HELP. Use the grouping method to factor the polynomial below completely.
x^3 – 5x^2 + 3x - 15
A. (x^2 + 5)(x-3)
B. (x^2 - 3)(x+5)
C. (x^2 - 5)(x+3)
D. (x^2 + 3)(x - 5)

9514 1404 393

Answer:

  35 miles

Step-by-step explanation:

The relevant relation is ...

  distance = speed × time

The total distance the trolley traveled is ...

  d = (20 mi/h) × (3.5 h) = 70 mi

The distance is the same in both directions, so the trolley traveled half this distance in one direction.

The trolley traveled 35 miles in one direction.

Answer:

A)   ± 54 cm^3 ( maximum possible error in volume )

B) i) 58.625 cm^3  ii) 49.625 cm^3

Step-by-step explanation:

A) using differential

edge of cube = 6 cm ,  maximum possible error = 0.5 cm

∴ side of cube ( x )= ± 0.5 cm

V = volume of cube

dv /dx = d(x)^3 / dx

∴ dv  = 3x^2 dx ---- ( 1 )

input values into 1

dv = 3(6)^2 * ( ± 0.5 )

    = ± 54 cm^3 ( maximum possible error in volume )

B) Using calculator

actual error in measuring volume when

i) radius = 6.5 cm instead of  6 cm

V1= ( 6.5)^3 = 274.625 ,  V = ( 6)^3 = 216

actual error = 274.625 - 216 = 58.625 cm^3

ii) radius = 5.5cm instead of 6cm

actual error = 49.625 cm^3

Answer:

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

The height of a projectile fired upward is given by the formula:

[tex]\displaystyle s = v_{0} t - 16t^2[/tex]

Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that v₀ = 128, find t such that s = 96.

Substitute:

[tex](96) = (128)t-16t^2[/tex]

This is a quadratic. First, we can divide both sides by -16:

[tex]-6 = -8t+t^2[/tex]

Isolate the equation:

[tex]t^2 - 8t + 6 = 0[/tex]

The equation isn't factorable, so we can consider using the quadratic formula:

[tex]\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

In this case, a = 1, b = -8, and c = 6. Substitute:

[tex]\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}[/tex]

Simplify:

[tex]\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}[/tex]

Hence, our two solutions are:

[tex]\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84[/tex]

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Answer:

Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.

Step-by-step explanation:

The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

12 resistors, which means that [tex]N = 12[/tex]

3 defective, which means that [tex]k = 3[/tex]

4 are selected, which means that [tex]n = 4[/tex]

To find an specific probability, that is, of x defectives:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = x) = h(x,12,4,3) = \frac{C_{3,x}*C_{9,4-x}}{C_{12,4}}[/tex]

Answer:

negative

Step-by-step explanation:

because when positive and negative integers are multiplied it results to a negative answer

Answer:

máy ...

xác suất để một máy tính bảng có hệ điều hành B sử dụng ổn định trong 2 năm đầu tiên. Add answer

Answer:

$3735

Step-by-step explanation:

2/5 = 8/20

8/20 + 7/20 = 15/20 = 3/4

3/4*4980 = 3735

Answer:

Step-by-step explanation:

When the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.

"It is a transformation in which the object is rotated about a fixed point. "

For given question,

Quadrilateral JKLM is rotated - 270° about the origin.

This means, quadrilateral JKLM is rotated 270° clockwise about the origin.

We know, if point P(x, y) is rotated 270° clockwise or 90° anticlockwise then  the coordinated of rotated point would be (-y, x).

From figure, the coordinates of the quadrilateral JKLM are:
J = (3, 3)

K = (5, -5)

L = (-3, -7)

M = (3, -3)

After rotating -270° about the origin the coordinates of the quadrilateral would be,

J' = (-3, 3)

K' = (5, 5)

L' = (7, -3)

M' = (3, 3)

And the image of the rotated quadrilateral J'K'L'M' is shown below.

Therefore, when the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.

Learn more about rotation here:

https://brainly.com/question/16710736

#SPJ2

Answer:

C) (f+g)(x)= 3x^3-2x^2+10x-12

Answer:

the answer of that is number C

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Pytago:

x[tex]x^{2} +7^{2} = 9^{2} \\\\x = \sqrt{9^{2} - 7^{2} } x = 4\sqrt{2}[/tex]

Answer:

14

Step-by-step explanation:

The area of a parallelogram is

A = bh where b is the base and h is the height

140 = b*10

Divide each side by 10

140/10 = 10b/10

14 = b

Answer:

The third choice is the correct one.

Step-by-step explanation:

The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.

Answer: The third answer is correct

Step-by-step explanation:

Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.

Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours

Step-by-step explanation:

Damien = X -21

Caitlyn = X

2X - 21 = 14

2X = 14 + 21

X = (14+21)/2

X = 7.5

Answer:

2 minutes and 5 seconds

Step-by-step explanation:

60+20+15+15+15= 125 Seconds ( 2 minutes and 5 seconds )

I added three fifteens as I don't know the number of chambelanes.

Hope it helps!

Answer:

It's letter b

Step-by-step explanation:

I hope this help

This question is solved using the conditional probability concept.

Using this concept, we find that:

First, the concept is presented.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

In which

P(A|B) is the probability of event A happening, given that B happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(B) is the probability of B happening.

----------------------------------------------------

Question a:

For relation with the formula presented above, I will change events A and B.

Event A: Person is infected.

Event B: Positive test.

Probability of a positive test:

Thus:

[tex]P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527[/tex]

Probability of a positive test and the person is infected.

85% = 0.85 out of 1/300. Thus:

[tex]P(A \cap B) = \frac{0.85}{300} = 0.0028[/tex]

Desired probability:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053[/tex]

0.053*100% = 5.3%, thus:

P(AIB)= 5.3%

---------------------

Question b:

Event A: Does not have the virus

Event B: Test negative.

Probability of a negative test:

Thus:

[tex]P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473[/tex]

Probability of a negative test and the person is not infected.

0.95 out of 299/300

Thus:

[tex]P(A \cap B) = \frac{0.95\times299}{300} = 0.9468[/tex]

Desired probability:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999[/tex]

0.999*100% = 99.9%, so:

P(A'|B') = 99.9%

A similar question can be found at https://brainly.com/question/24275491

Answer:

A)x>-3

Step-by-step explanation:

as the circle is not coloured this means that -3 is not included so the ones that have

[tex] \geqslant \\ \leqslant [/tex]

are not answers and these means smaller or equal to/greater or equal to.

As the line is going to the right this means that x is greater than -3 so we use > for greater.

so in the end we get that the answer is x > -3

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Out of 124 software users

This means that [tex]n = 124[/tex]

Assume the probability that a given software user will call technical support is 97%.

This means that [tex]p = 0.97[/tex]

Conditions:

[tex]np = 124*0.97 = 120.28 \geq 10[/tex]

[tex]n(1-p) = 124*0.03 = 3.72 < 10[/tex]

Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0[/tex]

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

Answer:

It is the first one, The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.

Step-by-step explanation:

Given:

The function is:

[tex]f(x)=x^2-x+1[/tex]

To find:

The result of the operation [tex]-f(x)=-(x^2-x+1)[/tex].

Solution:

If [tex]g(x)=-f(x)[/tex], then the graph of f(x) is reflected across the x-axis to get the graph of g(x).

We have,

[tex]f(x)=x^2-x+1[/tex]

The given operation is:

[tex]-f(x)=-(x^2-x+1)[/tex]

So, it will result in a reflection across the x-axis.

Therefore, the correct option is A.

Answer:

A) reflection across the x-axis.

Step-by-step explanation: I took the test

Answer:

The larger the sample size, the more accurate the estimation of the true population value.

Step-by-step explanation:

Given:

If x, y, and z are positive integers, then

[tex]2^x\times 3^y\times 5^z=54000[/tex]

To find:

The value of [tex]x+y+z[/tex].

Solution:

First we need to find the prime factors of 54000.

[tex]54000=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5[/tex]

[tex]54000=2^4\times 3^3\times 5^3[/tex]        ...(i)

We have,

[tex]54000=2^x\times 3^y\times 5^z[/tex]        ...(ii)

On comparing (i) and (ii), we get [tex]x=4,y=3,z=3[/tex].

The sum of [tex]x,y,z[/tex] is:

[tex]x+y+z=4+3+3[/tex]

[tex]x+y+z=10[/tex]

Therefore, the value of [tex]x+y+z[/tex] is 10.

Answer:

y = -1

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

If you add x to the left side of the equation you get positive 1/2x +3=7

you then would subtract 3 from 7 to get 4

this would leave you with 1/2x=4

if you divide 4 by 1/2 you get 8 as the answer.

Answer:

Step-by-step explanation:

a). Given expression in the question is,

   [tex]\frac{13822\times 623}{14}[/tex]

   Exact value of the expression will be,

   [tex]\frac{13822\times 623}{14}=615079[/tex]

b). By using approximations to 1 significant figure,

   13822 ≈ 10000

   623 ≈ 600

   14 ≈ 10

   615079 ≈ 60000

   Now use the expression,

   [tex]\frac{13822\times 623}{14}=\frac{10000\times 600}{10}[/tex]

                  = 60000

For this you just look at the sides.

Soh cah toa

This is good to remember.

Sin = opposite/ hypotenuse

Cos= adjacent/ hypotenuse

Tan = opposite/ adjacent

In this case you have TanZ, the side adjacent to the angle is 10 and the opposite to the angle is 24. So tanZ is 24/10 which simplifies to 12/5.

The hypotenuse is always the longest side, but the opposite and adjacent sides can change depending on the angle.

Answer:90 = ... 42 + 48) - 360

Step-by-step explanation: