Use the Remainder Theorem to evaluate f(10) for:
f(x) = 2x^3 – 14x^2 - 56x - 40

Answer:

\(Volume = 11488.21\)

\(Area = 2461.76\)

Step-by-step explanation:

Given

\(Radius, r = 14\ in\)

Shape: Sphere

Solving (a): The Volume

This is calculated as:

\(Volume = \frac{4}{3}\pi r^3\)

Take \(\pi\) as 3.14 and substitute 14 for r

\(Volume = \frac{4}{3} * 3.14 * 14^3\)

\(Volume = \frac{4}{3} * 3.14 * 2744\)

\(Volume = \frac{4 * 3.14 * 2744}{3}\)

\(Volume = \frac{34464.64}{3}\)

\(Volume = 11488.21\)

Solving (b): The Surface Area

This is calculated as follows:

\(Area = 4\pi r^2\)

Take \(\pi\) as 3.14 and substitute 14 for r

\(Area = 4 * 3.14 * 14^2\)

\(Area = 4 * 3.14 * 196\)

\(Area = 2461.76\)

The percent error of the house of the pizza would be 2.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.

We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.

WE know that Error = Actual value - Estimated value

Then Error = 14 - 12 = 2

Therefore, the percent error would be 2.

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The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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Answer:

-3.21538461538

Step-by-step explanation:

\(\mathrm{Equation\;Given:}\; 5+5x=\frac{12x-\frac{12}{5}\cdot \:7}{5}\)

\(\mathrm{Multiply\;both\;sides\;by\;5}:\)   \(5\cdot \:5+5x\cdot \:5=\frac{12x-\frac{12}{5}\cdot \:7}{5}\cdot \:5\)

\(\mathrm{Now\;we\;have\;}:\)  \(25+25x=12x-\frac{84}{5}\)

\(\mathrm{Subtract\;by\;sides\;by\;25}:\)   \(25+25x-25=12x-\frac{84}{5}-25\)

\(\mathrm{Thus\;we\;have}:\)  \(25x=12x-\frac{209}{5}\)

\(\mathrm{Subtracting\;12x\;from\;both\;sides}:\)  \(25x-12x=12x-\frac{209}{5}-12x\)

\(\mathrm{So\;then\;we\;have:}\) \(13x=-\frac{209}{5}\)

\(\mathrm{Now\;divide\;both\;sides\;by\;13}:\)  \(\frac{13x}{13}=\frac{-\frac{209}{5}}{13}\)

\(\mathrm{Hence\;we\;have}:\;\;x=-\frac{209}{65}\)

\(\mathrm{Decimal\;form}:-3.21538461538\)

Kavinsky

Answer:

\(( {2}^{ - 6} )(5)( {2}^{3} \times 5) {}^{2} \\ \\ = 2 {}^{( - 6 + (3 \times 2))} \times {5}^{(1 + 2)} \\ \\ = {2}^{0} \times {5}^{3} \\ \\ = 1 \times {5}^{3} \\ \\ = {5}^{3} \)

Answer:

mkhhikbyjhggfikmnikkfyujikok

Answer:

A. Triangle A= 16cm^2

Step-by-step explanation:

triangle A area=8×4=32

32÷2=16cm^2

triangle B area= 5×6=30

30÷2=15cm^2

so triangle A has the greater area of 16 cm^2

Answer:

A. 16cm2 triangle

Explanation in detail: triangle A area=84=32 32÷2=16cm^2 area of triangle B = 56=30

30÷2=15cm^2 As a result, triangle A has a bigger area of 16 cm2.

Step-by-step explanation:

Answer:

0.625 tons or 5/8 tons

Step-by-step explanation:

(5/2)/4

0.625 tons or 5/8

Answer:

  5/8 ton

Step-by-step explanation:

1/4 of 5/2 ton is on each tire, so the weight it is bearing is ...

  (1/4)(5/2 ton) = 5/8 ton

Each tire is bearing 5/8 ton.

_____

Additional comment

If that is a US short ton (2000 lb), then the weight on each tire is 1250 pounds. If the tires are inflated to 50 pounds per square inch, then the area of rubber on the road at each tire is 1250 lb/(50 lb/in^2) = 25 in^2. That's the size of a 5-inch square.

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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the answer is C 61 because 10x is 40 plus 21 is 61

Answer:

Option C

The answer is 61

Step-by-step explanation:

10x + 21 when x = 4

10(4) + 21

40 + 21 = 61

Thus, The answer is 61

-TheUnknownScientist 72

Answer:

possible

Step-by-step explanation:

Answer: x^4 + 2x + 2

Step-by-step explanation:

I just took the test. :)

Answer: x^4 + 2x + 2

Step-by-step explanation:

Big brain

Answer:

694

Step-by-stp explanation:

Answer:

whats the question?

Step-by-step explanation:

Answer:

1 m&m

Step-by-step explanation:

in order to find out how many will be left you will make the number of m&ms even causing it to have an even amount left over.

Answer:12

Step-by-step explanation:I did the math

The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.

Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.

This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.

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Answer:

Step-by-step explanation:

Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.

let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

The checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

The fertilizing techniques that would be most effective for each example are as follows:

1. Farm with numerous workers and sensitive crops:

a. UDP (Unchecked )

b. Precision management (Checked)

2. A gardener raising produce for a family:

a. UDP (Checked).

b. Precision management (Unchecked )

3. Company that delivers corn to 10 states:

a. UDP (Unchecked)

b. Precision management (Checked)

Please note that the checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

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Answer:

(5/2,9)

Step-by-step explanation:

Midpoint Formula: (((x1+x2)/2),((y1+22)/2))= (((-6+11)/2),((13+5)/2))= (5/2,9)

Hello!

For this you would just need to multiple straight across. Here's how you would set it up:

3/4 ·1/8

Then you would multiple 3 x 1 = 3

And 4 x 8 =32

Your answer should be 3/32, it cannot be simplified so that is the final answer :).

Based on the information provided, it is expected that after 18 months, the difference in the cost of the two plants is 240.

By following the sequence provided on the table, let's calculate the cost for each plant:

Plant A: 75, 110, 145, 180, 215, 250, 285, 320, 355, 390, 425, 460, 495, 530, 565, 600, 635, 670.

Plant B: 60, 110, 160, 210, 260, 310, 360, 410, 460, 510, 560, 610, 660, 710, 760, 810. 860, 910

Now, let's calculate the difference in cost:

910 - 670 = 240

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Answer:

\(\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }\)

\(\sqrt{9+36}\)

\(\sqrt{45}\)

Step-by-step explanation:

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Mr. X reduces his weight in a ratio of 4:17. This means that for every 4 units of weight he loses, his initial weight was divided into 17 equal parts.

To determine the ratio by which Mr. X reduces his weight, we need to compare his initial weight of 85 kg with his target weight of 65 kg.

The reduction in weight is calculated as the difference between the initial weight and the target weight, which in this case is 85 kg - 65 kg = 20 kg.

The ratio can be expressed as a fraction, where the numerator represents the reduction in weight and the denominator represents the initial weight:

Reduction in weight / Initial weight

Substituting the values, we have:

20 kg / 85 kg

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

(20 kg / 5) / (85 kg / 5) = 4/17

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The amount of fewer euros he would receive as a result of the delay is 20 E.

The percentage loss that was caused by the delay is -4%.

Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.

Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday

Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E

Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E

Difference = 500 E - 480 E = 20 E

Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1

Percentage loss = (480 / 500) - 1 = -0.04 = -4%

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