13. Determine which of the following are roots of
x³ - 12x - 16
Hint: Use Remainder Theorem

Answer:

f, x, 7, -2

Step-by-step explanation:

The value of B in the prism is 21 in²

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The given figure is a prism.

And,

B is the base of the prism.

Now,

The base of the prism is a rectangle.

So,

Area of a rectangle.

= length x width

= 7 x 3

= 21 in²

Thus,

The value of B in the prism is 21 in²

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1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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a=shorter leg

b=longer leg

c=hypotenuse

a=b-14

c^2=a^2+b^2

26^2=(b-14)^2+b^2

676=b^2-2*b*14+14^2+b^2

676=2b^2-28b+196

676-196=2(b^2-14b)

480=2(b^2-14b) Divide with 2

240=b^2-14b

b^2-14b=240

b^2-14b+7^2=240+7^2

Becouse: (b-7)^2=b^2-14b+7^2

(b-7)^2=240+49

(b-7)^2=289

b-7=sqroot(289)

You have two solutions:

b-7=17 and

b-7=-17

Becouse sqroot(289)=+/- 17

First solution: b-7=17

b=17+7=24

Second solution:

b-7=-17

b=17+7=-10

leg of triangle can not be negative number so:

b=24

a=b-14=24-14=10

a=10 b=24

c=sqroot(a^2+b^2)

c=sqroot(10^2+24^2)

c=sqroot(100+576)

c=sqroot(676)

c=26

The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.

What is cashback?

Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.

When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account

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Answer:

a edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

12

Answer:

Step-by-step explanation:

Volume of a pyramid is expressed as:

\(V = \frac{Base \ area * height}{3}\)

Base area = area of the rectangle = 5*9 = 45

Height of pyramid = 29

Substitute:

\(V = \frac{45 * 29}{3}\\V = 15*29\\V = 435 units^3\)

Hence the volume of the pyramid is 435units³

the answer is B) both expressions are equivalent to 76 when t=3

Hope this helps :)

Answer:

D

Step-by-step explanation:

Hope i helped :)

Answer:

A

Step-by-step explanation:

Answer:

$960

Step-by-step explanation:

110% = $880

10% = $80

120% = $960

Answer:

0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 39368, \sigma = 2367\)

What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe?

This is 1 subtracted by the pvalue of Z when X = 44520. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{44520 - 39368}{2367}\)

\(Z = 2.18\)

\(Z = 2.18\) has a pvalue of 0.985

1 - 0.985 = 0.015

0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

We need a sample size of at least 879 to be 99.5% confident that our estimate of the population mean will be within 1 of the true population mean.

To determine the required sample size, we use mathematical formula:

\(n = (z * σ / E) ^ 2\)

Where:

n: sample size

z: z-score corresponding to desired level of confidence (99.5%)

σ: population standard deviation

E: margin of error (1 in this case)

Substitute given values into formula:

\(n = (2.807 * 29.6 / 1) ^ 2\\n = 878.3\)

Hence, in order to be 99.5% confident that our estimate of the population mean would be within 1 of the actual population mean, we need a sample size of at least 879.

It's vital to remember that the estimate will be more accurate the larger the sample size. Larger sample numbers might, however, also be more costly and time-consuming to gather. Hence, while choosing the sample size, researchers must carefully weigh the trade-offs between the required level of confidence, the margin of error, and the resources at their disposal.

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Answer: The 290 millimeters long is the ribbon.

Step-by-step explanation:

To convert centimeters to millimeters

1 cm =10 millimeters

therefore,

29cm= 290 millimeters

Therefore, the ribbon is 290 millimeters long.

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Answer:

uh l.m.a.o this is why im failing math

Step-by-step explanation:

lol

Answer:

-⅜ is between -1 and 0

⅞ is between 0 and 1

-2½ is between -3 and -2 ( in the mid )

2½ is between 2 and 3 ( in the mid )

The maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

A special kind οf relatiοn knοwn as a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn generates exactly οne value fοr each input value. Because οne is mapped tο twο different values, the abοve graph depicts a relatiοnship rather than a functiοn. Hοwever, if οne were instead mapped tο a single value, the relatiοnship mentiοned abοve wοuld becοme a functiοn.

Additiοnally, οutput values can be equal tο input values. We knοw that the square rοοt functiοn is an increasing functiοn, which means that the value οf the functiοn increases as the input value increases.

Therefοre, tο find the maximum value οf the functiοn, we need tο find the maximum value οf h.

Assuming that the lighthοuse is οn the hοrizοn, which is apprοximately 3 miles away, we can use the Pythagοrean theοrem tο find the height οf the lighthοuse:

\(h^2 = (3)^2 - (15)^2h^2 = 9 - 225h^2 = -216\)

Since we cannοt take the square rοοt οf a negative number, there is nο real height fοr the lighthοuse that wοuld make it visible frοm a ship 15 feet abοve the water level.

Therefοre, the maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

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The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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given a parabola in standard form

y

=

a

x

2

+

b

x

+

c

then the x-coordinate of the vertex can be found using

∙

x

x

vertex

=

−

b

2

a

y

=

x

2

−

6

x

+

5

is in standard form

with

a

=

1

,

b

=

−

6

,

c

=

5

⇒

x

vertex

=

−

−

6

2

=

3

substitute this value into equation for y-coordinate

y

vertex

=

3

2

−

6

(

3

)

+

5

=

−

4

⇒

vertex

=

(

3

,

−

4

)

the axis of symmetry is vertical and passes through the

vertex with equation

x

=

3

to find x-intercepts let y = 0

⇒

x

2

−

6

x

+

5

=

0

the factors of + 5 which sum to - 6 are - 1 and - 5

⇒

(

x

−

1

)

(

x

−

5

)

=

0

equate each factor to zero and solve for x

x

−

1

=

0

⇒

x

=

1

x

−

5

=

0

⇒

x

=

5

⇒

x

=

1

and

x

=

5

←

x-intercepts

graph{(y-x^2+6x-5)(y-1000x+3000)=0 [-10, 10, -5, 5]}

Answer:

Step 2 is wrong. It's 16n-14. Not -16n+14.

Step-by-step explanation:

Do -16n+14, then add both sides.

16n=-14+18

16n+14n= -14n+18+14n

30n=18

30n/30 18/30

n=3/5

Answer:

I don't see any answer choices, but read my explanation

Step-by-step explanation:

Any line with a slope of 3 would be parallel to y=3x+2.

For example,

y=3x+4

y=3x-1

y=3x

All of these lines are parallel to the original equation

The maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are:

Lower bound = 9.5

Upper bound = 30

In basketball, players can score 1, 2, 3 (or even 4 or 5 points) during a possession.

Players who score five points are fouled in the act of shooting a three-pointer and making the shot.

Players who score four points attempt a three-pointer and make the subsequent foul shot.

Players who score three points go beyond the 3-point line, in bounds.  

Players who score two points go inside the 3-point line, in bounds.

Players who score one point make free throws.

Basketball scores =  1, 2, 3, 4, 5 points

Median = 3 per possession

9.5   10  12.5   15   15.5   18.5   20  21.5  25    26   30    30

Thus, the maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are 9.5 and 30.

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Relative Frequency of Scores

30 30 26 25 20 15 10 9.5 12.5 15.5 18.5 21.5

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

Answer:

Step-by-step explanation:

Consider the given data of pulse rate and age of females

The null and alternative hypothesis is

\(H_0: \mu _1= \mu_2=\mu_3\)

\(H_1\): at least one of the mean is different from the others

The significance level is 0.05

The test statistic is F = 7.93

The Critical value is F = 3.06

Also, P-value is 0.0005

From the provided result it is clear that the P-value is less than the significance level , so researchers rejects the null hypothesis.

Therefore, the researcher conclude that there is sufficient evidence to rejection that the female from the three age bracket have the same mean pulse rate

On the basis of provided data , it is clear that the pulse rate of female affected by three age bracket

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

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The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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Answer:

The answer should be B.

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)