Complete the remainder of the
table for the given function rule

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]

[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]

⇒ 198x - 12x² = 0

[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]

By solving for x:

x = 0 or x = [tex]\dfrac{33}{2}[/tex]

Again:

V = 99x² - 4x³

[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]

At x = [tex]\dfrac{33}{2}[/tex]

[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]

[tex]\implies 198 - 12 \times 33[/tex]

= -198

Thus, at maximum value;

[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]

Recall y = 99 - 4x

when at maximum x = [tex]\dfrac{33}{2}[/tex]

[tex]y = 99 - 4(\dfrac{33}{2})[/tex]

y = 33

Finally; the volume V = x² y is;

[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]

[tex]V =272.25 \times 33[/tex]

V = 8984.25 inches³

Step-by-step explanation:

12-(-8)=4

12+8=20

because - - sign +

Answer:

as the sample size increases, the margin of error decreases

Answer:

[tex]2360m^2[/tex] of sheet steel are needed

Step-by-step explanation:

Given

The missing dimensions are:

[tex]Length = 5m[/tex]

[tex]Width = 6m[/tex]

[tex]Height = 8m[/tex]

[tex]n=10[/tex] --- number of containers

Required

The surface area of all containers

First, we calculate the surface area (A) of 1 container

[tex]A=2*(Length * Width + Length * Height + Width * Height)[/tex]

[tex]A=2*(5m* 6m+ 5m* 8m+ 6m * 8m)[/tex]

[tex]A=2*(30m^2 + 40m^2 + 48m^2)[/tex]

[tex]A=2*(118m^2)[/tex]

[tex]A=236m^2[/tex]

The surface area of 10 is:

[tex]Area = 10 * A[/tex]

[tex]Area = 10 * 236m^2[/tex]

[tex]Area = 2360m^2[/tex]

Answer:

C

Step-by-step explanation:

the probability of the outcome being greater than 63 is x≥63

Answer:

The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Answer:

354.

Step-by-step explanation:

De acuerdo a la sucesión 11,18,25,32..., para encontrar el término que se ubica en la posición 50​ se debe realizar el siguiente razonamiento lógico-matemático:

32 - 25 = 7

25 - 18 = 7

18 - 11 = 7

Así, los números van subiendo de 7 en 7. Por lo tanto, para determinar el número que se ubica en la posición 50 debe realizarse el siguiente cálculo:

(7 x 49) + 11 = X

343 + 11 = X

354 = X

Por lo tanto, el término que se ubica en la posición 50 es 354.

The answer is 1/x^2y^2

The given expression is [tex] \frac{ {x}^{0} y { - }^{3} }{ {x}^{2}y { - }^{1} } [/tex]

We know that any number raised with zero power equals 1. Thus, [tex] {x}^{0} = 1[/tex]

Hence, the expression becomes

[tex] \frac{y { - }^{3} }{ {x}^{2} y { - }^{1} } [/tex]

Now, apply the quotient rule,[tex] \frac{ {x}^{ \alpha } }{ {x}^{b} } = {x}^{ \alpha - b} [/tex]

Using this rule, we have

[tex] \frac{1}{ {x}^{2} y { - }^{1 - ( - 3)} } [/tex]

[tex] = \frac{1}{ {x}^{2} y { - }^{1 + 3} } [/tex]

Hence, the simplified expression is [tex] \frac{1}{ {x}^{2} {y}^{2} } [/tex]

Answer:

4.56% of the deliveries are likely to be outside the specification limits.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average weight was 95.0 grams. The standard deviation was 0.25 grams.

This means that [tex]\mu = 95, \sigma = 0.25[/tex]

What percentage of the deliveries is likely to be outside the specification limits (outside the interval of [94.5, 95.5])?

Less than 94.5, or more than 95.5. Since the normal distribution is symmetric, these probabilities are the same, so we can find one of them and multiply by two.

The probability that it is less than 94.5 is the p-value of Z when X = 94.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{94.5 - 95}{0.25}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

2*0.0228 = 0.0456

0.0456*100% = 4.56%

4.56% of the deliveries are likely to be outside the specification limits.

Answer:

78.54inches²

Step-by-step explanation:

Area of a circle=πr²

radius=½ diameter

=5inches

=π×(5inches)²

=π25inches²

=78.539816339744830inches²

rounded to the two decimal places=78.54inches²

Answer:

hsjsjsjsjaiisisudujsjsjsjsj

Answer:

[tex]Equation : \ y = \frac{4}{5}x + 4[/tex]

Step-by-step explanation:

To find equation of a line we will consider two points through which the lines passes .

Let it be  ( -5 , 0 ) and ( 0 , 4 )

Step 1 : Find the slope

             [tex]slope , m = \frac{y_2 - y_1}{x_2-x_1} = \frac{0-4}{-5-0} = \frac{-4}{-5} = \frac{4}{5}[/tex]

Step 2 : Equation of the line

             [tex](y - y_1) = m(x - x_1) \\\\or \\\\(y - y_2) = m (x -x _2)[/tex]

We will use the second point ( 0. 4)

                     [tex](y - 4) = \frac{4}{5}(x - 0)\\\\y = \frac{4}{5}x + 4[/tex]

Answer:

3

Step-by-step explanation:

r(x) = 0.01(x + 2)(x^2 - 9)

We are looking fo the value of x at which r(x) = 0.

We set the function equal to 0 and solve for x.

0.01(x + 2)(x^2 - 9) = 0

Divide both sides by 0.01. Factor x^2 - 9 as the difference of two squares.

(x + 2)(x + 3)(x - 3) = 0

x + 2 = 0  or  x + 3 = 0  or x - 3 = 0

x = -2  or x = -3  or x = 3

Since we are looking for a time after the experiment started, and it started at x = 0, we discard the negative answers, and we keep x = 3.

Answer: 3

Answer:

3

Step-by-step explanation:

EDMENTUM

Answer:

The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.

Step-by-step explanation:

Let the shorter leg be x.

Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).

Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:

[tex]a^2+b^2=c^2[/tex]

Where a and b are the side lengths and c is the hypotenuse.

The hypotenuse is 13 and the legs are x and (x + 7). Substitute:

[tex](x)^2+(x+7)^2=(13)^2[/tex]

Square:

[tex]x^2+x^2+14x+49=169[/tex]

Simplify:

[tex]2x^2+14x-120=0[/tex]

We can divide both sides by two:

[tex]x^2+7x-60=0[/tex]

Factor:

[tex](x-5)(x+12)=0[/tex]

Zero Product Property:

[tex]x-5=0\text{ or }x+12=0[/tex]

Solve for each case:

[tex]x=5\text{ or } x=-12[/tex]

Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:

[tex]x=5[/tex]

The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.

Answer:

Incorrect

Step-by-step explanation:

This interpretation is incorrect because it states that 98% of the data is with in the confidence interval.

or 98% of the laptop have screen size between 19.2 and 21.4 inches

However, the interpretation would have been correct if it would have stated as - Value of the population mean i.e mean size of the laptop screen lies within the confidence interval.

Answer:

69

Step-by-step explanation:

xvusvsuvtuvqYSQY

Answer:

4 serving cups

Step-by-step explanation:

Given

[tex]Serving\ cup = \frac{1}{6}[/tex]

[tex]Rice\ cup = \frac{2}{3}[/tex]

Required

The number of serving cup (n)

This is calculated by dividing the rice cup by the serving cup

[tex]n = \frac{Rice\ cup}{Serving\ cup}[/tex]

[tex]n = \frac{2/3}{1/6}[/tex]

Rewrite as:

[tex]n = \frac{2}{3} \div \frac{1}{6}[/tex]

Change to multiplication

[tex]n = \frac{2}{3} * \frac{6}{1}[/tex]

[tex]n = \frac{12}{3}[/tex]

[tex]n=4[/tex]

Answer:

B

Step-by-step explanation:

Took quiz

The logarithmic function for the teacher who wrote the table of values with amount of hydrogen and pH level is given by f ( x ) = log ( 1/x )

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the function be represented as f ( x )

Now , the values of x are

x = { 1/10 , 1/100 , 1/1000 , 1/10000 , 1/100000 }

where x represents the amount of Hydrogen in moles per liter

And the values of f ( x ) = { 1 , 2 , 3 , 4 , 5 }

where y represents the pH level

So , when x = 1/10 , f ( x ) = 1

And , the logarithmic equation is given as

f ( x ) = log ( 1/x )

when x = 1/1000

f ( 1/1000 ) = log ( 1/1/1000 )

f ( 1/1000 ) = log ( 1000 )

f ( 1/1000 ) = 3

Therefore , the value of f ( x ) is log ( 1/x )

Hence , the logarithmic equation is f ( x ) = log ( 1/x )

To learn more about logarithm click :

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9514 1404 393

Answer:

  100 m

Step-by-step explanation:

One side between two angles is given, so we need to find the third angle. The sum of angles in a triangle is 180°, so the third angle is ...

  A = 180° -110°20' -13°20' = 56°20'

The law of sines can be used to find the length of side AB:

  AB/sin(C) = BC/sin(A)

  AB = BC·sin(C)/sin(A) . . . . multiply by sin(C)

  AB = (360 m)sin(13°20')/sin(56°20') ≈ 99.75253 m

The distance AB across the river is about 100 m.

The answer is A.

Hope this helps! can i have brainliest lol

Answer:

a

Step-by-step explanation:

Answer:

y = 1.19x

Step-by-step explanation:

y is the dependent variable (total cost)

x is the independent variable (number of pounds)

Answer:

the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour

Step-by-step explanation:

The computation of the standard deviation of the speeds of cars is shown below;

The z score for the top 1% is 2.326

So,

= (75 - 61) ÷ standard deviation = 2.326

Standard deviation is

= 14 ÷ 2.326

= 6.0 miles per hour

Hence, the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour

92631

thats the answerrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

the answers is 92631

plz mark me as a brilliant

[tex]\sqrt[3]{a^2+b^2} = (a^2+b^2)^{\frac{1}{3}}[/tex]

Sui believes that the two cylinders have an equal volume is correct.

The volume of cylinder = Base area×Height

=(πr²)×(height)

This is also true for oblique cylinder.

Both cylinders have same height and radius also so, both cylinders have equal volume.

V=πr²h

V=π×(5)²×11.5

V=903.208m³

It can also be visualized that the oblique cylinder have circular pieces. These pieces can be solid together to form a regular cylinder with the same height (i.e. 11.4 m). So both the cylinders have equal volume.

A cylinder is a three-dimensional shape in geometry. A cylinder is round and has a top and bottom in the shape of a circle. The top and bottom are flat and always the same size.

Thus, Sue is correct, and it's true that the two cylinders shown in the diagram have equal volumes.

Learn more about cylinders here,

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Answer:

-2 and 0

Step-by-step explanation:

EZ

Answer:

D

[tex]x + 40 \degree = 180\degree \\ x = 180\degree - 40\degree \\ x = 140\degree[/tex]

Answer:

x = 140°

Step-by-step explanation:

x and 40° are adjacent angles and sum to 180° , then

x + 40° = 180° ( subtract 40° from both sides )

x = 140°

Answer:

1) 40 degrees

2) 140 degrees

3) 110 degrees

4) 70 degrees

5) 70 degrees

Explanation:

Use the curved protractor they have created you, and count every dash as 10 degrees. Keep in mind that the whole thing equals 180 degrees, and half would equal 90 degrees. Some call it a right angle.

Let me know if my answer is correct for the other users that will see this message. Thank you!

-kiniwih426

Answer:

[tex]\frac{22}{3}[/tex]

Step-by-step explanation:

x + y + y + z + z + x = 2x + 2y + 2z = 22

x + y + z = 22

22 ÷ 3 = [tex]\frac{22}{3}[/tex]