(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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Help me please I need to show my work
Answer:
x=33
Step-by-step explanation:
all angles in a triangle sum to 180 degrees
x+2x+(2x+15) = 180 <---- simplify this
5x+15 = 180
5x=165
x = 33
The function f represents the 1000 revenue in dollars the school can 800 expect to receive if it sells 220 – 12x coffee mugs for x dollars 600 each. 400 200 Here is the graph of ƒ. 2 4 6 8 10 12 14 16 18 20 price (dollars) Select all the statements that describe this situation. a. At $2 per coffee mug, the revenue will be $96. b. The school expects to sell 160 mugs if the price is $5 each. c. The school will lose money if it sells the mugs for more than $10 each. d. The school will earn about $1000 if it sells the mugs for $10 each. e. The revenue will be more than $70o if the price is between $4 and $14. f. The expected revenue will increase if the price per mug is greater than $10. g. The domain for this situation is about 0 - 9. h. The domain for this situation is about 0 - 18.25. revenue (dollars)
The function f represents the 1000 revenue in dollars the school can 800 expect to receive if it sells 220 – 12x coffee mugs for x dollars 600 each.
The statements that accurately describe this situation are:
False. The revenue at $2 per mug is $336, not $96.True. The school expects to sell 160 mugs if the price is $5 each.False. The revenue is maximized when the price per mug is around $9, so selling mugs for more than $10 does not necessarily result in a net loss.True. The revenue at $10 per mug is approximately $1000.True. The revenue is always above $700 if the price is between $4 and $14.False. The revenue is maximized when the price per mug is around $9, so the expected revenue will not increase if the price per mug is greater than $10.The domain for this situation is about 0-18.25. This is the set of all possible values for x, the price per mug. From the graph, we can see that the maximum price per mug that yields a positive revenue is around $18.25. Therefore, any value of x between 0 and 18.25 is in the domain.To learn more about the functions:
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Maths work …………………………
Answer:
by similarity
as these questions are usually solve by similarity
Pls help me I will make u brainest
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?
3
4
5
6
7
8
9
We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?The divisors of 10 are 1, 2, 5, and 10.
To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.
We need to select 2 distinct divisors and find their product.
The possible pairs are:
1 and 2, product = 21 and 5, product = 51 and 10, product = 102 and 5, product = 102 and 10, product = 205 and 10, product = 50Therefoore, we can obtain 6 different numbers.
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please help!!
4.
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
How to solve:The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
They cover almost equal distances from their starting points:
24 miles ≈ √12²+21² miles
b) They encounter each other.
c) The angle at one vertex measures 30 degrees.
d) e) As shown in the attached picture, it is an almost right triangle.
f) Together, they cover a total distance of 57 miles (12+21+24).
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the product of 2 rational numbers is 16/3.If one of the rational number is -26/3,find the other rational number
Answer:
- [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
let n be the other rational number , then
- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]
[a number × its reciprocal = 1 ]
multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]
n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex] ( cancel the 3 on numerator/ denominator )
n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]
I need help please
Answer:
64 sq cm
Step-by-step explanation:
triangle area = 1/2*b*h (×4 because 4 triangles)
square area = lw
Write the equation of a line perpendicular to `y=3` that goes through the point (-5, 3).
Answer:
The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.
Step-by-step explanation:
To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.
To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).
The equation of the vertical line passing through the point (-5, 3) is:
x = -5
This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).
So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.
Answer:
x= -5
Step-by-step explanation:
The perpendicular line is anything with x= __.
x= -5 however, will go through the point (-5, 3) and that is our answer.
4 1/2 divided by 3 (fraction problem)
Answer: 9/6 or 1 1/2
Step-by-step explanation:
9/2 ÷ 3
KCF (keep, change, flip)
9/2 × 1/3
Solve.
Final answer: 9/6
hope i helped :)
Goods with a cost price of R200 are sold at a mark-up of 100%. The selling price is:
If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:
Selling price = Cost price + Mark-up
Mark-up = 100% x Cost price
= 100% x R200
= R200
So the mark-up is R200.
Selling price = Cost price + Mark-up
= R200 + R200
= R400
Therefore, the selling price of the goods is R400.
the whole problem is in the pic below
Answer:
301.733% increase
Step-by-step explanation:
how long will a car take to travel 140km averaging a speed of 35km/h
Answer:
Step-by-step explanation:
To calculate the time it will take a car to travel 140km at an average speed of 35km/h, we can use the formula:
time = distance ÷ speed
Plugging in the given values, we get:
time = 140km ÷ 35km/h
time = 4 hours
Therefore, it will take a car 4 hours to travel 140km at an average speed of 35km/h.
Answer:
ㅤ
Car will take 4 hours
ㅤ
Step-by-step explanation:
ㅤ
[tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{Time = \dfrac{Distance}{Speed}}}}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Distance)} = 140 \: km}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Speed)} = 35 \: km/hr}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Applying \: Formula:-}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Required_{(Time)} = \bigg(\dfrac{\cancel{140}}{\cancel{35}}\bigg)} \: hr}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\leadsto{\sf{Required_{(Time)} = 4 \: hr}}}}}[/tex]
ㅤ
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Time = \dfrac{Distance}{Speed}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Speed = \dfrac{Distance}{Time}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Distance = Speed \times Time}}}[/tex]
suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. how long would it take the two painters together to paint the house?
It would take the two painters together eight hours to paint the house
Step-by-step explanation: Given that, One painter can paint the entire house in twelve hours. The second painter takes eight hours to paint a similarly-sized house. To find, How long would it take the two painters together to paint the house? Suppose one painter takes x hours to paint the house.
Therefore, the other painter will take x-4 hours to paint the same house. According to the question, [tex]1/x+1/(x-4)=1/12+1/8[/tex] Multiply by LCM, [tex]8(x-4)=12x+12(x-4)8x-32=6x+484x=80x=20[/tex]Therefore, the first painter will take 20 hours to paint the house. The second painter will take 16 hours (20-4). Together they will take, [tex]1/20+1/16=0.1+0.0625=0.1625[/tex] Thus, they will take 6.1538 hours which can be rounded to 4.8 hours.
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If a car runs at a constant speed and takes 3 hrs to run a distance of 180 km, what time it
will take to run 100 km?
Answer:
100 minutes
Step-by-step explanation:
We know
It takes 3 hrs to run a distance of 180 km.
180 / 3 = 60 km / h
60 minutes = 60 km
40 minutes = 40 km
What time it will take to run 100 km?
60 + 40 = 100 minutes
So, it takes 100 minutes to run 100 km.
[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answer:
576 books.
Step-by-step explanation:
134+254+188=576 books in total.
Answer:
576
Step-by-step explanation:
This is literally easy!
Checked books are 134 + 254 + 188 = 576
WILL GIVE BRAINLIEST 15 POINTS PLEASEE Fill in the blanks pleaseee
Therefore, we have the values of:
a = -g(x) for -10 < x < -8
b = lower limit of the range where g(x) = -6
c = -C for -1 < x < 1
d = upper limit of the range where g(x) = 4
e = we cannot determine the value of e based on the given information.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.
Here,
We can find the values of a, b, c, d, and e by examining the given information:
For -15 < x < -10: g(x) = -(-10) = 10
For -10 < x < -8: g(x) = -a
For -1 < x < 1: g(x) = -C
For b < x < l: g(x) = -(-6) = 6
For 10 < x < 15: g(x) = -8
For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.
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With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
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Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
Find the surface area of the regular pyramid. Round your answer to two decimal places.
solve for x using a tangent and a secant line
Check the picture below.
[tex]11^2=(x+3)(3)\implies 121=3x+9\implies 112=3x \\\\\\ \cfrac{112}{3}=x\implies 37.3\approx x[/tex]
use the formula for the sum of a geometric series to find the sum or state that the series diverges. (use symbolic notation and fractions where needed. enter dne if the series diverges.) (4^3 / 5^3) + (4^4 / 5^4) + (4^5 / 5^5) = ________--
The sum of the geometric series is 3904/3125.
By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.
Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;
The first term, a = 4³/5³
Common ratio, r = 4/5
The number of terms, n = 3
We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;
S_n = a(1 - rⁿ) / (1 - r)
S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]
S₃ = {(64/125) [1 - (64/125)]} / [1/5]
S₃ = (64/125) [(125-64)/125] [5/1]
S₃ = (64/125) (61/125) (5)
Therefore, S₃ = 3904/3125.
Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.
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A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using ἁ =0.05 instead of ἁ =0.05
c. using ἁ =0.05 instead of ἁ =0.01
d. giving the drug to 25 randomly selected students instead of 50.
e. using a two-sided test instead of a one-sided test.
The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.
The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.
To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.
However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.
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Can somebody help me, please
Answer:
uh I don't even know what this is
Answer: x = 500
Step-by-step explanation:
Use the Pythagorean Theorem
a²+b²=c²
300² + 400² = x²
90000 + 160000 = x²
250000 = x²
√250000 = √x²
500 = x
hope i explained it :)
The value of 5^2000+5^1999/5^1999-5^1997
Answer:
We can simplify the expression as follows:
5^(2000) + 5^(1999)
5^(1999) - 5^(1997)
= 5^(1999) * (1 + 1/5)
5^(1997) * (1 - 1/25)
= (5/4) * (25/24) * 5^(1999)
= (125/96) * 5^(1999)
Therefore, the value of the expression is (125/96) * 5^(1999).
Step-by-step explanation:
QRT=(3x+5)
TRS=(10x-7)
Find the measure of each angle.
Answer:
I'm sorry, but the given expressions QRT and TRS do not seem to correspond to angles. They appear to be algebraic expressions involving variables x. Without further information or context, it is not possible to determine any angles or measures of angles.
Please provide additional information or clarify the question.
Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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assuming that the p-value to test that the population mean number of errors for the ethanol group (e) is greater than the population mean number of errors for the placebo group (p) is 0.0106 and using a 1% significance level, what is the best conclusion from this hypothesis test in the context of the problem?
The best conclusion from this hypothesis test in the context of the problem is that we can reject the null hypothesis. The null hypothesis for this problem is that the errors is not greater than the population mean.
What is the best conclusion?The null hypothesis for this problem is that the population mean number of errors for the ethanol group is not greater than the population mean number of errors for the placebo group.
In other words, the null hypothesis is: H₀: μe ≤ μp. The alternative hypothesis is that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group. In other words, the alternative hypothesis is: H₁: μe > μp.
The p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the p-value is 0.0106, which is less than the significance level of 0.01. This means that the observed test statistic is significant at the 1% level, and we reject the null hypothesis.
Therefore, we conclude that there is evidence to suggest that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group.
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If y varies inversely with x and y is = to 100 x = 25 what is the value of y when x=10
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=25\\ y=100 \end{cases} \\\\\\ 100=\cfrac{k}{25}\implies 2500=k\hspace{12em}\boxed{y=\cfrac{2500}{x}} \\\\\\ \textit{when x = 10, what's "y"?}\qquad y=\cfrac{2500}{10}\implies y=250[/tex]
machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested
The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.
To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:
A = $4,000.00(1 + 0.045/365)^(365*4)
A = $4,000.00(1.0001234)^1460
A = $4,889.68
The final amount is $4,889.68, which means that the interest earned is:
Interest = $4,889.68 - $4,000.00 = $889.68
We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:
$1.197204 / $1.00 = 1.197204
Interest earned = $889.68 x 1.197204 = $1,064.08
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