Write the fraction below in its simplest form
5(x+6)5 (x-7) 5 (x+8)
15(x+6)⁹ (x−7)(x−8)
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Answer:

2

Step-by-step explanation:

1 + 1 = 2

I hope my answer helps you :)

Answer:

2 or Window

Step-by-step explanation:

1 + 1 = 2

OR

1 + 1 = WINDOW!

If the given function is f '(t) = 16/(1 + t²), the value of the function f will be f = 16 tan (t) - 24.8.

It is described as a particular kind of relationship with a set domain and range. Every value in the domain has a specific relationship with one value in the range, according to the function.

Given that,

f '(t) = 16/(1 + t²)

f(1) = 0

In order to find f integrate the function,

f = ∫(16/(1 + t²)) dt

f = 16 ∫1/(1 + t²) dt

f = 16 tan t + C

As, f(1) = 0

0 = 16 tan 1 + C

C = - 16(1.55) = -24.8

Thus, the value of function is f = 16 tan (t) - 24.8.

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Answer:

2. ......................

Answer:

y = 2x - 7

Step-by-step explanation:

y = mx + b

m is known (m=2):

y = 2x + b

Since one point is known (3,-1), you can solve for b:

-1 = 2(3) + b

b = -7

So the equation is:

y = 2x - 7

The function that models the number of bottles, B, collected during week n is; B(n) = 256(¹/₂)ⁿ⁻¹

The formula for the nth term of a geometric sequence is;

aₙ = arⁿ⁻¹

where;

a is first term

r is common ratio

n is position of term

We are given that;

a = 256 bottles

r = ¹/₂

Thus;

B(n) = 256(¹/₂)ⁿ⁻¹

Thus, we conclude that B(n) represents the required function.

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Answer:

D

Step-by-step explanation:

If 48 times 1/4 is 12, 12 divided by 1/4, the inverse operation, is 48.

The surface area of the cube is increasing at a rate of 49 cm²/min.

If the length of an edge of a cube is l cm.,

its volume V is l3 and surface area A is 6l2.

Differentiating V=l3 w.r.t. time,

we get,

dV/dt = 3l2dldt

dV/dt=10 cm3min,

when l=90

dl/dt=103×902

=12430

As A=6l2

dA/dt =12l×dldt

=12×90×12430

=49 cm2min

The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume.

It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth.

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Answer:

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

Add up all the numbers to get the end of month figure.

Convert mixed fractions to sum of whole and fractions, then combine whole numbers and fractions, bringing all to common denominator of 16.

A total of 112 combinations are possible out of all possible combinations  when a coin is tossed  10 times and having total of 4 tails and have different start and end faces.

For the given question we have 2 conditions:

condition 1:

when the start turn have head face then the end turn must have tails face as it is given that start and end have different faces.

so in this case 1st and last position is fixed so we have exactly 8 positions.

and given that out of 10 times there must be total of 4 tails and we discussed that last face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.

so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is = 8 combination 5  = [tex]8_C__5[/tex] =56 ways

conditon 2:

 when the start turn have tail face then the end turn must have head face as it is given that start and end have different faces.

so in this case 1st and last position is fixed so we have exactly 8 positions

and given that out of 10 times there must be total of 4 tails and we discussed that first face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.

so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is =8 combination 5 =  [tex]8_C__5[/tex] =56 ways

so total number of ways is = no. of ways condition 1+ no. of ways condition 2 = 56 +56 = 112 ways

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The answer is 0.109, or choice B. The probability that only six of 8 Internet users buy their clothes exclusively online is 0.109.

The probability that only 6 out of 8 Internet users buy their clothes exclusively online can be calculated using the binomial distribution. The probability of a single Internet user buying their clothes exclusively online is 0.5, and the probability of an Internet user not buying their clothes exclusively online is 0.5.

The probability of 6 out of 8 Internet users buying their clothes exclusively online can be calculated using the formula:

P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2

Plugging in the values, we get:

P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2

= 28 * (0.5)^6 * (0.5)^2

= 28 * (0.015625) * (0.25)

= 0.109

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Complete Question:

Fifty percent of the people that use the Internet buy their clothes exclusively online. Find the probability that only six of 8 Internet users buy their clothes exclusively online. Round to three decimal places.  explain answer in 100 words.

A. 0.750

B. 0.109

C. 0.438

D. 0.004

Answer: 20 days

Step-by-step explanation:

First, we find the food provisioned for 1 man will last for how many days

Take 80 times 30 = 2400 days

Now we know that 40 more joined

80 + 40 = 120 serve

So, we take 2400 divided by 120 = 20 days

Answer:

16%

Step-by-step explanation:

Let's assume the original price of the item was Rs. 100.

After the price increased by 45%, the new price became:

New price = Original price + (45% of Original price)

New price = 100 + (0.45 x 100)

New price = Rs. 145

Now, the price dropped by 20% from the increased price of Rs. 145:

Final price = New price - (20% of New price)

Final price = 145 - (0.2 x 145)

Final price = Rs. 116

We can calculate the overall change in price by finding the difference between the final price and the original price:

Overall change in price = Final price - Original price

Overall change in price = 116 - 100

Overall change in price = 16

So, the price increased by Rs. 16. To find the percentage increase, we can use the formula:

Percentage increase = (Overall change in price / Original price) x 100%

Plugging in the values, we get:

Percentage increase = (16 / 100) x 100%

Percentage increase = 16%

Therefore, the price of the item increased by 16%.

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The percentage by which the price increased is; 16%

Percentage Increase

Let the price of an item be denoted as x

Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x

Now, the price after inflation decreased by 20% or 0.2. Thus;

Final price is now; 1.45x(1 - 0.2)

⇒ 0.8(1.45x)

⇒ 1.16 x

Since the original price is x, then;

Difference in price = 1.16x - x

Difference in price = 0.16x

In percentage, this difference in price represents a 16% increase.

The complete question is;

Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?

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Answer: The sum of the first 75 terms for the following sequence is 10,200

Step-by-step explanation: To find the sum of the first 75 terms for the following sequence, we have to first find the 75th term for which the formula used here will be,

[tex]a_{75\\} = a_{1} + (n-1)d\\ = -10 + (74-1)(4)\\ = -10 + 292\\ = 282[/tex]

So, the 75th term of this arithmetic progression is 282

Now we will find the sum of the first 75 terms,

[tex]S_{n} = n(a_{1} + a_{75} )/ 2\\ =75(-10 + 282)/2\\ =75(272)/2\\ =20400/2\\ =10200[/tex]

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Answer:

y = 18 + 12x

Step-by-step explanation:

To find the total cost Mr. Montenegro pays in dollars when x shirts are ordered, we can use the equation y = 18 + 12x, where y is the total cost in dollars and x is the number of shirts ordered. This equation takes into account the delivery fee of $18 and the cost of each shirt, which is $12. Therefore, we can use the equation y = 18 + 12x to find the total cost Mr. Montenegro pays when he orders x shirts.

bit strings of length 12 contain a) exactly three 1s is 220 b) at most three 1s is 2700 c) atleastthree1s is 220 d) an equal number of 0s and 1s is 66.

a) To calculate the number of bit strings of length 12 containing exactly three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3).The solution is 12C3 = 220.

b) To calculate the number of bit strings of length 12 containing at most three 1s, we can use the summation formula. The formula is sum of nCr, where n is the total number of bits (12) and r is the number of 1s (3). So, the answer is (12C0 + 12C1 + 12C2 + 12C3) = 2700.

c) To calculate the number of bit strings of length 12 containing at least three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3). The solution is 12C3 = 220.

d) To calculate the number of bit strings of length 12 containing an equal number of 0s and 1s, we can use the combination formula. The formula is nCr

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There can be 8 possible outcomes present in the sample space

The probability that one switch is not working is 3% or 0.03

We need to find the number of possible outcomes in the sample space that can be possible

The first switch can be working or not

The second switch might be working or not

so does the third switch, it might be working or not working

And each switch is independent to one another

The number of outcomes can be

2 x 2 x 2 = 8

Therefore, the number of outcomes are there in the sample space is 8

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Answer:

60

Step-by-step explanation:

Let x = number of people at the party.

0.9x wore red dresses.

2/25x wore green dresses.

rest of people wore white dresses

The rest of the people is

x - 0.9x - 2/25 x

x - 0.9x - 0.08x = 15

0.02x = 15

x = 750

0.9x = 675 (red)

2/25 x = 60 (green)

0.02x = 15 (white)

Answer: 60

The number of homes in a community of 12, 000 which would be heated by electricity, given the rate of houses heated, is c. 3,360 homes

To find the number of homes in the community which would be heated by electricity, first find the percentage of homes that are heated according to the U.S. Census :

= Number of houses heated / Total number

= 7 / 25

= 28 %

When given a community of 12, 000 homes therefore, the number of homes which would be heated are:

= Percentage of houses heated x Community size

= 28 % x 12, 000

= 3,360 homes

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Answer:

c. 3,360 homes

Step-by-step explanation:

The approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) is [tex]-\frac{2}{3}[/tex]

As per the given data we have determine the value of approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y).

A contour or a contour line may be defined as the line of intersection of a level surface with the surface of ground.

This means every point on a contour line has the same altitude as that of the assumed intersecting surface.

The set of the curves f(x, y)=c

From the given contour plot the curves intersects with the line y = 5 are f( x,  y ) = 12 and f (x, y) = 10

f(x, y) = 12 intersects the line y = 5 at the point x = 3

So, f(3,5) = 12

f(x, y) = 10 intersects the line y = 5 at the point x = 6

so, f(6,5) = 10

[tex]$f_x(3,5)= \lim _{h \rightarrow 0} \frac{f(3+h, 5)-f(3,5)}{h}$[/tex]

Where approximate h = 3

[tex]f_x(3,5) & =\frac{f(3+3,5)-f(3,5)}{3}[/tex]

[tex]=\frac{f(6,5)-f(3,5)}{3}[/tex]

[tex]=\frac{10-12}{3}[/tex]

[tex]f_x(3,5) & =\frac{-2}{3}[/tex]

Therefore the answer is [tex]-\frac{2}{3}[/tex].

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Approximate  [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) shown below.

Diagram attached at the end of solution

Answer:

y > -2/3x + 2, y [tex]\geq[/tex] x

[tex]\left \{ {{y > -2/3x + 2} \atop {y \geq x}} \right.[/tex]

Step-by-step explanation:

Knowledge Needed

A system of linear inequalities is graphing 2 lines.

If the line's y side is less than it's x-side (y </ [tex]\leq[/tex] x), shade below.

If the line's y side is greater than it's x-side (y </ [tex]\leq[/tex] x), shade above.

If the line is dotted, it is < or >.

If the line is filled in, it is [tex]\leq[/tex] or [tex]\geq[/tex].

Where both regions are shaded is the solution.

Question

Examine the dotted line.

1) We know it is < or > because it is dotted.

2) We know it is y > .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 2.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is -2/3.

y > -2/3x + 2

Examine the solid line.

1) We know it is [tex]\geq[/tex] or [tex]\leq[/tex] because it is solid.

2) We know it is y [tex]\geq[/tex] .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 0.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is 1.

y [tex]\geq[/tex] 1x + 0

y [tex]\geq[/tex] x

The solution to the linear inequality is when both lines are shaded in (true), which means both lines are the solution together.

y > -2/3x + 2, y [tex]\geq[/tex] x

Answer:

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

Find the lines first, then determine inequalities based on the shaded region and types of lines.

One line has positive slope and passes through the origin. Its x and y-coordinates are same, hence it is:

The shaded region is above this line and the line is solid, therefore the inequality is:

The second line has a negative slope and it has y-intercept at (0, 2), x- intercept at (3, 0).

Its slope is m = (0 - 2)/(3 - 0) = - 2/3.

So the line is:

Again, the shaded region is above the line, and the line is dashed, hence the inequality is:

Answer:

h = 20 mean h can only be 20

h < 20 means h can only be a number that is smaller than 20, can't be exactly 20

Step-by-step explanation:

h = 20

This means the variable h can only be 20; it can't be lower or higher than 20.

h < 20

This means the variable h can only be smaller than 20; this means the number can only be below 20 and can't be exactly 20.

Joan saved a total of $78 from her $390 weekly income each week.

What is percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage means 1 part from hundreds and represented by the symbol '%'. Percentages have no dimensions. Therefore, it is called a dimensionless number.

Percentage = (value/total value)× 100

We have, Joan's income = $390/week

Saving = 20% from her weekly salary.

We have to calculate how much does she save each week. Joan save 20% of her weekly income (i.e $390). let Joan saved $x each week from her sallary. The saved income in dollars each week by Joan i.e ($x) is equals to 20% of 390

x =( 20/100)× 390

=> x = 390/5

=> x = 78

Hence, Joan saves $78 each week.

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Answer: Solution: 0.625

Step-by-step explanation: First, you have to set up the fraction as a division problem, so we have to remember that when making a fraction to a decimal, the numerator becomes the dividend, and the denominator becomes the divisor, which the dividend goes inside the bracket, and the divisor goes outside the bracket. Now, you would divide as usual, and get 0.625. I hoped this helped!  NOTE: I put in an attachment to show what I'm talking about.

Answer:

Step-by-step explanation:  do 5÷8 and u get 0.625

Answer:

  45

Step-by-step explanation:

You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.

From the first point, 9 segments can be drawn.

From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)

From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:

  9(10)/2 = 45

45 line segments can be drawn.

__

Additional comment

This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.

Answer: C -  square root of 74

Step-by-step explanation: took the test and got it right. hope this helps.

have a good day :)

Answer:

[tex]\sqrt{74}[/tex]

Step-by-step explanation:

A correct statement about sampling distributions is: Sampling distributions of means get closer to normality as the sample size increases.

The correct answer is an option (A)

In this question we have been given few statements.

We need to select a correct statement about sampling distributions.

We know that the sampling distribution is nothing but a probability distribution that is obtained through repeated sampling of a specific population.

Also according to central limit theorem, sampling distribution of means approaches normal when the sample size increases.

Therefore Sampling distributions of means get closer to normality as the sample size increases.

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Answer:

y = -6x - 4

Step-by-step explanation:

Slope intercept form:

y = mx + b

m is the slope

b is the y-intercept

To find the slope, you take two points from the line and plug them into the following equation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Let's use (0, -4) and (-2, 8):

[tex]\frac{8-(-4)}{-2-0} = \frac{12}{-2}=-6[/tex]

So m = -6

We know that the y-intercept (b) is -4, so we can plug everything into the equation:

y = -6x - 4

Answer:

40

Step-by-step explanation: