Charlie saves $28.35 each month for 6 months. In the seventh month, he only saves $10.70.

How much money will Charlie have saved after 7 months?

In conclusion, x = 5 is the equation of a vertical line across the location (5,2).

A vertical line is one that is straight up and down and lacks a horizontal component, giving it an arbitrary slope. As a result, it has the equation x = c, where c is the x-coordinate of any point on the line. Since the line in this instance goes through the coordinates (5,2), its equation is x = 5.

This is due to the fact that the line is vertical and does not slant left or right, therefore every point on it will have an x-coordinate of 5. Since the line travels through point (5,2), the equation x = 5 includes all potential points along the line.

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Answer:

98.6607 pounds

Step-by-step explanation:

11.81 times 8.354 = 98.6607

\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

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

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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The following are the solutions to the given problem:A. Cost of Equity Capital:Given,Beta of the firm = 1.00Risk-Free Rate (Rf) = 3.5%Equity Risk Premium = 6%Cost of Equity (Re) = Rf + Beta*(Equity Risk Premium)Re = 3.5% + 1.00(6%)Re = 9.5%B. After-Tax Cost of Debt:Given,

Pre-tax cost of debt = 4.5%Tax rate = 40%

After-tax cost of debt (Rd) = Pre-tax cost of debt x (1 - Tax Rate)Rd = 4.5% x (1 - 0.40)Rd = 2.7%C. Weighted Average Cost of Capital (WACC):Given,

Weightage of Equity (We) = 100 million shares / 100 million shares + 250 million of debtWe = 28.57%Weightage of Debt (Wd) = 250 million of debt / 100 million shares + 250 million of debt

Wd = 71.43%WACC = (We x Re) + (Wd x Rd)WACC = (28.57% x 9.5%) + (71.43% x 2.7%)WACC = 3.91%D. Cost of Equity after Restructuring:Given,New Default Spread = 3 x Old Default SpreadOld Default Spread = 2.7% - 3.5%Old Default Spread = -0.8%New Default Spread = 3 x -0.8%

New Default Spread = -2.4%New After-tax Cost of Debt (Rd) = 2.7% + (-2.4%)Rd = 0.3%New Weightage of Debt (Wd) = 750 million of debt / 100 million shares + 750 million of debt

Wd = 88.24%New Weightage of Equity (We) = 100 million shares / 100 million shares + 750 million of debtWe = 11.76%New Cost of Equity (Re) = 9.5%Re = 9.5%New WACC

= (We x Re) + (Wd x Rd)New WACC = (11.76% x 9.5%) + (88.24% x 0.3%)New WACC = 0.53%E. After-tax Cost of Debt after Restructuring:Given,

New After-tax Cost of Debt (Rd) = 0.3%F. WACC after Restructuring:New WACC = 0.53%G. Value (Price) per Share for the Remaining Shareholders in the Company:Given,

New Shares = 500 million / $11 per share = 45,454,545 shares New Equity Shares = 100 million shares + 45,454,545 shares = 145,454,545 shares Value of Equity = 145,454,545

shares x $11 per shareValue of Equity = $1,600,000,000Value per Share for the Remaining Shareholders in the Company = $1,600,000,000 / 100 million sharesValue per Share for the Remaining Shareholders in the Company = $16.00 per share.

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Answer:

6x^3-5x^2

Step-by-step explanation:

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

4x^3+x^2+2x^3-6x^2

4x^3+2x^3+x^2-6x^2

6x^3+x^2-6x^2

6x^3-5x^2

The simplest form of the given expression \((4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\) is,

\(6x^{3} - 5x^{2}\).

Here, given expression is,

\((4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\)

What is simplest form of equation?

The simplest form is the smallest possible equivalent fraction of the number.

Now,

Simplest form of expression,

\((4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\\4x^{3} +x^{2} +2 x^{3} -6x^{2} \\6x^{3} - 5x^{2}\)

Hence, The simplest form of the given expression \((4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\) is, \(6x^{3} - 5x^{2}\).

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Answer:

80 apples are in the bag

Step-by-step explanation:

24/n=30/100

24x100=2400

2400/30=80

80 apples in total

The difference between the selling price and the cost price is the profit he earned.

Profit = Selling Price - Cost Price

Profit = $216 - $180

Profit = $36

To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :

Percentage Profit = (Profit : Cost Price) * 100%

Percentage Profit = ($36 : $180) * 100%

Percentage Profit = 0.2 * 100%

Percentage Profit = 20%

Therefore, his percentage profit is 20%.

Complete Question

The complete question is shown on the first uploaded image

Answer:

Population

All undergraduate college students at the  researcher's university ,

Sample

The 107 undergraduate college students who returned the questionnaire

Step-by-step explanation:

From the question we are told that

   The list of undergraduate college students obtained from her university is  n= 1196

     The number of student that are randomly selected is  n =  500

      The number of e-mail that was returned is  k = 107

     The proportion that believes that the federal student loan program needs to be completely overhauled is  \(\^{p} = 0.71\)

Generally the population for this particular study is

All undergraduate college students at the  researcher's university ,

this is because they are the total pool of data from which the statistical sample are randomly selected from

Generally the sample for this particular study is

The 107 undergraduate college students who returned the questionnaire

 this is because this data provides us with an insight on the perspective of all undergraduate college students at the researcher's university about federal financial  aid

Answer:

Dan, because he types 60 words per minute.

Step-by-step explanation:

Jim: 3850/70 = 55 words/minute

David: 3300/60 = 55 words/minute

Dan: 2400/40  = 60 words/minute

\(\huge\fbox{Answer ☘}\)

\(7(8) - 6 \div 2 + (a)3 = 107 \\ 56 - 3 + 3a = 107 \\ 53 + 3a = 107 \\ 3a = 107 - 53 \\ 3a = 54 \\ a = \cancel\frac{54}{3} = 18\)

hope helpful~

The value of A in the expression is 18

The expression is given as:

\((7)8 - 6 \div 2 + (A)3 = 107.\)

Evaluate the quotient

\((7)8 - 3 + (A)3 = 107.\)

Open all brackets

\(56 - 3 +3A = 107.\)

Subtract 3 from 56

\(53 +3A = 107.\)

Subtract 53 from both sides

\(3A = 54\)

Divide both sides by 3

\(A = 18\)

Hence, the value of A in the expression is 18

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Answer:

\(\huge\boxed{120 \textdegree}\)

Step-by-step explanation:

In order to solve for m∠TSP, we can use basic angle relationships and equations.

Let’s assume m∠PSW is \(x\)°

We know that if two angles are supplementary, their angle lengths will add to 180°.

We also know that m∠TSP is twice as large as PSW. Since PSW is represented as x°, TSP will be 2x°.

We can add these two angles together and get 180°. Then you can solve for x (PSW)

So we know that x (PSW) is 60°. However, the question asks for the measure of TSP. We know that TSP is twice as large as PSW, so we can multiply PSW (60) by 2.

\(60 \cdot 2 = 120\)

So m∠TSP is 120°.

Hope this helped!

Answer:

Should be the 2nd choice.

Answer:

1.727 x 10^4

Step-by-step explanation:

2.26 x 10^4 = 22 600

5.33 x 10³ = 5330

22 600 - 5330 = 17 270

17 270 = 1.727 x 10^4

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

c

Step-by-step explanation:

the square root of 106 is 10.

29

Answer:

Step-by-step explanation:

The function is continuous for x > 0 . The derivative is defined on that interval and is equal to ...

  f'(x) = -2x . . . . . for x > 0

Then at x = 1, the derivative is ...

  f'(1) = -2(1)

  f'(1) = -2

__

The function has a jump discontinuity at x=0, so the derivative does not exist at that point. A condition for the existence of the derivative is that the function is continuous at the point of interest.

P(A) given that A and B are independent is; 35%

P(A|B) is defined as a conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B"

Now, the formula to find P(A|B) is;

P(A|B) = P(A∩B) / P(B)

Where;

P(A∩B) = P(A) *  P(B)

Thus;

P(A|B) = (P(A) *  P(B))/(P(B)

Plugging in the relevant values gives;

0.35 = P(A)

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Answer:

If I directly give you the answers they won't help you...so I've shown you how to do the questions instead

Step-by-step explanation:

8/9 + 5/6 (make them have the same denominator)

= 48/54 + 45/54

= 93/54 (make it a mixed fraction)

1 and 39/54

(The second and third one are done the same way... make them have the same denominator by using their equivalent fractions (e.g 1/2 = 2/4), add the numerators ONLY... simplify the result)

1 and 6/9 divided by 5/6

(make the first number an improper fraction)

1 x 9 + 6 = 15 (this is the numerator...the denominator remains the same)

15/9 divided by 5/6 (reciprocate the number after the division sign and then change the division sign to a multiplication sign)

15/9 x 6/5

(Then simplify. e.g the 5 in 6/5 can be divided by the 15 in 15/9)

3/9 x 6/1

(The 6 in 6/1 and the 9 in 3/9 have a common factor... 3)

3/3 x 2/1

(3/3 = 1)

1 x 2

=2

(The other questions are done in the same way... Make the mixed fraction an improper fraction(This means the denominator is larger than the numerator)... reciprocate the number after the division sign (This means flipping it (e.g 2/3 becomes 3/2) then change the division sign to a multiplication sign and either directly multiply the result or simplify it first by dividing numerators with denominators (e.g instead of 9/3 x 12/4 = 108/12 = 9, you could say 1 divided 3 = 4 thus 9/1 x 4/4 (which is = 1) thus 9 x 1 = 9). Either way you should get the same answer whichever way you choose.

PS: YOU COULD ALSO USE A CALCULATOR TO CONFIRM YOUR ANSWER

#1

#2

#3

#4

#5

Answer:

Step-by-step explanation:

Given parameters:

              1 mile = 6 x 10⁴ inches

Average human hair  = 3 x 10⁻³ inches

Unknown:

How many times longer is a mile than a human hair;

Solution:

 Since we know that a mile 6 x 10⁴ inches , we can compare this quantity to the human hair;

     Number of times  = \(\frac{6 x 10^{4} }{3 x 10^{-3} }\)

     Number of times  = 2 x 10⁴⁺³

     Number of times  = 2 x 10⁷

So, a mile is 2 x 10⁷ times longer than the human hair.

Answer:

tan(θ)= dn/de

θ=arctan(dn/de)

Step-by-step explanation:

The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Wood 1:

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

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Answer:

Slopes of parallel lines are equal

Step-by-step explanation:

On a coordinate plane, quadrilateral ABCD is shown. Point A is at (-2, -2), point B is at (-3, 4), point C is at (2, 2), and point D is at (3, -4).

The slope of the line segment BC is:  

\(\dfrac{4-2}{-3-2} =-\dfrac{2}{5}\)

The slope of the line segment AD is:

\(\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}\)

The slope of the line segment CD is:

\(\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6\)

The slope of the line segment BA is:

\(\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6\)

Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

Answer:

c.) on edg.

Step-by-step explanation:

got it right :)

Answer:1/20

Step-by-step explanation:

trust

Answer:

1/20

Step-by-step explanation:

5 divided by 100 is =20

5divided by 5 is =1

=1/20

Answer:

Step-by-step explanation:

?

The total surface area of the given composite figure is: 66 m²

To find the total surface area, we will simply find the area of each surface and add it up to get the total.

Area of a rectangle is given by the formula:

Area = Length * Width

Thus:

Total surface area = 2(1 * 4) + 2(5 * 2) + (2 * 2) + (2 * 5) + (9 * 2) + (1 * 2) + (4 * 2) = 8 + 20 + 10 + 18 + 2 + 8

= 66 m²

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