The graph provided show the volume (in cubic inches) of air in a balloon as it changes
over time.
What is the volume of the balloon in cubic inches after 10 seconds?

Answer:

Step-by-step explanation:

The critical numbers of the function is \(1.18$.\)

As per the question we have to determine the critical numbers of the function.

The number “c” has to be in the domain of the original function (the one you took the derivative of). If the number isn’t in the domain (for example, if there is a removable discontinuity at x = 0), then that number isn’t a critical number.

We have given,

\($$f(x)=x^{-6} \ln x$$\)

For critical numbers \(\mathrm{f}^{\prime}(\mathrm{x})=0$ of $\mathrm{f}^{\prime}(\mathrm{x})$\) is undefined.

Now,

\($$\begin{aligned}\mathrm{f}^{\prime}(\mathrm{x}) & =\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{-6} \ln x\right) \\& =\mathrm{x}^{-6} \times \frac{\mathrm{d}}{\mathrm{dx}}(\ln \mathrm{x})+\ln \mathrm{x} \times \frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{-6}\right) \\& =\mathrm{x}^{-6} \times \frac{1}{\mathrm{x}}+\ln \mathrm{x} \times\left(-6 \mathrm{x}^{-7}\right) \\& =\mathrm{x}^{-7}(1-6 \ln x)\end{aligned}$$\)

We will use product rule,

\(\frac{d}{d x}(f . g)=f \cdot g^{\prime}+g \cdot f^{\prime}$$\)

Now,

\($$\begin{aligned}\mathrm{f}^{\prime}(\mathrm{x}) & =0 \\\mathrm{x}^{-7}(1-6 \ln \mathrm{x}) & =0 \\1-6 \ln \mathrm{x} & =0 \\\mathrm{x} & =\mathrm{e}^{\frac{1}{6}}=1.18\end{aligned}$$\)

Therefore, critical number is \(\mathrm{x}=\mathrm{e}^{\frac{1}{6}}=1.18$.\)

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Answer:

After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected

As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that

H₀ > z

Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.

Step-by-step explanation:

critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;

reject H₀

There is sufficient evidence to reject the claim.

Answer:

Part is A. Part B is underestimate. Part C (for the choose drop-off boxes are these: 1# < 2# < 3# <

Step-by-step explanation:

I took the test, hope it helps.

Step-by-step explanation:

Let's represent "a number" with x. We want to find the difference between x and 6, so we know that it is a subtraction problem. So far, we have the expression:

x - 6

We also know that this expression is less than 1. So, we are left with:

Now, let's solve for x.

x - 6 < 1 <--- Let's add 6 to both sides

Answer:

x - 6 < 1

Step-by-step explanation:

Answer:

f(g(3) = 1

Step-by-step explanation:

f(g(3)

Step one: Plug in 3 for X

g(x)= 2x - 5  ->  g(3) = 2 * 3 - 5

Step two : Solve ( By Using PEMDAS)

g(3) = 6 -5

g(3) = 1

Answer:

By flipping the second fraction (finding its reciprocal) we change the equation mathematically. In order to maintain the equation mathematically, we must turn the division question into a multiplication question.

Step-by-step explanation:

The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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Answer:

C

Step-by-step explanation:

because 6 as a positive is less than 12 as a positive and the lines around indicate absolute value

The value y is -36.

Proportionality is the property of two variables being in a multiplicative relation to a constant.

Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,

y ∝ xz

Let k be the Proportionality constant,

y = kxz

-60 = k*4*-5

k = 3

When x = 4 and z = -3

y = 3*4*-3

y = -36

Hence, The value y is -36.

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Answer : your answer should be 536

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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According to the unitary method,

A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.

B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.

Unitary method:

In math, unitary method refers the process of finding the value of a single unit, and based on this value.

Given,

Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.

Here we need to find the following:

A) The time take for Peter to finish the job alone

B) The time taken for Emily and Peter to finish the job together

Let us consider x be the time taken for Peter to finish the job alone.

So, based on the given question we can write it as,

=> 1/6 + 1/8 + 1/x = 1/2

=> (8 + 6)/48 + 1/x = 1/2

=> 14/48 + 1/x = 1/2

=> 7/24 + 1/x = 1/2

=> 1/x = 1/2 - 7/24

=> 1/x = 12 -7/24

=> 1/x = 5/24

=> x = 24/5

=> x = 4.8

So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.

Then the time taken for Emily and Peter to finish the job together is calculated as,

=> 5/24 + 1/6

=> 5 + 4/ 24

=> 9/24

=> 3/8

Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.

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Answer: i think its d

Step-by-step explanation:

The graph of the function y = -2x + 1/3 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = -2x + 1/3

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

124

Step-by-step explanation:

Following PEMDAS,

multiplication comes first, 52x2 equals 104

Then add 20 to 104

124

Answer:

124

Step-by-step explanation:

20+50x2

20+104

124

Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

The speed of the boat in still water is 14 mph.

Answer:

A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.

Step-by-step explanation:

In this case the equation has one solution.

A value of x that makes the equation true is -3, which when substituted into the equation and simplified makes the equation turns into -5=-5.

A value of x that makes the equation false is 1, which when substituted into the equation and simplified makes the equation turns into 15=-5.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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Answer:

C. <w and <y

Step-by-step explanation:

<t and <x are corresponding angles, therefore they are congruent to each other by the corresponding angles theorem.

<w and <y are also corresponding angles and are therefore also congruent.

<x and <z are congruent also based on the vertical angles theorem.

<t and <z are alternate exterior angle, and are therefore congruent also.

So, from the pairs of angles given as options, the only given pair of angles that are congruent would be:

<w and <y

The mass of the sugar that is contained in the juice is 19.6 g.

In mathematics, a proportion is a statement that two ratios are equal. A ratio is the relationship between two quantities, usually expressed in the form of a fraction.

To solve a proportion, you can use cross-multiplication. Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa.

We know that;

24.5 g of sugar is contained in 250 ml of the juice

x g of sugar is contained in 200 mL of the juice

x = 24.5 * 200/250

x = 19.6 g

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Answer:

3h

Step-by-step explanation:

Answer:

$9 = 1hr

32hr=???

Step-by-step explanation:

1 x 32 = 32

9 x 32 = 288

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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