What values of the numbers a and b does the function f(x) = axe^ {bx^2} have the maximum value f(3) = 6?

Answer:

5/24 or 20.8%

Step-by-step explanation:

Probability that the 7th grader is a boy = number of boys/(total kids) = 4/(4+4) = 1/2

Probability that the 8th grader is a boy = 5/(5+7) = 5/12

Probability that both are boys = 1/2*(5/12) = 5/24 or 20.8%

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

Answer:

the smaller batch

Step-by-step explanation:

Proportion of coconut in the smaller batch = 2/1 = 2

Proportion of coconut in the bigger batch = 5/3 = 1.67

2 is greater than 1.67. So, the proportion of sugar in the smaller batch is stronger

Answer:

3f(x)−2g(x)

=3(2x−1)−2(x2)

=6x−2x2−3

Step-by-step explanation:

I hope it will help you....

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Answer:

3 f(x) – 2 g(x)

Step-by-step explanation:

The test statistic for this sample and the p-value for this sample is  t = 0.467.

Given:

sample of size n=305

M=83.6

SD=14.9.

Significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4

To find the Test statistic

\(test=\frac{\bar x-\mu}{\frac{s.t}{\sqrt{n} } }\)

    \(=\frac{82.4.6-83.6}{\frac{14.9}{\sqrt{305} } }\)

     \(0.467\)

P-value:

With t = 0.467.

p-value = (1 - 0.467)

0.533 > 0.001

So, fail to reject H₀

Therefore, the failing to reject the Null Hypothesis.

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Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Calculation with Lagrange multipliers of its optimum restricted places,

\(f_x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ g_x = 2x\\\\f_y = 1 \ \ \ \ \ \ \ \ \ \ \ \ \ g_y = 2y\\\\\)

Set the multiplier formulas for Lagrange:

\(f_x = \lambda g_x \to 2 = \lambda 2x ............ (i)\\\\f-y = \lambda g_y \to 1 = \lambda 2y................ (ii)\\\\constraint: \\\\\to x^2 + y^2 = 5 .................... (iii)\\\\Taking \ (i)\ divides\ (ii), \ (assuming\ \lambda \neq 0)\\\\\frac{2}{1}=\frac{\lambda 2x}{\lambda 2y}=\frac{x}{y}\\\\\therefore \\\\2y = x\\\\Sub\ into\ (iii)\ to\ find\\\\4y^2 + y^2 = 5 \to y = \pm 1\\\\\)

We get solutions (x,y)=(2,1) and (−2,−1) if combined with 2y = x. These are all the identical points we obtained in (c) and we know the f(2,1) is the max, whereas f(−2, −1) is a minimum.

Answer:

1.54

Step-by-step explanation:

the z-score is calculated with the formula z= ( raw score - mean) / standard deviation

z= (236 - 193) / 28

z= 43 / 28

z= 1.5357

Answer:

The point of their intersection is (-3,-5)

Answer:

V = 7385.28

Step-by-step explanation:

Formula of the volume of a cylinder: V = pi*r^2*h

Since you are told to replace pi with 3.14, now plug in the numbers that you are given into the formula...

V = (3.14)(14)^2*(12)

= 7385.28

Notes: Remember you always have to divide your radius in half if it gives you a diameter, BUT since in this question it's given, you don't have to do any extra work :)

The probability that the first card drawn is a spade and the second card is a club is 1/16.

In probability theory, the multiplication rule or product rule is a formula used to compute the probability of an outcome that can be accomplished by a sequence of multiple events that are independent of one another. The formula for multiplication rule is given as:

P(A and B) = P(A) * P(B|A)

Given, that a card is drawn from a standard deck and replaced, after the deck is shuffled, another card is pulled. The first card drawn is a spade.

So, the probability that the first card drawn is a spade is:

P(S) = 13/52 = 1/4 (there are 13 spades in a deck of 52 cards)The second card is a club.

Therefore, the probability that the second card is a club is:

P(C) = 13/52 = 1/4 (there are 13 clubs in a deck of 52 cards). Since the card is replaced after the first draw, each of the two events are independent.

Therefore, the probability that the first card drawn is a spade and the second card is a club is:

P(S and C) = P(S) * P(C) = 1/4 * 1/4 = 1/16.

Therefore, the probability that the first card drawn is a spade and the second card is a club is 1/16.

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Answer:

y=2x+4

Step-by-step explanation:

2 is the slope, you can see that with rise over run. 4 is the y intercept

Answer:

y=2x+4

Step-by-step explanation:

Look at the y-axis if the point that touches the y-axis is 4

Then the slope is 2

you go down 2 which is -2 (Since down is negative)

and you go left 1 which is -1 (Since left is negative)

now the equation looks like this:

y=-2/-1x+4

Simplify: (negative and negative cancel each other out making it positive)

y=2x+5

Answer:b

Step-by-step explanation:

Answer: Has one real solution

Answer:

B. One Real solution

Step-by-step explanation:

edge 2021

Answer:

15

Step-by-step explanation:

To find the common denominators for 2/3 and 1/5, just look at the denominators for both of the fractions, 3 and 5

Multiply 3 and 5, which is 15. 15 is the common denominator.

Answer:

1

Step-by-step explanation:

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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Answer:

mean = total divide by nõ of items

mean = 31•855

Step-by-step explanation:

add the total ..you will get

318•55

divide by 10

318•55 ÷ 10

31•855

Answer:

Step-by-step explanation:

Henry X blue

Rachel 5 blue and Y black

Jack 3 times the total of pens ( blue & black)

So

X + 5 + Y for Henry and Rachel

Jack : 3( X + 5 + Y)

Jack has 3X + 15 + 3Y.

Pens of jack 3X + 15 Blue & 3Y black.

The expression that represents the perimeter of the frame is (8x+24) inches. Option C

From the question, we are given that dimensions of the photograph is 5 inch × 7 inchIt is given that the dimensions of the frame are 2x inches larger than the dimensions of the photograph. Thus, the dimensions of the frame is (2x+5) inches × (2x+7) inches.

Since, the frame is in rectangular shape. Perimeter of a rectangle = 2(Length + Width)

= 2(2x+5+2x+7)

= 2(4x+12)

= 8x+24 inches.

Thus, the perimeter of the frame is represented by the expression (8x+24) inches.

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The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

y = 2x² + 4x

now, for, x= 0 , y = 0

for, x= 1, y = 6

for, x= 2, y = 16

Hence, The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

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Answer:

12.56

Step-by-step explanation:

find the circumference of the circle : 2πr

C=2(12)(3.14)

C=75.36

the length of the arc is: arc length will be (60/360) one 1/6 of the total circumference.

(60/360)(75.36)= 12.56

Answer:

x = 3.

Step-by-step explanation:

To find x all you need to do is 78 divided by 26.

78 ÷ 26

Which is 3.

So x is 3.

Answer:

x= 78

Step-by-step explanation:

isolate the varible by dividing each side by the factors and i got x =78.

The definite integral in part (a) cannot be evaluated using only Gamma or Beta functions.

To evaluate the integral ∫√√z e^(-√z) dz using only Gamma or Beta functions, we need to express the integrand in terms of such functions. However, the integrand in this case does not have a direct representation in terms of Gamma or Beta functions. Therefore, we cannot evaluate the integral using only those functions.

Part (b):

To evaluate the integral ∫(e^x)^2 (e^(2x) + 1)^(-3) dx using only Gamma or Beta functions, we can make a substitution: let u = e^x. Then, du = e^x dx, and the integral becomes ∫u^2 (u^2 + 1)^(-3) du. This can be rewritten as ∫u^2 (1 + u^(-2))^(-3) du.

Now, we can rewrite the integrand using the Beta function as (1/u^2)^(-3/2) * (1 + u^(-2))^(-3) = Beta(-3/2, -3) = Γ(-3/2)Γ(-3)/Γ(-6/2).

Using the properties of the Gamma function, we have Γ(-3/2) = -4√π/3, Γ(-3) = 2, and Γ(-6/2) = -4√π/15. Substituting these values back into the expression, we get (-4√π/3)(2)/(-4√π/15) = 10/3.

Therefore, the value of the integral ∫(e^x)^2 (e^(2x) + 1)^(-3) dx is 10/3.

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Answer:

Please check the explanation in the attached diagram.

Answer:

the answer is b

Step-by-step explanation:

-5+12=7

Answer:

D

Step-by-step explanation:

X= 12-7

X=5

Hope this was helpful

The probability that all three dice are going to show up the same number is 1/3025.

We are going to solve this question using probability. Here, it has been given that there are three dice that show the numbers from 11 to 66. This means that one dice is going to show = 55 outcomes (i)

All three dice together are going to show = 55*55*55 = 166375 outcomes (ii)

No. of exclusive events when the dice are going to show the same number = 55 times (iii)

We know the formula = Probability of any event = \(\frac{(No. of exclusive events)}{No. of possible outcomes}\)

Using this formula and the values of (ii) and (iii), we get -

= 55/166375

= 1/3025

Therefore, upon using the formula for probability we are able to determine the probability of the three dice showing the same number.

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The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.

Toothpaste company

Large tubes

Small tubes

1) Sparkling

100 per hour

200 per hour

2) Bright White

100 per hour

250 per hour

3) Fresh!

200 per hour

250 per hour

4) Mint

150 per hour

150 per hour

Formula for comparative advantage is

CA=rate of producing large tubes/rate of producing small tube

For 1 Sparkling:

CA = 100/200

CA = 0.5

For 2 Bright White:

CA = 100/250

CA = 0.5

For 3 Fresh:

CA = 200/250

CA = 0.8

For 4 Mint:

CA = 150/150

CA = 1

thus, to place the companies in order of greatest comparative advantage to least comparative advantage in  producing large tubes of toothpaste is 4, 3, 1, 2.

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Complete question:

Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in

producing large tubes of toothpaste.

2.1.3.4

4.1,2,3

4,3,1,2

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