312 Algebra 1 - 4th Nine Weeks
ASSIGNMENT
Simplify the rational
6x(x+3)(x-2)
3(x-2)(x +9)

complete question:

If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?

A parallelogram with a base of 10 centimetres and a height of 8 centimetres.

Answer:

area = 48 cm²

Step-by-step explanation:

A parallelogram is quadrilateral with 4 sides formed by 2 pair of parallel lines. The area of a parallelogram is represented as follows :

area of parallelogram =  B × H

where

B = breadth

H = height

According to the question the height and the base each reduced by 2 cm.

The new base = 10 - 2 = 8 cm

The new height = 8 - 2 = 6 cm

area = B × H

area = 8 × 6

area = 48 cm²

Answer:

The correct answer is 161700.

Step-by-step explanation:

Total number of members of the senate of 107th congress is 100 in which there are 53 republicans, 42 democrats and 5 independents.

A new committee is to be formed from these 100 congressmen to study the benefits of arts in education.

Number of senators required to head the new committee is 3.

Therefore total number of ways 3 members are selected in the population of 100 congressmen is given by [tex]\left[\begin{array}{ccc}100\\3\end{array}\right][/tex] = 161700.

Thus there are 161700 ways one can select 3 senators to head a committee.

High Risk because returns are not guaranteed, but time frames are set

—Speculation

Moderate Disk because expectations of returns are reasonable and average

—Growth

Low Risk because of steady Interest without fluctuation in value

—Savings

In investment terms, growth corresponds to high risk as returns aren't guaranteed, savings relate to low risk due to steady interest income, and speculation signifies moderate risk as it has reasonable return expectations.

The types of investment can be associated with different levels of risk as follows:

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Answer:

The sidewalk moves at 0.5 ft/sec

Josie's speed walking on a non-moving ground is 3.5ft/sec

Step-by-step explanation:

Let x represent the speed of the side walk and y represent her walking speed

It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk

Distance = speed × time

176 = (x+y)×44

44x+44y = 176

x+y = 4 .......1

It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction).

21 = (y-x)7

7y - 7x = 21

y - x = 3 ......2

Add equation 1 to 2

2y = 7

y = 3.5 ft/sec

From equation 1

x + y = 4

x = 4 - 3.5 = 0.5

x = 0.5 ft/sec

The sidewalk moves at 0.5 ft/sec

Josie's speed walking on a non-moving ground is 3.5ft/sec

Answer: Josie's speed walking on a non-moving ground is 3.5 ft/sec

The side walk moves at 0.5 Ft/sec

Step-by-step explanation:

Let x represent Josie's speed walking on a non-moving ground.

Let y represent the speed of the sidewalk.

It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It means that the total speed at which she moved is

(x + y) ft/sec

Distance = speed × time

Therefore,

176 = 44(x + y)

Dividing both sides by 44, it becomes

4 = x + y- - - - - - - - - - - - - -1

It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction). It means that the total speed at which she moved is (x - y) ft/sec

Therefore,

21 = 7(x - y)

Dividing both sides by 7, it becomes

3 = x - y- - - - - - - - - - - - - -2

Adding equation 1 and 2, it becomes

7 = 2x

x = 7/2 = 3.5 ft/sec

Substituting x = 3.5 into equation 2, it becomes

3 = 3.5 - y

y = 3.5 - 3 = 0.5 ft/sec

Given:

The length of a rectangle is 5 less than its width.

The area of the rectangle is 84 square feet.

We need to determine the quadratic equation in standard form that represents the area of the rectangle.

Dimensions of the rectangle:

Let l denote the length of the rectangle.

Let w denote the width of the rectangle.

Since, it is given that the length is 5 less than its width, it can be written as,

[tex]l=5-w[/tex] and [tex]w=w[/tex]

Area of the rectangle:

The area of the rectangle can be determined using the formula,

[tex]A=length \times width[/tex]

Substituting A = 84, [tex]l=5-w[/tex] and [tex]w=w[/tex], we get

[tex]84=(5-w)\times w[/tex]

[tex]84=5w-w^2[/tex]

Adding both sides of the equation by w², we have;

[tex]w^2+84=5w[/tex]

Subtracting by 5w on both sides, we get;

[tex]w^2-5w+84=0[/tex]

Thus, the quadratic equation in standard form for the area of the rectangle is [tex]w^2-5w+84=0[/tex]

The level of production (x) that will maximize the profit is approximately 36 units.

The profit is the revenue (R(x)) minus the cost (C(x)). So, we have:

P(x) = R(x) - C(x)

Given Functions:

Cost Function: C(x) = 45,000 + 100x + x³ dollars

Revenue Function: R(x) = 4000x dollars

Substitute the given functions into the profit function:

P(x) = R(x) - C(x)

P(x) = 4000x - (45,000 + 100x + x³)

P(x) = 4000x - 45,000 - 100x - x³

Simplify the profit function:

P(x) = -x³ + 3900x - 45,000

Find the critical points by differentiating the profit function and setting it to zero:

P'(x) = -3x² + 3900

Set P'(x) = 0 and solve for x:

-3x² + 3900 = 0

-3x² = -3900

x²= 1300

x = ±√1300

x = ±36.06

Evaluate the second derivative (P''(x)) to determine if these critical points are maxima or minima:

P''(x) = -6x

Substitute the critical points (x = ±36.06) into P''(x):

P''(x)= -6(36.06)

= -216.36 (negative value)

Since the second derivative is negative at x ≈ ±36.06, it confirms that x = 36.06 is a maximum point.

So, the level of production (x) that will maximize the profit is approximately 36 units.

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To determine the level of production that maximizes profit, we calculate the profit function, differentiate it to find critical points, and then identify the maximum. The critical points are found by setting the first derivative of the profit function to zero and solving for x.

To determine the level of production x that will maximize the profit for the manufacturer, we first need to calculate the profit function. Profit, P(x), is the difference between total revenue, R(x), and total cost, C(x).

The profit function is defined as P(x) = R(x) - C(x). Using the given cost function C(x) = 45,000 + 100x + x^3 dollars and the revenue function R(x) = 4000x dollars, we get:

P(x) = 4000x - (45,000 + 100x + x^3)

This simplifies to:

P(x) = -x^3 + 3900x - 45,000

To find the production level that maximizes profit, we need to determine the critical points by differentiating P(x) and setting the derivative equal to zero. The derivative of P(x) is:

P'(x) = -3x^2 + 3900.

Setting P'(x) = 0 gives:

-3x^2 + 3900 = 0

Solving for x yields two critical points, but only one will maximize profit. We can find this maxima by testing which value of x gives the higher P(x) or by using the second derivative test. After finding the correct value of x, we round it to the nearest whole number as the final answer.

Answer:

C(2010) = $1312 using linear approximation.

Step-by-step explanation:

The full complete question is attached to this solution.

The full table is given as

Year | 1970 | 1980 | 1990 | 2000

Cash |$180 |$262 |$564 | $938

we are told to use linear approximation to obtain C(2010)

Linear approximation, Mathematically, results in

C(2010) = C(2000) + C'(t) [t]

where t = years since 2010 = (Year - 2000)

Linear approximation gives C'(t) as the rate of change of C with time

C'(t) = (ΔC/Δt)

We will be using the latest year for this approximation.

ΔC = C(2000) - C(1990) = 938 - 564 = $374

Δt = 2000 - 1990 = 10

C'(t) = (374/10) = $37.4 per year.

C(2010) = C(2000) + C'(t) [t]

t = 2010 - 2000 = 10

C(2000) = $938

C'(t) = $37.4 per year

C(2010) = 938 + (37.4)(10) = $1312

Hope this Helps!!!

The amount, C(2010), of cash per capita in circulation in the year 2010 = $1312.

The full table is given as

Year | 1970 | 1980 | 1990 | 2000

Cash |$180 |$262 |$564 | $938

we are told to use linear approximation to obtain C(2010)

Linear approximation, Mathematically, results in

C(2010) = C(2000) + C'(t) [t]

where t = years since 2010 = (Year - 2000)

Linear approximation gives C'(t) as the rate of change of C with time

C'(t) = (ΔC/Δt)

We will be using the latest year for this approximation.

ΔC = C(2000) - C(1990) = 938 - 564 = $374

Δt = 2000 - 1990 = 10

C'(t) = (374/10) = $37.4 per year.

C(2010) = C(2000) + C'(t) [t]

t = 2010 - 2000 = 10

C(2000) = $938

C'(t) = $37.4 per year

C(2010) = 938 + (37.4)(10) = $1312.

Complete question:

Sample space for the experiment is {B, E, I, L , R , S, T }  .

Hence option D is correct.

Given, that the word IRRESISTIBLE .

An experiment consist of selecting a letter at random from the letters in the given word.

The number of distinct letters in the word is 7 i.e I is 3 times in the word but consider it as single letter.

Therefore the appropriate sample space for the experiment is {B, E, I, L , R , S, T } .

Thus the option D is correct.

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The sample space for an experiment consists of all possible outcomes or events that can occur. In this case, the experiment involves selecting a letter at random from the letters in the word "IRRESISTIBLE."

The appropriate sample space for this experiment would be the set of all individual letters that can be selected from the word. Therefore, the sample space is:

Sample space = {I, R, E, S, T, I, B, L}

Each element of the sample space represents a possible outcome of the experiment, which is selecting a specific letter from the word "IRRESISTIBLE."

It is important to note that the sample space only includes the individual letters as outcomes, and it does not consider the order or repetition of the letters in the word.

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Answer: [tex].47[/tex]

3 tenths is written as

Decimal: [tex].3[/tex]

Fraction: [tex]\frac{3}{10}[/tex]

17 hundredths is written as

Decimal: [tex].17[/tex]

Fraction: [tex]\frac{17}{100}[/tex]

Add

[tex]3/10+17/100[/tex]

[tex]=.47[/tex]

Fraction Form

[tex].47=\frac{47}{100}[/tex]

Answer:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]

And replacing we got:

[tex] E(X) = 1*0.05 +2* 0.3 +3* 0.4 +4*0.25 = 2.85[/tex]

So we are going to expect about 2,85 automobiles for this case.

Step-by-step explanation:

For this case we define the random variable X as "number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.)" and we know the distribution for X is given by:

X         1         2       3         4

P(X)  0.05  0.30  0.40   0.25

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete

For this case we can calculate the epected value with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]

And replacing we got:

[tex] E(X) = 1*0.05 +2* 0.3 +3* 0.4 +4*0.25 = 2.85[/tex]

So we are going to expect about 2,85 automobiles for this case.

The expected number of automobiles at Lakeside Olds at opening time can be calculated as a weighted average, resulting in an expectation of approximately 3 cars.

The expected number of automobiles lined up at Lakeside Olds at opening time would be calculated by multiplying each number of automobiles by its respective probability and then adding up those products. This is essentially calculating a weighted average.

So for the given data:

Add up those results: 0.05 + 0.60 + 1.20 + 1.00 = 2.85. Thus, on a typical day, Lakeside Olds should expect approximately 3 automobiles to be lined up at opening time.

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Answer:

0.6848

Step-by-step explanation:

Mean of \hat{p} = 0.453

Answer = 0.453

Standard deviation of \hat{p} :

= \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.453(1-0.453)}{100}} = 0.0498

Answer = 0.0498

P(0.0453 - 0.05 < p < 0.0453 + 0.05)

On standardising,

= P(\frac{0.0453-0.05-0.0453}{0.0498} <Z<\frac{0.0453+0.05-0.0453}{0.0498})

= P(-1.0044 < Z < 1.0044) = 0.6848

Answer = 0.6848

Using the Central Limit Theorem, it is found that the mean of the sampling distribution of the sample proportions is 0.453.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem:

By the Central Limit Theorem, the mean is [tex]\mu = p = 0.453[/tex].

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The relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is not irreflexive, asymmetric, or intransitive.

To determine whether the relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is irreflexive, asymmetric, or intransitive, we will analyze each property.

Therefore, the relation R2 is none of the given properties (irreflexive, asymmetric, or intransitive).

Answer:

d AND C

Step-by-step explanation:

Answer:

D. 144 cubic meters

Step-by-step explanation:

Volume of triangular prism(V)= Area of a triangle(A)×height of the prism(H)

That is,

V=AH

Where,

A=Area of a triangle

H=Height of the prism

Given,

A=1/2× base×height=16 square meters

Height=9 meters

Therefore,

Volume of triangular prism=16 square meters×9 meters

=144 cubic meters

Answer: D. 144 cubic meters

Step-by-step explanation:

A triangular prism consists of 2 triangular faces(base) and 3 rectangular faces.

The formula for determining the volume of a triangular prism is expressed as

Volume = area of the triangular base × height of the prism

Area of triangular base = 1/2 base × height

From the information given,

Height of prism = 9 meters

Area of triangular base = 16 square meters

Volume of the triangular prism = 16 × 9 = 144 cubic meters

Answer:

44

Step-by-step explanation:

Input 8 into x

f(8)=6(8)-4

f(8)=48-4

f(8)=44

Answer:

p = 0.574197

Step-by-step explanation:

There are 14000 ballots left.

The lead is 2174, so he needs to lead at least 2175 in these 14000 ballots.

He does so if he gets at least 8088 votes.

If P(x >= 8088) = 0.20, then the corresponding z score to this is, by table/technology,

z = 0.841621234

Now, as

z = (x - u) / s

and

u= n p

s = sqrt(n p(1-p))

Then

0.841621234 = (8088 - 14000*p) / sqrt(14000p(1-p))

Solving for p here,  

p = 0.574197

Answer:

21 weeks.

Step-by-step explanation:

To start, you have to get the pounds lost per week.

12/3=4

4 pounds lost per week.

Next, find out how many weeks it takes by solving this equation,

4x=84

Divide 84/4=21

Therefore, it took 21 weeks to lose 84 pounds.

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

Equations

The following equation will be solved

[tex]\displaystyle \frac{2}{x+3}-\frac{3}{4-x}=\frac{2x-2}{x^2-x-12}[/tex]

Changing signs of the second term on the left side

[tex]\displaystyle \frac{2}{x+3}+\frac{3}{x-4}=\frac{2x-2}{x^2-x-12}[/tex]

Operating

[tex]\displaystyle \frac{2(x-4)+3(x+3)}{x^2-x-12}=\frac{2x-2}{x^2-x-12}[/tex]

Simplifying denominators, provided

[tex]x^2-x-12\neq 0[/tex]

[tex]2(x-4)+3(x+3)=2x-2[/tex]

Operating

[tex]2x-8+3x+9=2x-2[/tex]

Solving

[tex]\boxed{x=-1}[/tex]

Since

[tex](-1)^2-(-1)-12=-10\neq 0[/tex]

Solution (1)

Answer:

  y = 2x^2 -x -3

Step-by-step explanation:

It can be convenient to use the quadratic regression capability of a graphing calculator or spreadsheet. That's what we did in the attachment.

__

Fill in the given points in the equation to find three linear equations in a, b, c.

  3 = a(2^2) +b(2) +c

  7 = a(-2)^2 +b(-2) +c

  -2 = a(1^2) +b(1) +c

Subtracting the last equation from the first two gives ...

  (3) -(-2) = (4a +2b +c) -(a +b +c)   ⇒   5 = 3a +b

  (7) -(-2) = (4a -2b +c) -(a +b +c)   ⇒   9 = 3a -3b . . . . . [eq5]

Subtracting the second of these equations from the first gives ...

  (5) -(9) = (3a +b) -(3a -3b)   ⇒   -4 = 4b

  b = -1

Dividing [eq5] by 3 gives ...

  3 = a - b

  3 = a -(-1)

  2 = a

Using the original 3rd equation, we have ...

  -2 = a +b +c

  -2 = 2 +(-1) + c

  -3 = c . . . . . . . . subtract 1

The desired quadratic is ...

  y = 2x^2 -x -3

Final answer:

The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.

Explanation:

The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:

[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]

To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.

After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.

Answer:

28.57℅

Step-by-step explanation:

If last year attendance was 860 and the attendance increases to 1204:

Attendance increment = 1204-860

= 344

%increase = increment/current attendance × 100%

% increase = 344/1204 × 100

℅ increase = 34400/1204

% increase = 28.57%

Therefore the percentage increase from last year is 28.57℅

Step-by-step explanation:

By definition, the area of a rectangle is given by:

A = w * lA=w∗l

Where,

w: width of the rectangle

l: length of the rectangle

We then have the following expression for the area:

A = k ^ 2 + 19k + 60A=k

2

+19k+60

What we must do is factorize the expression following the following steps:

1) Find two numbers that are equal to 19

2) Find two multiplied numbers equal to 60

We have then:

A = (k + 15) (k + 4)A=(k+15)(k+4)

Therefore, the width of the rectangle is:

w = (k + 4)w=(k+4)

Answer:

Thats correct! The answer is B. (2nd option.) I took edge.

Step-by-step explanation:

Answer:

t = -2.69 , p = 0.0078

Step-by-step explanation:

We have the following data:

Sample Mean = x = 24.444

Sample Standard Deviation = s = 2.45

Sample size = n = 18

Josh wants to test that mean number is lesser than 26. So our test value is 26 i.e.

u = 26

Since Josh wants to test that mean would be fewer than 26, so this would be a left tailed test with a less than sign in Alternate Hypothesis. Therefore, the hypothesis would be:

[tex]H_{o}: u\geq 26\\H_{a}: u<26[/tex]

Since, we do not know the value of Population standard deviation, and we have the value of sample standard deviation, we will use One-Sample t-test for the population mean.

The formula to calculate the test-statistic would be:

[tex]t=\frac{x-u}{\frac{s}{\sqrt{n}}}[/tex]

Substituting the values in this formula gives us:

[tex]t=\frac{24.444-26}{\frac{2.45}{\sqrt{18}}}\\t=-2.69[/tex]

This means, the test statistic would be -2.69

Since, the sample size is 18, the degrees of freedom would be:

Degrees of freedom = df = n - 1 = 17

To find the p-value we need to check the p-value against test statistic of 2.69, with 17 degrees of freedom and One-tailed test. This value comes out to be:

p-value = 0.0078

Therefore, the correct answer would be:

t = -2.69 , p = 0.0078

Answer:

33.66 cm

Step-by-step explanation:

Multiply to find the product.

Answer:

20 knives

Step-by-step explanation:

the ratio of fork to knives is [tex]\frac{4}{5}[/tex] and their are 16 forks, so we put the ratio of fork and knives equal to number of fork and knives so its:

[tex]\frac{4}{5}[/tex] = [tex]\frac{16}{x}[/tex]  We cross multiply

80 = 4x Divide both  side by 4

x = 20

we can check too

16/20 if we simplify, its give us 4/5

There are 20 knives in Isabella's kitchen.

The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5.

Given that there are 16 forks in the drawer, we can set up a proportion to find the number of knives:

4/5 = 16/X

Cross multiply to get: 4X = 80

Divide by 4 to find X = 20

Therefore, there are 20 knives in Isabella's kitchen drawer.

Answer:

x/2=5+4=9

x=9*2=18

x=18!

Answer:

4

Step-by-step explanation:

The sum of the first n terms of a geometric series is:

S = a₁ (1 − r^n) / (1 − r)

Given n = 6, S = 15624, and r = 5:

15624 = a₁ (1 − 5^6) / (1 − 5)

a₁ = 4

Final answer:

The answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.

Explanation:

Can Segments Form a Triangle?

To determine if the segments with lengths of 1 and 8 can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have two sides that are each 8 units long, and one side that is 1 unit long.

Let's add the lengths of the two shorter segments: 1 + 8 = 9.

This sum is greater than the length of the other segment, which is 8. Now, we will check the sum of the other two possible pairs:

Since all combinations of the sums of two sides are greater than the third side, these segments can indeed form a triangle.

Thus, the answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.

Answer:

a. The percentage of adult men that will fit through the door without bending is 0.

b.  The percentage of adult women that will fit through the door without bending is 0.

c. No, it is not adequate. There must be another technical reasons to not use a larger door.

d. The doorway height that would allow 60% of men to fit without bending is 70.1 inches.

Step-by-step explanation:

a. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of men's height N(μ=69.5, σ=2.4).

We can calculate the z-score as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-69.5}{2.4}=\dfrac{-17.9}{2.4}=-7.4583[/tex]

[tex]P(X<51.6)=P(z<-7.4583)=0[/tex]

The percentage of adult men that will fit through the door without bending is 0.

b. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of women's height N(μ=63.8, σ=2.6).

We can calculate the z-score as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-63.8}{2.6}=\dfrac{-12.2}{2.6}=-4.6923[/tex]

[tex]P(X<51.6)=P(z<-4.6923)=0[/tex]

The percentage of adult women that will fit through the door without bending is 0.

c. No, it is not adequate. There must be another technical reasons to not use a larger door.

d. We can calculate this finding a z-value z1 for which P(z<z1)=0.60.

Looking in a standard normal distribution table, the value for z1 is z1=0.25335.

Then, transforming to our adult men's height distribution, we have:

[tex]X=\mu+z\sigma=69.5+0.25335*2.4=69.5+0.6=70.1[/tex]

The doorway height that would allow 60% of men to fit without bending is 70.1 inches.

Answer 39916800

Step-by-step explanation:

The probability that all hip-hop songs are played consecutively is 0.18%.

To calculate the probability that all hip-hop songs are played consecutively, to consider the total number of possible song arrangements and the number of arrangements where all hip-hop songs are consecutive.

The total number of song arrangements calculated using the concept of permutations. Since there are a total of 11 songs on the playlist, the number of possible arrangements is 11!.

Now, let's calculate the number of arrangements where all hip-hop songs are played consecutively treat the 6 hip-hop songs as a single unit or block. This means  6! ways to arrange the hip-hop songs within that block.

Since we have 5 rock songs remaining, we can arrange them in 5! ways.

Therefore, the total number of arrangements where all hip-hop songs are played consecutively is 6! ×5!.

To calculate the probability, we divide the number of favorable outcomes (where all hip-hop songs are played consecutively) by the total number of possible outcomes:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = (6! × 5!) / 11!

Calculating the numerical value:

Probability = (720 × 120) / 39,916,800

Probability ≈ 0.00180

To know more about probability here

https://brainly.com/question/32117953

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