Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c · ·d. b. The critical points of f' (x) are same as the critical points of f(x) c. The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. d. All of the statements are false. e. Every local maximum a global maximum

Answers

Answer 1

The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.

What is a critical value of a function?

The critical value is the value of x for which the double derivative of the function f(x) becomes zero.

When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either

a maxima or a minima.

Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.

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Related Questions

Rajani is carrying 9.725 kg of vegetables and Mamta is carrying 8.50 kg of vegetables. Who is carrying more and how much?​

Answers

Rajini is carrying more, since 9.725 kg = 9725 g and 8.50 kg = 8500 g, and 9725 is more than 8500.

To find out how much more vegetables Rajini is carrying, you have to SUBTRACT Mamta’s amount from it.

So: 9725 g - 8500 g = 1025 g

and 1025 g = 1.025 kg

Answer: Rajini is carrying 1.025 kg more vegetables than Mamta.

Answer:

Step-by-step explanation:

let Rajani be carrying r = 9.725kg

let Mamata be carrying m = 8.500kg

difference = r - m = 9.725 - 8.500 = 1.225kg

hence Rajani is carrying 1.225kg more than Mamata

For each of the statements below, is it true with Correlation, Regression, Both, or Neither? Please explain. Thank You!
1. Requires a measure for both variables'individual variances
2. Can be tested for statistical significance
3. Provides a way to predict a specific value of one variable (such as weight) from the value of another variable (such as height)

Answers

True of both correlation and regression. Both requires a measure for both variables individual variances.True of both correlation and regression. Both can be tested for statistical significance.True of regression. Regression provides a way to predict a specific value of one variable from the value of another variable.

1. Correlation is a bivariate analysis that measures the strength of association between two variables and the direction of the relationship. Regression is a statistical method to determine the strength and character of the relationship between one dependent variable and a series of other variables (known as independent variables). So, both correlation and regression require a measure for both variables individual variances.

2. We can test for the statistical significance of a correlation coefficients by performing a hypothesis test on the correlation coefficients. And it's also possible to perform hypothesis tests on the regression slope on the values which is being estimated using a regression analysis. So, both correlation and regression can be tested for statistical significance.

3. Correlation helps us to test the strength of association between two variables. But regression helps us to predict one of the variables from the other. So, it is true for a regression. It is only regression which provides a way to predict a specific value of one variable from the value of another variable.

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An architect is designing a home and needs to create a rectangular bedroom. The bedroom must be 425 ft2 and must be 8 ft longer than it is wide. What are the width and length of the bedroom?

Answers

The width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.

What is the area of the rectangle?

The area of the rectangle is length x breadth. The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.

Let w be the width of the bedroom and l be the length of the bedroom.

The width of the bedroom is 8 feet shorter than the length, so the length is w + 8.

The area of the bedroom is the product of its width and length, or w * (w + 8).

We can set up the equation 425 = w * (w + 8) and solve for w.

First, we can rewrite the equation as 425 = w^2 + 8w.

Then, we can complete the square by adding (8/2)^2 = 16 to both sides:

425 + 16 = w^2 + 8w + 16

441 = w^2 + 8w + 16

We can rewrite the left side of the equation as (w + 4)^2, which gives us:

(w + 4)^2 = 441

Taking the square root of both sides gives us:

w + 4 = 21

Subtracting 4 from both sides gives us:

w = 17

Therefore, the width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.

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10 points cause it not thay hard for yall

Answers

Answer:

6,63,9 and 90

Step-by-step explanation:

The slope of the table is 9.

36/4 is equal to 9.

54/9 = 6

7*9=63

81/9=9

10*9=90

PLEASE ASAP HURRY PLEASE

Mario set a goal to run 170 miles this month to prepare for a marathon. So far this month, he has run 85 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.

A. m over 85 equals 170; m = 14,450 miles

B. m − 85 = 170; m = 255 miles

C. m + 85 = 170; m = 85 miles

D. 85m = 170; m = 2 miles

Answers

The equation to show how many miles Mario has left to run this month to reach his goal is C. m + 85 = 170; m = 85 miles.

How to illustrate the equation?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement

In this situation, Mario set a goal to run 170 miles this month to prepare for a marathon and far this month, he has run 85 miles.

Let the remaining miles be m.

This will be illustrated as:

m + 85 = 170

Collect like terms

m = 170 - 85

m = 85

In conclusion, the correct option is C

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Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE

Answers

The answer to your problem is $26

A large university accepts 70% of the students who apply. Of the students university, 25% actually enroll. If 20,000 students apply, how many enroll?

Answers

Answer:

350 enrolled

Step-by-step explanation:

.7 x 20000 = 1400

.25 x 1400 = 350

Answer:

3500

Step-by-step explanation:

20000 * 0.70 = 14000

14000 * 0.25 = 3500

K
Factor the trinomial.
b²-13b+40

Answers

Answer: (b-8)(b-5)

Step-by-step explanation:

Find the multiple of 40 that adds up to -13 while being mutiplied by multiples of b^2

1*-5=-5

1*-8=-8

-8-5=13

-8*-5=40

(b-8)(b-5)

Which of the following conclusions do you draw if the p-value is not small enough to convincingly rule out chance?
a. We cannot reject the null hypothesis.
b. We accept the null hypothesis.
c. We are convinced that chance alone produced the observed results.
d. We accept the alternative hypothesis.

Answers

The conclusion is option A, we cannot reject the null hypothesis.

What is hypothesis?

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

The null hypothesis cannot  be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.

Therefore, we can not reject the hypothesis.

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O
Yaritza made 25% of her free throws over the season. If she shot 160 free throws, how
many did she make?
Divide/scale down to solve for the missing percent.
attempts
percent
Submit Answer
25
BB
A
160
100
0
attempt 1 out of 2 by

Answers

Yaritza made 25% of her free throws over the season. If she shot 160 free throws, 40 many did she make. Using the concept of percentage.

What is Percentage?

When a fraction of a whole is represented as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

When the denominator is 100, percentages are really just fractions. The percent sign (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

An easy way to solve this problem is by first finding 50%.

To find 50% of 160

= 160 × (50/100)

= 80

So, 160.0 becomes 80.

Then, because 25% is half of 50% to find the answer divide 80 by 2.

Therefore, Yaritza made 40 of her 160 free throws.

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someone please answer this question and give the right answer please!

Answers

The area of the rectangle is 4 (7-2) unit².

What is rectangular shape?

A rectangle is a quadrilateral with four equal vertices and parallel sides of equal length.

Given, the sides of the rectangle are 4 and 7.

And in the diagram,

The rectangle overshadowed by the rectangle having the sides 4 and 2.

So, the sides of the shaded rectangle are 4 and (7-2).

So, the area of the rectangle

= length x width

= 4 x (7-2)

= 4 (7-2)

Therefore, the area is 4 (7-2) unit².

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PLEASE HURRY ASAP I NEED TO FINISH!!
Pete was building a doghouse for his dog, Chip. He made the door 32 inches tall. The height of the door was four times the height of the window in the doghouse.

Write an equation to determine the height of the window.

A. 32 equals h over 4
B. 32 = 4h
C. 32 = 4 + h
D. 32 = h − 4

Answers

Answer:

Step-by-step explanation:

B

PLEASE ANSWER CLEARLY WITH THE EQUATION



A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. The students rented 2 more small cars than large cars, which altogether can hold 46 people. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.

Answers

There were 6.75 small cars rented and 1.75  large cars total were rented.

How to find the Equation?

Let x represent the quantity of little cars rented, and y represent the quantity of big cars rented.

The system of equations below is based on the statements that have been provided:

5x + 8y = 51

x = y + 5

If we replace (1) with the value of x from (2), we get

5(y+5) + 7y = 46

5(y) + 5(5) + 7y = 46

5y + 25 + 7y = 46

12y = 46 -25

12y = 21

y = 1.75

Adding the value of y to (2) yields x = 1.75 + 5 = 6.75.

There were 6.75 small cars rented.

1.75  large cars total were rented.

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Let f(x) be a polynomial with a leading coefficient of 6 and a constant term of 5. Which of the following cannot be true?

Answers

Answer:  f(0) = 3   (choice B)

====================================================

Reason:

The leading coefficient is 6, which is the coefficient of the leading term (aka the first term). The constant is 5, which is the last term.

Here are some examples of what f(x) could be.

[tex]f(\text{x}) = 6\text{x}^2+\text{x}+5\\\\f(\text{x}) = 6\text{x}^3+2\text{x}^2-7\text{x}+5\\\\f(\text{x}) = 6\text{x}^5+4\text{x}^3-81\text{x}^2+5[/tex]

The middle terms don't matter and neither does the exponent on the leading term.

So this is what the general template would look like

[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\[/tex]

where n is a positive integer.

If we were to plug in x = 0, then all of the terms involving x go to zero. They cancel out. The only thing left standing would be the "5" at the very end.

So,

[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\f(0) = 6*0^{n}+\ldots+5\\\\f(0) = 0+0+\ldots+0+0+5\\\\f(0) = 5\\\\[/tex]

In short, the constant value is the y intercept of the polynomial curve. It allows us to quickly spot it without having to do much (or any) math.

This is why choice B is a false statement.

The other answer choices cannot be proven true or false since we don't have enough information about this particular function.

Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.
(20 POINTS!!!!!!!! SHOW YOUR WORK PLEASE!!!!)

Answers

Answer:

y = 3x - 1

y = 3x + 2

Step-by-step explanation:

Here Is The Right Lined Up Answer,

If You Expected It As A Photo Lined For An

Easier Review I Don't Have The 'Capture Photo' Button

But I Can Reuse/Repost, Here It Is:

There You Are, I Hope This Helped You Out

Don't Get Stressed You WILL Get 100%

By: LocalLesMara

When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit. How much medicine would be usual dose for a 18 month old weighing 18 pounds? milligrams

Answers

First let’s confirm that the 18 month old is in the age range for the dose they gave. (It is)

Then convert 18 pounds into kg
1 pound = 0.454 kg
18 pounds = 18 • 0.454 = 8.172 kg

Now how many mg of medication for 8.172kg?

5mg/1 kg = x mg/8.172
Cross multiply
5 • 8.172 = 40.86 mg is the dose

Please LMK if you have questions

what is the rate of change of the function y=7/4x-2

Answers

Answer:

7/4

Step-by-step explanation:

The rate of change is the slope or the change in y over the change in x.

The rate of change it’s equal as ( slope ) when you see the number that’s has the X like in this example

7/4x

That is the rate of change ( Slope )

A barn is in the shape of a pentagonal prism with the dimensions shown. The volume of the barn is 9072 cubic feet. Find the dimensions of each half of the roof.

(Help I cannot solve this-)

Answers

According to the given information the dimensions of each of the roof is 12 feet.

Mathematical concepts include volume.

The amount the three-dimensional space that's also occupied is measured in volume. To define it quantitatively, a variety of imperial either Us or metric system, in addition to SI-derived units such as the cubic meter but instead liter), are widely utilized. A symbiotic relationship exists between volume and length (cubed).

What does mathematic volume mean?

Mathematics refers to volume as the measurement of internal space in a specific 3D object. A fish tank, for instance, is three feet long, one foot broad, and two feet high. Expanding the length, that width, and the height results in the volume, which is equal to six when 3x1x2 is used. Consequently, the fish tank can hold 6 cubic feet of water.

Briefing:

According to the given picture

a = 18 ft,

b = 8ft,

c = 36ft and h = x

[tex]\begin{matrix}V=a\times b\times c+\frac{a\times h}{2}\times c\\\9072=18\times8\times36+\frac{18\times x}{2}\times36\\9072=5184+324\times x\\\x=12\\\end{matrix}[/tex]

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Answer: 15

Step-by-step explanation: I submitted 12 and that was wrong, answer is 15

Question 2 of 15
Is this relation a function? Justify your answer.

Answers

the only criteria, really, to be a function is to assign exactly 1 y-value to every valid x-value. not 2 or 0 y-values.

we see here, x = 2 has one assigned y-value : y = 3.

x = 4 has y = 9.

x = 6 has y = 10.

x = 9 has y = 5.

there is no indication that there are more valid x-values.

each x-value used has exactly 1 y-value.

so, the criteria is fulfilled. it is a function.

Mariam has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $311.60.
She buys 4 bicycle reflectors for $7.18 each and a pair of bike gloves for $19.94.
She plans to spend some or all of the money she has left to buy new biking outfits for $76.57 each.

What is the greatest number of outfits Mariam can buy with the money that's left over?

Answers

Answer: 2

Step-by-step explanation:

the for this answer is two

Solve for Input of Function Given Output
Given } h(x)=-3 x-5 solve for x when } h(x)=-2

Answers

Step-by-step explanation:

put the value of h(x) in the function like in the above figure.

Need help with this question.



580 lb to kg

(Round to the nearest hundredth as needed)

Answers

Answer:

264 kg.

Step-by-step explanation:

To convert from pounds to kilograms, divide the number of pounds by 2.20462. In this case, we have:

580 lb / 2.20462 = 263.74 kg

So, rounded to the nearest hundredth, the answer is 264 kg.

Y-2=1/3(x+6) write in standard form

Answers

Answer:

2x+3y = -15

Step-by-step explanation:

A DVD costs $18.99 plus 6.5% sales tax. What is the total cost if the DVD?

Answers

Answer:

Step-by-step explanation:

To determine the total cost of the DVD, you need to calculate the amount of sales tax and add it to the cost of the DVD.

The sales tax is equal to the cost of the DVD multiplied by the sales tax rate:

Sales tax = $18.99 * 6.5% = $1.23

To determine the total cost, you need to add the cost of the DVD to the sales tax:

Total cost = $18.99 + $1.23 = $20.22

So the total cost of the DVD is $20.22.

Fun fact-

Washington Sales Tax. State Sales Tax: 6.5%

In which direction does the parabola defined by the equation y = 4x + 4 open?

Answers

Hence, given parabola is defined in Negative Y direction. -Y direction

Which of the several equation types are there?

Either identity equations or conditional equations classify an equation. Every value of the variables has a corresponding identity. Only particular values of the variables are valid for a conditional equation. The equals symbol ("="), which divides two expressions, denotes an equation.

Here,

Given : y = 4[tex]x^{2}[/tex] + 4

Thus,

 General Guidance The answer provided below has been developed in a clear step by step manner.

Step: 1 Given parabola equation is,

=> y = -4[tex]x^{2}[/tex]+4

=>y-4=-4x2 -4x2 =

=> (y-4) == y-4 = 4

This is the equation of a downward parabola. Hence this parabola is defined in negative Y direction.

Explanation: Upward parabola is given by [tex]x^{2}[/tex] = 4AY, And downward parabola is [tex]x^{2}[/tex] = - 4Ay

Hence, given parabola is defined in Negative Y direction. -Y direction

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Hannah wants to have $ 5500 to help pay for a new deck in 10 years. If she wants to put her money into an account earning 5.5% interest compounded continuously, how much should she invest now, so that she will have $ 5500 in 10 years?
Payment amount =

Answers

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5500\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &10 \end{cases} \\\\\\ 5500=Pe^{0.055\cdot 10} \implies \cfrac{5500}{e^{0.055\cdot 10}}=P\implies 3173.22\approx P[/tex]

Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week

Answers

The sales Jamie made for the week is $530

How to find Jamie sales for the week

information from the problem

Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales

Jamie makes $229.50 in one week, her sales for that week = ?

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

15% = 15 percent

= 15 / 100

= 0.15

Let Jamie's sales for the week be x

total earning = 150 + 0.15x

229.50 = 150 + 0.15x

229.50 - 150 = 0.15x

0.15x = 79.5

x = 79.5 / 0.15

x = 530

The sales for the  week is $530

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The value of a car can be represented by the equation V = 16,000(0.93)t, where V is the value of the car and t is the age of the car in years. What is the meaning of the number 0.93 in the equation?

As the age of the car increases by 1 year, the value of the car decreases by $ 93.

As the age of the car increases by 1 year, the value of the car decreases by 7%.

As the age of the car increases by 1 year, the value of the car decreases by $ 7.

As the age of the car increases by 1 year, the value of the car decreases by 93%.

Answers

As the age of the car increases by 1 year, the value of the car decreases by 7%. The correct option is B.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the value of a car can be represented by the equation V = 16,000(0.93)t, where V is the value of the car and t is the age of the car in years.

As the age of the car increases by 1 year, the value of the car decreases by 7%. The correct option is B.

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A doctor has 2 doses of flu protection vaccine left. He has 5 women and 8 men who want the medication. If the
names of 2 of these people are selected at random, determine the probability that 2 men's names are selected
The problem is to be done without replacement. Use combinations to determine the probability.

Answers

The required probability for the 2 men's names are selected is 0.358.

Given that,
A doctor has 2 doses of flu protection vaccine left. He has 5 women and 8 men who want the medication.
The names of 2 of these people are selected at random, determining the probability that 2 men's names are selected is to be determined,

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The number of ways to select 2 men = 8C2 = 28
The number of ways to select 2 people from 13 = 13C2 = 78
The probability of the 2 men's names being selected = 28 / 78 = 0.358


Thus, the required probability for the 2 men's names are selected is 0.358.

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if n is an integer,what is the sum of the next three consecutive even integers greater than 2n

Answers

The sum of the next three consecutive even integers greater than 2n, where n is an integer, is: Sum = 6n + 12

What is the sum of the next three consecutive even integers?

We know that n is an integer number, we want to find the sum of the next three consecutive even integers greater than 2n2n is already an even integer, and consecutive even integers are given by adding 2 to the smaller one.

Then the 3 consecutive integers larger than 2n are:2n + 22n + 42n + 6

The sum of these 3 gives:(2n + 2) + (2n + 4) + (2n + 6)3*(2n) + 2 + 4 + 66n + 12

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The specific time requirements (in hours) for each product are as follows: Machining, hours Polishing, hours Assembling, hoursProduct I 3 1 2Product II 2 1 1Product III 2 2 2Product IV 4 3 1The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the productare Birr 360, Birr 240, Birr 360 and Birr 480, respectively. The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.3. A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. Make the mathematical model for the given problem.4. Discuss few areas for application of quantitative analysis in your organization or organization you are familiar with for decision making.5. Take the data of the output of your organisation summarise them with some tool (like bar chart, pie chart, etc.) and discuss the result. Give your opinion to improve the results in the future. With _____, the emphasis is on helping the buyer realize the synergy of carrying all associated products of the same brand or manufacturer.A. Solo exchange transactionsB. Insight sellingC. Cross-sellingD. UpgradingE. Full-line selling