i am pretty sure you add up all of them
The percent change in the numerator for the cash coverage ratio, considering the changes in EBIT and depreciation, is 12.5%. Meanwhile, the percent change in the denominator, based on the interest expense, is 33.33%.
Explanation:The cash coverage ratio is a measure of a company's ability to pay off its obligations and is calculated by adding depreciation and EBIT and then dividing by the interest expense. For this question, we are looking at the percent change in the numerator, which is EBIT + depreciation, and the denominator, which is the interest expense. With EBIT going from $30m to $33m, depreciation going from $10m to $12m, and interest expense going from $6m to $8m we can calculate as follows.
The original numerator value was $40m (EBIT of $30m + depreciation of $10m) and the new numerator is $45m (EBIT of $33m + depreciation of $12m). So, the percent change in the numerator of the cash coverage ratio is ((45-40)/40)*100 = 12.5%. The original denominator was $6m and the new denominator is $8m. Thus, the percent change in the denominator of the cash coverage ratio is ((8-6)/6)*100 = 33.33%.
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The range of which function includes –4?
Answer:
[tex]y=\sqrt{x} -5[/tex]
Answer:
The function [tex]f(x)=\sqrt{x-5}[/tex]
Step-by-step explanation:
The Range of any function is complete set of all possible resulting values of the dependent variable , after substituting the domain.
so, the function [tex]f(x)=\sqrt{x-5}[/tex] has range [tex]f(x)$\geq$ -5[/tex]
This includes - 4 .
Hence, the function is [tex]f(x)=\sqrt{x-5}[/tex] .
PLEASE HELP ME OUT :) Independent or Dependent?
Also, is there an easier way to determine if these are independent or dependent other than working out the entire problem? (Not trying to be lazy. My school website uses common core learning which explains each problem in, seemingly, the most difficult way possible for most different types of algebra and geometry)
Answer:
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
Step-by-step explanation:
Two events A and B are independent if the occurrence of A does not affect the probability of B.
On the other hand The probability of A given B is defined as:
[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]
When two events are independent then:
[tex]P (A\ and\ B) = P (A) * P (B)[/tex]
So if the two events A and B are independent this means that:
[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]
[tex]P (A | B) = P (A)[/tex]
Which makes sense because if the events are independent then the probability of A not being affected by B.
So to solve this problem identify in what cases
[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]
When this happens those events are independent
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
Find the area of the triangle.
Answer: 118.3 m^2
Step-by-step explanation:
Use Heron's formula: √s(s-a)(s-b)(s-c)
s= a+b+c/2
13+18.2+22.3/2 = 26.75
√26.75(26.75-13)(26.75-18.2)(26.75-22.3)
√26.75(13.75)(8.55)(4.45)
√13994.34609
118.297701 = 118.3 m^2
Sophie Ruth is eating a 505050-gram chocolate bar which contains 30\%30%30, percent cocoa. How many grams of cocoa are in the chocolate bar?
Answer:
15 g
Step-by-step explanation:
30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g
Answer:
15g
Step-by-step explanation:
Investigation Circles: Investigation 2
I need help with the worksheet
Explanation:
1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.
"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."
__
2. We know from the first question that ...
circumference/diameter = π
And we know that ...
diameter = 2·radius
Then the following are true:
A. circumference = π · diameter
B. circumference = (2·radius) · π
__
3. The expressions in order evaluate to approximately ...
4.0, 3.45, 3.31, 3.24
Of these, the last is closest to pi (3.14....). The appropriate choice is ...
D. (10·5)/15.4
__
4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.
Find the area of the triangle
Answer:
Step-by-step explanation:
A=BH/2
A=9x12/2
A=54
Answer: 54
Step-by-step explanation:
A = base * height ÷ 2
A = 12 * 9 ÷ 2
A = 108 ÷ 2
A = 54
Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.
His answer is f(x) = (
)2 – 5.
Hm, it seems like his answer is off. The image is what I got.
Answers:
X+3
Step-by-step explanation:
I got it right
Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square. Also find the area of the square.
Answer:
the point r would be located at (4,3)
Step-by-step explanation:
granted that the quadralaterel is a square that would mean that all side lengths are equal and the distance between points x and q is 3 meaning that the same would have to be said about the distance between s and r
The graphs of two cosine functions are shown below.
The function whose graph is B was obtained from the function whose graph is A by one of the following changes. That change was:
the addition of a negative constant
a change in amplitude
a phase shift
a period change
Answer:
"the addition of a negative constant"
Step-by-step explanation:
Please note the following points of functions regarding transformations:
1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant
2. If there is a phase shift, the function would be horizontally transformed
3. If there is a period change, the function would be horizontally compressed/stretched
4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.
We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.
Point (-4, 3) lies in Quadrant I II III IV
Answer:
Quadrant II
Step-by-step explanation:
I attached an image of the quadrants system.
You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.
Quadrant I
Degrees: 0-90
X values: positive (+)
Y values: positive (+)
Quadrant II
Degrees: 90-180
X values: negative (-)
Y values: positive (+)
Quadrant III
Degrees: 180-270
X values: negative (-)
Y values: negative (-)
Quadrant IV
Degrees: 270-360
X values: positive (+)
Y values: negative (-)
John was born in 1951 and has been contributing to his own retirement plan as well as
Social Security for many years. John was trying to decide if he wanted to retire at 62 years of age rather than at 66 when he would reach full retirement age. According to the Social Security laws, John would receive a 25% reduction in his Social Security if he retired at 62. John went to the Social Security website and discovered that if he retired at 66 he would receive $2,460 a month in retirement from Social Security. How much would he receive if he retired at 62 rather than at 66?
a. $1,650 a month
b. $1,845 a month
c. $1,500 a month
d. $1,745 a month
Answer:
[tex]\boxed{\text{b. \$1845 a month}}[/tex]
Step-by-step explanation:
Amount if retired at 66 = $2460/mo
Less 25 % = 0.25 × 2460 = -615
Amount if retired at 62 = $1845/mo
John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.
4x2+3x=0 please solve this by using quadratic formula
Answer:
x= 0 and x=-3/4
Step-by-step explanation:
[tex]4x^2 + 3x =0[/tex]
We need to solve this equation using quadratic formula.
The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
for the type of equation
[tex]ax^2 +bx+c=0[/tex]
So, for our given equation:
a= 4
b= 3
c=0
putting values in the formula
[tex]x=\frac{-3\pm\sqrt{9-0}}{8}\\x=\frac{-3\pm3}{8}\\x=\frac{-3+3}{8}\,and\, x=\frac{-3-3}{8}\\x=\frac{0}{8}\,and\, x=\frac{-6}{8}\\x=0\,and\, x=\frac{-3}{4}[/tex][/tex]
so, x= 0 and x=-3/4.
(6Q) Find the domain and range.
Answer: Option a.
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
We have the function [tex]f(x) = 2x + cosx[/tex]
Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]
The domain and range of h(x) are all real numbers
The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]
Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].
Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)
The range of f(x) will be equal to the union of the range of g(x) and h(x)
Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)
Gustavo earns 8 dollars per hour plus 10% of his sales. Write an equation that models Gustavo's total earnings, E, when he works x hours and has a total of y sales in dollars. you do not need to solve the equation.
Answer:
e = 8x + 0.1y
Step-by-step explanation:
If Gustavo makes no sales at all, he still gets $8 per hour worked (x). We can model this part with this equation:
e = 8x
But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y). So the equation becomes:
e = 8x + 0.1y
or you can express it this way:
e = 8x + y/10
which is the same thing just written differently.
Which equation represents the perpendicular bisector of the given line segment?
A) x = 0
B) y = 0
C) y = x
D) x = 10
Answer:
Option D. [tex]x=10[/tex]
Step-by-step explanation:
step 1
Find the midpoint of the given line segment
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
[tex]A(5,10),B(15,10)[/tex]
substitute the values
[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]
[tex]M=(10,10)[/tex]
step 2
Find the equation of the perpendicular bisector
we know that
The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)
therefore
the equation is equal to
[tex]x=10[/tex]
Answer:
10
Step-by-step explanation:
In ®A shown below, radius AB is perpendicular to chord XY at point C. If XY=24 and AC=5 cm, what is the radius of the circle?
ANSWER
B. 13cm
EXPLANATION
The radius of the circle becomes the hypotenuse of the right triangle formed.
We can use the Pythagoras Theorem to obtain,
AC²+CY²=r²
This implies that,
r²=5²+12²
r²=25+144
r²=169
Take positive square root to get;
r=√169
r=13
AB and AC are two equal chord of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.
OA is the bisector of ∠BAC.
Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.
P divides BC in the ratio 6:6=1:1.
P is mid-point of BC.
OP ⊥ BC.
In △ ABP, by pythagoras theorem,
AB2=AP2+BP2
BP2=36−AP2 ....(1)
In △ OBP, we have
OB2=OP2+BP2
52=(5−AP)2+BP2
BP2=25−(5−AP)2 .....(2)
From 1 & 2, we get,
36−AP2=25−(5−AP)2
36=10AP
AP=3.6cm
Substitute in equation 1,
BP2=36−(3.6)2=23.04
BP=4.8cm
BC=2×4.8=9.6cm
Sasha has a fever of 103°F. What is Sasha’s fever in degrees Celsius?
32°C
39.4°C
66.9°C
71°C
39.4 degrees Celsius
Hope this helps :)
Answer:
39.4°C
Step-by-step explanation:
The equation for fahrenheit to celsius is
(°F − 32) × 5/9 = °C
With our variable of 103 plugged in it is
(103°F − 32) × 5/9 = 39.444°C
Therefore, her fever is 39.4°c
Can someone help please
Answer:
62 Sunday papers were sold
Step-by-step explanation:
Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:
1.50 · x + 0.75 · (x/2) = 116.25
Multiplying by 2, this becomes ...
3.00x +0.75x = 232.50
3.75x = 232.50
Dividing by the coefficient of x gives ...
232.50/3.75 = x = 62
The number of Sunday newspapers sold is 62.
What is the area of triangle ABC? Round your final answer to the nearest cm.
Answer:
A = 21.65 cm squared
Step-by-step explanation:
The basic area formula for a triangle is
[tex]A= \frac{1}{2}bh[/tex]
We have our base as 5, so we can find the height using right triangle trig. Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base. Using the tangent ratio to find side BC:
[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to
5 tan(60) = x so
x = 8.66
Filling in for the area:
[tex]A= \frac{1}{2}(5)(8.66)[/tex] so
A = 21.65 cm squared
Answer both questions please
1.) The diameter of a circle is 10cm.What is the approximate circumference? Use 3.14 for pi
2.) The radius of a circle is 3 inches. What is the approximate area? Use 3.14 for pi.
Answer:
31.4cm
Step-by-step explanation:
C = 2*pi*r
2r = d
2r=10
r=5
C = 2*5*pi
C = 10*3.14
C = 31.4cm
Solve x^2 +5x-10=0. How do you solve this
Answer:
(-5 +/- sqrt(65))/2
Step-by-step explanation:
To solve this, we can use the quadratic formula!
So,
x = (-b +/- sqrt(b^2-4ac))/2a
x = (-5 +/- sqrt(25+40))/2
x = (-5 +/- sqrt(65))/2
So (-5 +/- sqrt(65))/2 is our answer.
The pie store is having a 20% , percent off sale on all of its pies. If the pie you want regularly costs $18 dollar sign, 18, how much would you save with the discount?
20% off, means that 20% of the regular price is how much you would save.
Multiply the original price by 20%
18 x 0.20 = 3.6
The discount is $3.60
Frank and his family are going to the grand opening of a circus there is a special price on tickets this weekend tickets cost 36 each this is a 60% of the cost of a regular price ticket. What is the cost of a regular price ticket?
Answer:
60
Step-by-step explanation:
(This is not how teachers usually teach you)
First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.
Answer:
The cost of a regular price ticket is $60.Step-by-step explanation:
Givens
Tickets cost $36 each, which represents 60% of the regular price.To find the regular price for tickets, we can use the rule of three.
If $36 represents 60%, how much would represents 100%?
[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]
Therefore, the cost of a regular price ticket is $60.
Please please help me
Answer: 5 Vertices
Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.
It takes Ahmed 50 seconds on his bike to reach his friend's house 250 meters away. What is his average speed?
It takes 5 meters per second.
If you divide 250 by 50 you would get his average speed
The average speed of Ahmed is 5 meters per second.
Important information:
Time taken by Ahmed = 50 secondsDistance = 250 metersWe need to find the average speed of Ahmed.
Average speed:Formula for average speed is:
[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Using this formula, the average speed of Ahmed is:
[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]
[tex]\text{Average Speed}=5[/tex]
Thus, the average speed of Ahmed is 5 meters per second.
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I need help getting started please
Check the picture below.
so, the triangular prism is really 2 triangles and 3 rectangles stacked up to each other at the edges. Let's simply get the area of each shape and sum them up, and that's the area of the prism.
[tex]\bf \stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{6})(\stackrel{height}{5.2}) \right]}+\stackrel{\textit{right-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{left-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{base rectangle}}{(8\cdot 6)} \\\\\\ 31.2+48+48+48\implies 175.2[/tex]
Answer:
The surface area = 175.2 mm²
Step-by-step explanation:
Formula:-
Area of rectangle = lb
Area of triangle = bh/2
It is given a triangular prism.
To find the surface area
Surface area = 3 Rectangle area + 2 triangle area
Rectangle area = 3 * lb
= 3 * 8 * 6
= 144 mm²
Triangle area = 2 * bh/2 = bh
= 6 * 5.2 = 31.2²
Total area = 144 + 31.2 = 175.2 mm²
The midsegment of a trapezoid is 11 cm in length. If one of the trapezoid's bases is 17 cm long, what is the length of the other base?
Answer:
x must be 5
Step-by-step explanation:
Recall that the area formula for a trapezoid is
A = (average of base lengths)(width)
Here we have
17 cm + x
(average of base lengths) = 11 cm = ----------------
2
So 2(11 cm) = 17 cm + x, or
22 cm = 17 cm + x
Then x must be 5.
To find the length of the other base of the trapezoid with a midsegment of 11 cm and one base of 17 cm, use the average property of the midsegment. The calculation reveals the other base is 5 cm in length.
Explanation:The question is about finding the length of the other base of a trapezoid when the length of the midsegment and one of the bases is known. The midsegment of a trapezoid is parallel and equal to the average of the two bases. Therefore, if the midsegment is 11 cm and one base is 17 cm, the other base can be found by setting up the equation:
Midsegment = (Base1 + Base2) / 2
Substitute the known values:
11 = (17 + Base2) / 2
Multiplying both sides by 2 gives:
22 = 17 + Base2
Subtracting 17 from both sides gives:
Base2 = 22 - 17
Base2 = 5
Thus, the length of the other base of the trapezoid is 5 cm.
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A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
4046.56 cm3
Step-by-step explanation:
The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.
Your volume will be [tex]5 * \frac {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]
A stove costs $695 will be on sale next week for 20% off its regular price. What is the amount of savings
Answer:
It would be 139$
Step-by-step explanation:
In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.
What equation/thing is happening to this number to get this solution? My book is just telling me "use a calculator" but it doesn't explain it any further. Please help!
Answer:
Use the square root function on your calculator
Step-by-step explanation:
Look at the third line down, where is says that 936 = AD^2. If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function. After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator. The square root of 936 is 30.59417