Mathematics College

## Answers

**Answer 1**

Answer:

1/16

Step-by-step explanation:

Substituting the given value of x into the equation, we get ...

## Related Questions

One integer is 1/3 times another. The sum of their squares is 90. What are the two integer?

### Answers

Answer:

Hence, the two integers could be:

3 and 9

0R

-3 and -9

Step-by-step explanation:

Let the two integers be denoted by a and b.

It is given that:

One integer is 1/3 times another.

i.e. let

i.e.

Also,

The sum of their squares is 90.

i.e.

Hence, when a=3 we have:

and when,

then b=-9

One integer is 3 more than 5 times another. The product is 54, what are the two integers?

### Answers

Answer:

The two integers are 18 and 3.

Step-by-step explanation:

Consider the provided information.

It is given that One integer is 3 more than 5 times another.

Let us consider the integer is x.

Then 3 more than 5 times of x is:

The product of the provided two numbers is 54. i.e.

Use the formula of the quadratic equation:

For the equation the solutions are:

By comparing the obtained equation with the above equation, it can be concluded that a = 5, b = 3 and c = -54. Substitute the these values in the above formula.

or

or

or

As we have given that numbers are integer, therefore ignore

Thus, the value of x is 3 or one number is 3.

Then 3 more than 5 times of x is: 3 + 5(3) = 18.

Therefore, the two integers are 18 and 3.

on physical examine a 34 year old patient had following cardiac parameters. The approximate amt of blood in LV (preload) =80cc, HR 100. What is his cardiac output (CO)?

### Answers

Answer:

8 Liters/minute

Step-by-step explanation:

Cardiac output is defined as the volume of blood pumped by the left ventricle or right ventricle per unit time.

Heart rate is the number of heart beats per minute.

Stroke volume is the amount of blood pumped from the left ventricle per beat.

Amount of blood in LV=Stroke volume = 80 cc/beat=0.08 L/beat

Heart rate=100 beats/minute

Cardiac output (CO)= Stroke volume×Heart rate

Cardiac output (CO)=0.08×100

Cardiac output (CO)=8 L/minute

Name and describe the methods for determining a marketing budget.

### Answers

Answer: There are several ways in which we can determine our marketing budget. Some of these are given below:

1. Percentage of revenues:

Under this method we usually take a fixed percentage of our revenues and further allocating this amount for marketing. We will choose the percentage that works best for us.

2. Percentage of net sales:

This method determines our marketing budget as a fraction of our net sales. This method will take a lot of trial and error to find the percentage that works well for our company.

3. Industry specific:

Nowadays, industries have specific projections as to the amount they will need to spend on marketing . The best way to get these numbers is to find a firm that represents our industry and ask them to provide us with averages. We can then refine the actual costs.

4. Objective/task oriented

This is model that works by setting out goals, planning out the tasks and then estimating the cost for all of these tasks. It works greatly for firms who have a immense knowledge about measurements and information of their business processes.

Three workers at a fast food restaurant pack the take-out chicken dinners. John packs 45% of the dinners, Mary packs 25% of the dinners and Sue packs the remaining dinners. Of the dinners John packs 4% do not include a salt packet. If Mary packs the dinner 2% of the time the salt is omitted. Lastly, 3% of the dinners do not include salt if Sue does the packing. If you find there is not salt in your purchased dinner what is the probability that Mary packed your dinner?

### Answers

Answer:0.5625

Step-by-step explanation:

If John packed the dinner

probability of salt less dinner==0.018

If Mary packed the dinner

probability of salt-less dinner ==0.005

If sue packed the dinner

probability of salt-less dinner ==0.009

Total proportion of salt-less dinner=0.032

probability that dinner is salt-less and mary packed it==0.5625

Last year, a person wrote 128 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance?

### Answers

Answer: The mean number of checks written per day =

Step-by-step explanation:

Given : A person wrote 128 checks in last year.

Consider , the last year is a no-leap year.

The number of days in ;last year = 365 days

Let X be the number of checks in one day.

Then ,

The mean number of checks written per day =

Now X follows Poisson distribution with parameter .

Then ,

Matrix question. Please write the detailed formula and explanation/definition of how you did this, thanks. A=131 232 B= \bigl(\begin{smallmatrix} 211 \\ 323 \\ 211 \end{smallmatrix}\bigr)

a) What is A+B?

b) What is A x B (A times B) ? what is the multiplication formula for 3*3 matrix? How about the multiplication formula for 2*2 matrix and 4*4 matrix?

c) Are A and B invertible? WHY?

### Answers

Answer:

a.A+B can not find out

b.=

=

=

In similar way multiply two matrix of order

c.No,because A is not a square matrix and determinant of B is zero.

Step-by-step explanation:

We are given that two matrix

A=

B=

In matrix A , two rows and 3 columns therefore, the order of matrix

In matrix B, 3 rows and 3 columns therefore, the order of matrix B is

a.A+B can no find because when add two matrix then the order of two matrix should be same .

b.

When we multiply on matrix to other matrix then number of columns of first matrix equals to number of rows of second matrix.

Therefore, number of columns of matrix A is equals to number of rows of matrix B.So, we can multiply

=\times

=

Formula for multiply of matrix of order

Let A and B are square matrix of order

Let A= and B=

=

In similar way we multiply of matrix of order and matrix multiply of order

Let A and B are matrix of order

Let

=

In similar way we multiply two matrix of order

C.Matrix A is not a square matrix .Therefore, it is not a invertible matrix.

Therefore, the determinant of B is equal to zero therefore, inverse of matrix B does not exist.

Hence, Both matrix A and B are no invertible.

If Ana devotes all her time to making fudge, she can make 3 pounds of fudge an hour, and if he devotes all her time to making toffee, she can make 2 pounds of toffee an hour. If Leo devotes all his time to making fudge, he can make 4 pounds of fudge an hour, and if he devotes all his time to making toffee, he can make 5 pounds of toffee an hour. According to The Principle of Comparative Advantage, Ana and Leo will be able to produce more overall if:

### Answers

Answer: If Ana produce more furge and Leo produce more toffee.

Step-by-step explanation:

Comparative advantage: A country or a person has a comparative advantage in producing a commodity if the opportunity cost of producing that commodity is lower in that country as compared to the other country.

Here Ana or Leo will gain comparative advantage only when they are selling the good they are specializing in and they would specialize in that good which would have lower opportunity cost for them.

(a) For Ana who devoted all of her time to making either 3 pounds of fudge or 2 pounds of toffee,

the opportunity cost for making 1 pound of furge is = 2/3 = 0.66

the opportunity cost for making 1 pound of toffee is = 3/2 = 1.5

(b) For Leo who devoted all of her time to making either 4 pounds of fudge or 5 pounds of toffee,

the opportunity cost for making 1 pound of furge is = 5/4 = 1.25

the opportunity cost for making 1 pound of toffee is = 4/5 = 0.8

Above calculations clearly shows that Ana has a comparative advantage in producing furge because opportunity cost of making furge is lower than the Leo, so he devotes most of his time to produce furge.

Whereas Leo has a comparative advantage in producing Toffee because opportunity cost of making toffee is lower than the Ana, so he devotes most of his time to produce toffee.

It cost Maria 20 cents to mail a postcard and 33 cents to mail a letter. She sent either a postcard or a letter to each of 18 people and spent $4.38. Let x represent the number of postcards she wrote. What would be the expression for the number of letters? How many postcards did Maria send?

### Answers

Answer: The the expression for the number of letters =

Maria sent 12 postcards

Step-by-step explanation:

Given : Cost of mail a postcard =20 cents

Cost of mail a letter = 33 cents

Since 1 dollar = 100 cents

Total money spent by Maria =

Let x represent the number of postcards she wrote.

The the expression for the number of letters =

According to the question we have ,

Hence, Maria sent 12 postcards and 6 letters .

List price List price: Divide 7434 items between four people, A,B,C and D in the proportions: 3:6:8:4. How many items do B and D get?

### Answers

Answer:

B 2124

D 1416

Step-by-step explanation:

Take the ratio

A B C D Total

3 6 8 4 21 (3+6+8+4 = 21)

B gets 6 out of every 21 items

Take that fraction times the total items

6/21 * 7434 = 2124

D gets 4 out of every 21 items

Take that fraction times the total items

4/21 * 7434 = 1416

Answer: B get = 2124 items and D get = 1416 items

Step-by-step explanation:

Total number of items = 7434

Dividing ratio between A, B, C and D = 3:6:8:4

∴ the items divided in this ration are as follows:

=

Hence,

A get = 1062 items

B get = 2124 items

C get = 2832 items

D get = 1416 items

So, B get 2124 items and D get 1416 items out of the 7434 items.

Let T: P_3 rightarrow P_3 be the linear transformation satisfying T(1) = 2x^2 + 2, T(x) = 4x - 9, T(x^2) = -4x^2 + x - 2. Find the image of an arbitrary quadratic polynomial ax^2 + bx + C. T(ax^2 + bx + c) =

### Answers

Answer:

Step-by-step explanation:

Let T: be the linear transformation

We have to find the image of an arbitrary quadratic polynomial

We know that linear transformation satisfied the property

Therefore,

Substitute all given values in right place

Hence, the image of an arbitrary quadratic polynomial

.

Let A elementof M_n(R) be a diagonalizable matrix with tr(A^2) = 0. Prove that A is the zero matrix.

### Answers

Answer with Step-by-step explanation:

Let A element of (R) be a diagonalizable matrix with given

We have to prove that A is the zero matrix

Le A= be any matrix of order

Trace : Trace is defined as the sum of diagonal elements of a matrix.

Therefore,

We know that square of an positive or negative element is positive

Therefore, it is necessary that when tr(=0

When all elements of matrix are zero then the matrix should be zero matrix.

Hence, A is a zero matrix .

Several years ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 65.1 inches. (a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.16. Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an alphaequals0.10 level of significance.

### Answers

Answer:

(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Solution:

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis: In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis :

Alternative Hypothesis : 63.7" alt="H_1: \mu>63.7" align="absmiddle" class="latex-formula">

b)The P-value for this test is 0.16.

Solution: The p-value represents the probability of getting a sample mean height of 65.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

Solution:

p- value = 0.16

\apha" alt="p-value> \apha" align="absmiddle" class="latex-formula">

Since the p - value is high .

So, we will accept the null hypothesis

So,

Hence The mean height is 63.7 inches

In multiple regression analysis, residual analysis is used to test the requirement that ___________. The number of independent variables included in the analysis is correct The variation in the residuals is the same for all predicted values of Y The independent variables are the direct cause of the dependent variable The prediction error is minimized

### Answers

Multiple regression analysis is used to make a linear model capable of giving predicting an output variable using two or more independent variables. Analysis of the residual is used to to test if the variation in the residuals is the same for all predicted values of y.

- Residual values gives the difference between the actual and predicted value of a model.

- Residual analysis in linear regression is used to test the appropriateness of a linear model for a given data set.

- Since, the number of independent variables in multiple regression exceeds 1 ; then variation in the predicted values are analysed using the result of the residuals.

Therefore, residual analysis in multiple regression tests the variation in the residuals is the same for all predicted values of y.

Learn more :brainly.com/question/18405415

Answer: The predicted error is minimized.

Step-by-step explanation:

Ideally, residual analysis is used in a linear regression model to measure the appropriateness of the model by examining the residual plots on the graph.

And, residual referred as a difference between the noticed value of the dependent variable (y) and the estimated value (ŷ).

Residual = Noticed value - Estimated value

e = y - ŷ

Lane French has a bad credit rating and went to a local cash center. He took out a $100 loan payable in two weeks at $113.50. What is the percent of interest paid on this loan?

### Answers

Answer: Percent of interest paid on this loan annually = 351% p.a

Step-by-step explanation:

Given that,

principal amount = $100(loan)

time period = 14 days

interest amount (SI) = $13.50

we have to calculate the rate of interest (i),

Simple interest(SI) = principal amount × rate of interest (i) × time period

13.50 = 100 × i ×

i =

i = 3.51

i = 351% p.a.

John has won the mega-bucks lottery, which pays $1, 000, 000. Suppose he deposits the money in a savings account that pays an annual interest of 8% compounded continuously. How long will this money last if he makes annual withdrawals of $100, 000?

### Answers

Answer:20.91

Step-by-step explanation:

Given

Principal amount invested=

Rate of interest=8%

Annual Withdrawl=

compound interest is given by

A=

Therefore reamining Amount after certain years

Net money will become zero after t year

=0

t=20.91 years

Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,341 interest on $51,700 at 4%. What was the time using exact interest?

### Answers

Answer:237 days

Step-by-step explanation:

Interest=1341

Principal

rate of interest

We know

Simple Interest=

=

=

=

Jason received an invoice for $5,000, and the invoice was dated on August 26 with terms of 2/10, n/45 EOM. Please answer the following questions: (1) How much did Jason owe if the bill is paid by September 26?

(2) When will be the last day that Jason can receive the cash discount?

(3) When will be the last day that Jason has to pay for this bill?

### Answers

Step-by-step explanation:

Consider the provided information.

Jason received an invoice for $5,000, and the invoice was dated on August 26.

Part 1)

We need to find the bill Jason needs to pay by September 26.

n/45 means invoice amount should be paid within 45 days after the august 26.

From August 26 to September 26 Jason complete a month.

Thus, Jason just need to pay only $5,000. Which is the invoice amount.

Part 2)

The last day of discount can be calculated by 2/10.

Here, the 2/10 represents that discount of 2% within 10 days.

Now, calculate the 10 days form August 26.

The 10 days from August 26 is September 5.

Hence, September 5 is the last day that Jason can receive the cash discount.

Part 3)

Now, we need to calculate the last day that Jason has to pay for the bill.

n/45 means invoice amount should be paid within 45 days after the august 26.

Hence, the sum of the invoice should be paid within 45 days of August 26, whatever the date.

2. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2017. The average usage was found to be 375kWh. From past years in the March quarter the population standard deviation of the usage was 81k Assuming the standard deviation is unchanged and that the usage is normally distributed ; A. Determine the interval of 95% confidence for the average kilowatt-hours for the population. B. Determine the 99% confidence interval. C. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 20kWh from the sample mean? (This would mean an error amount of 20kWh.)

### Answers

Answer:

Step-by-step explanation:

Given that n =30, x bar = 375 and sigma = 81

Normal distribution is assumed and population std dev is known

Hence z critical values can be used.

For 95% Z critical=1.96

Margin of error =

Confidence interval = 375±29

=(346,404)

B) 99% confidence

Margin of error = 2.59*Std error =38

Confidence interval = 375±38

=(337, 413)

C) For 90%

Margin of error = 20

Std error = 20/1.645 = 12.158

Sample size

Atleast 44 people should be sample size.

In your own words, explain the problem of correlation vs. causation. Why are causation and correlation very different?

### Answers

Answer:

Step-by-step explanation:

Correlation means that two or more events happen together. They are related to one another by being caused by the same thing.

Causation has a definite order. The first event has some cause that is comes before the second event. One event caused the other.