What is the completely factored form of this polynomial?

4x³+12x²+9

The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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To complete the conversion, the following will be gotten:

12880 m

Using conversion technique,

8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k

we have to cancel out similar units in the numerator and denominator.

Therefore,

8 mi / 1 × 1.61 k / 1 mi × 1000m / 1k

8 / 1 × 1.61  / 1  × 1000m / 1 = 12.88 / 1 × 1000m

Hence,

12.88 / 1 × 1000m = 12880 m

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Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

Answer:

$2.50

Step-by-step explanation:

6.25/2.5=2.5

Answer:

33, 66, 81

Step-by-step explanation:

180-99= 81, so angle TUM is 81 degrees.

Angle T + angle M = 99. Solving for x, x= 11.

Angle T= 33

Angle M= 66

Angle TUM= 81

Answer:

37.76

Step-by-step explanation:

it easssyy i guess

The correlation of the data shown on the graph is 1

In this question, the graph represents the given parameter

From the graph, we have the following observations

When the change (increase) in the x values causes a change (increment) in the y values, then the correlation is positive

From the list of options, we have

-1, -0.5 and 0 are not positive values

This means that the correlation is (c) 1

Hence, the correlation of the data is 1

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The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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The tangent line approximation at x= 29.2 is

L(x) = 2x - 1 or L(29.2) = 57.4

The intuitive idea is that a tangent plane “just touches” a surface at a point. The formal definition mimics the intuitive notion of a tangent line to a curve. Let z = f(x,y) be the equation of a surface S in R3, and let P=(a,b,c) be a point on S.

A function f differentiable at tangent.

x=a, we can find that the slope of the tangent of y=f(x) at (a,f(a)) can be found by writing . ). The resulting tangent line through (a,f(a)) and the gradient m=f'(a) is the point-gradient given by

y−f(a)=f'(a)(x−a) has an equation of the form This can also be expressed as y=f'(a)(x−a)+f(a).

Replacing the variable y by the expression L(x) yields points (a, f( a)) called L(x)=f′(a)(x−a)+f(a). , L(x) is just the new name for the tangent, and

f(x)≈L(x) for x near a.

f(x) = 2x - 1

x= 29.0 near to 29.2

f(29.0) = 58 - 1 = 57

f'(x) = 2

So, the point is (29.0, 57) and slope of tangent is 2 .

Tangent line , 57 = 2(29) + b

=> b = -1

then equation is 2x - 1 = y

We to calculate tangent line approximation give as an approximation for at x = 29.2

Tangent line approximation,

y = 2 (29.2) - 1 = 57.4

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The given question is incomplete, complete question is:

Suppose and f (x) = 2x - 1 , what does the tangent line approximation give as an approximation for x= 29.2??

Answer:

there are 52 cards in a deck so the chance is a red card (or not a red card) is 26 out of 52.

Step-by-step explanation:

The solution is 12/13

The probability that the selected card is not an ace but a red card is 12/13

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the probability of the selected card is not an ace but a red card be P

Now , the equation will be

Mason randomly chooses a card from a standard deck of playing cards

So , the probability that the card is a red card is

There are 26 red cards in the deck of 52 cards

So , the probability of selecting a red card = 26/52

Now , from the 26 red cards , the probability that the card is not an ace would be = 26 - ( Ace of hearts + Ace of diamonds )

And ,

The probability of the selected card is not an ace but a red card P = 24/26

The probability of the selected card is not an ace but a red card P = 12/13

Therefore , the value of P is 12/13

Hence , the probability is 12/13

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Answer:

105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

Decimal calculation steps
(1101001)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (105)₁₀

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

0.48£

Step-by-step explanation:

(3x8)/50=0.48£

Step-by-step explanation:

Answer:

Current worth of stock is $141.538

Current worth of stock rounded to nearest cent is $142

Step-by-step explanation:

price of stocks= $141

percentage increase in price of stocks = 1.8% of initial price of stock

dollar value increase in price of stocks = 1.8% of initial price of stock

increase in price of stocks = 1.8% of  $141

increase in price of stocks = 1.8/100 * $141 =$ 253.8/100 = $2.538

Current worth of stock = initial price of stock+increase in price of stocks

substituting the value of initial price of stock and increase in price of stocks we have

Current worth of stock =$141 + $2.538 = $141.538

Since we need to find stock worth now, to nearest cent, as after decimal there .5 and any value greater than or equal to .5 is rounded to one then after rounding,  $141.538 becomes  $142

The graph that would best show the data collected from measuring the volume of a balloon at varying temperatures is a scatter plot graph.

The frequency table is used to show how often a certain result is given. For example, if we roll a dice 100 times we can use this table to display how often each number came up, which can look like:

10 times

30 times

25 times

20 times

5 times

10 times

A bar graph is often used to compare groups or track changes over time. For example, we can measure how many cars pass by certain points in an hour and use a bar graph to display how many cars passed by each place during that hour by representing each place with its own bar, whose height will tell us the number of cars. This would not be the graph we use because we are comparing changes in a single balloon, not in groups of balloons.

The first option is a circle graph, which is used when one thing contains varying percentages within it. The circle graph can display how much of the total is comprised by each sub-division. This is not the kind of graph we are looking to use because it would be incapable of displaying varying values for the same variable.

The graph that would best show the data collected from measuring the volume of a balloon at varying temperatures is a scatter plot graph because this kind of graph can represent two different variables and is used to compare the relationship between them, in this case, the volume of the balloon and the temperature.

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complete question:

Which type of graph would best show the data collected from measuring the volume of a balloon at varying temperatures?

circle graph

frequency table

bar graph

scatter plot

Answer: banana- 88

Orange-55

Apple-143

Step-by-step explanation:

220 divided by 5, times 2,

that’s the banana trees

220 divided by 4, that’s the oranges

Add the answers together

Take the answer away from 220 that’s the apples

Answer:

y = 6h  h = hour

Step-by-step explanation:

Step-by-step explanation:
So the center of the circle is x. This means any straight line through that point is the diameter of the circle. So the radius is half of the diameter. So if the radius of the circle is 7 inches and line YZ is the diameter, then to find the answer just multiply the radius by 2.

So

7 x 2 = 14

The length of the line YZ is then 14 inches, because the line is the diameter of the circle.

The above equation represents this situation, where the new price is 25% off the original price. Calling P to the original price, and solving for new price,

That is, the new price is 75% of the original price

The expression 1 - 0.25P also represents the price of the item

Answer:

here

Step-by-step explanation:

C and D is the answer

The correct statement are;

B. Katarina has 375 star stickers.

D. 75% of the stickers are stars.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars.

Now,

Since, Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars.

Hence, The number of hearts = 25% of 500

                                              = 25/100 × 500

                                              = 25 × 5

                                              = 125

And, Number of stars = 500 - 125

                                  = 375

                                  = 75% of 500

Thus, The correct statement are;

B. Katarina has 375 star stickers.

D. 75% of the stickers are stars.

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Answer:(2I3O-9247)

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)

so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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The value of angle A and C is 14° and 121° respectively

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

The sum of angle in a triangle is 180°

Therefore 45+6x-5+x-7 = 180

collect like terms

45-5-7+6x+x =180

33+7x = 180

7x = 180 - 33

7x = 147

x = 147/7

x= 21

therefore the value of angle A = ( 21-7) = 14°

and angle C = 6(21) - 5

C = 126-5

C = 121°

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Answer:

$20

Step-by-step explanation:

$10 ÷ 8 = $1.25 ($1.25 per inch)

$1.25 x 16 = $20

A 16 inch pizza will sell for $20

Hope this helped :)