Assume the heights in a male population are normally distributed with mean 70.3 inches and standard deviation 4.1 inches. If a randomly selected male’s height is at the 75th percentile, how tall is he (to the nearest tenth of an inch)?

Answer:

x =1

Step-by-step explanation: Correct solution

[tex]4=-2(x-3) \\\\\mathrm{Switch\:sides}\\-2\left(x-3\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x-3\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x-3=-2\\x-3+3=-2+3\\\\Simplify\\x = 1[/tex]

Answer:

(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Step-by-step explanation:

Given:

u = (−2, 3, 1)

=> u = -2i + 3j + k                           --------------------------(i)

v = (−1, −1, 2)

=> v = -i - j + 2k                                --------------------(ii)

3u − 2v − 4w = (3, 2, −3)

=> 3u − 2v − 4w = 3i + 2j - 3k             ------------------(iii)

(A) TO FIND THE VECTOR w

Let:

w = (a, b, c) = ai + bj + ck

(a) Substitute u, v and w into equation (iii)

3u − 2v − 4w = 3i + 2j - 3k

3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k

(b) Solve the equation in step (a) by opening the brackets and collecting like terms

(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k

open brackets

-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k

collect like terms

-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k

i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k

(c) Solve for a, b and c in step (b)

Comparing both sides of the equation, we have;

-4 - 4a = 3              ----------(*)

11 - 4b = 2              -----------(**)

-1 - 4c = -3             ------------(***)

From (*)

4a = -4 - 3

4a = -7

a = [tex]\frac{-7}{4}[/tex]

From (**)

4b = 11 - 2

4b = 9

b = [tex]\frac{9}{4}[/tex]

From (***)

-1 - 4c = -3

4c = -1 + 3

4c = 2

c = [tex]\frac{2}{4}[/tex]

c = [tex]\frac{1}{2}[/tex]

Remember that

w = (a, b, c)

w = ai + bj + ck

Therefore,

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(B) TO FIND -2u + 3v - 5w

Remember that;

u = (−2, 3, 1)

v = (−1, −1, 2),

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Substitute u, v, w into the expression as follows;

-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Expand

(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]

Collect like terms

(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])

Solve

([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Answer:

3663 bacteria

Step-by-step explanation:

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the sets be A and B

A = { 7 , 8 , 9 , 10 }

B = { 9 , 10 , 11 , 12 }

The intersection of sets A and B is the set of all ements which belongs to both A and B.

The intersection of sets A and N is denoted by ( A ∩ B ) and read as A intersection B.

A ∩ B = { 7 , 8 , 9 , 10 } { 9 , 10 , 11 , 11 , 12 }

Now, list the elements which are present in both sets. A ∩ B = { 9 , 10 }

Hope I helped!

Best regards!

Answer:

its a

Step-by-step explanation:

Answer:

The temperature drops 4° every hour

Step-by-step explanation:

Step 1:

24° ÷ 6

Step 2:

24 : 6 = 4 : 1

Answer:

4

Hope This Helps :)

Answer:

[tex]\boxed {\tt -4 \textdegree \ per \ hour }[/tex]

Step-by-step explanation:

This question asks us to find the average rate of change in temperature per hour.

Therefore, we must divide the temperature change by the hours.

[tex]rate \ of \ change =\frac{temperature \ change}{hours}[/tex]

The temperature dropped 24 degrees in 6 hours. Since it dropped, the change was negative.

[tex]temperature \ change = -24 \textdegree \\hours = 6 \ hours[/tex]

Substitute the values into the formula.

[tex]rate \ of \ change =\frac{-24 \textdegree}{6 \ hours}[/tex]

Divide.

[tex]rate \ of \ change = - 4 \textdegree / hour[/tex]

The average change in temperature was -4° per hour. The temperature dropped 4 degrees each hour.

Answer:

Why is college important? It’s a question you may have heard among friends, or perhaps you’ve even wondered yourself about the benefits of earning a degree. And it’s a good question to be asking as you consider your future—and everything that will include, from earnings potential to starting or switching your career. Here are five facts you should know as you consider the value of a college education.

1. People with college degrees earn more on average.

According to averages calculated by the US Bureau of Labor Statistics (BLS), people with a bachelor’s degree earn around 64% more per week than individuals with a high school diploma, and around 40% more than those with an associate’s degree. Those with an associate’s degree earn around 17% more than those with a high school diploma.

Over the course of a year (52 weeks), those percentage differences add up. For example, if you compare the average median annual earnings for those with a bachelor’s degree to those with a high school diploma, you’ll discover a difference of almost $24,000 per year in income.

2. College can help you expand your network.

Salary is far from the only answer for why is college important. You may have heard this before, but who you know and who your friends know is important. No matter how talented you are, a strong network can help you start and advance in your career.

At an Art Institutes school, you’ll not only have the chance to connect with instructors* who have worked in their fields, but you can also meet students in a variety of creative fields. These diverse connections may well benefit you in the future. Plus, you can also participate in professional groups, community activities, and industry conferences where you can grow your circle even more. Your Career Services department may also connect you with alumni in your field and can continue to provide networking support after graduation!

3. Gaining new skills can help enhance your current career.

Building your skill set and industry knowledge can help you move forward in your current career, and the skills you learn go beyond the obvious. At The Art Institutes, not only can you build your technical and artistic skills, but you can also develop your critical thinking, communication, and teamwork.

Earning your degree can demonstrate to a current employer that you’re serious about your career, and that you’re prepared to take on bigger projects and more responsibility. In the long term, when you apply to new jobs in your field, having a degree can provide you with a competitive edge. Even if the job doesn’t require a degree, your education—along with the quality of your work—may help you stand out among applica

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 3/4 acres in 3 3/8 days = 9 6/8 acres in 3 3/8 days

(72 + 6)/8 = 78/8

(24 + 3)/8 = 27/8

78/8 divided by 27/8 = 78/27 = 26/9 or 2 8/9 acres/day

Answer:

B) -6 (w - 4) + 8w = 2 (w + 9) has no solution

Step-by-step explanation:

Answer:

For each one it is shown below

Step-by-step explanation:

The computation of the prime time viewing percentage for the following data is shown below:l;

but before that we need do the total which is

= 6.2% + 8.1% + 7.4% + 6.4% + 3.1% + 2.8%

= 34%

Now for each one the viewing percentage is

For ABC

[tex]= \frac{6.2}{34}[/tex]

= 18.24%

For CBS

[tex]= \frac{8.1}{34}[/tex]

= 23.82%

For NBC

[tex]= \frac{6.4}{34}[/tex]

= 18.82%

For Warner brothers

[tex]= \frac{3.1}{34}[/tex]

= 9.12%

For fox

[tex]= \frac{7.4}{34}[/tex]

= 21.76%

For UPN

[tex]= \frac{2.8}{34}[/tex]

= 8.24%

Answer:

Step-by-step explanation:

x   - the length of the first piece

2x    - twice the length of the first piece (the length of the second piece)

6x   - six times the  length of the first piece

two inches more:

6x+2    - the length of the third piece

first + second + third = 47 in  {total length of the pieces of steel}

x + 2x + 6x + 2 = 47

9x + 2 = 47

9x = 45

x = 45:9

x = 5 in

first piece:   5 in

second piece: 2×5 = 10 in

third piece:   6×5 + 2 = 30 + 2 = 32 in

Steps to solve:

-2x - 4 > 8

~Add 4 to both sides

-2x > 12

~Divide -2 to both sides

x < -6

Best of Luck!

Answer:

Total earnings per week

=18114.8¢

Step-by-step explanation:

He receives 14.20¢ per paper, 6 days a week.

He receives 50¢ for the Sunday paper.

He delivers

124 daily papers each day

He earns= 124*14.20*6

He earns=10564.8¢

151 Sunday papers each week.

He earns= 151*50

He earns= 7550¢

Total earnings per week

=10564.8+7550

=18114.8¢

Answer:

Area=84.5833333333

Step-by-step explanation:

Answer:

Step-by-step explanation:

To make this easy, convert them both into improper fractions.

Multiply 7x4= 28 + 1 = 29/4

Multiply 11 x 2 = 22 +3= 25/2

29/4 x 25/2 = 725/8

simplified it is 90 5/8

Hope this helps :)

Answer:

A) 48 feet

B) 4 seconds

C) 0.54 seconds and 3.46 seconds

Step-by-step explanation:

So we have the function:

[tex]h(t)=64t-16t^2[/tex]

Which represents the height h(t) of the ball after t seconds.

A)

To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:

[tex]h(1)=64(1)-16(1)^2[/tex]

Simplify:

[tex]h(1)=64-16[/tex]

Subtract:

[tex]h(1)=48[/tex]

So, after 1 second, the height of the ball is 48 feet above the ground.

B)

To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:

[tex]0=64t-16t^2[/tex]

Solve for t. Factor out a 16t:

[tex]0=16t(4-t)[/tex]

Zero Product Property:

[tex]16t=0\text{ or } 4-t=0[/tex]

Solve for t:

[tex]t=0\text{ or } t=4[/tex]

We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.

C)

To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:

[tex]30=64t-16t^2[/tex]

First, divide everything by 2 to simplify things:

[tex]15=32t-8t^2[/tex]

Subtract 15 from both sides:

[tex]-8t^2+32t-15=0[/tex]

Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:

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

Substitute:

[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]

Simplify:

[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]

Use a calculator. Approximate:

[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]

So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.

And we're done :)

Answer:

-5 -9 -13....

Step-by-step explanation:

17-4=13 so you basically minus 3 each time.

Answer:

x could be anything. you have to have a equation to solve for x.

Step-by-step explanation:

Answer:

Low estimate

Step-by-step explanation:

2 5/6 rounded is 3 so the total would be 11 hours if everything is rounded.

Answer:

The answer is low

Answer:

A and B

Step-by-step explanation:

Quadratic Equations: f(x) = a(bx - h)² + k

Quadratic equations always have a degree of 2. That means that we will always have an x² term. Of the 4 choices, only A and B offer a term of x², making them a quadratic.

Answer:

Y = 5x - 3/2 + x^2

Y = x^2 + 5x - 2

Step-by-step explanation:

The function must contain x^2.

That is have a degree of 2.

Answer:

Hey there!

-8=x+11/2

-16/2=x+11/2

-27/2=x

Let me know if this helps :)

Answer:  -27/2     or        -27

Step-by-step explanation:

You didn't use parentheses so the equation isn't clear.  

I answered for both possibilities.

                  [tex]-8=x+\dfrac{11}{2}\\\\\\-8-\dfrac{11}{2}=x\\\\\\-\dfrac{16}{2}-\dfrac{11}{2}=x\\\\\\\large\boxed{-\dfrac{27}{2}=x}[/tex]

                                                    [tex]-8=\dfrac{x+11}{2}\\\\\\-8(2)=\dfrac{x+11}{2}(2)\\\\\\-16=x+11\\\\\\-16-11=x\\\\\\\large\boxed{-27=x}[/tex]

Answer:

No

Step-by-step explanation:

For the smaller figure to be a scaled copy, the figure would have to be half as wide as well,

Answer:

Answer is 54 . IT is the correct answer

Step-by-step explanation:

Hope it is helpful for you

Answer:

$430

Step-by-step explanation:

Step 1:

300 - 50

Step 2:

350 + 20

Step 2:

370 + 60

Answer:

$430

Hope This Helps :)

Answer:

13 m

Step-by-step explanation:

The distance x is:

x = √12² + (13 -8)² = √144 + 25 = √169 = 13 m

Answer:

Yes

Step-by-step explanation:

Pi is a rational number, because it goes on forever.

Answer:

y = -5x + 32

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write in known variables

slope m = -5

y = -5x + b

Step 2: Find b

7 = -5(5) + b

7 = -25 + b

b = 32

Step 3: Write linear equation

y = -5x + 32

Answer:

y - 7 = -5(x - 5)

Step-by-step explanation:

We are given that a line has a slope of -5 and contains the point (5,7).

We want to write the equation of this line.

The equation of this line can be written in three ways:

Either one of these ways works, but let's use point-slope form, as that form is the easiest.

We can immediately substitute the values into the formula to get the equation.

We can start with the slope; replace m with -5 in the formula.

[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]

Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:

y - 7 = -5(x - 5)

Answer:

D) 7 1/5

Step-by-step explanation:

2 2/5 is equivalent to 12/5 then if you divide it by 1/3 you will get 7 1/5 or 7.2

solution

Answer:

here we go 6×4+3

now 24+3

hence the answer is

27 ans

Answer:

x = -2

Step-by-step explanation:

f(x) = 6 x + 3×4

f(x) = 6 x + 12

6 (x + 2) = f(x)

x = -2

Hope I helped! Please label me as Brainliest!

Answer:

The side length is irrational

Step-by-step explanation:

Because the square root of 23 or 20+3 is a non-perfect square root and it's a never ending decimal.

Answer:

There are 11550 possible selections

Step-by-step explanation:

Given

[tex]Men = 7[/tex]

[tex]Women = 11[/tex]

Required

How many ways can 4 men and 4 women be selected

The keyword in the question is SELECTION and it means COMBINATION;

So, number of selection is:

[tex]Number = Men * Women[/tex]

[tex]Number = ^7C_4 * ^{11}C_4[/tex]

This gives

[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]

[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]

[tex]Number = 7 * 5 * 330[/tex]

[tex]Number = 11550[/tex]

Hence;

There are 11550 possible selections