The correct solution of the expression is,
⇒ 16 / e¹²ˣ
We have to given that;
The value of Expression is,
⇒ (2e⁻³ˣ)⁴
Now, We can simplify as;
⇒ (2e⁻³ˣ)⁴
⇒ 2⁴ × e⁻¹²ˣ
⇒ 16e⁻¹²ˣ
⇒ 16 / e¹²ˣ
Thus, The correct solution of the expression is,
⇒ 16 / e¹²ˣ
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A man is flying in a hot air balloon in a straight line at a constant rate of 5' per second while keeping it at a constant altitude. As he approaches the parking lot of a market. , he notices that the angle of depression from his balloon to a friend's car in the parking lot is 34ﾟ. A minute and a half later after flying directly over his friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36ﾟ At that time what is the distance between him and his friend?
The distance is given as 272.98 feet.
What is Angle of Depression?The measurement of the angle of depression relates to the formation between a horizontal line and the observer's sightline to an object or point that exists beneath their level.
Therefore, it demonstrates the formed degree between the observer's line of vision towards a subject and the horizontal flatness visible when looking downwards at it from afar.
This notion is prevalent throughout trigonometry and play a vital role in areas including surveying, navigation and architecture. The degrees obtained from this practice are generally calculated via angles, with a complete 90-degree measure indicative of viewing straight downward over the designated target.
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Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college
with no student loan debt. This is her only job, and she makes a salary that allows her to
bring home $3,300 a month. She's not married and has no children or anyone else who
is supported by her income. Over the past year, she has given a total of $3,960 to charity.
Her address is 1234 Main St., New York, NY 12345, and her Social Security number is
123-45-6789.
Note that the above prompt requires you to under stand what a W-4 form is and how to complete one.
What is the process for comleting the W-4 form?Rbecca needs to s tart by entering your personal information in boxes 1-4, including your name, address, Social Security number, and filing status. In this case, Rebecca Kate Foster's information is:
Box 1: Rebecca Kate Foster
Box 2: 1234 Main St.
Box 3: New York, NY 12345
Box 4: 123-45-6789
Box 5: Single
In box 6, write "1" since Rebecca only has one job.
Rebecca can claim the standard deduction or itemize deductions in box 7. She may benefit from itemizing deductions because she has donated $3,960 to charity in the last year.
Rebecca can claim whatever excess tax withholding she wants each paycheck in box 8. She may not need to withhold any further taxes because she has no dependents and is not married. If she prefers, she can leave this section blank.
Rebecca can claim any extra withholding for the year in box 9. If she anticipates to owing taxes at the end of the year, she may want to withhold more from each paycheck to prevent a hefty tax payment later. If she anticipates a reimbursement, she should withhold less. She can use the IRS's withholding calculator to determine the right amount.
Finally, sign and date the form in box 5 before submitting it to your company.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
DIRECTIONS Read the scenario below and fill out the W-4 form using the information provided. Then, read the W-2 form and answer the questions that follow. W-4 Form Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college with no student loan debt. This is her only job, and she makes a salary that allows her to bring home $3,300 a month. She’s not married and has no children or anyone else who is supported by her income. Over the past year, she has given a total of $3,960 to charity. Her address is 1234 Main St., New York, NY 12345, and her Social Security number is 123-45-6789.
Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
Answer: A
Step-by-step explanation: -87
Determine what the project’s ROE will be if its EBIT is –$50,000. When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.
-5.67%
-5.4%
-5.13%
-6.48%
Universal Exports Inc. is also considering financing the project with 50% equity and 50% debt. The interest rate on the company’s debt will be 10%. What will be the project’s ROE if it produces an EBIT of $140,000?
19.13%
21.38%
22.50%
24.75%
What will be the project’s ROE if it produces an EBIT of –$50,000 and it finances 50% of the project with equity and 50% with debt? When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.
-18.21%
-20.94%
-20.03%
-23.67%
The return on equity (ROE) for a project financed with 100% equity or 50% equity and 50% debt, given different levels of earnings before interest and taxes (EBIT) are 20.3%, -5.4%, 36.2% and -20.3% respectively. So, the correct answers are A), B), A) and A). if Galaxy Corp. proceeds with a recapitalization then Basic earning power (BEP), Return on assets (ROA), Net income are likely to increase. The correct option is A), B) and E).
ROE = EBIT*(1 - T)/Total Equity
Where T is the tax rate and Total Equity is the amount of equity used to finance the project.
If the EBIT is $145,000, then
ROE = $145,000*(1 - 0.30)/$500,000 = 20.3%
Therefore, the answer is 20.3%. So, the correct answer is A).
If the EBIT is -$45,000, then
ROE = -$45,000*(1 - 0.30)/$500,000 = -5.4%
Therefore, the answer is -5.4%. So, the correct answer is B).
If the project is financed with 50% equity and 50% debt at an interest rate of 11%, then the cost of equity can be calculated as follows
Cost of Equity = EBIT*(1 - T)/Total Equity
Cost of Debt = Interest Rate*(1 - T)
Weighted Average Cost of Capital (WACC) = Cost of Equity*(Equity/Total Capital) + Cost of Debt*(Debt/Total Capital)
ROE = EBIT*(1 - T)/Total Equity
ROE = [$145,000*(1 - 0.30)/($500,0000.50)] + [$145,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]
ROE = 36.2%
Therefore, the answer is 36.2%. So, the correct answer is A).
If the project is financed with 50% equity and 50% debt at an interest rate of 11%, and the EBIT is -$45,000, then
ROE = -$45,000*(1 - 0.30)/($500,0000.50) + [-$45,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]
ROE = -20.3%
Therefore, the answer is -20.3%. So, the correct answer is A).
If Galaxy Corp. proceeds with the recapitalization, the cost of debt is likely to increase since the firm is issuing new long-term debt. Therefore, the cost of debt (rdrd) will increase.
However, the basic earning power (BEP) and return on assets (ROA) are likely to increase since the firm will have a higher proportion of debt in its capital structure, which will increase the financial leverage of the firm.
As a result, the net income of the firm may also increase. The cost of equity (rsrs) may or may not change depending on how the market perceives the increased financial risk associated with the higher debt level.
Therefore, the items that are likely to increase are Basic earning power (BEP), Return on assets (ROA), Net income. The correct answer is A), B) and E).
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--The given question is incomplete, the complete question is given
" Universal Exports Inc. is considering a project that will require $500,000 in assets. The project will be financed with 100% equity. The company faces a tax rate of 30%. What will be the ROE (return on equity) for this project if it produces an EBIT (earnings before interest and taxes) of $145,000?
20.3%
22.3%
13.2%
14.2%
Determine what the project’s ROE will be if its EBIT is –$45,000. When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.
-7.6%
-5.4%
-6.3%
-5.7%
Universal Exports Inc. is also considering financing the project with 50% equity and 50% debt. The interest rate on the company’s debt will be 11%. What will be the project’s ROE if it produces an EBIT of $145,000?
36.2%
32.9%
24.7%
26.3%
What will be the project’s ROE if it produces an EBIT of –$45,000 and it finances 50% of the project with equity and 50% with debt? When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.
-20.3%
-19.3%
-21.3%
-26.4%
Galaxy Corp. currently is financed with 10% debt and 90% equity. However, its CFO has proposed that the firm issue new long-term debt and repurchase some of the firm’s common stock. Its advisers believe that the long-term debt would require a before-tax yield of 10%, while the firm’s basic earning power is 14%. The firm’s operating income and total assets will not be affected. The CFO has told the rest of the management team that he believes this move will increase the firm’s stock price. If Galaxy Corp. proceeds with the recapitalization, which of the following items are also likely to increase? Check all that apply.
Basic earning power (BEP)
Return on assets (ROA)
Cost of debt (rdrd)
Cost of equity (rsrs)
Net income"--
Consider the sequence 4,323,313,3
The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
4, 3 2/3, 3 1/3, 3....
In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term
Take for instance
2nd = 4 - 1/3 = 3 2/3
3rd = 3 2/3 - 1/3 = 3 1/3
4th = 3 1/3 - 1/3 = 3
And so on
This means that
First term, a = 4Common difference, d = -1/3So, the explicit rule is
f(n) = a + (n - 1)d
This gives
f(n) = 4 - 1/3(n - 1)
Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)
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Complete question
Consider the sequence 4,3 2/3,3 1/3, 3....
What is the explicit rule for this sequence
I need help please to solving this problem
The height of the tower is given as follows:
h = 22.5 ft.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The reflection means that the two triangles are similar in this problem, hence the proportional relationship for the equivalent side lengths is given as follows:
3/13.5 = 5/h
Then the height is obtained as follows:
3h = 5 x 13.5
h = 5 x 13.5/3
h = 22.5 ft.
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Translate the sentence into an equation.
The quotient of a number and 8 is 16.
What is the solution to the equation?
One-half
2
128
164
Answer:
128
Step-by-step explanation:
To translate the sentence into an equation, we can use the following formula: number / 8 = 16. This equation shows that we are dividing a number by 8 and getting a result of 16. To solve for the number, we can multiply both sides of the equation by 8. This gives us the equation number = 16 x 8, which simplifies to number = 128. Therefore, the solution to the equation is 128.
Answer:
128
Step-by-step explanation:
got it right on edge
find the inverse of the function f(x)=-1/25x^2, x<0
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
What is an inverse function ?If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
We have to find the inverse of the function.
The inverse, interchange the variables solve for y,
Now,
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Hence,
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
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(06.06 MC)
The table below shows the amount of money, in cents, Celine had in her savings account after different
number of years:
Years 251463
Money in
36 112 12 85 150 60
cents
Approximately, what will be the amount of money, in cents, that Celine will save in 12 years?
250
300
400
200
Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300
How to determine the equation of line of best fit?In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by
y = 26.9x - 18.5
when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;
y = 26.9(12) - 18.5
y ≈ 300 cents.
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The list represents the number of students who checked books out of the library in a 10-day period.
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
Find the median and interpret its meaning as it relates to the number of students checking out books.
A. The median is 32, and it represents the difference in the lowest and highest number of students who checked books out.
B. The median is 83, and it represents the highest number of students who checked books out.
C. The median is 40, and it represents the most common number of books that students checked out.
D. The median is 50, and it represents the typical number of students who checked books out.
For the given rectangular equation give its equivalent polar equation
Answer:
The last option
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
Step-by-step explanation:
Given equation is 6x - y = 14
To convert an equation in rectangular(cartesian) form, f(x, y) to polar f(r, θ) we use the following information
x = rcosθ
y = rsinθ
Substituting for x and y in the original rectangular equation 6x - y = 14,
6(rcosθ) - rsinθ = 14
Factoring out r on the left side,
r(6cosθ - sinθ) = 14
which gives
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
That would be choice 4
Here is question 5 of 6. Thank you for the help
The critical value for a two-tailed test at the 0.05 significance level is 1.96.
The null hypothesis is that there is no difference in the proportion of men and women intending to vote for Donald Trump, and the alternative hypothesis is that there is a difference.
The test statistic is given by:
z = (p1 - p2) /√[(p×(1-p)×(1/n1 + 1/n2),
where p = (x1 + x2) / (n1 + n2) and x1 and x2 are the number of successes in samples 1 and 2 respectively, and n1 and n2 are the sample sizes of samples 1 and 2 respectively.
In this case, x1 = 120, x2 = 132, n1 = 250, and n2 = 240.
Plugging these values into the equation gives us z = 0.906.
Since the test statistic does not exceed the critical value, we fail to reject the null hypothesis. That is, there is not convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.
Therefore, the critical value for a two-tailed test at the 0.05 significance level is 1.96.
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10. Bond A is zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying
$100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual
compounding, what is the yield to maturity on Bond B?
*Make sure to input all percentage answers as numeric values without symbols,
0.0600.
The yield to maturity on Bond B is 9%
How to calculate the yield to maturityWe know that Zero Coupon Bond Value= F/(1+r)^t
F= Face Value =100
r= Rate of interest
t= time to maturity =2Yrs
Price= F/(1+r)^t
84.18 = 100/(1+r)^t
(1+r)^t=100/84.18
(1+r)^2=1.18793
1+r=(1.18793)^(1/2)
r = 1.089922 - 1
r = 8.9922%
r = 9% (Approx)
In conclusion, the yield to maturity on Bond B is 9%
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How do you find Exponential Decay Rate?
1+b
1-b
Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?
You owe $2,264 on a credit card at a 14.7% APR. You pay $500.00 month. How many months does it take to pay off your balance?
Answer: 5.5 months
Explanation:
To calculate the number of months it will take to pay off your credit card balance, we can use the formula for the time it takes to pay off a balance with fixed monthly payments:
n = -log(1 - (r * b) / p) / log(1 + r)
where:n is the number of months it will take to pay off the balancer is the monthly interest rate (which is the annual percentage rate divided by 12)b is the balance owedp is the fixed monthly paymentFirst, let's calculate the monthly interest rate r:
r = 0.147 / 12 = 0.01225
Next, we can substitute the values into the formula:
n = -log(1 - (0.01225 * 2264) / 500) / log(1 + 0.01225)
Using a calculator, we can simplify this to:
n = 5.5 months
Solve the simultaneous equation graphically : x + y = 3 and 3x - y = 1.
( Taking the range of values of x from - 1 to +3
Answer:
x + y = 3 and 3x - y = 1.
Step-by-step explanation:
For the equation x + y = 3, we can find the x-intercept by setting y = 0 and solving for x:
x + 0 = 3
x = 3
So the x-intercept is (3, 0). Similarly, we can find the y-intercept by setting x = 0 and solving for y:
0 + y = 3
y = 3
So the y-intercept is (0, 3). We can plot these two points and draw a straight line through them to represent the equation x + y = 3. The resulting line has a slope of -1 and a y-intercept of 3.
For the equation 3x - y = 1, we can find the x-intercept by setting y = 0 and solving for x:
3x - 0 = 1
x = 1/3
So the x-intercept is (1/3, 0). Similarly, we can find the y-intercept by setting x = 0 and solving for y:
3(0) - y = 1
y = -1
So the y-intercept is (0, -1). We can plot these two points and draw a straight line through them to represent the equation 3x - y = 1. The resulting line has a slope of 3 and a y-intercept of -1.
Now, we can visually determine the point where the two lines intersect, which represents the solution to the simultaneous equation. We can do this by looking at the graph and finding the point where the two lines intersect. Using the given range of values of x from -1 to +3, we can plot the two lines and find their intersection point:
[i dont know wheres the graph image but just show it so you can explain that]
The intersection point is approximately (1.1, 1.9), which is the solution to the simultaneous equation x + y = 3 and 3x - y = 1.
gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
(NEED HELP!!!)
There are 32 cm² of frosting will take to cover the outside.
Given that;
Base of house = 2 cm
And, Height of house = 3 cm
Since, The shape of house is like a prism.
We know that;
Area of Prism is,
SA = 2B + ph,
where B, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.
Hence, We get;
SA = 2 × (2 × 2) + 2 (2 + 2) × 3
SA = 8 + 24
SA = 32 cm²
Hence, There are 32 cm² of frosting will take to cover the outside.
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Let the vector v have an initial point at (1,−1) and a terminal point at (7,2) what is the direction angle?
The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.
The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.
To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.
Let's first find the components of the vector v
v = <7 - 1, 2 - (-1)> = <6, 3>
Now, we can find the direction angle as follows
θ = arctan(3/6)
θ = 0.4636 radians (in decimal form)
To convert this to degrees, we can multiply by 180/π
θ ≈ 26.57°
Therefore, the direction angle of the vector v is approximately 26.57 degrees.
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Find the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
A. (x - 2)2 + (y - 5)2 = 169
B. (x - 2)2 + (y - 5)2 = 25
C. (x + 3)2 + (y + 7)2 = 169
D. (x + 3)2 + (y + 7)2 = 25
(x+3)²+(y+7)²=169 is the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The radius of the circle is 13
The equation of circle in standard form is (x-h)²+(y-k)²=r²
(h, k) is centre of circle
(-3, -7) is centre
(x+3)²+(y+7)²=13²
(x+3)²+(y+7)²=169
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A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
Help plss will give brainliest and points
The new coordinates of dilated rectangle by scale factor of 1/4 are J(1, 2), K(3, 2), L(3, 1), and M(1, 1) we can draw figure.
We are given the coordinates of the vertices of a rectangle J(4,8), K(12,8), L(12,4), and M(4,4).
To dilate the rectangle by a scale factor of 1/4, we need to multiply each coordinate by 1/4.
Multiplying each x-coordinate by 1/4
x-coordinate of J: 4 * 1/4 = 1
x-coordinate of K: 12 * 1/4 = 3
x-coordinate of L: 12 * 1/4 = 3
x-coordinate of M: 4 * 1/4 = 1
Multiplying each y-coordinate by 1/4
y-coordinate of J: 8 * 1/4 = 2
y-coordinate of K: 8 * 1/4 = 2
y-coordinate of L: 4 * 1/4 = 1
y-coordinate of M: 4 * 1/4 = 1
Therefore, the coordinates of the dilated rectangle are: J(1,2), K(3,2), L(3,1), and M(1,1).
Using these new coordinates, we can draw the dilated rectangle by plotting the four vertices on a coordinate plane.
The dilated rectangle has the same shape and orientation as the original rectangle, but it has been reduced in size by a scale factor of 1/4.
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A motorboat travels 234 miles in 6 hours going upstream. It travels 342 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current
The boat is moving at 48 mph while the current is moving at 9 mph in still water.
To solve this problemLet's use the letters "B" for the boat's speed in still water and "C" for the current's speed.
The boat's effective speed upstream is B - C because it is moving against the current.
Since the boat is moving downstream against the tide, its effective speed is equal to B plus C.
Based on the supplied data, we can construct the following two equations:
234 = 6(B - C)
342 = 6(B + C)
Making these equations simpler:
39 = B - C
57 = B + C
Now that we have added the two equations, we may solve for B and C:
39 + 57 = 2B
96 = 2B
B = 48
Therefore, the boat's speed in calm water is 48 mph.
To find C, we can rewrite one of the initial equations with this value as a substitute:
39 = 48 - C C = 9
Thus, the current is moving at a 9 mph velocity.
Therefore, the boat is moving at 48 mph while the current is moving at 9 mph in still water.
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PLEASE HELP ASAP WILL GOVE BRAINLIEST NEED THIS AWNSERED IN 15 MINUTES
The segment lengths on the right triangle are given as follows:
JL = 13.[tex]KL = 13\sqrt{3}[/tex]What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.The sum of the internal angle measures of a triangle is of 180º, hence the missing angle is given as follows:
m < L = 180 - (30 + 60)
m < L = 90º.
Hence the segment JL represents the hypotenuse of the figure.
JL is opposite to the angle K, hence it's length is obtained as follows:
sin(30º) = JL/26
1/2 = JL/26
2JL = 26
JL = 13.
Segment KL is adjacent to the angle of 30º, hence it's length is obtained as follows:
cos(30º) = KL/26
[tex]\frac{\sqrt{3}}{2} = \frac{KL}{26}[/tex]
[tex]2KL = 26\sqrt{3}[/tex]
[tex]KL = 13\sqrt{3}[/tex]
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Mr Greenwood paid $11 for 5 buns and 2 sausages last week. His wife bought 8 such buns and 4 such sausages for $19.60 this week.
(a)
How much was each bun?
(b) How much was each sausages?
Answer:
Step-by-step explanation:
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If x and y vary directly and y is 2 when x is 3, what is why when x is 2
Step-by-step explanation:
Direct variation means y = k x
when y = 2 x= 3
2 = k *3
2/3 = k
so the variation becomes y = 2/3 x
when x = 2
y = 2/3 (2)= 4/3
Factor cards is a one - player game using numbered cards. To begin with, all cards are in a central pile with their numbers visible. At each turn , exactly one card is moved from the central pile to the score pile and one or more cards are moved from central pile to the discard pile according to these rules.
Rule 1: A card may be moved to the score pile only if the number on the card has at least one of its factors, other than itself, still on the central pile.
Rule 2: When a card is moved to the score pile, all the cards that have factors of its number and are still in the central pile are moved to the discard pile.
Play stops when no card in the control pile has a factor other than itself in the central pile. The players score is the sum of all numbers on the cards in the score pile at the end of play.
In the following questions, the game starts with 20 cards numbered 1 to 20 and are therefore called 20-games.
A) Show steps that will produce a score of more than 100 points in a 20- game
B) What is the maximum score for a 20- game. Explain why it is the maximum
C) Explain why every 20- game ends with 8 or fewer cards in the score pile .
The match terminates as soon as the central heap runs out of cards whose factor are not present elsewhere, resulting in a score of 92 - falling short from 100.
How to explain the informationIt should be noted that to acquire a higher point achievement, alternative approaches can be tested; however, reaching beyond the hundred mark is not guaranteed.
Conversely, with each 20-game, the final outcome should contain 8 or fewer pieces in the tally pile since there are strictly 17 cards eligible to be shifted into this collection. Subsequently, due to the 138 maximum points potential (stated in part B), and the entire set amounting for 210 points - the minimum count for items within the discard pool will be 3 (as calculated from 20 - 17).
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Find the percent of the number
13% of 50
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{13\% of 50}}{\left( \cfrac{13}{100} \right)50}\implies 6.5[/tex]
Answer: 6.5
Step-by-step explanation: You can find the percent of a number by multiplying the two together such as 50(0.13). This will give you the answer of 6.5.
Is it 65 and 5 bag variability????
The estimate of the population mean is 80 and the variability in the distribution is 120
The estimate of the population meanHere, we have
The dot plots
From the dot plots, we can see that the data are normally distributed
This means that the mean, the median and the mode are equal
From the distribution of the random variable, we have the following readings
mean = 80Hence, the estimate of the population mean is 80
The variability in the distributionHere, we use the range
So, we have
Variability = Highest - Least
This gives
Variability = 140 - 20
Variability = 120
So, the variability in the distribution is 120
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In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale.
For m
The measure of ∠BPO is 48°.
How to find the measure of ∠BPO?Since PD bisects ∠BPA, we can say:
∠AOC = ∠BOC .
Thus, ∠ BOC = 42°
Since PB is tangent to the circle, PBO = 90°.
Looking at triangle PBO, we can say:
∠BPO + ∠PBO + ∠BOC = 180 (angles in a triangle add up to 180)
∠BPO + 90 + 42 = 180
∠BPO + 132 = 180
∠BPO = 180 - 32
∠BPO = 48°
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6-Tel, Inc. is a telecommunication services provider looking to expand to a new territory Z; it is analyzing whether it should install its own telecom towers or lease them out from a prominent tower-sharing company T-share, Inc.
Leasing out 100 towers would involve payment of $5,000,000 per year for 5 years. Erecting 100 news towers would cost $18,000,000 including the cost of equipment and installation, etc. The company has to obtain a long-term secured loan of $18 million at 5% per annum. Owning a tower has some associated maintenance costs such as security, power and fueling, which amounts to $10,000 per annum per tower.
The company's tax rat is 40% while its long-term weighted average cost of debt is 6%. The tax laws allow straight-line depreciation for 5 years. Determine whether the company should erect its own towers or lease them out.
Answer:
The present value of leasing the towers is $19,576,000 while the present value of erecting new towers is $20,273,000. Therefore, the company should lease the towers.
Step-by-step explanation: