In circle K with mLJKL = 112 and
JK = 7 units find area of sector JKL.
Round to the nearest hundredth.
Answers
Area of the sector JKL is 47.89 unit²
How the area of the sector is calculated
From the figure
Given that
JKL is a sector that subtends ∠JKL at the center of the circle JL.
The radius of the circle is KL or JK
Area of a sector = θ/360 * πr²
where
r is the radius
θ is angle subtended at the center
m∠JKL = 112⁰ = θ
JK = 7 units = radius
Therefore,
Area = 112/360*π(7)²
A = 112/360 * 3.142 * 49
= 17243.296/360
= 47.89 unit²
Therefore, area of the sector JKL is 47.89 unit²
Related Questions
please help :wildlife society wants to investigate the effects of a chemical spill on the growth of various types of fish. Scientists will start by measuring the lengths and weights of a sample of fish in the area. Which of the following samples should be selected for this study?
A.
fish in local lakes
B.
fish in oceans worldwide
C.
fish at the local zoo
D.
pet fish owned by local citizens
Answers
Find the product.
-1(5) =
Answers
Answer:
-5
Step-by-step explanation:
when you multiply a number by -1 it becomes its opposite
A company needs 150,000 items per year. It costs the company $640 to prepare a production run of these items and $7 to produce each item. If it also costs the company $0.75 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized.
Answers
The requried x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.
To find the number of items that should be produced in each run to minimize the total costs of production and storage, we can use the following steps:
Let x be the number of items produced in each run. The total cost of production and storage (C) can be expressed as:
C(x) = (640/150,000) + (7x) + (0.75 * 150,000 / x)
The first term (640/150,000) represents the cost of preparing a production run, the second term (7x) represents the cost of producing each item, and the third term (0.75 * 150,000 / x) represents the cost of storing each item.
To minimize the total cost, we need to find the value of x that minimizes the function C(x). We can do this by taking the derivative of C(x) with respect to x and setting it equal to zero:
C'(x) = 0
Now, let's find the derivative of C(x):
C'(x) = d/dx [(640/150,000) + (7x) + (0.75 * 150,000 / x)]
C'(x) = 0 + 7 - (0.75 * 150,000 / x²)
Now, set C'(x) equal to zero and solve for x:
7 - (0.75 * 150,000 / x²) = 0
0.75 * 150,000 / x² = 7
150,000 / x² = 7 / 0.75
150,000 / x² = 9.333...
Now, solve for x:
x² = 150,000 / 9.333...
x² ≈ 16,071.43
x ≈ sqrt(16,071.43)
x ≈ 126.77
Since x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.
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A researcher claims that the mean annual cost of raising a child (age 2 and under) by husband-wife families in the U.S. is $13,960. In a random sample of husband-wife families in the U.S. the mean annual cost of raising a child (age 2 and under) is $13,725. The sample consists of 500 children and the population standard deviation is $2,345. At the α = 0.10, is there enough evidence to reject the claim? Use the p-value approach.
Answers
Answer:
[tex]z=\frac{13725-13960}{\frac{2345}{\sqrt{500}}}=-2.24[/tex]
[tex]p_v =2*P(z<-2.24)=0.0251[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 13960 at 10% of signficance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=13275[/tex] represent the sample mean
[tex]\sigma=2345[/tex] represent the sample standard deviation
[tex]n=500[/tex] sample size
[tex]\mu_o =68[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is 13960, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 13690[/tex]
Alternative hypothesis:[tex]\mu \neq 13690[/tex]
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{13725-13960}{\frac{2345}{\sqrt{500}}}=-2.24[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2*P(z<-2.24)=0.0251[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 13960 at 10% of signficance.
c - 12 > 30, if c = 13
Answers
Answer:
False
Step-by-step explanation:
Substitute 13 in for c
c - 12 > 30
13 - 12 > 30
1 > 30
This is false, because 1 is not greater than 30
The solution:
c - 12 > 30
Add 12 to both sides
c > 42
Write an inequality for each statement.
1. Lacrosse practice will not be more than 45 minutes.
2. Mario measures more than 60 inches in height
Write an inequality for each statement.
1. Lacrosse practice will not be more than 45 minutes.
2. Mario measures more than 60 inches in height
3. More than 8000 fans attended the first football game of the Wizard amd Arrowhead Stadium in Kansas City, Missouri. Write an inequality to describe attendance.
3. More than 8000 fans attended the first football game of the Wizard amd Arrowhead Stadium in Kansas City, Missouri. Write an inequality to describe attendance.
Answers
Answer:
1. [tex]l \leq 45[/tex] ( in this inequality, the time can be less than or equal to 45, but no more than 45)
2. [tex]m > 60[/tex] (Mario's height is more than 60.)
3. [tex]f > 8000[/tex] (More than 8000 fans attended.)
Please help!!
Which expression is equivalent to 10 - 8?
Choose 1 answer:
Answers
Answer:
Option A is the right answer choice.
Step-by-step explanation:
10 plus a negative number is the same as subtracting it as a positive
Is a triangle whose side measure 12 ft, 16 ft and 20 ft a right triangle?
Answers
Answer:
This is a Right Triangle
Step-by-step explanation:
12=a 16=b 20=c
Now lets solve
a^2+b^2=c^2
144+b^2=c^2
144+256=c^2
144+256=400
c^2=400
The square root of 400 is 20..
This IS a Right Triangle
Yes, a triangle with sides of lengths 12ft, 16ft and 20ft is a right triangle. This is proven by using the Pythagorean theorem, which these side lengths satisfy.
Explanation:To verify if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In the triangle you provided with sides of lengths 12 ft (a), 16 ft (b), and 20 ft (c, as the hypotenuse is usually the longest side), you would plug those values into the equation: 12² + 16² = 20²?
144 + 256 = 400?
400 = 400
Because the equation is true, this proves that the triangle is indeed a right triangle.
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The table shows information about the numbers of hours 30 children spent on their tablets one evening. a) find the class interval that contains the median. B)work out an estimate for the mean number of hours
Answers
(a) The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex] (b)The estimated mean number of hours is 1.8 hours.
To analyze the data and answer the questions about the time 30 children spent on their tablets one evening, let's break it down step by step.
(a) The median is the value that separates the higher half from the lower half of the data. For 30 children, the median position will be the average of the 15th and 16th values in the ordered data set.
Given the frequencies:
- [tex]\( 0 < h \leq 1 \): 6[/tex] children
- [tex]\( 1 < h \leq 2 \):[/tex] 13 children
- [tex]\( 2 < h \leq 3 \):[/tex] 7 children
- [tex]\( 3 < h \leq 4 \): 4[/tex] children
To find the median class interval, we need to determine where the 15th and 16th values fall.
Cumulative frequency:
[tex]- \( 0 < h \leq 1 \): 6\\ - \( 1 < h \leq 2 \): 6 + 13 = 19\\ - \( 2 < h \leq 3 \): 19 + 7 = 26\\ - \( 3 < h \leq 4 \): 26 + 4 = 30[/tex]
From the cumulative frequency:
The 15th and 16th values fall within the second class interval [tex]\( 1 < h \leq 2 \),[/tex] because the cumulative frequency reaches 19 in this interval.
The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex]
(b) To estimate the mean, we'll use the midpoint of each class interval and multiply by the frequency of that interval, then divide by the total number of children.
Determine the midpoints of each class interval:
[tex]- \( 0 < h \leq 1 \): midpoint = \( \frac{0 + 1}{2} = 0.5 \)\\ - \( 1 < h \leq 2 \): midpoint = \( \frac{1 + 2}{2} = 1.5 \)\\ - \( 2 < h \leq 3 \): midpoint = \( \frac{2 + 3}{2} = 2.5 \)\\ - \( 3 < h \leq 4 \): midpoint = \( \frac{3 + 4}{2} = 3.5 \)[/tex]
Multiply each midpoint by its respective frequency:
[tex]- \( 0.5 \times 6 = 3 \)\\ - \( 1.5 \times 13 = 19.5 \)\\ - \( 2.5 \times 7 = 17.5 \)\\ - \( 3.5 \times 4 = 14 \)\\[/tex]
Sum these products:
[tex]\[ 3 + 19.5 + 17.5 + 14 = 54 \][/tex]
Divide by the total number of children to find the mean:
[tex]\[ \text{Mean} = \frac{54}{30} = 1.8 \][/tex]
The estimated mean number of hours is 1.8 hours.
The complete question is:
The table shows information about the numbers of hours 30 children spent on their tablets one evening.
Number of hours (m) Frequency
D<h<1 6
1<h<2 13
2<h<3 7
3<h<4 4
a) Find the class interval that contains the median.
b) Work out an estimate for the mean number of hours.
Two tanks of brine are connected via two tubes. Tank 1 contains x(t) pounds of salt in 500 gallons of brine, and tank 2 contains y(t) pounds of salt in 500 gallons of brine. Brine is pumped from tank 1 to tank 2 at a rate of 50 gallons/min and brine is pumped from tank 2 to tank 1 at the same rate of 50 gallons/min, ensuring that the total volume of brine in the tanks remains constant over time.
a) Show that x(t) and y(t) satisfy the differential equations x'= − (1/10)x + (1/10)y ; y' = (1/10)x − (1/10)y.
b) If initially tank 1 contains no salt, and tank 2 contains 10 pounds of salt, use the method of elimination to find x(t) and y(t).
Answers
a. Salt flows into tank A at a rate of
(y(t)/500 lb/gal) * (50 gal/min) = y(t)/10 lb/gal
and out at a rate of
(x(t)/500 lb/gal) * (50 gal/min) = x(t)/10 lb/gal
so the net rate of change of the amount of salt in tank A is
[tex]x'(t)=\dfrac{y(t)}{10}-\dfrac{x(t)}{10}[/tex]
Similarly, you would find
[tex]y'(t)=\dfrac{x(t)}{10}-\dfrac{y(t)}{10}[/tex]
b. We have
[tex]x'=-\dfrac x{10}+\dfrac y{10}\implies x''=-\dfrac{x'}{10}+\dfrac{y'}{10}[/tex]
Notice that x' = -y', so
[tex]x''=-{2x'}{10}\implies 5x''+x'=0[/tex]
Solve for x: the characteristic equation
[tex]5r^2+r=r(5r+1)=0[/tex]
has roots [tex]r=0[/tex] and [tex]r=-\frac15[/tex], so
[tex]x(t)=C_1+C_2e^{-t/5}[/tex]
Again using the fact that y' = -x', we then find
[tex]x'(t)=-\dfrac{C_2}5e^{-t/5}\implies y'(t)=\dfrac{C_2}5e^{-t/5}\implies y(t)=C_1-C_2e^{-t/5}[/tex]
Given that x(0) = 0 and y(0) = 10, we find
[tex]\begin{cases}0=C_1+C_2\\10=C_1-C_2\end{cases}\implies C_1=5,C_2=-5[/tex]
Calculations the mean of 13, 8, 12, 10, 27
Answers
Answer:
14
Step-by-step explanation:
M = (13+8+12+10+27)/5
= 70/5
= 70 : 5
= 14
The weights of six animals at the zoom are shown in the table below
5
24
38
52
66
85
What is the mean absolute deviation? Round to the nearest tenth
Answers
Answer:
22.7
Step-by-step explanation:
To find the mean absolute deviation (MAD), first find the mean (or average).
μ = (5 + 24 + 38 + 52 + 66 + 85) / 6
μ = 45
Next, subtract the mean from each value and take the absolute value.
|5 − 45| = 40
|24 − 45| = 21
|38 − 45| = 7
|52 − 45| = 7
|66 − 45| = 21
|85 − 45| = 40
Sum the results and divide by the number of animals.
MAD = (40 + 21 + 7 + 7 + 21 + 40) / 6
MAD ≈ 22.7
Aiden needs to find the percent of shaded squares in the bar diagram. Which model should he use? plz help
Answers
Answer: C
Step-by-step explanation:
Answer:
It might be C
Step-by-step explanation:
I am so sorry if it is the wrong answer. I didn't have a test about this.... :(
a student says the prime factors of 17 are 1 and 17. Is the student correct? explain.
Answers
Answer:
Correct
Step-by-step explanation:
1. Factors
Are whole numbers that can divide the number completely.
2. Prime number
Number of factors that can be express in form of prime factorisation.
Prime factorisation of a number can be done by repeated division by prime numbers (number is written as the product of its prime factors)
For example, 17
List of factors, 1 and 17
Prime number, 17
Prime factorisation, 1×17=17
So why prime numbers cannot be express in form of prime factorisation?
Because, a prime number can only be divided by 1 or itself, so it cannot be factored any further. Not like the other number.
Brainliest would be appreciated :)
Final answer:
The student is incorrect; 17 is a prime number, and the only prime factor of 17 is 17 itself. The number 1 is not considered a prime factor as it is not a prime number.
Explanation:
No, the student is not correct in stating that the prime factors of 17 are 1 and 17. Prime factors are numbers that are both prime and divide the original number without leaving a remainder. The definition of a prime number is a number greater than 1 that has no positive divisors other than 1 and itself. In the case of 17, it is indeed a prime number, so it cannot have any prime factors other than itself. Therefore, the only prime factor of 17 is 17.
The number 1 is not considered a prime factor, as it is not a prime number because it does not meet the basic criterion of having exactly two distinct natural number divisors: 1 and itself. Examples of prime factors can be seen in other numbers, such as 15, whose prime factors are 3 and 5, both of which are prime numbers that divide 15 without leaving a remainder. In contrast, 17 can only be divided evenly by 1 and 17, and since 1 is not a prime number, 17 is the sole prime factor of 17.
A researcher collected data of systolic blood pressure and weight for 5 patients, as are shown in the table below.
Patient Systolic Blood Pressure (in mmHg) Weight (in lbs)
1 145 210
2 155 245
3 160 260
4 156 230
5 150 219
1. Draw a scatter plot of systolic blood pressure (response) versus weight (regressor).2. What is the direction of the association?
Answers
Answer:
We can see the details in the pic.
Step-by-step explanation:
We can see the details in the pic shown.
A model of a soccer ball is made up of regular pentagons and hexagons.
A soccer ball is made up of regular pentagons and hexagons.
The side length of one of the pentagons measures 2 inches and the apothem measures about 1.38 inches. What is the area of one of the pentagons? State your answer to the nearest tenth.
square inches
The side length of one of the hexagons measures 2 inches and the apothem measures about 1.73 inches. What is the area of one of the hexagons? State your answer to the nearest tenth.
square inches
Answers
Answer:
- pentagon area= 6.9
-hexagon area=10.4
Answer:
Pentagons: 6.9 square inches
Hexagons: 10.4 square inches
Step-by-step explanation: i got it right on edge
Evaluate the following expression. Round your answer to two decimal places.
Answers
Answer: 2.18
Step-by-step explanation:
log(11)/log(3)=2.18
Answer:
2.18
Step-by-step explanation:
I just did it and got it right
Find the slope of the line that passes through the two points below (-4,9) and (8,7)
Answers
Answer:
-1/6
Step-by-step explanation:
The slope of the line can be found by
m = (y2-y1)/(x2-x1)
= (7-9)/(8 - -4)
-2 /(8+4)
-2/(12)
-1/6
Identify if there is a relationship between the variables.
No, there is no relationship because the points are
all up and down.
Yes, the relationship displayed shows arm span
increasing as height increases.
O Yes, the relationship displayed shows arm span
decreasing as height increases.
Answers
Answer:
increases
Step-by-step explanation:
Answer:
the answer is:B
Step-by-step explanation:
Amy can run the 150 meter dash in 50 seconds. John can run 120 meters in 400 seconds. Who runs faster per second?
Answers
Answer:
Amy
Step-by-step explanation:
amy completed a longer distance in a shorter amount of time
rather than john completed a shorter distance in a longer time
pls mark me brainliest
Amy runs faster than John.
What is speed?Speed is defined as the ratio of distance of an object to the time taken to complete the distance.
Speed of any object can be calculated by the equation,
Speed = Distance / Time
Here, Speed of Amy = 150/50 = 3
Speed of John = 120/400 = 0.3
Amy runs at a speed of 3 meters per seconds and John runs at a speed of 0.3 meters per second.
Hence Amy runs faster than John.
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a four sectioned spinner is numbered 1-4. What is the probability you spin a 2, and then a 4?
Answers
Answer:
1/4 25%
Step-by-step explanation:
The spinner has 4 sides so the denomination is 4 and you are trying to get one of the 4 sides each so it would be a 1/4 chance for both answers so 25%
what is the exact circumference of the circle?
Answers
Answer:
40
Step-by-step explanation:
i need to know number 7
Answers
Answer:
it would be A. -25
Step-by-step explanation:
`for example if she sold 0 dollars worth of necklaces and she spent 25 dollars on supplies she would have lost 25 dollars so it would be -25.
Answer:A,-$25
Step-by-step explanation:
She bought the necklace. When she sold it, she sold it for $25 less than what she bought it for. Therefore, she lost $25, the same as -$25.
Height of rectangular prism if the volume is 334.8 meters
Answers
Only the volume is given, so you can already assume the rectangular prism is a cube, which in that case you can divide by 3 to get the answer.
Suppose Julio is a veterinarian who is doing research into the weight of domestic cats in his city. He collects information on 188 cats and finds the mean weight for cats in his sample is 10.97 lb with a standard deviation of 4.41 lb. What is the estimate of the standard error of the mean (SE)
Answers
Answer:
The standard error of the mean is 0.3216
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 188
Sample mean =
[tex]\bar{x}= 10.97\text{ lb}[/tex]
Sample standard deviation =
[tex]s = 4.41\text{ lb}[/tex]
We have to estimate the standard error of the mean.
Formula for standard error:
[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]
Putting values, we get,
[tex]S.E =\dfrac{4.41}{\sqrt{188}} = 0.3216[/tex]
Thus, the standard error of the mean is 0.3216
The regression equation Credits = 17.9 − 0.09 Work was estimated from a sample of 21 statistics students. Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job. (Round your answers to 1 decimal place.) (a) Choose the correct statement. An increase in the number of hours worked per week increases the expected number of credits. A decrease in the number of hours worked per week decreases the expected number of credits. An increase in the number of hours worked per week decreases the expected number of credits. (b) Choose the right option. The intercept is not meaningful as a student who works outside may not earn any credits. The intercept is meaningful as a student may not have a job outside of school. (c) If Work = 0, then Credits = . If Work = 60, then Credits = .
Answers
Answer:
Step-by-step explanation:
Hello!
Given the regression equation
Credit= 17.9 - 0.09 Work
That was estimated from a sample of n= 21 statistic students.
Y: number of college credits taken
X: number of hours worked per week at an outside job
a)
The estimation for the slope is -0.09
As you see the estimated slope is negative, this means that the association between the two variables is indirect or inverse. Meaning, when the number of Work increases, the number of Credit decreases. (negative regression)
The correct option is: "An increase in the number of hours worked per week decreases the expected number of credits."
b)
The estimation for the intercept is 17.9
In general, the intercept is the estimated average of Y when X=0. You can interpret the intercept of this equation as "the value of Credits earned by a student that does not work outside of school"
The correct option is: " The intercept is meaningful as a student may not have a job outside of school. "
c)
If Work=0, then Credit= 17.9 (As explained in item b)
By replacing the value in the equation: Credit= 17.9 - 0.09 * 0= 17.9
If Work=60, you replace it in the equation and:
Credit= 17.9 - 0.09 Work= 17.9-0.09*60= 12.5
If the student works 60 hs outside of school it is expected that he takes 12.5 college credits.
I hope this helps!
The correct answers are that an increase in work hours decreases the number of expected credits, the intercept is meaningful as it represents the credits for a student not working, and credits equal to 17.9 when work hours are zero and 12.5 when work hours are 60.
The regression equation given is Credits = 17.9 - 0.09 Work, where Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job.
(a) From this equation, we can see that for an increase in the number of hours worked (Work), the number of expected credits (Credits) decreases because the coefficient of Work is negative (-0.09). So, the correct statement is: An increase in the number of hours worked per week decreases the expected number of credits.
(b) Regarding the intercept, it is meaningful since it represents the expected number of credits a student would take if they did not work at all (Work = 0). Therefore, the correct option is: The intercept is meaningful as a student may not have a job outside of school.
(c) If Work = 0, then Credits = 17.9. If Work = 60, then Credits = 17.9 - 0.09(60) = 17.9 - 5.4 = 12.5.
Individuals filing federal income tax returns prior to March 31 had an average refund of $1102. Consider the population of "last-minute" filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15).
a. A researcher suggests that one of the reasons that individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.
b. For a sample of 600 individuals who filed a return between April 10 and April 15, the sample mean refund was $1050 and the standard deviation was $500. Compute the p-value.
c. Using α =.05, what is your conclusion?
d. Test the hypotheses using the critical value approach (α = 0.025).
Answers
Answer:
a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.
[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]
b) P-value = 0.0055
c) The null hypothesis is rejected.
There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.
d) Critical value tc=-1.96.
As t=-2.55, the null hypothesis is rejected.
Step-by-step explanation:
We have to perform a hypothesis test on the mean.
The claim is that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund ($1102).
a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.
[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]
b) The sample has a size n=600, with a sample refund of $1050 and a standard deviation of $500.
We can calculate the z-statistic as:
[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1050-1102}{500/\sqrt{600}}=\dfrac{-52}{20.41}=-2.55[/tex]
The degrees of freedom are df=599
[tex]df=n-1=600-1=599[/tex]
The P-value for this test statistic is:
[tex]P-value=P(t<-2.55)=0.0055[/tex]
c) Using a significance level α=0.05, the P-value is lower than the significance level, so the effect is significant. The null hypothesis is rejected.
There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.
d) If the significance level is α=0.025, the critical value for the test statistic is t=-1.96. If the test statistic is below t=-1.96, then the null hypothesis should be rejected.
This is the case, as the test statistic is t=-2.55 and falls in the rejection region.
A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run. During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time since the start of the run. Write a differential equation that describes this relationship, where k is a positive constant?
Answers
Answer:
[tex]\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}[/tex]
Step-by-step explanation:
Given
The jogger’s position: p(t)
We can express the acceleration a as follows
[tex]a=\frac{d^{2}p}{dt^{2}}[/tex]
then
[tex]\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}[/tex]
only if
[tex]0 min\leq t\leq 1 min[/tex]
The required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].
Given information:
A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run.
During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time.
Let a be the acceleration of the jogger.
So, the expression for acceleration can be written as,
[tex]a=\dfrac{d}{dt}(\dfrac{dP(t)}{dt})\\a=\dfrac{d^2P(t)}{dt^2}[/tex]
Now, the acceleration is proportional to square root of time.
So,
[tex]a\propto \sqrt t\\a=k\sqrt t\\\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex]
Therefore, the required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].
For more details about differential equations, refer to the link:
https://brainly.com/question/1164377
please help, im so confused!
Which point is on the graph of the function
f(x) = One-half(2)x?
(0, 1)
(0, 2)
(1, One-half)
(1, 1)
Answers
Answer:
D (1,1)
Step-by-step explanation:
Answer:
D. (1,1)
Hope it works!
Step-by-step explanation:
5.Richard Miyashiro purchased a condominium and obtained a 30-year loan of $196,000 at an annual interest rate of 8.20%. (Round your answers to the nearest cent.)
(a) What is the mortgage payment?
$
(b) What is the total of the payments over the life of the loan?
$
(c) Find the amount of interest paid on the mortgage loan over the 30 years.
$
6.
Marcel Thiessen purchased a home for $205,700 and obtained a 15-year, fixed-rate mortgage at 7% after paying a down payment of 10%. Of the first month's mortgage payment, how much is interest and how much is applied to the principal? (Round your answer to the nearest cent.)
interest $
applied to the principal $
Answers
Answer:
5 a) PMT=$1,465.60
b) Total Payments=$527,616
c) Total Interest=$331,616
6a) Interest=$1,079.93
b) Principal=$584.07
Step-by-step explanation:
a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.
-The monthly mortgage payment can be calculated as follows:
[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})[/tex]
Where:
PMT is the monthly mortgage paymentr is the annual interest raten,t is the number of annual payments and time in years respectively-We substitute to solve for PMT:
[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})\\\\=196000[\frac{(0.082/12)}{1-(1+\frac{0.082}{12})^{-12\times30}}]\\\\=\$1,465.60[/tex]
Hence, the monthly mortgage payment is $1,465.60
b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:
[tex]\sum(payments)=PMT\times nt\\\\=1465.60\times 12\times 30\\\\=\$527,616.00[/tex]
Hence, the total amount of payments is $527,616
c. The amount of interest paid over the loan's term is obtained by subtracting the principal loan amount from the total payments made:
[tex]Interest=Payments-Principal\\\\=527,616.00-196,000.00\\\\=\$331,616[/tex]
Hence, an interest amount of $331,616 is paid over the loan's term.
6 a) We first obtain the effective loan amount by subtracting the down-payment:
[tex]Loan \ Amount= Regular \ Price -Downpayment\\\\=205700-0.1(205700)\\\\=\$185,130[/tex]
The interest paid on the first mortgage payment is calculated as below:
[tex]I=\frac{r}{n}\times P\\\\I=Interest\\r=interest \ rate\\n=Payments \ per \ year\\P=Outstanding \ loan \ balance\\\\\therefore I=\frac{0.07}{12}\times 185130\\\\=\$1,079.93[/tex]
Hence, the amount of interest in the first payment is $1,079.93
b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;
[tex]Principal \ Paid=PMT-Interest\\\\PMT=A[\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}}]\\\\=185130[\frac{(0.07/12)}{1-(1+\frac{0.07}{12})^{-180}}\\\\=1664.00\\\\\\Principal \ Paid=1664.00-1079.93\\\\=\$584.07[/tex]
Hence, the amount of principal applied is $584.07