WILL GIVE BRAINLIEST! NEED QUICK HELP ASAP! Photo added! least common denominator x^3/x^2+4x+4 and -9/x^2+5x+6

WILL GIVE BRAINLIEST! NEED QUICK HELP ASAP! Photo Added! Least Common Denominator X^3/x^2+4x+4 And -9/x^2+5x+6

Answers

Answer 1

The denominator( s ) we are given are [tex]x^2 + 4x + 4[/tex], and . The first thing we want to do is factor the expressions, to make this easier -

[tex]x^2 + 4x + 4[/tex]

This expression is a perfect square, as ( x )^2 = x^2, ( 2 )^2 = 4, 2 * ( x ) * ( 2 ) = 4x. Thus, the simplified expression should be the following -

[tex]( x + 2 )^2[/tex]

The other expression is, on the other hand, not a perfect square so we must break this expression into groups and attempt factorization -

[tex]x^2 + 5x + 6,\\\left(x^2+2x\right)+\left(3x+6\right),\\x\left(x+2\right)+3\left(x+2\right),\\\left(x+2\right)\left(x+3\right)\\\\Factored Expression = \left(x+2\right)\left(x+3\right)[/tex]

Combining ( x + 2 )^2 and ( x + 2 )( x + 3 ), the expression that contains factors of each is ( x + 2 )^2 * ( x + 3 ), or in other words the LCM.

Solution = [tex]\left(x+2\right)^2\left(x+3\right)[/tex]


Related Questions

06:Pretest 06:Quadrilaterals
27. Which statement is true?
O All squares are quadrilaterals,
O All quadrilaterals are parallelograms,
All rectangles are squares,
O All quadrilaterals are squares,

Answers

Answer:

all squares are quadrilaterals

All squares are quadrilaterals. A quadrilateral is a 4 vertices figure, and a square has 4 vertices.
PLEASE MARK BRAINLIEST!!!!!!!!! Thanks

15 3/4 is what decimal

Answers

The answer is 15.75
3/4 = .75
15 + .75 = 15.75!
Hope this helped!

Brainly is much appreciated!

━━━━━━━☆☆━━━━━━━

▹ Answer

15.75

▹ Step-by-Step Explanation

3 ÷ 4 = .75

15 + .75 = 15.75

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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4x+y=10 Complete the missing value in the solution to the equation. (left parenthesis ( -),−6)

Answers

Answer:  x = 4

4x - 6=10

4x = 10 + 6

4x = 16

[tex]x = \frac{16}{4}[/tex]

x = 4  ←  the missing value

Therefore the the solution is (4,-6) of the equation 4x+y=10 .

Hope this helped You!

Find the lateral​ (side) surface area of the cone generated by revolving the line segment y equals seven halves x ​, 0 less than or equals x less than or equals 5​, about the​ x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height

Answers

Answer:

[tex]Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

Step-by-step explanation:

Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

and which in our case, we can obtain the following:

[tex]y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }[/tex]

Recall as well that [tex]0\leq x\leq 5[/tex], which gives us the limits of integration:

[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]

If we compare it with the geometry formula:

Lateral surface of cone = [tex]\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }[/tex]

which is exactly the expression we calculated with the integral.

If a varies inversely with b, and a=12 when b=1/3, find the equation that relates a and b

Answers

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.
A) List all outcomes in the event A that all three vehicles go in the same direction.
B) List all outcomes in the event B that all three vehicles take different directions.C) List all outcomes in the event C that exactly two of the three vehicles turn right.D) List all outcomes in the event D that exactly two vehicles go in the same direction.E) List outcomes in D'.F) List outcomes in C ∪ D.G) List outcomes in C ∩ D.

Answers

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Someone pls help me

Answers

The slope greater than one would be the last image, because for every step in x, you get more than one y step.

The slope between 1 and 0 would be the second image

And the slope less than 0 would be the third image

a city grid of Anytown, USA is shown on the grid below the fire department is represented by the quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid below to represent two vertices of the new?fire Department quadrilateral ABCD:

What could be the ordered pairs of representing vertices C and D of quadrilateral ABCD so that the new fire department to congruent to the old fire department?

Answers

Answer:

C(1, 1)D(4, 1)

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Average rate of change from G from x=1 to x=4 is

Answers

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Compute the critical value z Subscript alpha divided by 2 that corresponds to a 86​% level of confidence.

Answers

Answer:

z = 1.476

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.86}{2} = 0.07[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]

The answer is z = 1.476

What is the measure of BAC ? Pls help

Answers

Answer:  m∠BAC =36.87°

It is given, but maybe difficult to see.

Step-by-step explanation: If you had to calculate it yourself, you need a scientific calculator or a conversion chart. You could figure the sine by dividing the  length of the opposite side, 6 by the length of the hypotenuse, 10. you get sine=0.6  

Then use the calculator or chart to get the angle.

input sin^-1 (0.06)

Assume that T is a linear transformation. Find the standard matrix of T:R2→R2T:R 2→R 2 first rotates points through −3π/4−3π/4 radian (clockwise) and then reflects points through the horizontal x1x 1-axis.

Answers

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Thomas wants to invite Madeline to a party. He has an 80% chance of bumping into her at school. Otherwise, he’ll call her on the phone. If he talks to her at school, he’s 90% likely to ask her to a party. However, he’s only 60% likely to ask her over the phone. What is the probability of Thomas inviting Madeline to the party at school?

Answers

Answer:

84%

Step-by-step explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

[tex]P_1 = 20\% * 60\% = 12\%[/tex]

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

[tex]P_2 = 80\% * 90\% = 72\%[/tex]

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

[tex]P = P_1 + P_2[/tex]

[tex]P = 12\% + 72\% = 84\%[/tex]

Lisa is in charge of planning a reception for 3600 people. She is trying to decide which snacks to buy. She has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.



Favorite Snack Number of People



Brownies 32



Cookies 22



chips 56



other 65



Based on the above sample, predict the number of the people at the reception whose favorite snack will be chips. Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answers

Answer:

The expected number of the people at the reception whose favorite snack will be chips is 1152

Step-by-step explanation:

Given

The data in the above table and

Reception = 3600

Required

Predict the number of the people at the reception whose favorite snack will be chips.

The first step is to determine the total number of samples;

[tex]Total = Brownies + Cookies + Chips + Other[/tex]

[tex]Total = 32 + 22 + 56 + 65[/tex]

[tex]Total = 175[/tex]

The next step is to determine the fraction of people whose favorite is chips

[tex]Fraction = \frac{Chips}{Total}[/tex]

[tex]Fraction = \frac{56}{175}[/tex]

The product of the above fraction and the expected number of people in the reception is the solution to this question;

[tex]Expected\ Number = \frac{56}{175} * 3600[/tex]

[tex]Expected\ Number = \frac{56* 3600}{175}[/tex]

[tex]Expected\ Number = \frac{201600}{175}[/tex]

[tex]Expected\ Number = 1152[/tex]

Hence, the expected number of the people at the reception whose favorite snack will be chips is 1152

Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years. Set up the two equations that can be used to find each of their ages. Constraint 1: The solution must satisfy the ratio of their ages. Constraint 2: The solution must satisfy the sum of their ages. Only constraint would be met if Mrs. Lang is 32 and Jill is 8. Only constraint would be met if Mrs. Lang is 45 and Jill is 15.

Answers

Answer:

The two equations that can be used to find each of their ages are [tex]x=4 \times y[/tex] and [tex]x+y=60[/tex] .

Step-by-step explanation:

We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.

Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.

Now, according to the question;

The first condition states that Mrs. Lang is 4 times as old as her daughter Jill, that means;

                                     [tex]x=4 \times y[/tex]   ----------------- [equation 1]

The second condition states that the sum of their ages is 60 years, that means;

                                 [tex]x+y=60[/tex]

                                [tex]4y + y = 60[/tex]     {using equation 1}

                                  [tex]5y=60[/tex]

                                   [tex]y=\frac{60}{5}[/tex]

                                   y = 12 years

Now, putting the value of y in equation 1 we get;

                               [tex]x=4 \times y[/tex]

                               [tex]x= 4 \times 12[/tex] = 48 years

Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.

Answer:

Mrs. Lang is 48 and her daughter is 12 years old.

Step-by-step explanation:

find the local and/or absolute extrema for the function over the specified domain. (Order your answers from smallest to largest x.) f(x)

Answers

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Which linear inequality is represented by the graph?
ysx-1
yzx-1
3 4 5
y< 3x - 1
y > 3x - 1

Answers

Answer:

y>3x -1 is the right answer

Find the surface area of this composite solid.

Answers

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

The correct is A to this question

g Steel used for water pipelines is often coated on the inside with cement mortar to prevent corrosion. In a study of the mortar coatings of the pipeline used in a water transmission project in California, researchers noted that the mortar thickness was specified to be 7/16 inch. A very large sample of thickness measurements produced a mean equal to 0.635 inch and astandard deviation equal to 0.082 inch. If the thickness measurements were normally distributed, approximately what proportion were less than 7/16 inch?

Answers

Answer:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.635,0.082)[/tex]  

Where [tex]\mu=0.635[/tex] and [tex]\sigma=0.032[/tex]

We are interested on this probability

[tex]P(X<0.4375)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Based only on the given information, it is guaranteed that AD = CD.

Answers

Answer:

Not really, actually it depends on the shape given whether it's a rectangle, a square etc. Because you can't conclude that the shape of a rectangle with such dimensions could be guaranteed.

Determine whether the sequence is arithmetic, geometric, or neither:
-2, -4,-8, -16,...
a) arithmetic b)geometric
c) neither

Answers

The answer is B it’s B BBbBbBbBbBbBbBbBbBbBbbbb

Answer:

b)  geometric

Step-by-step explanation:

Notice that each new term is derived by multiplying the previous term by 2.  Thus:  the first term is -2 and the common ratio is 2.  This is a geometric sequence.

What is the horizontal asymptote of the function f (x) = StartFraction (x minus 2) Over (x minus 3) squared EndFraction?

Answers

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

What is an asymptote?

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

What is the horizontal asymptote?

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

How to solve this problem?

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

Learn more about horizontal asymptotes here -

https://brainly.com/question/14357352

#SPJ2

Answer:

c

Step-by-step explanation:

Maria’s office is located at (–7,–5) on the coordinate plane. Her home is located at (4,–6) and the supermarket is located at (–2,–6). When returning back from the office, she first goes to the supermarket to buy some groceries, and then goes back home. Find the total distance she traveled from her office to home.

Answers

Answer:

Total distance= 15.055 unit

Step-by-step explanation:

Distance between the first journey i.e from her office to the supermarket is calculated as follows given the coordinates.

(-5,-7) and (4,-6)

The distance between those tow points

Is

= √((4-(-5))² +( (-6)-(-7))²)

= √(9²+1²)

= √ 81+1

= √ 82

= 9.055

Noe the distance between the second journey traveled i.e from the supermarket to her house is calculated as follows given the coordinates.

(4,-6) and (-2,-6)

Distance= √((4--2)² +( -6--6)12

Distance = √(4+2)² + 0

Distance = √ 6²

Distance = 6

Total distance= 9.055 + 6

Total distance= 15.055

anyone mind lending a helping hand (asap!?!?)

Answers

Answer:

Q9 X=42.5

Step-by-step explanation:

let unknown angle be x

cos x=45/61

X=cos^-1 45/61

X=42.463...

X=42.5 (1 decimal place)

Please help me the venn diagram is wrong too im confused on how to do this :(((

Answers

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

A chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth. Because there might be variability from one bolt to another, the chemist decides to use a randomized block design, with the bolts of cloth considered as blocks. She selects five bolts and applies all four chemicals in random order to each bolt. The resulting tensile strengths follow. Analyze the data from this experiment (use α = 0.05) and draw appropriate conclusions.



Bolt


Chemical 1 2 3 4 5


1 73 68 73 71 67


2 73 67 75 72 70


3 75 68 78 73 68


4 73 71 75 75 69

Answers

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate

Answers

Answer:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=25, p=0.85)[/tex]  

The probability mass function for the Binomial distribution is given as:  

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

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

What is the equation of the line that is parallel to the given line and passes through the point (12, -2)? A) y = -6/5x + 10 B) y= -6/5x + 12 C) y = -5/6x -10 D) y = 5/6x - 12

Answers

Answer:

D

Step-by-step explanation:

Parallel lines are those that have the same slope, or coefficient of x.

Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):

slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6

So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.

The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.

Here, our slope is 5/6 and our given point is (12, -2). So plug these in:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-2)=(5/6)(x-12)[/tex]

[tex]y+2=\frac{5}{6} x-10[/tex]

[tex]y=\frac{5}{6} x-12[/tex]

This matches D, so we know that it's the correct answer.

~ an aesthetics lover

The answer is D I just took the test

Solve the following system by substitution.

y = - 3x + 11
5x + y = 21

Answers

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Is 47 a prime number or composite?

Answers

Answer:

Prime number

Step-by-step explanation:

A prime number has 2 factors.

A composite number has more than 2 factors.

47 has the factors 1 and 47.

47 is a prime number.

Answer:

47 is prime.

Step-by-step explanation:

Its factors are 1 and 47.

If a number has only 2 factors, then it's prime.

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