Use factoring to prove that 16⁵+16⁴ is divisible by 17.

The value of c that satisfies the Mean Value Theorem for this problem are given as follows:

A. [tex]4\sqrt{3}[/tex]

The function for this problem is given as follows:

f(x) = x + 48/x.

The bounds of the interval are given as follows:

a = 3, b = 16.

The derivative of the function is given as follows:

f'(x) = 1 - 48/x².

The numeric value of the derivative at x = c is given as follows:

f'(c) = 1 - 48/c²

The numeric values of the functions at the bounds are given as follows:

Then the value of c is obtained as follows:

1 - 48/c² = 0/16

1 - 48/c² = 0

48/c² = 1

c² = 48

c = square root of 48.

[tex]c = \sqrt{16 \times 3}[/tex]

c = [tex]4\sqrt{3}[/tex]

Option A, as we have to be reminded that the interval is [3,16], hence the negative root is not considered.

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The gold, silver, and bronze medals can be awarded in 720 ways.

What is Permutation?

The permutation is the number of ways to arrange the specified number of things out of the total available number of things, it is calculated by using excel function(=PERMUT(r, n)).

Given data,

n=10, r=3

Number of ways   gold, silver, bronze can be awarded to 10 finalists is = nPr =10P3

=720

720 ways gold ,silver and bronze can  be arranged.

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The work is done in compressing the spring from a length of 15 inches to a length of 13 inches are the 0.897ftlb.

Work Done:According to the paintings-power theorem, the internet paintings performed on an item equals the alternate withinside the power of the item . If the simplest alternate withinside the power located is withinside the capability power (say U) of the item, then the internet paintings performed W=△U.

Answer and Explanation:When a spring is compressed x in with the aid of using a pressure F,

F=kx, where k is the spring constant.

Since it's miles for the reason that the spring is compressed to 8in from 21in, that is, a compression of (21−eight)=13in, we obtain

F=kx⇒k=Fx=10lb1312ft=12013lbft−1.

Using the theorem, the internet paintings performed on an item equals the alternate withinside the power of the item. In this situation the simplest alternate in power is withinside the capability power of the spring while it's miles compressed with the aid of using x gadgets of duration, which is 12kx2. (k is the spring constant.)

The capability power of the spring while it's miles compressed to 15cm=0.5k(21−1512)2

The capability power of the spring while it's miles compressed to 13cm=0.5k(21−1312)2

Work Done equals the alternate withinside the capability power while it's miles compressed from 15in to 13in

=0.5k[(21−1312)2−(21−1512)2]=0.512013[(21−1312)2−(21−1512)2]≈ 0.897ftlb

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LCD = 12

Equivalent Fractions with the LCD

11/12 = 11/12

1/2 = 6/12

Solution:

Rewriting input as fractions if necessary:

11/12, 1/2

For the denominators (12, 2) the least common multiple (LCM) is 12.

LCM(12, 2)

Therefore, the least common denominator (LCD) is 12.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

11/12 = 11/12 × 1/1 = 11/12

1/2 = 1/2 × 6/6 = 6/12

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The expected number of colleges to which the student is admitted .2344

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colours. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.

Let X= college to which student is admitted

We are given with n=7 and p=1/6

P(X=2)=⁷P₂[tex]\frac{1}{6^{2} }(1-\frac{1}{6}) ^{7-2}[/tex]

=.2344

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Answer:

x = 4°

Step-by-step explanation:

The box in the top right angle of the diagram lets us know that all of these angles equal 90°  !

To find x, we just need to do simple algebra and use the info above.

21x + 6 = 90 °

21x = 90 - 6

21x = 84

x = 84 / 21

x = 4°

Answer:

Step-by-step explanation:

The coordinate point of intersection on the graph will be at (1.5, 4.5)

Given the equations Dimitri wrote expressd as:

y = 3x

y = x + 3

Since they are both y-values, we can equate the right hand side to have:

3x = x + 3

3x - x = 3

2x = 3

x = 3/2

x = 1.5

Get the value of y:

y = 3x

y = 3(1.5

y = 4.5

Answer:

I don't know this problem or the answer

The required probability of P(Girls/Sophomore) is 0.9.

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

Here,
Data are shown in the table, P(Girls/Sophomore) is to be determined.
In order to determine the probability of the girls over Sophommer,
From,
P(A|B) = P(A ∩ B) / P(B)
P(Girl  | Sophomore ) = P(Girl ∩ Sophomore ) / P(Sophomore)
Substitute the value in the above equation,

P(Girls/Sophomore) = 9 / 10

Thus, the required probability of P(Girls/Sophomore) is 0.9.

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The answer is A

It's multiples by 8 each time

Answer:

[tex]1. = \frac{18}{12} [/tex]

[tex]2. = \frac{39}{30} [/tex]

[tex]3. = \frac{5}{15} [/tex]

[tex]4. = \frac{18}{14} [/tex]

[tex]5. = \frac{13}{20} [/tex]

Answer:vertical



Step-by-step explanation:

Answer: B

Step-by-step explanation:

y = 72.49x0.50

Answer:

B

Step-by-step explanation:

edge2023 and because i said so ;)

56 * (28/5) shows how the distributive property can be used to evaluate 7 times 8 and four-fifths.

7 times 8 = 56

4/5 = 28/5

Using the distributive property:

7 * 8 * (4/5) = (7 * 8) * (4/5) = 56 * (4/5) = 56 * (28/5) = 56 startfraction 28 over 5 endfraction

The distributive property states that for any numbers a, b, and c, a * (b + c) = a * b + a * c. To evaluate 7 times 8 and four-fifths, we can use the distributive property to separate the two factors. First, we calculate 7 times 8, which is equal to 56. Then, we calculate four-fifths, which is equal to 28/5. We then use the distributive property to multiply the two factors together, which is (7 * 8) * (4/5). This simplifies to 56 * (4/5) which is equal to 56 startfraction 28 over 5 endfraction.

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Answer: ≈0.71

Step-by-step explanation: The real decimal would be 0.70710678118655. Yes, I know it is a big number. So, after doing some calculations, I got 0.5, remember we need to find the square root of 0.5. So, after finding that, I got 0.70710678118655. Which, your answer wants it to be rounded, so it would be D: ≈0.71

Your query has an answer of Extras charges = $999.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Detailed explanation:

Data

Total cost: $11.325

8% state tax

$53 for license plates

$40 for an emissions inspection.

Process

1.- Determine the 8% of the car's cost.

11325 ———————— 100%

x ———————- 8%

x = (8 x 11325)/100

x = 90600/100

x = $1,066.16 in state taxes

2. Determine the entire cost.

Charges total $906 plus $53 plus $40.

= $ 999

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Answer:

all yes

Step-by-step explanation:

AB = A'B' → yes

If AC // BD, then A'C' // B'D' → yes

m∠ABC < m∠A'B'C → No

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Quadrilateral ABCD.

After rotation of 90 degrees, Quadrilateral A'B'C'D'.

We see that,

The side length of the quadrilateral remains the same after rotation.

The parallel sides of the quadrilateral remain the same after rotation.

The angle of the quadrilateral remains the same after rotation.

Thus,

AB = A'B'.

If AC // BD, then A'C' // B'D'.

m∠ABC = m∠A'B'C.

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Answer:

y = 126

Step-by-step explanation:

The Probability that the student will arranged in order from shortest to tallest is 2.505210.

Probability is a branch of math which deals with the numerical description of certain events is to occur. It is the ratio of the numbers of favorable outcomes to the total number of outcomes. When solving probability problems we need to consider series of random experiments or experiments that involve several different aspects, such as drawing two cards from a deck or rolling several dice. the ability to calculate relative frequencies requires counting the number of possible outcomes of the experiment

If a class has 11 students who are to be randomly assigned seating in the order of shortest to tallest.

The total outcomes= 11! = 39916800

here the total favorable outcome is 1.so,

Probability = 1 / 39916800

                   = 2.505210

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To rewrite the expression tan 0 x csc 0 in terms of sine and cosine, we can use the following trigonometric identities:

The reciprocal identity: csc 0 = 1/sin 0

The tangent identity: tan 0 = sin 0/cos 0

The Pythagorean identity: sin^2 0 + cos^2 0 = 1

Substituting these identities into the given expression, we get:

tan 0. csc 0 = (sin 0/cos 0) * (1/sin 0)

Using the reciprocal identity and the Pythagorean identity, we can simplify this expression further to get:

tan 0. csc 0 = (sin 0 * 1)/(cos 0 * sin 0)

Next, we can cancel out the sin 0 term on the numerator and denominator to get:

tan 0. csc 0 = 1/cos 0

Finally, we can use the Pythagorean identity again to rewrite the denominator as:

tan 0. csc 0 = 1/sqrt(1 - sin^2 0)

Therefore, the final simplified expression is:

tan 0. csc 0 = 1/sqrt(1 - sin^2 0)

This is the final answer.

Answer:

No, I do not agree with Buffett as the wealthy barely have any struggles, and them only paying less than a dollar in taxes will make the government add to the less fortunate. Meaning: If a large number of people aren't paying taxes, the government would not be getting a certain amount of money p/m&yr (per month and year), and that's a huge problem because hundreds of thousands of dollars are being spent every day.  And where does the government get that income? We, the givers. And so if they aren't reaching that expectation, where will they get it from? And it's likely that they will add to the less fortunate. Which is terrible. That can lead to putting thousands of people in debt leaving them miserable with nothing

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The change rate at the top of the mt is given as - 2.5 ° / hr

 at the base it is 1/5th of this number

1/5 * -2.5   =  - 0.5 °C  per hour

The multiplicative rate of change of the exponential function is 1.5

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The general form of the geometric sequence is an=a1r(n−1),

where r is the common ratio

a1 is the first term

n is the placement of the term

Now, use the geometric sequence formula to solve for the rate:

an=a1r^(n-1)

6.75=4.5r^(2-1)

6.75=4.5r

6.75/4.5=r

r= 1.5

and if you want to make sure just multiply each number by 1.5 and see if it gets you the next number

4.5 4.5×1.5=6.75 (holds true)

6.75 6.75×1.5=10.125 (holds true)

10.125 10.125×1.5=15.1875 (holds true)

15.1875

1.5 is the multiplicative rate.

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141.472 N of drag force is applied in 1.6m wide and 1.4m high car travelling at 10m/s

Drag force is the net force in the direction of flow experienced by any item moving through a fluid and is caused by pressure and shear stress forces acting on the surface of the object.

Formula of drag force is given by:

[tex]F_d = \frac{1}{2}C_dAPv^2[/tex]

where

[tex]F_d[/tex] = drag force (N)

[tex]C_d[/tex] = drag coefficient (1.05 for moving car)

P = density of fluid (1.2 kg/m3 for air at NTP)

v = flow velocity (m/s)

A = characteristic frontal area of the body

A = height * width

=> 1.6*1.4

so A=2.24 [tex]m^2[/tex]

and v=10 m/s

so [tex]F_d[/tex] = 1/2* 1.05 * 2.24 *( 1.2 *10*10)

=> 0.5*1.05*2.24 *122

=> 143.472 N

so [tex]F_d[/tex]  = 143.472 N

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Equation that represents the height of parasail (y) based on the speed of the motorboat (x) is given by y sinβ = Xt

What is parasail?

A kind of sports game where a person climbs in a parachute and the parachute is tied to a moving motorboat.

Generally, parasail is tied with a motorboat by a special chord. The position of chord of parasail is not properly perpendicular to the direction of boat moving on. There is an angle between the chord and horizontal surface of motorboat.

Let the angle is denoted by β

The vertical height of parasail over the boat=h

the length of chord that means distance from boat to the parasail = y

speed of boat = X

As per trigonometric formula, opposite/ hypotenuse = sinβ

                                        sinβ = h/y

   hence, height of parasail over the boat surface, h= y sin β

                             Now, from the height, speed and time equation

                          height = speed × time

 at time t, the height of parasail ysinβ  which attached to a boat of speed X can be represent by the equation.

             y sinβ = Xt

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Answer:

The oceans – the largest CO2-reservoir

Step-by-step explanation:

The oceans absorb substantial amounts of carbon dioxide, and thereby consume a large portion of this greenhouse gas, which is released by human activity.

The ocean is a natural 'reservoir' for dissolved carbon dioxide.

We have,

The _____________  is a natural 'reservoir' for dissolved carbon dioxide.

Oceans absorb large amounts of carbon dioxide consuming a large portion of greenhouse gas such as carbon dioxide which is released by human activity.

Oceans are the largest carbon dioxide reservoir.

Thus,

The ocean is the answer.

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Answer:

500 grams

Step-by-step explanation:

you doubled the people, so you would need to double the flour.

Answer:

no. Only Lin is right.

Step-by-step explanation:

As you can see, 2.5 and d are multiplied with each other. To get rid of the 2.5, though, you’d have to do the inverse operation, which is division.

hope this helps

Step-by-step explanation: