The formula for the area of a rectangle is A-ly, where A is the area, I is the length, and w is the width. If a rectangle has an area of 1800 square feet, and the length is twice the distance of the width, determine the width. ​

The largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x² , is equals to the 20√15/ 9 .

In optimizing the objective function f(x), solve for the critical points by putting the first derivative f′(x), equals to zero. Then the objective function is evaluated at the critical points to determine the it's minimum or maximum. We have, a rectangle with base as x-aixs and both upper vertices on the curve y = 5 − x², which is a parabola equation. Thus width of the rectangle is based from the equation of the parabola y= 5 - x² --(1)

Area of rectangle is expressed as A = xy , where x -->length of it and y-->width or vertices of curve. The length of the rectangle with base x- axis is equal to 2x. Therefore, the area is A = w× l

= 2x( 5 - x² )

A = 10x - 2x³ --(2)

If area is maximum, then dA/dx = 0

Differentiating the equation (2) with respect to x

dA/dx = 10 - 6x²

so, 10 - 6x² = 0

=> 6x² = 10

=> x² = 10/6

=> x² = 5/3

=> x = ±√5/3

but x represents the length so, it's value always be positive. Thus, x = √5/3. The area is equal to A = 10x - 2x³

= 10(√5/3) - 2(√5/3)³

=> A = 10√5/3 - 10/3(√5/3)

=> A = √5/3( 10 - 10/3) = 20√5/3√3

=> A = 20√15/ 9 ( using rationalzation )

Hence, the required area is 20√15/ 9 .

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Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

y = $100.00 - $10.00x is the equation for the total amount of money in the savings account after x weeks.

The y-intercept represents the initial deposit of $100.00 and the slope is -10

a. Let's call the amount of money saved each week "s" and

let's call the total amount of money in the savings account after "x" weeks "y".

Since the amount saved each week is the same, we can express the total amount of money in the savings account as:

y = $100.00 + sx

We know that at the end of the 5th week, the total amount in the savings account is $50.00. So we can set up the following equation:

$50.00 = $100.00 + 5s

solving for s:

$50.00 - $100.00 = 5s

-$50.00 = 5s

-10 = s

So the equation for the total amount of money in the savings account after x weeks is:

y = $100.00 - $10.00x

b. In the context of this problem, the slope represents the amount of money that is saved each week.

In this case, the slope is -10, meaning that $10.00 is saved each week. The y-intercept represents the initial deposit of $100.00.

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Answer:

6

Step-by-step explanation:

(3√3)^2/3 = (∛3)²  X ∛(√3)²  

= 3

27^2/3 = (∛27)²

= 3² = 9

9^-1/2 = 1/√9

= 1/3

so the answer is  3 + (9 X 1/3)

= 3 + 3

= 6

Answer:

The Answer is 8m square

Step-by-step explanation:

2m is the width

4m is the length

Answer:

52m²

Step-by-step explanation:

First since its only showing the front, top, and right side of the shape you count up all of the cubes you see.

Amount of cubes on each side:

Front: 6 cubes

Top: 8 cubes

Side: 12 cubes

6+8+12=26 cubes

But there is 6 sides total on the shape. Because we only did 3 sides, to get the final answer you multiply it by 2.

26×2=52

Final answer: 52m²

Mercury will sink

(sorry if Im wrong)

Answer:

Sink.

Step-by-step explanation:

Mercury is a quicksilver and hence will sink.

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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Answer:

1/3

Step-by-step explanation:

The length of the second trial will be equal to 2(⁵/₈) miles.

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 two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Of the three individuals carrying an affected gene, there is a 2/3 probability for the individuals to be carriers because of the inheritance of the alleles.

Refer the image for a pedigree analysis. When both of the parents are carriers for a particular gene, there is 2/3 possibility of the affected individual to be carriers. One individual, here, remains unaffected while another is affected with the trait. We can also illustrate this with the help of a Punnett square. When the parents are taken as heterozygous autosomal recessive carriers for a particular trait, they will exhibit the described result.

This is explained in accordance with the Mendelian's laws of inheritance. A trait, illness, or disease can be passed down through families in a number of different ways, one of which is autosomal recessive. Two copies of a defective gene are required for an autosomal recessive disorder to manifest as a disease or trait. According to the law of segregation, a parent may have two different alleles for a specific gene, each present in one copy of the chromosome. One allele of each gene is carried by each sex cell as a result of segregation.

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Answer:

82

Step-by-step explanation:

Answer:

\(P = 48 in\),\(A= 120in^2\)

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

Answer:

A is the correct answer

Step-by-step explanation:

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

34

Step-by-step explanation:

I count up with my brain

Answer:

34 maybe, not totally positive.

Step-by-step explanation:

HAVE A SAVAGE DAY

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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The ratio is  15+\(r_2\) : \(12+r_1\).

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here surface area of the cylinder = \(2\pi rh+2\pi r^2\) square unit

=> A = \(2\pi r(h+r)\) square unit.

Now Height = 12 in , radius = r1 then,

=> \(A_1 = 2\pi r_1(12+r_1)\) -----> 1

Now Height = 15 in , radius = r2 then,

=>\(A_2=2\pi r_2(15+r_2)\)-------> 2

Now the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder then,

=>\(2\pi r_2(15+r_2) : 2\pi r_1(12+r_1)\)

=>\(15+r_2:12+r_1\)

Hence the ratio is \(15+r_2:12+r_1\).

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Answer:

25:16

Step-by-step explanation:

I took the

Answer:

6

Step-by-step explanation:

7×6=42 so 6 is x so this is your answer

Answer:

-6 or 6

Step-by-step explanation:

7x|x|=42 (divide both sides)

|x|=6 (separate into possible cases)

x=6

x=-6  (the equation has two solutions)

hope this helps!

Using a system of equations, the number of children and adults who attended the movies is as follows:

A system of equations is two or more equations solved concurrently.

A system of equations is also known as simultaneous equations.

The total number of people who went to the movies = 100

The unit cost of adult tickets = $4

The unit cost of children tickets = $2

The total sales = $276

Let the number of children who attended the movies = x

Let the number of adults who attended the movies = y

x + y = 100 ... Equation 1

2x + 4y = 276 ... Equation 2

Multiply Equation 1 by 2:

2x + 2y = 200 ... Equation 3

Subtraction Equation 3 from Equation 2:

2x + 4y = 276

-

2x + 2y = 200

2y = 76

y = 38

Substitute y = 19 in equation 1:

x + y = 100

x + 38 = 100

x = 62

Check in Equation 2:

2x + 4y = 276

2(62) + 4(38) = 276

124 + 152 = 276

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Answer:

27

Step-by-step explanation:

3x - 2x²

3 × -3 = -9

2 × -3 = -6

-9 - (-6²)

-9 - (-36)

-9 + 36

36 - 9

36 - 9 = 27

Answer:

if the lines are parallel, that means they have to have the same slope in order to stay parallel to one another. so the slope of both the green and red lines is 1/5

Answer:

after reflection over y axis

a 9,7

b 9,6

c 0,6

d 0,7

Answer:

have a good day

Step-by-step explanation:

i support u

Answer:

15

Step-by-step explanation:

The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.

The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.

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is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

Answer:

16/15

Step-by-step explanation:

The LCM of 5 and 3 is 15

4/5 + 1/3 = 12 / 15 + 4 / 15 = 16 / 15

Answer:1.13333333333 also known as 1.13 repeat

Step-by-step explanation:

The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.

Given:

- Each correct question is worth 10 points.

- Every student receives an additional 555 bonus points.

Let's calculate the mean and standard deviation of YY:

Mean of YY:

The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:

μY = μX * 10 + 555

Substituting the value of μX from the given information:

μY = 1.95 * 10 + 555

μY = 19.5 + 555

μY = 574.5

Therefore, the mean score of a random student (YY) is 574.5.

Standard Deviation of YY:

The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:

σY = σX * 10

Substituting the value of σX from the given information:

σY = 0.8 * 10

σY = 8

Therefore, the standard deviation of the random student's score (YY) is 8.

Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

that a randomly chosen student answered correctly. Here is the probability distribution of X along with

summary statistics:

0

1

2

2.

3

X = # correct

P(X)

0.05

0.20

0.50

0.25

Mean: Hex = 1.95

Standard deviation: Ox 0.8

Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give

every student 5 additional bonus points. Let Y represent a random student's score.

What are the mean and standard deviation of Y?

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The zeros of a function are the values of x that, when evaluated in the function, make the output of the function to be zero.

A function is written in general form as y = f(x)

That notation says that, when we use the input "x" in a given function, that function "transforms" that input x into an output "y"

So y = f(x) is the value that the function takes for the input x.

A zero is an input of the function such that:

0 = f(x)

So the zeros are the inputs that have an output of zero, in this case you know that the function has a zero at 3, and as you can see, when x = 3, the function intercepts the x-axis, which is the axis defined by y = 0.

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