Find the volume of a cone with a base radius of 5 in. and a height of 12 in.

Answers

Answer 1

Answer:

V = 314

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

Given:

r = 5

h = 12

Work:

V = πr²(h/3)

V = 3.14(5²)(12/3)

V = 3.14(25)(4)

V = 314

Answer 2

Answer:

The volume of the cone is 311.1in³.

Step-by-step explanation:

V = ⅓Bh where B = πr²

V = ⅓πr²h

V = ⅓(22/7)(5²)12

V = 0.33(3.142)(25)12

V = 311.1in³


Related Questions

Suppose that y varies directly with x and y = 3 when x = 9. What is y when x = 18?

Answers

Answer:

y = 6

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in y = 3 and x = 9, and solve for k

y = kx

3 = k(9)

1/3 = k

So, the equation is y = 1/3x

Plug in 18 as x and solve for y

y = 1/3x

y = 1/3(18)

y = 6

So, when x = 18, y = 6


The labor charges for mechanics is $54 an hour. The
standard deviation is $4 an hour. Find the minimum percentage of
data values that lie within the range of $48 to $60 an hour for the
mechanic's labo

Answers

The minimum percentage of data values that lie within the range of $48 to $60 an hour for the mechanic's labor is 86.64%.

To find the minimum percentage of data values that lie within the range of $48 to $60 an hour for the mechanic's labor.

We need to calculate the z-scores for both values and use a z-table to find area under the normal curve between those two scores.

First, we calculate the z-score for $48 an hour:

z = (48 - 54) / 4 = -1.5

Next, we calculate the z-score for $60 an hour:

z = (60 - 54) / 4 = 1.5

Using a standard normal distribution table, we can find that the area under the curve between -1.5 and 1.5 is approximately 0.8664 or 86.64%.

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The first pentagon is dilated to form the second pentagon.

Drag and drop the answer to correctly complete the statement.

Will Mark Brainlist =)

Answers

Answer:

2

Step-by-step explanation:

Answer:

2 is answer i promise

Step-by-step explanation:


Find the exact value of tan A in simplest radical form

Answers

Answer:

12.68 de

Step-by-step explanation:

At the football game they sold $4 pizzas and $2 sodas which made the school$260 the number of Sodas sold was five more than three times a number of pizzas sold determine the amount of pizza and sodad sold

Answers

[tex]\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}[/tex]

[tex]\Huge \textsf{Step-by-step explanation}[/tex]

[tex]\LARGE \bold{\textsf{Step 1: Assign Variables}}[/tex]

[tex]\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}[/tex]

[tex]\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}[/tex]

[tex]\large \bold{ \textsf{From the problem, we know that:}}[/tex]

[tex]\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}[/tex]

[tex]\large \bold{ \textsf{We can use this information to write two equations:}}[/tex]

[tex]\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}[/tex]

[tex]\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}[/tex]

[tex]\LARGE \bold{\textsf{Step 3: Solve the system of equations}}[/tex]

[tex]\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}[/tex]

[tex]\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}[/tex]

[tex]\large \textsf{Simplifying this expression gives us:}[/tex]

[tex]\textsf{10\textit{p} + 10 = 260}[/tex]

[tex]\large \textsf{Subtracting 10 from both sides:}[/tex]

[tex]\textsf{10\textit{p} = 250}[/tex]

[tex]\large \textsf{Dividing both sides by 10}[/tex]

[tex]\textsf{\textit{p} = 25}[/tex]

[tex]\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}[/tex]

[tex]\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}[/tex]

[tex]\large \textsf{So, 25 pizzas and 80 sodas were sold.}[/tex]

----------------------------------------------------------------------------------------------------------

Find m QRS? who can help me?​

Answers

Answer:

m<PRS+m<PRQ=m<QRS.

17 + 17 = 34

m<QRS=34

Help will mark brainliest show steps pls

Answers

Answer:

at first , you need the sum of both equations . It will be like :

2y= 0 + 2

Y=1

_____

now that you know the value of Y , place it in the one of the equation that you like , forexample i place it in the second equation and find out that the value of x is ( -3/2)

1= 2X+5

-4=2X

X= -2

Hope it helps , good luck ^.^

Y = -2x - 3
Y = -2 + 5

-2x - 3 = 2x + 5

x= -2

y= -2 x (-2) -3

y= 1

( x, y) = (-2, 1)

The answer is (-2, 1)

HELP

Is x+7 a factor of p(x)

Answers

Answer:

No

Step-by-step explanation:

Because the remainder is not zero

I just need this and that it

Answers

The answer is J hdjdghsksjdbgeshsh

The fastest clapper in the world can clap 720 times in 60 seconds. What is the unit rate? *

Answers

Answer: 12 claps per second

Step-by-step explanation: divide both by 60 and yield 12 times -1 second

Someone please help me I’ll give out brainliest please dont answer if you don’t know

Answers

Answer:

-9p+3

plz mark me as brainliest

what is the volume of the prism 8 1/2 m 7 m 4 m

Answers

Answer:

Step-by-step explanation:

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

Answer:

Step-by-step explanation:

Volume of prism = length * width * height  

                            = 8 1/2 *  7 * 4

                            [tex]= \frac{17}{2}*7*4\\\\=17 * 7 * 2\\\\= 238 cubic m[/tex]


What is the area of the triangle in square yards?
6 yd.
15 3/4 yd.

Answers

Answer:

6x15 2/4 yd dividedby 2

Step-by-step explanation:

do the math and u get ur answer

the difference between a low-cost provider strategy and a focused low-cost strategy is

Answers

The difference between a low-cost provider strategy and a focused low-cost strategy lies in their scope and target market. A low-cost provider strategy aims to achieve a cost advantage over competitors while targeting a broad market segment.

A low-cost provider strategy involves offering products or services at a lower cost compared to competitors while targeting a broad customer base. The focus is on achieving economies of scale, operational efficiencies, and cost reduction across the value chain to deliver products or services at competitive prices. This strategy aims to attract a large customer base through cost advantages and can be employed in various industries.

In contrast, a focused low-cost strategy narrows down the target market to a specific segment or niche. Instead of targeting a broad market, the company focuses on serving a particular group of customers with specialized needs or preferences. By understanding the unique requirements of this specific segment, the company can tailor its offerings and operations to provide lower costs, thereby gaining a competitive edge within that niche market. This strategy allows for a more concentrated effort and customization to cater to the specific demands of the chosen market segment.

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CAN SOMEONE HELP ME PLEASE

Answers

It seems like it is a 1:3 ratio.
y = 12
3(2x + 1) = 4x + 9
6x + 3 = 4x + 9
6x = 4x + 6
2x = 6
x = 3
Since they are similar the proportions of the figure would be equal
3/9 = 2x + 1/ 4x + 9
4x + 9 = 3(2x + 1)
4x + 9 = 6x + 3
2x = 6, x = 3
3/9 = 4/y
y = 12
Solution: x = 3, y = 12

Craig opened a savings account and deposited $600.00 as principal. The account earns 2%
interest, compounded annually. What is the balance after 6 years?
Use the formula A =
1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

Answers

Answer:

the answer is 675.70 or 4,504.33

Step-by-step explanation:

the right answer is that

Solve the problem. Round your answer to one decimal place. Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%. Round to the nearest hundredth of a degree. Select one: О 99.12°F O 97.28ºF 98.78°F O 98.40°F

Answers

The temperature that separates the top 7% from the bottom 93% is 98.78°F.

To solve this problem, we need to use the concept of the normal distribution. In a normal distribution, data is symmetrically distributed around the mean, with the majority of values falling within a certain range determined by the standard deviation. In this case, we are given a normal distribution of human body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F.

To find the temperature that separates the top 7% from the bottom 93%, we need to locate the value on the distribution that corresponds to the 93rd percentile. The 93rd percentile represents the point below which 93% of the data falls. Conversely, the top 7% of the data lies above this point.

Using statistical tables or a calculator, we can determine the z-score corresponding to the 93rd percentile. The z-score measures the number of standard deviations a given value is away from the mean. Once we find the z-score, we can use it to calculate the temperature value.

In this case, the z-score corresponding to the 93rd percentile is approximately 1.475. We can then use the z-score formula: z = (x - mean) / standard deviation. Rearranging the formula to solve for x (the temperature value), we get x = (z * standard deviation) + mean. Plugging in the values, we find x = (1.475 * 0.62) + 98.20 = 98.78°F.

Therefore, the temperature that separates the top 7% from the bottom 93% is approximately 98.78°F. This means that 93% of human body temperatures are below 98.78°F, while the top 7% are above this value.

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consider the function f(x)=x−2x 1. (a) find the domain of f(x).

Answers

The domain of the function f(x) = x² - 2x + 1 is all real numbers, which is denoted as (-∞, +∞).

To find the domain of the function f(x) = x² - 2x + 1, we determine the set of all possible values for x that make the function well-defined.

The given function is a polynomial-function, and polynomial functions are defined for all real numbers. So, the domain of f(x) = x² - 2x + 1 is the set of all real numbers, which can be represented as (-∞, +∞).

It means that any real-number can be substituted into the function, and it will give a valid output. There are no limitations on the possible values of x in this case.

Therefore, the domain is all real numbers.

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The given question is incomplete, the complete question is

Find the domain of the function f(x) = x² - 2x + 1.

Find the length of the side labeled x. Round intermediate values to the nearest 10th. Use the rounded values to calculate the next value. Round your final answer to the nearest 10th

Answers

Answer:

16.0(?)

Step-by-step explanation:

I’m not really sure if it’s correct. But I’m assume it’s correct.

HELP PLEASE

Marcus works at the grocery store. He earns 8.75 per hour. Last week he worked 6.5 hours. How much did Marcus make last week?

Answers

20 dollars bev b h h b g v v v v.

. A rectangle has its base on the x-axis and its upper two vertices on the semi-circle y = V1 - 32. What is the largest area the rectangle can have? 1 6 1

Answers

The largest area the rectangle can have is -1024 square units.

To solve the given problem, follow the steps given below:

Step 1: Sketch the given graph on a coordinate plane as shown below:

Step 2: Let's assume that the base of the rectangle is x units and its height is y units.

Step 3: As the base of the rectangle is on x-axis, we have the length of the base as the x-coordinate of the upper two vertices of the rectangle.

Now, the x-coordinate of the upper two vertices of the rectangle lie on the given semicircle whose equation is y = V1 - 32.

So, we can write:

y = V1 - 32x^2 = (y + 32)^2 ⇒ x^2 = y^2 + 64y + 1024

Step 4: Now, we can write the area of the rectangle as: A = base × height= x × y

Using the value of x from equation (1), we get: A = (y^2 + 64y + 1024)1/2 y

So, we have an equation for area in terms of y. Let's differentiate it with respect to y to find the maximum value of A. dA/dy = (y^2 + 64y + 1024)-1/2 (2y + 64)

By equating dA/dy = 0, we get: 2y + 64 = 0y = -32

Substituting the value of y in equation (2), we get:x^2 = 1024 ⇒ x = ±32

The given rectangle lies in the first quadrant.

Hence, the length of the base of the rectangle is x = 32 units.

So, we have the dimensions of the rectangle as length = 32 units and breadth = height = y = -32 units.

However, as the length and breadth of the rectangle cannot be negative, we cannot consider the negative value of y.

Therefore, the maximum area of the rectangle is: A = base × height= 32 × (-32)= -1024 sq. units

Hence, the largest area the rectangle can have is -1024 square units.

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The checkbook balance of Hercher Company is $1,955.81. The bank statement shows a balance of $3,142.11. The statement shows interest earned of $31.55 and a service charge of $22.80. There is a deposit in transit of $3,991.88. In further analyzing the statement it was discovered that the bank collected a note for $3,100.000. Hercher Co. forgot to deduct a check for $850 during the month. There is a check outstanding for $2,919.43. What is the reconciled balance?

Answers

Answer:

Reconciled balance $3,142.11

Step-by-step explanation:

The computation of the reconciled balance is shown below:

Debit balance as per check book $1,955.81

Add: interest earned $31.55

Collection of note $3,100

Outstanding checks $2,919.43

Less: service charges -$22.80

Less: deposit in transit -$3,991.88

Less: forgot a check -$850

Reconciled balance $3,142.11

The same would be relevant and considered too

what is the distance between -2 1/2, -5 3/4

Answers

Answer:

Step-by-step explanation:

it's kinda confusing b/c of the minus signs.. huh...  but -5 is less than -2 sooo

start with

-2 1/2  - (-5 3/4 )

=5 3/4 - 2 1/2

=5 3/4 - 2 2/4

=23/4 - 10/4

=13/4

there you go...  :)

if you want it back in proper fractions

3 1/4

The density of mercury is 13.5 times greater than the density of water. If you were to build a barometer that used water instead of mercury to record the standard pressure at sea level, what would be the height of that barometer? Assume that the mercury barometer is 76 centimeters, or 29.92 inches, long (this is the standard atmospheric pressure at sea level). View Available Hint(s) The density of mercury is 13.5 times greater than the density of water. If you were to build a barometer that used water instead of mercury to record the standard pressure at sea level, what would be the height of that barometer? Assume that the mercury barometer is 76 centimeters, or 29.92 inches, long (this is the standard atmospheric pressure at sea level). 110.29 centimeters (43.42 inches) 5.63 centimeters (2.21 inches) 89.5 centimeters (35.24 inches) 1026 centimeters (403.92 inches)

Answers

Answer:

h = 403.92in or 1026cm

Step-by-step explanation:

Given

Let x represent the density of mercury, and y the density of water.

[tex]y = 13.5x[/tex]

[tex]Mercury\ barometer =76cm[/tex] or [tex]Mercury\ barometer =29.92in[/tex]

Required

Determine the height of the barometer

At standard atmospheric pressure, the relationship between the mercury barometer and the height (h) of the barometer is:

[tex]h = 13.5 * Mercury\ barometer[/tex]

In centimeters, we have:

[tex]h = 13.5 * 76cm[/tex]

[tex]h = 1026cm[/tex]

In inches, we have:

[tex]h = 13.5 * 29.92in[/tex]

[tex]h = 403.92in[/tex]

Match the word to its description. The difference between the lowest and highest value 1. mode The middle value 2. mean 3. median The most frequent value PP 4. range The average​

Answers

Answer:

range

Step-by-step explanation:

The difference between the lowest and the highest number is called the range. The middle value is the median (it's in the "mid"dle, median) The mean is the average. And the mode is the most frequent value.

A local store owner is interested in finding the mean age of her customers. She randomly surveys 82 customers and records their age. Identify the population, sample, variable, type of variable, parameter, and statistic.

Answers

Population: The set of all possible customers in the store.

Sample: The 82 customers randomly surveyed.

Variable: Age of the customers Type of variable: Quantitative parameter

Parameter: The mean age of all the customers in the store.

Statistic: The sample mean age of the 82 customers surveyed.

Analysis: The mean age of all customers is a parameter since the store owner is interested in knowing the mean age of all the customers that come to her store.

The store owner will be interested in collecting data on all the customers who come to her store. Since this will be difficult, she will sample some customers instead. The store owner randomly surveyed 82 customers, which is the sample size. The variable of interest is the age of the customers. This is a quantitative variable since it is measured using numerical values. The sample mean age of the 82 customers surveyed is a statistic.

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Melanie's dance class was 100 minutes long. If 1/8 of the time was spent
stretching, how many minutes were spent stretching?

Answers

Answer:

12.5 minutes

Step-by-step explanation:

Multiply 1/8 by 100. Convert 25/2 to a decimal by dividing 25 by 2. The answer is 12.5 minutes.

Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z<0.75? a.0.7223 b.0.7734 Oc 0.9127 d.0.6915 QUESTION 26 Given the least squares regression line y-3 x-3, which of the following is true? a. The relationship between x and y is positive. b. The relationship between x and y is negative. c. As x decreases, y increases. d. None of the answer options is correct.

Answers

The least squares regression line y-3 x-3 is (a) "The relationship between x and y is positive."

To get the area under the standard Normal curve corresponding to Z < 0.75, we can use the standard Normal distribution tables. The tables provide the cumulative probability up to a given Z-score.

Looking up the value of 0.75 in the standard Normal distribution table, we find that the corresponding area is approximately 0.7734.

Therefore, the answer is (b) 0.7734.

Regarding the least squares regression line y = 3x - 3, we can make the following observations:

a. The relationship between x and y is positive: This is true because the coefficient of x (3) is positive, indicating a positive relationship between x and y.

b. The relationship between x and y is negative: This is false because the coefficient of x (3) is positive, indicating a positive relationship between x and y.

c. As x decreases, y increases: This is false because as x decreases, y will also decrease based on the equation y = 3x - 3.

d. None of the answer options is correct: This is false because option (a) "The relationship between x and y is positive" is correct.

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Jess is having a private party at the bowling alley. The party costs $99 plus %3 per person who attends.

Answers

Answer:

Total cost= 99 + 2.97x

Step-by-step explanation:

Giving the following information:

Fixed cost= $99

Variable cost= 3% per person

First, we need to calculate the 3% of 99:

Unitary variable cost= 99*0.03= $2.97

Now, we establish the total cost structure:

Total cost= 99 + 2.97x

x= number of people in attendance

Finally, suppose 200 people attend the party:

Total cost= 99 + 2.97*200

Total cost= $693

Need someones help on this!

Answers

Answer:

x^3

Step-by-step explanation:

quotient property of exponents

I think the answer is c. x^3

Other Questions
Consider this forecast surface weather map from the National Weather Service. The grey lines are isobars, drawn every 4 mb. Five points labeled A, B, C, D and E are shown. Each point is on an isobar, so it is easy to determine the sea-level pressure at each point. The table below gives the elevation (in meters) of each point that is not at sea level:B: 25 m below sea level (this is Death Valley)C: 1600 m (Denver, approximately)D: 180 m (note that the Great Lakes are NOT at sea level)E: 370 m (near State College) Complying with environmental laws and regulations to avoid fines and lawsuits would be an objective to demonstrate:Select one:a. Nudgingb. Corporate social responsibilityc. Corporate mandated. Vicarious liability Select a specific institution. Identify this institution and utilizing its published MCR analyze costs and revenue of at least 3 specific departments. Then, evaluate implications of this volume to the facilitys future income stream. Question 3 Question 3a Assume you are the Minister of Finance and Economic Planning for Ghana, in charge of Fiscal Policy. The Research Director of the Ministry brought you the following data on Ghana for the previous fiscal year, 2021. An examination of the data reveals that, during the fiscal year 2021, households in Ghana saved 20% of their disposable income (Y) and spent the rest on consumption. In addition, GH5,000.00 was spent on Consumption expenditure (C), which is independent of income and Gross Private Investment (I) was GH7,000.00. Total Government expenditure (G) which stood at GHe8,000.00 was supposed to be financed by a lump sum tax of GH2,000.00 (independent of income) and a proportional tax rate of 25% of national income. Exports (X) stood at GH 2,500.00. In addition, the country's import (M) during the previous fiscal year comprises of GH1,000.00 which was independent of the country's national income and 10% which was dependent of the country's national income. Given these data on Ghana for the previous year: i. Compute the equilibrium level of income (Y), Consumption (C), Tax (T) and Savings (S). (Hint: C = a + byd; T = To+tY and M = M + mY) Determine the Government fiscal stance. (10 marks) (1 mark) iii. If the full employment level of national income is GH40,000.00, determine the income gap. iv. What fiscal policy would be appropriate to address this gap? (1 mark) (1 mark) V. If there is an increase in export to GH4,000.00, find the new level of equilibrium income. (2 marks) vi. Show how a GH 2,000 increase in government spending financed by a GH$2,000 increase in taxes will affect the level of national income. (2 marks) Question 3b Gross Domestic Product (GDP) is not a good measure of welfare in an economy. Discuss. (3 marks) A supermarket CEO claims that 26% of customers that enter the store purchase milk or bread. A survey of 320 customer showed that 67 customers purchased bread or milk on their trip to the store. Assuming the CEO's claim is correct, determine (to 4 decimal places):1. the standard error for the sampling distribution of the proportion.2. the probability that the sample proportion is no more than that found in the survey. Have China, India, Japan, South Korea and Singapore experiencedthe catch-up effect (also known as convergence theory)? Explaindifferences with Australia and the USA. Discount loan (interest and principal at maturity). Chuck Ponzi has talked an elderly woman into loaning him $10,000 for a new business venture. She has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the $10,000 with an annual interest rate of 11% over the next 15 years. Determine the cash flow to the woman under a discount loan, in which Ponzi will have a lump-sum payment at the end of the contract. What is the amount of payment that the woman will receive at the end of years 1 through 14? A company produces packets of soap powder labeled "Giant Size 32 Ounces. The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 or and a standard deviation of 0.3 or. To ad having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 or. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a bes have to be for it to be labeled overweight? 33.82 or 634,15 or 34.6202 31.80 o QUESTION 7 Some researchers have noted that adolescents who spend a lot of time playing video or computer games are at greater risk for depression and violence. This is an example of a a single-blind experiment, because the subjects knew they were playing games ha valid conclusion, because more time yields more aggression is a positive association c. a paired data experiment, because we are studying both aggression and game playing dan observational study with larking variables that may explain the association. QUESTIONS A company produces packets of soap poeder held"Chante 12 mes. The actual weight of top powder in a box una distribution of 33 oranda de roso having dised customers, the company box fit considered underwright if it weh less 1902. To avoiding help the best way does best be for is to be weled overweight XXX b.34.15 34.620 0.31.80 OR QUESTION 4 The time needed for college students to complete a certainpaper and pencil maze follows a Normal distribution, with a mean of 80 seconds and a standard deviation of 6 seconds. You wish to see if the mean time je is changed by meditation, so you have a group of 8 college students meditate for 30 minutes and then complete the mare. It takes them an average of 1-74 seconds to complete the mare. Use this information to test the hypotheses Hg: -80, Ha80 at significance level a-0.02. You conclude that a. Ha should be accepted. bHo should be rejected. Hy should not be rejected. d. this is a borderline case and so decision should be made. 11 12 15 16 17 22 24 29 33 38 what is the median An account linked with another account that has an opposite normal balance and that is subtracted from the balance of the related account is a(n):A) Accrued account.B) Contra account.C) Temporary Account.D) Clearing account.E) Permanent Account. Explain the Decision-making method (High and low Methods) withexamples. Find the non-parametric equation of the plane with normal (5,6,6)-5,6,6 which passes through point (5,6,0)5,-6,0.Write your answer in the form Ax+By+Cz+d=0Ax+By+Cz+d=0 using lower case x,y,zx,y,z and * for multiplication. Please Do Not rescale (simplify) the equation. Let X1, X2, ..., Xm be a random sample from a population with mean mu1 and variance of sigma1^2=, and let Y1, Y2, ... , Yn be a random sample from a population with mean mu2 and variance sigma2^2, and that X and Y samples are independent of one another. Which of the following statements are true? Xbar is normally distributed with expected value mu1 and variance sigma1^2/m Ybar is normally distributed with expected value mu2 and variance sigma2^2/m Xbar-Ybar is normally distributed with expected value mul-mu2 and variance (sigma1^2/m+sigma2^2/n). Xbar-Ybar is an unbiased estimator of mul-mu2. All of the above statements are true. Touch may communicate many different meanings includinga.all of the above. b.control. c.positive emotionsd.playfulness. Explain the full story of Garland, including up to Amy Coney Barrett. Did Trump and Mitch McConnell as in accordance with the constitution? As CRO of Lakeside Bank, a bank that has 15 million of fixed-rate assets, 30 million of rate-sensitive assets, 25 million of fixed-rate liabilities, and 20 million of rate-sensitive liabilities. Conduct a gap analysis for Lakeside Bank and show what will happen to bank profits if interest rates rise by 4 percentage points. Answer all parts (a) to (e) of this question. If a firm produces quantities q1 and q2 of two goods, its total cost is: C = q1 + q 2 1 + q 2 2 q1q2. The goods are sold in competitive markets at prices p1 > 1 and p2.(a) [10 marks] Write down an expression for the profit of the firm. Obtain and provide an economic interpretation for the first-order profit-maximising conditions.(b) [10 marks] Using the Cramers rule, find the quantities q1 and q2 that satisfy the first order conditions.(c) [10 marks] Find the second-order conditions for profit maximisation. For what values of are the second-order conditions satisfied?(d) [10 marks] Assume the second-order condition is satisfied. Use calculus to determine the way in which the supply of good 2 varies with a rise in p1. Explain why it depends on the sign of .(e) [10 marks] Assume the second-order condition is satisfied. If p1 = 0.5 and p2 = 1, under which condition about will good 1 be supplied by the firm? Explain the economic intuition behind the results. Cullumber Corporation issued 368 shares of $10 par value ordinary shares and 123 shares of $50 par value preference shares for a lump sum of $16,587. The ordinary shares have a market price of $20 per share, and the preference shares have a market price of $90 per share. Prepare the journal entry to record the issuance. Consider the set S = {(o,p,q,r): op-qr =0 }Provide a counterexample to show that this set is not a subspace of R4 If the alternate hypothesis is justifiably directional (rather than non-directional), what should the researcher do when conducting a t test? O a one-tailed test O a two-tailed test O set the power to equal B O set to be less than the significance level