = 1/4 gr * 60 mg per gr = 15 mg

Hence, for 10 mg per ml:

Dosage = 15 mg /  10 mg per ml = 1.5 ml

The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

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A. The pair of linear equations are: x + y = 55 and y = x + 25

B. Number of time she spend running everyday is: 15 minutes.

C. It is not possible.

A system of equations consist of linear equations that have unknown variables whose values make the linear equations in the system true.

Part A: To write a pair of linear equations, do the following,

Let x represent the time Jackie runs

Let y represent the time Jackie dances

We are given that, Jackie runs and dances for a total of 55 minutes every day, therefore, the first linear equation would be:

x + y = 55 --> equation 1

We are also given that Jackie dances for 25 minutes longer than she runs, therefore, the second linear equation would be:

y = x + 25 --> equation 2

Therefore, the two pair of linear equations that shows the relationship between the number of minutes Jackie runs and dances everyday are:

x + y = 55

y = x + 25

Part B: Substitute y = (x + 25) into equation 1

x + y = 55 --> equation 1

x + x + 25 = 55

2x + 25 = 55

2x = 55 - 25

2x = 30

x = 15

Therefore, the number of time she spend running everyday is: 15 minutes.

Part C:

If she spent 45 minutes dancing (y = 45), and x = 15, substitute the values into x + y = 55 to find out if it is possible.

15 + 45 = 55

60 = 55 (not true)

Therefore, it is not possible.

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Answer:

Step-by-step explanation:

D because the quadratic formula is basically [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]±

so if we place the equation D into the formula

a = 1

b = +3

c = +24

we can clearly say that D eq is correctly used and can be.

The statements that apply to the algebraic expression are

The complete question is added as an attachment

The statement is given as:

Twice the difference of a number and six

Represent the number with n.

So, the statement becomes

Twice the difference of a n and six

Twice means 2 *

So, we have

2 * difference of a n and six

Express difference as minus i.e. -

So, we have

2 * (n - 6)

Hence, the expression is written as 2(n - 6)

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Answer:

d = [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The distance between two points is found by

d = [tex]\sqrt{( x2-x1)^2 + ( y2-y1)^2}[/tex] where (x1,y1) and (x2,y2) are the two points

d = [tex]\sqrt{(-2 - -1)^2+(-6 - -14)^2 }[/tex]

d =[tex]\sqrt{( -2+1)^2 + (-6+14)^2}\\[/tex]

d = [tex]\sqrt{(-1)^2 +( 8)^2 }[/tex]

d = [tex]\sqrt{1+64}[/tex]

d = [tex]\sqrt{65}[/tex]

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3

First  

x -3 = 0 , make it equal to 0 and add 3 to both sides

x = 3

Then we write all the coefficients and continue with

a pattern of multiply by 3 and add to the next coefficient.

See attachment.

Answer:

Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.

Step-by-step explanation:

Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 70, \sigma = 40, n = 50, s = \frac{40}{\sqrt{50}} = 5.66[/tex]

The probability that the sample average will exceed $75 is one subtracted by the p-value of Z when X = 75, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (75 - 70)/5.66

Z = 0.88

Z = 0.88 has a p-value of 0.8106.

1 - 0.8106 = 0.1894.

0.1894 = 18.94% probability that the sample average will exceed $75.

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The equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

The given parameter is

constant rate of 20 kilometers per hour.

This means that

Rate = 20km per hour

When Seb bikes for t hours, the distance is

d = rate * t

This gives

d = 20t

Hence, the equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

This means that

t = 5

So, we have:

d = 20 * 5

Evaluate

d = 100

Hence, Seb will travel 100 kilometers if he bikes at this rate for 5 hours

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Answer:

1. d=20t

2. 50

The required answers are calculated by using the simple interest formula:

a. She needs to deposit $793.65 in the account each month

b. The total money she put into an account for a year is $285,714.29

c. The total interest she earns is $514,285.71

The formula for the simple interest is

A = P(1 + RT)

Where,

A - amount after T years

P - principal amount

R - the rate of interest

T - time (years)

It is given that,

A = 8,00,000

T = 30 years

R = 6% = 0.06

So,

a. Finding the amount needs to deposit in the account each month:

We have A = P(1 + RT)

⇒ P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

Thus, the amount needs to deposit in the account for each month

= P/T×12

= 285,714.29/30×12

= $793.65

b. Finding the total money that she put into account:

That is nothing but,

P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

c. FInding the total interest:

We have I = A - P

⇒ I = 8,00,000 - 285,714.29

∴ I = $514,285.71

Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71

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Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.

Velocity is distance divided by time, hence:

v = d/t

A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:

12 + r = 46/t

r = 46/t - 12

Downstream, the time is of t + 2 hours, hence:

12 - r = 46/(t + 2)

r = 12 - 46/(t + 2)

Hence, equaling the values for r:

46/t - 12 = 12 - 46/(t + 2)

46/t + 46/(t + 2) = 24

[tex]\frac{46t + 92 + 46t}{t(t + 2)} = 24[/tex]

92t + 92 = 24t² + 48t

24t² - 44t - 92 = 0

Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:

r = 46/t - 12 = 46/3 - 12 = 3.33 mph.

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The probability that the student plays football is 20/33.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the student plays football = total number of students who play football / total number of students

The probability that the student plays football = 40/66 = 20/33

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Answer:

(x-5)(x+1)

Step-by-step explanation:

x² - 4x + 5 = (x-5)(x+1)

a) The preparation of a traditional income statement for Carbon Company is as follows:

Carbon Company

Sales revenue                         $600,000

Costs:

Materials               $ 101,300

Energy                       21,590

Setups                      24,360

Purchasing              26,200

Customer service   20,200

Long-term labor     29,400

Administrative        30,700     $253,750

Operating Income                  $346,250

b) The preparation of an activity-based income statement for Carbon Company is as follows:

Carbon Company

Sales revenue                                                                     $600,000

                   Resources supplied    Unused Resources   Used Resources

Materials               $ 101,300                     $ 2,300              $99,000

Energy                       21,590                         2,210                  19,380

Setups                      24,360                                0                 24,360

Purchasing              26,200                         7,800                  18,400

Customer service   20,200                         9,700                 10,500

Long-term labor     29,400                         4,650                 24,750

Administrative        30,700                         5,950                 24,750        

Total                   $253,750                      $32,610              $221,140

Operating Income                                                            $378,860

                          Unused Resources Capacity     Cost Driver Volume

Resources used

Materials                        $ 2,300                                 9,000 pounds

Energy                               2,210                        380 machine-hours

Setups                                     0                                         87 setups

Purchasing                      7,800                         80 purchase orders

Customer service           9,700                                         70 returns

Long-term labor              4,650                              330 labor-hours

Administrative                5,950                              450 labor-hours

Materials $ 101,300

Energy 21,590

Setups 24,360

Purchasing 26,200

Customer service 20,200

Long-term labor 29,400

Administrative 30,700

Sales revenue  $600,000

                   Resources supplied       Unused Resources   Used Resources

Materials               $ 101,300                         $ 2,300              $99,000

Energy                       21,590                             2,210                  19,380

Setups                      24,360                                    0                 24,360

Purchasing              26,200                             7,800                  18,400

Customer service   20,200                             9,700                 10,500

Long-term labor     29,400                             4,650                 24,750

Administrative        30,700                             5,950                 24,750        

Total                   $253,750                          $32,610              $221,140

Thus, the traditional income statement for Carbon Company shows an operating income of $346,250, while the activity-based income statement shows an operating income of $378,860.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

According to given figure,

Angle 11, Angle 20 and Angle 16 forms angles of a triangle,

so, by angle sum property of a triangle :

[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]

[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

600

Step-by-step explanation:

250/1 times 6/ 100 times 40/1

Answer: Choice 3

Step-by-step explanation:

Oof, this is a tough one. But anyways

Angle 19 + Angle 20 = 180

So Angle 20 = 180 - Angle 19

As l and m are parallel, Angle 20 = Angle 6 from the z rule

So Angle 6 = 180 - Angle 19

Substitute the information given at the start into the equation

2x - 4 = 180 - (5x - 8)

180 - 5x + 8 = 2x - 4

7x = 192

x = 27.42

From what we have found earlier, Angle 20 = Angle 6 so

Angle 20 = 2x - 4 = 2 * 27.42 - 4 = 50.85 rounding it to 50.9

So the answer is 50.9 or Choice 3

Answer:

See below

Step-by-step explanation:

[tex]A = \{2, 4, 6\}[/tex]

[tex]A^c =\{1, 3, 5\}\\B = \{4, 5, 6\}\\B^c = \{ 1,2, 3\}[/tex]

To prove 1 we have

[tex](A \bigcup B) = \{2, 4, 6\} \bigcup \{4, 5, 6\} = \{2, 4, 5, 6\}\\(A \bigcup B) ^c =\bold{\{1,3\}}\\A^c \bigcap B^c = {\{1, 3, 5\} \bigcap \{1, 2, 3\} =\bold{\{1,3\}}\\[/tex]

Hence proved

To prove 2

[tex](A \bigcap B) = \{2, 4, 6\} \bigcap \{4, 5, 6\} = \{4, 6\}\\\\(A \bigcap B)^c = \bold{\{1,2, 3, 5\}}\\A^c \bigcup B^c = \{1, 3, 5\} \bigcup \{1, 2, 3\} = \bold{\{1,2,3,5\}}\[/tex]

Hence proved

Notes

The complement of a set is the set of all elements not in the set

Here the set of all outcomes is {1, 2, 3,4,5, 6}

So if A = {2, 4, 6} then the complement of A s=is the set of outcomes not in A ie the set {1, 3, 5} which is the set of odd numbers on a die throw

The union of two sets is the set of all elements in both sets without duplication

The intersection of two sets is the set of all elements common to both sets

Taking squares on both sides leads to

[tex]\sqrt{-x + 6} = x - 6[/tex]

[tex]\left(\sqrt{-x + 6}\right)^2 = (x - 6)^2[/tex]

[tex]-x + 6 = x^2 - 12x + 36[/tex]

[tex]x^2 - 11x + 30 = 0[/tex]

[tex](x - 5) (x - 6) = 0[/tex]

Solving for [tex]x[/tex], we get

[tex]x - 5 = 0 \text{ or } x - 6 = 0[/tex]

or

[tex]x = 5 \text{ or } x = 6[/tex].

Evaluating both sides of the starting equation at these solutions, we have

[tex]\sqrt{-6 + 6} = 6 - 6 \implies 0 = 0[/tex]

which is true, so [tex]\boxed{x=6}[/tex] is a valid solution. However,

[tex]\sqrt{-5 + 6} = 5 - 6 \implies \sqrt1 = -1 \implies 1 = -1[/tex]

which is not true, so [tex]\boxed{x=5}[/tex] is an extraneous solution.

The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D

9√4.000

= 4.000/9

= 0.444

Approximately,

= 0.4

Fraction

This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.

Decimal

This is a number expressed in the decimal system (base 10).

Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.

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Answer:

750 - y(y-5) = 0

Step-by-step explanation:

Area is Length times width.  In a rectangle we have two lengths and 2 widths.

We can use y to represent the length.  The width would be y-5.

Area = LW

750 = y(y-5) or another way to write this is

750 - Y(y-5) = 0

Answer:

C

Step-by-step explanation:

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

The correct option is:

b. Most of students' test scores are around the mean.

A large range indicates that there is a significant difference between the highest and lowest scores in the set.

On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.

When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

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Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.

First, find the income shortfall:

= 75,017 - 54,000

= $21,017

The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:

= 6% - 2% inflation

= 4%

The future value is:

= Income shortfall x future value interest factor, 4%, 29 years

= 21,017 x 3.1187

= $65,545.72

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