Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 66 \ln x + 135[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]Logarithmic Differentiation: [tex]\displaystyle y' = \frac{66}{x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $70,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $2900 per performance, and your jazz ensemble is charging $800 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.) C(x, y)
Answer:
The monthly cost function for the scenario C(x,y) is;
C(x,y) = 70,000 + 2900x + 800y
Step-by-step explanation:
Let C represent the monthly cost in dollars.
x represent the number of performances by the cabaret artist per month
and y represent the number of hours of jazz per month
Given;
monthly costs of $70,000
regular cabaret artist is charging you $2900 per performance.
Per month = $2900x
your jazz ensemble is charging $800 per hour.
Per month = $800y
The monthly cost function for the scenario C(x,y) is the sum of all the costs;
C(x,y) = 70,000 + 2900x + 800y
If f(x) = 2x – 1 and g(x) = 3x + 5, then (f o g)(x) is equal to
Answer:
(f◦g)(x) = 6x +9
Step-by-step explanation:
Use g(x) as the argument to f(x) and simplify.
(f◦g)(x) = f(g(x)) = f(3x +5) = 2(3x +5) -1
(f◦g)(x) = 6x +9
The range of the secant function is?
Answer:
1. Where are the vertical asymptotes on the graph of the secant function?
choice A: x = π /2 + nπ
2. The range of the secant function is
answer: y ≤ -1 or y ≥ 1
3. What is the period of the secant function?
Choice C : 2π
Step-by-step explanation:
there are 3 questions on this page.
correct on edge
The range of secant is y ≤ -1 or y ≥ 1.
What is a range in the function?The range of a function is the set of its possible output values.
As we know the vertical asymptotes of the secant function
x = π /2 + nπ
and, The range of the secant function is
y ≤ -1 or y ≥ 1
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Simon walks a total of 45.55 miles in March and 35.7 miles in April.
How many miles does Simon walk in all in March and April?
Enter your answer
Answer:
81.25
Step-by-step explanation:
45.55 + 35.7
Answer:I hope that helps
Step-by-step explanation:
Rachel bought two coloring books.
One had 134 pictures and the other
had 309. After one week she had
already colored 145 of the pictures,
How many pictures does she still have
to color?
Answer:
298 pictures
Step-by-step explanation:
One coloring book has 134 pictures, and other one has 309 pictures. The total will be addition:
134 + 309 = 443 pictures
Rachel colored 145 of them all, so subtract 145 from 443:
443 - 145 = 298
She still has 298 pictures left.
Answer:
298
Step-by-step explanation:
Total pictures:
134 + 309
443
Already coloured: 145
To be coloured: 443 - 145
= 298
If f[6} = x ^ -2x , find: f [6} =
Answer:
1/ 6^12
Step-by-step explanation:
f[x} = x ^ (-2x)
f(6) = 6 ^ (-2*6)
= 6 ^ -12
We know the negative exponent moves it to the denominator
= 1/ 6^12
(1) Saad had a box that is 15cm by 20cm by 22cm. What is the volume of the box?
(2) jake is redoing her kitchen. It measures 18ft by 19 ft. If wallpaper costs $1.29 per foot, how much will it cost her to wallpaper the kitchen?
Answer:
Question1:volume=6600cm^3
Question2:cost=$441.18
Step-by-step explanation:
Question 1:
volume=length x width x height
Volume=15 x 20 x 22
Volume=6600cm^3
Question 2:
area of kitchen=length x width
Area of kitchen=18 x 19
Area of kitchen=342ft^2
$1.29 for 1ft^2
$b for 342ft^2
$b=342 x1.29
$b=$441.18
10 percent of what number is 350
Answer:
3500
Step-by-step explanation:
multiply 10*350
Wich shapes can the the shaded area be divided into to find the area
Answer:
A. a rectangle and a triangle
Answer:
a) rectangle and triangle, then add both to fin the total area.
Step-by-step explanation:
A major building contractor has 10 new floor plans that she would like to start using in the homes she builds. She wants to know whether her homes will sell for a higher price in the city or the suburbs. She builds two homes—one in the city and one in the suburbs—for each of the 10 floor plans. She uses the same real estate agency to sell all 20 homes and then she calculates the difference in selling price (city – suburb) for each of the floor plans. What is the most appropriate test to analyze her data? a. Two Proportion Z Test b. One Sample T Test c. One Proportion Z Test d. Independent Samples T Test e. Paired T Test
Answer: d. Independent Samples T Test
Step-by-step explanation: Independent Samples T Test is commonly used when you want to compare the means of two independent groups and determine if there is evidence that the the associated means are significantly different.
For this test, the data must have: continuous dependent variable; independent variable is categorical (two or more groups); cases that have values on both variables; the obervations are independent, i.e. the groups don't interfere on each other; random sample of data for the population; normal distribution of the dependent variable for each group; homogeneity of variances and no outliers.
Each groups should have at least 6 subjects and have the same number of individuals in each group.
The hypothesis in this test can be expressed as:
H₀: μ1 = μ2 or μ1 - μ2 = 0
H₁: μ1 ≠ μ2 or μ1 - μ2 ≠ 0
Solve: tan(x)-cos^2(x)=sin^2(x)
Answer:
x = 45 degrees +180 n where n is an integer
Step-by-step explanation:
tan(x)-cos^2(x)=sin^2(x)
Add cos^2(x) to each side
tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)
tan(x)=sin^2(x)+ cos^2(x)
We know that sin^2(x)+ cos^2(x) = 1
tan (x) =1
Take the inverse tan of each side
tan ^-1 ( tan x) = tan ^-1 (1)
x = 45 degrees +180 n where n is an integer
Answer:
Pi/4+kpi
Step-by-step explanation:
X= 45 degrees and on unit circle that is pi/4
Nancy shot a 24 on 4 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes?
Answer:
108
Step-by-step explanation:
"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:
score/18 = 24/4
Multiplying by 18, we get ...
score = 18(24/4) = 18(6) = 108
Nancy can expect a score of 108 on 18 holes.
the height of the two triangular faces is 5.2 centimeters. the surface area of the triangular prism is ____ square centimeters.
The surface area of the triangular prism is 171.2 square centimeters.
From the given triangular prism,
Area of base (rectangle) = Length×Breadth
= 8×6=48 square centimeter
So, area of 3 congruent rectangles = 3×48
= 144 square centimeter
Here, area of a triangle = 1/2 × Base × Height
= 1/2 ×6×5.2
= 15.6 square centimeter
So, area of 2 congruent triangles= 2×15.6
= 31.2 square centimeter
Total surface area = 144+31.2
= 171.2 square centimeter
Therefore, the surface area of the triangular prism is 171.2 square centimeters.
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382
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x-3)2 + (y – 5)2 = 6
(x - 3)2 + (x - 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
(x+3)^2 + (y+5)^2 = 36
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--3)^2 + (y--5)^2 = 6^2
(x+3)^2 + (y+5)^2 = 36
Will give brainliest please explain how
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = [tex]2^{\frac{5}{2} }[/tex] = [tex]2^{x}[/tex]
x = 5/2
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = =
x = 5/2
On the Red Trail, the distance between point A and point B is 7.3 kilometers. You walked this distance back and forth. What is the distance you walked in meters?
Answer:
[tex]d = 14,600\,km[/tex]
Step-by-step explanation:
The distanced travelled is equal to twice the distance between points A and B. The distance that was walked in meters is:
[tex]d = 2\cdot (7.3\,km)\cdot \left(\frac{1000\,m}{1\,km} \right)[/tex]
[tex]d = 14,600\,km[/tex]
Final answer:
The total distance walked on the Red Trail, back and forth, when converted from kilometers to meters, is 14,600 meters.
Explanation:
The question asks for the total distance walked in meters if a person walks from point A to point B and back on the Red Trail, where the distance between point A and point B is 7.3 kilometers.
Firstly, we know that 1 kilometer equals 1,000 meters. Therefore, to find the distance in meters for a single trip from point A to point B, we multiply 7.3 kilometers by 1,000:
7.3 km × 1,000 = 7,300 metersSince the trip was made back and forth, the total distance covered is twice the distance of a single trip:
Total distance = 2 × 7,300 meters = 14,600 metersTherefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.
What is the value of this expression when a=3 and b=-1?
Answer:
1/4
Step-by-step explanation:
[tex](\dfrac{3(3)^{-2}(-1)^6}{2(3)^{-1}(-1)^5})^2=[/tex]
[tex](\dfrac{\frac{1}{3}}{-\frac{2}{3}})^2=[/tex]
[tex](-\dfrac{1}{2})^2=[/tex]
[tex]\frac{1}{4}[/tex]
Hope this helps!
How do I write the exponent expression below in numbers
Three to the sixth power all divided by two
Answer:
(3^6)/2
Step-by-step explanation:
make sure everything as the numerator is in parenthesis
You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 99% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $ 12 comma 260 with a standard deviation of $ 800. Suppose that the interval is calculated to be (11693 comma 12827 ). How could the sample size and the confidence coefficient be altered in order to guarantee a decrease in the width of the interval?
Answer:
If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:
[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The width of the confidence interval is just defined as two times the margin of error:
[tex] Width = 2ME[/tex]
And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%
By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.
Step-by-step explanation:
For this case w ehave the following info given from the problem
[tex] n =17[/tex] represent the sample size for the cars selected
[tex]\bar X = 12260[/tex] represent the average price for the cars sold
[tex] s= 800[/tex] represent the standard deviation for the solds
And we have a 99% confidence interval for the true average price for the cars given:
[tex]11693 \leq \mu \leq 12827[/tex]
And we know that the confidence interval for the true mean is given by this formula:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:
[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The width of the confidence interval is just defined as two times the margin of error:
[tex] Width = 2ME[/tex]
And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%.
By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.
A study in 2010 reported that 3 in 4 adults in a relationship met their significant other using an online dating site. Recently a popular magazine 'People' claimed that that number has changed. To test this claim a telephone survey of 600 randomly selected adults in a relationship was completed. Of the 600 adults, 480 said that they met their significant other using an online dating site. Does this provide evidence that the proportion has changed? Use α = 0.05, to test the magazine's claim. Conditions: 1. The sample is 2. n p 0 ( 1 − p 0 ) 10 3. n 0.05 N Hypotheses: H 0 : p 0.75 H 1 : p 0.75 Test Statistic: The test statistic is a test statistic. The value of the test statistic is . p-value: The value of the p-value is . Decision: Because the p-value is than α = 0.05, we the null hypothesis. Conclusion: The data the claim that the proportion has changed
Answer:
Step-by-step explanation:
From the given information,
The required correct answers are,
1. The sample is:
b) simple random sample
2. np0 (1-p0) ___ 10
a) greater than or equal to
3. n ___ 0.05N
b) less than or equal to
Hypotheses:
4. H0:p___0.75
d) =
5. H1:p___0.75
a) ≠
6. The test statistic is a
a) z test statistic
7. test statistic=2.8284
8. p-value=0.0047
Decision:
Because p-value less than Alpha=0.05, we reject null hypothesis.
Conclusion:
The data support the claim that the proportion has changed.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
p = 3/4 = 0.75
For the alternative hypothesis,
p ≠ 0.75
Considering the population proportion, probability of success, p = 0.75
q = probability of failure = 1 - p
q = 1 - 0.75 = 0.25
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 480
n = number of samples = 600
P = 480/600 = 0.8
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.8 - 0.75)/√(0.75 × 0.25)/480 = 2.53
Recall, population proportion, P = 0.75
The difference between sample proportion and population proportion(P - p) is 0.8 - 0.75 = 0.05
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.75 - 0.05 = 0.7
the p for the right tail is 0.75 + 0.05 = 0.8
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the test z score in the right tail 1 - 0.9943 = 0.0057
We would double this area to include the area in the left tail of z = - 2.53. Thus
p = 0.0057 × 2 = 0.0114
Because alpha, 0.05 > than the p value, 0.0114, then we would reject the null hypothesis.
Therefore, at 5% significance level, this data provide evidence that the proportion has changed.
Which expression is the result of
10x2 + 50x = ?
Step-by-step explanation:
10x2 + 50x
10x ( x +5)
Is the result
Maria and her friends went on a bike ride. The start and end times are shown below how long did they Ride
Start time: 1:09
End time: 2:05
Maria and her friends rides for 56 minutes
Duration of timeDuration is defined as the length of time that something lasts. Eg. When a film lasts for two hours, this is an example of a time when the film has a two hour durationHow to solve the problem?GivenStart time = 01:09
End time = 02:05
From start and end time we can see that there is 4 minutes to complete 1 hoursSo to find total time we need to subtract 4 minutes from 1 hours i.e 60 minutes∴ Ride Time = 60-4
∴ Ride Time = 56 minutes
Therefore the total ride time that Maria and her friend rode is 56 minutes
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1+2x-3x-4 I need it please
Answer:
Simplified as -3 - x
Step-by-step explanation:
I know, you want to simplify this answer.
So.
1 + 2x - 3x - 4 = 1 - x - 4 = -3 - x
What is the domain of the function Y equals cube root x
Final answer:
The domain of the function y = x^(1/3) (cube root of x) is all real numbers, which is expressed as (-∞, +∞).
Explanation:
The domain of a function describes all the possible values of 'x' for which the function is defined. In the case of the function y = cubic root of x, which is written as y = x^(1/3), the function is defined for all real numbers because you can take the cubic root of any real number, negative, positive, or zero. Hence, the domain of the function y = x^(1/3) is all real numbers, which mathematically is expressed as (-∞, +∞). This is different from the function y = x^2, where the domain must often be restricted to nonnegative numbers to have a well-defined real inverse function.
Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 24 men and 3 women. (Enter your probabilities as fractions.) (a) Find the probability that both appointees are men. (b) Find the probability that one man and one woman are appointed. (c) Find the probability that at least one woman is appointed.
Answer:
[tex](a)\dfrac{92}{117}[/tex]
[tex](b)\dfrac{8}{39}[/tex]
[tex](c)\dfrac{25}{117}[/tex]
Step-by-step explanation:
Number of Men, n(M)=24
Number of Women, n(W)=3
Total Sample, n(S)=24+3=27
Since you cannot appoint the same person twice, the probabilities are without replacement.
(a)Probability that both appointees are men.
[tex]P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}[/tex]
(b)Probability that one man and one woman are appointed.
To find the probability that one man and one woman are appointed, this could happen in two ways.
A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.P(One man and one woman are appointed)[tex]=P(MW)+P(WM)[/tex]
[tex]=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}[/tex]
(c)Probability that at least one woman is appointed.
The probability that at least one woman is appointed can occur in three ways.
A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.Two women are appointedP(at least one woman is appointed)[tex]=P(MW)+P(WM)+P(WW)[/tex]
[tex]P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}[/tex]
In Part B, [tex]P(MW)+P(WM)=\frac{8}{39}[/tex]
Therefore:
[tex]P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}[/tex]
UPOOD
The area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square,
If the side length of a square is 4 inches, its area is
16.6 square inches and its perimeter is
074 Inches.
Reset
Next
Answer:
If the side length of a square is 4 inches, it's Area is 16 inches, and Perimeter is 16 inches.
Step-by-step explanation:
Given that the Area = s²
Perimeter = 4s
Side length of the square = s
If the length of a square is 4 inches, then applying the above formulas, we have
s = 4 inches
Area = 4² = 16 inches
Perimeter = 4s = 4×4 = 16 inches
Final answer:
The area of a square with a side length of 4 inches is 16 square inches and its perimeter is 16 inches. Doubling the side length to 8 inches yields an area that is four times greater, 64 square inches, due to the squared relationship between side length and area.
Explanation:
Understanding Square Area and Perimeter
A student has posed a question about the properties of squares. We are given that the side length of a square is 4 inches. From this, we can calculate the square's area and perimeter. The area of a square is found by squaring the length of its side (s2), which in this case would be 4 inches × 4 inches = 16 square inches. The perimeter is the length around the square, calculated by multiplying the side's length by 4, yielding 4 inches × 4 = 16 inches.
By understanding the formulas for area (s2) and perimeter (4s), students can solve many geometrical problems related to squares. For instance, if the dimensions of a square are to be doubled, the new side length would be 4 inches × 2 = 8 inches, resulting in an area of 8 inches × 8 inches = 64 square inches, which is four times the original area, demonstrating that the area scales with the square of the linear dimensions.
What function do you use to find the angle of a vector, when you know its components?
Answer:
[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]
Step-by-step explanation:
If we are given components of a vector then we can find the angle between them.
Suppose we are given a vector v
[tex]v = (x, y)[/tex]
Where x is the horizontal component and y is the vertical component.
The angle can be found by using
[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]
The magnitude of the vector v can be found using
[tex]v = \sqrt{x^{2}+y^{2}}[/tex]
Example:
Lets do a quick example:
[tex]v = (2, 4)[/tex]
The angle of the vector is
[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]
The magnitude of the vector is
[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]
What percent is 7 out of 40?
Answer:
17.5%
Step-by-step explanation:
Convert fraction (ratio) 7 / 40 Answer: 17.5%
Answer:
17.5
Step-by-step explanation:
7/40 = 17.5
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How can you isolate the variable x-3=7
to get the variable alone you need to add three to both sides
x-3=7
+3 +3
-----------------
x= 10
Answer:
Step 1: Bring like terms together Step 2: Add variable to both sides Step 3: Simplify Step 4: Add the constant to both sides Step 5: Simplify Step 6: Divide by the coefficient Step 7: Solve Step 8: Test your solution Answer: 10
Step-by-step explanation:
A company issues 7% bonds with a par value of $200,000 at par on January 1. The market rate on the date of issuance was 6%. The bonds pay interest semiannually on January 1 and July 1. The cash paid on July 1 to the bond holder(s) is:
Answer:
The cash paid to the bondholder on July 1 is Z = $7000
Step-by-step explanation:
From the question we are told that
The percentage bond issued by the company is [tex]n = 7[/tex]%
The par value of the bond is [tex]V =[/tex]$200,000
The market rate is [tex]r = 6[/tex]%
So we are told that the bonds pay interest semiannually on January 1 and July
So the cash paid to the bondholder on July 1 is mathematically evaluated as
Z = [tex]V * \frac{7}{100} * \frac{1}{2}[/tex]
substituting value
Z = [tex]200000 * \frac{7}{100} * \frac{1}{2}[/tex]
Z = $7000
Final answer:
The cash paid on July 1 to bondholders for the company's 7% bonds with a par value of $200,000 is $7,000. This is calculated by first determining the annual interest payment and then dividing by two for the semiannual payment.
Explanation:
Understanding Bond Interest Payments
The question revolves around how much cash is paid to bondholders on July 1 for a company that issued 7% bonds with a par value of $200,000 at par when the market rate was 6%. Since the bonds were issued at par, this implies that the bond's stated interest rate matches the market interest rate at the time of issuance. However, the market rate later does not affect the fixed payments of a bond issued at par.
The interest payment for this bond would be calculated using the face value and the stated annual interest rate, which is then divided by two since interest is paid semiannually. The calculation is as follows:
Calculate the annual interest payment: $200,000 (par value) × 7% (interest rate) = $14,000.Divide the annual interest by two for the semiannual payment: $14,000 ÷ 2 = $7,000.Therefore, the cash paid on July 1 to the bond holder(s) is $7,000.