What is the product?
(x - 3)(2x2 - 5x + 1)
N
273 - 2 + 16x + 3
2x3 - 11X2 + 16x + 3
O 2x3 - 11x2 + 16x - 3
O 2x3 - x2 + 16x - 3

Answer:

  1/3

Step-by-step explanation:

The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.

  [tex]\displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}[/tex]

Answer:

a) E(X) = 71

b) V(X) = 20.59

Sigma = 4.538

Step-by-step explanation:

The question is incomplete:

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015).

Suppose we randomly select 100 tweets.

a) What is the expected number of these tweets with no reaction?

b) What are the variance and standard deviation for the number of these tweets with no reaction?

This can be modeled with the binomial distribution, with sample size n=100 and p=0.71, as the probability of no reaction for each individual tweet.

The expected number of these tweets with no reaction can be calcualted as the mean of the binomial random variable with these parameters:

[tex]E(X)=n\cdot p=100\cdot 0.71=71[/tex]

The variance for the number of these tweets with no reaction can be calculated as the variance of the binomial distribution:

[tex]V(X)=np(1-p)=100\cdot0.71\cdot0.29=20.59[/tex]

Then, the standard deviation becomes:

[tex]\sigma=\sqrt{V(X}=\sqrt{20.59}=4.538[/tex]

Answer:

Option (1)

Step-by-step explanation:

Quadratic equation is given as,

2x² + 8 = 0

Let the function is,

f(x) = 2x² + 8

f(x) = 2(x - 0)² + 8

Now we will prepare the table for every input value,

x    -2      -1         0        1          2

y     16      10       8        10        16

By plotting these points we get a parabola having vertex at (0, 8).

Graph of the given function doesn't touches or intersects the x-axis.

And we know if a graph has no x-intercept, function graphed will have no real solution.

Therefore, function f(x) will have no real solutions.

Option (1) will be the answer.

Answer:

1234567891011121314151617181920

Answer:

11.62 ounces

Step-by-step explanation:

Answer:

3 1/3

Step-by-step explanation:

8-5=3=3 1/3.

hope u understand

Answer:

14 years 3 months.

Step-by-step explanation:

5 + 8 = 13 years

6 + 9 = 15 months = 1 year 3 months.

Total = 14 years 3 months.

Answer:

Ground distance of Bob  from his friends house = 61 ft (Approx)

Step-by-step explanation:

Given:

Length of string = 75 ft

Angle with the ground = 35°

Find:

Ground distance of Bob  from his friends house.

Computation:

Using trigonometric application:

⇒ Cos [tex]\theta[/tex] = Base / Hypotenuse

⇒ Cos 35° = Base / 75

⇒ 0.819 = Base / 75

⇒ Base = 61.425 ft

Ground distance of Bob  from his friends house = 61 ft (Approx)

Answer:

-7

Step-by-step explanation:

The numerator of a  fraction is 1 more than  twice its denominator.

Let the denominator=x

Therefore, the numerator=2x+1

The fraction is: [tex]\dfrac{2x+1}{x}[/tex]

If 4  is added to both the  numerator and the denominator, the fraction reduces to 3.

Therefore:

[tex]\dfrac{2x+1+4}{x+4} =3[/tex]

First, we solve for x

[tex]\dfrac{2x+5}{x+4} =3[/tex]

Cross multiply

2x+5=3(x+4)

Open the bracket on the right-hand side

2x+5=3x+12

Collect like terms

3x-2x=5-12

x=-7

Therefore, the denominator of the fraction, x=-7

The percentage of change in productivity from April to May is found to be 6.66%.

A change in labour productivity reflects an output change that cannot be accounted for by a change in the number of hours worked. The development of technology over time might lead to an increase in output per hour enhanced employee skills.

We must first determine the number of man hours worked in April in order to compute the percentage change in productivity:

8 employs worked for 40 hours along with 7 employs worked for 10 hours in a week( total 4 weeks in April).

Input of April is,

= 8×40 + 7×10×4

= 1560 hours

To determine the productivity in April, divide the total sales by the number of man hours:

= 45000/1560

= 28.846

8 employs worked for 40 hours along with 9 employs worked for 15 hours in a week( total 4 weeks in April).

Input of May is,

= 8×40 + 9×15×4

= 1820 hours

To determine the productivity in April, divide the total sales by the number of man hours:

= 56000/1820

= 30.769

Finding the difference between productivity in each month and dividing by April's productivity percentage yields the percent change in productivity:

= [tex]\frac{30769-28.846}{28.846}[/tex]×[tex]100[/tex]

= 6.66 %

Therefore, the productivity from April to May increased by 6.66%.

To know more about how to find percentage change, here

https://brainly.com/question/809966

#SPJ2

Answer:

(0.5, 2)

Step-by-step explanation:

Since the y coordinates are the same, the distance is between the x values

4 - -3

4+3 = 7

The distance is 7

1/2 the distance would be the center

7/2 = 3.5

Add this to the left coordinate

The x coordinate of the center is -3 + 3.5 = .5

The y coordinate is 2

Answer:

C.  (x + 4)(x + 5).

Step-by-step explanation:

We need 2 numbers whose product is + 20 and whose sum is + 9.

They are + 5 and + 4 , so

x2 + 9x +20

= (x + 4)(x + 5).

Answer:

the mathematical model is : [tex]-\frac{1}{A}= kt - \frac{1}{50}[/tex]

Step-by-step explanation:

Given that:

Let A(t) to be the amount of oil in the barrel at time t.

However; Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel.

Then,

[tex]\frac{dA}{dt} \ \alpha \ A^2[/tex]

[tex]\frac{dA}{dt}= KA^2[/tex]

Initially the 100 -gallon barrel is half-full of oil

So, A(0) = 100/2 = 50

[tex]\frac{dA}{dt}= KA^2 \ \ \ \ \ \ :A(0)=50[/tex]

The variable is now being separated as:

[tex]\frac{dA}{A^2}=kdl[/tex]

Taking integral of both sides; we have:

[tex]\int\limits\frac{dA}{A^2}=\int\limits \ kdt[/tex]

[tex]-\frac{1}{A}= kt +C[/tex]

However; since A(0) = 50; Then

t = 0  ; A =50 in the above equation

[tex]-\frac{1}{50}= 0 +C[/tex]

[tex]C = - \frac{1}{50}[/tex]

Thus; the mathematical model is : [tex]-\frac{1}{A}= kt - \frac{1}{50}[/tex]

Answer:

12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft

Step-by-step explanation:

Given that truck can hold = 504 [tex]ft^{3}[/tex] i.e.

Volume, V = 504 [tex]ft^{3}[/tex]

Length of cargo space = 12 ft

Let width of cargo space = w ft

As per question statement:

Let height of cargo space = (w-1) ft

To find: The Dimensions of Cargo Space

Formula for Volume of Cargo Space:

V = Length [tex]\times[/tex] Width [tex]\times[/tex] Height

Putting the given values and conditions:

504 = 12 [tex]\times[/tex] [tex]w \times (w-1)[/tex]

[tex]\Rightarrow w(w-1) = \dfrac{504}{12}\\\Rightarrow w^{2} -w = 42\\\Rightarrow w^{2} -w - 42=0\\\Rightarrow w^{2} -7w +6w -42 =0\\\Rightarrow w(w -7) +6(w -7) =0\\\Rightarrow (w -7)(w+6) = 0\\\Rightarrow w =7, -6[/tex]

Dimensions can not be negative, so width, w = 7 ft

Height = (w-1) = 7-1 = 6 ft

So, the dimensions are 12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft.

Answer:

The solution is X<18

Step-by-step explanation:

When Mason was solving the inequality he subtracted two from the equation instead of adding two to solve for x.

X-2<16

X<18

Answer:

Step-by-step explanation:

x - 2 < 16

We eliminate 2 to isolate the variable, x by adding 2 to both sides. -2 + 2 = 0.

x < 18

We can test this because 17 is less than 18. Pretend x = 17

17 < 18✅

Mason subtracted 2, instead of adding 2.

In order to graph this, put an open circle at 18, and the arrow should point to the left.

Hope this helps ;D

Answer:

When the are intercepted by other lines (math)

Existing, happening at the same time (definition)

Answer:

Sin(2x)+sin(x)+cos(2x)-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

9x + 2y = 24  (A)

y = 6x + 19 ------ > y - 6x = 19 * (-2) -------> -2y + 6x = -38 (B)

(A) + (B)

15x = -14

x = -14/15

y = 6 * (-14/15) + 19 = -28/5 + 19 = 67/5

Answer:

A. 9x + 2y = 24  

Answer:

a) January 24(24 de Enero)

b) Paula will have made 5 visits(Paula habrá hecho 5 visitas). Mario will have made 4 visits(Mario habrá hecho 4 visitas).

Step-by-step explanation:

When two events, A and B, happen every x and y days, respectively, they will happen on the same day in each lcm(x,y) days. lcm(x,y) is the lesser common multiple of x and y which is not 0.

In this question:

Paula each 5 days

Mario each 6 days

Multiples of 5: {0, 5, 10, 15, 20,25,30, ...}

Multiples of 6: {0, 6, 12, 18, 24, 30, ...}

a) ¿Cuándo volvieron a coincidir?

lcm(5,6) = 30

30 days from December 24, which is January 24(24 de Enero).

b) ¿Cuántas visitas habrá hecho cada uno?

Paula visits each 5 days.

30 is 6th non-zero multiple of 5. This means that on January 24 will be her 6th visit. So she will have made 5 visits.

30 is the 5th non-zero multiple of 6. This means that on January 24 will be her 5th visit. So he will have made 4 visits.

They aren't independent since the probability uses all the cards in the deck

So at the first deal we have the chance of 26/52 of getting a red card, at the second deal we have the chance of a 25/51 of getting another red card, so they aren't independent

Answer:

Standard score z=0.07

Step-by-step explanation:

The z-score, or standard score, represents an equivalent value for X but in the standard normal distribution, where μ=0 and σ=1.

For X=28.3 in a normal distribution with μ=26.3 and σ=28.1, the standard score can be calculated as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{28.3-26.3}{28.1}=\dfrac{2}{28.1}=0.07[/tex]

This value is 0.07 standard deviations right to the mean.

In the picture attached, we have located the z-score.        

Answer:

x = 18°

y = 6

Step-by-step explanation:

in a parallelogram:

Any two opposite sides are congruent

and any two opposites angles are congruent:

then

y + 4 = 10

and 3x = 54

then

y = 6

and x =  54/3 = 18

Answer:

x= 18 , y = 6

Step-by-step explanation:

A parallelogram has two opposite sides equal and parallel hence;

y + 4 = 10

y = 10 -4 = 6

Similarly

54 = 3x( opposite angle of a parallelogram are the same because it's congruent)

3x = 54

x = 54/ 3 = 18°

To be congruent means to have the same shape, size and form but can be flipped.

Answer:

The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Step-by-step explanation:

We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.

We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.

This probability is equal to the proportion of black area in the total area of the cube.

We can define the side of the original cube as A=5a, being a the side of the small cubes.

The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:

[tex]S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2[/tex]

The total area of the 125 small cubes is:

[tex]S=125(6a^2)=750a^2[/tex]

Then, the ratio of black surface to the total surface is:

[tex]s_b/s=(150a^2)/(750a^2)=0.2[/tex]

Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Answer:

  15x+10

Step-by-step explanation:

The area of a rectangle is given by the formula ...

   A = LW

Fill in the given values and simplify.

  A = (3x+2)(5)

  A = 15x +10

The area of the rectangle is 15x+10.

Answer:

[tex]15x + 10[/tex]

Step-by-step explanation:

[tex]area = length \times width \\ = 3x + 2 \times 5 \\ = 5(3x + 2) \\ = 15x + 10[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

undefined

Step-by-step explanation:

We can find the slope by using the formula

m = (y2-y1)/(x2-x1)

m = (8 - -4)/97-7)

   = (8+4)/(7-7)

   = 12/0

We cannot divide by 0 so the slope is undefined

Answer:

38.76% probability that between 13 and 17 of these young adults lived with their parents

Step-by-step explanation:

I am going to use the normal approxiation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

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 samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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].

In this problem, we have that:

[tex]p = 0.142, n = 125[/tex]

So

[tex]\mu = E(X) = np = 125*0.142 = 17.75[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.142*0.858} = 3.9025[/tex]

What is the probability that between 13 and 17 of these young adults lived with their parents?

Using continuity correction, this is [tex]P(13 - 0.5 \leq X \leq 17 + 0.5) = P(12.5 \leq 17.5)[/tex], which is the pvalue of Z when X = 17.5 subtracted by the pvalue of Z when X = 12.5. So

X = 17.5

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

[tex]Z = \frac{17.5 - 17.75}{3.9025}[/tex]

[tex]Z = -0.06[/tex]

[tex]Z = -0.06[/tex] has a pvalue of 0.4761

X = 12.5

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

[tex]Z = \frac{12.5 - 17.75}{3.9025}[/tex]

[tex]Z = -1.35[/tex]

[tex]Z = -1.35[/tex] has a pvalue of 0.0885

0.4761 - 0.0885 = 0.3876

38.76% probability that between 13 and 17 of these young adults lived with their parents

Answer: Tamera invited 21 guests while Adelina invited 26 guest.

Step-by-step explanation:

x + (x-5) = 47  

x + x -5 = 47

2x  -5 =47

        +5   +5

2x= 52

x= 26    

26 -5  = 21