The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 150 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours

Answer:

19.4 in.

Step-by-step explanation:

Answer:

The volume of the pyramid is 126in^3

Step-by-step explanation:

To find the volume of a pyramid you need to use this formula which is

V=lw·h/3

V=9·6·7/3

V=54·7/3

V=126in^3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x^2−6x+9=5

Step 2: Subtract 5 from both sides.

x^2−6x+9−5=5−5

x^2−6x+4=0

Step 3:  a=1, b=-6, c=4

1x^2+−6x+4=0

Step 4: Quadratic formula (a) =1, b=-6, c=4

x= 6±√20 /2

Step 4: Last Step

x=3−√5

Explanation in words:

The first step of solving (x – 3)^2 = 5 is to use the quadratic formula. So the first step is to Simplify both sides of the equation which is the (x−3)^2. Our answer will led up to 5 after that.

Moving on to step 2 we will have to now subtract the 5 from both sides. So 5−5 = 0. So in this step, our answer is now led up to 0.

Now on the step 3 we will now have to use the formula named "quadratic formula". So in this case we will solve this equation with that formula       a=1, b=-6, c=4. At the end our answer will led up to x=3−√5.

Answer:

x=3+√5

x=3−√5

Hope this helps.

Answer:

Step-by-step explanation:

IG you wanted to solve for X ?   there are two answers ofc,  

x= 3-[tex]\sqrt{5}[/tex]

x=3+[tex]\sqrt{5}[/tex]

Answer:

The correct answer is "0.0000039110".

Step-by-step explanation:

The given values are:

[tex]Y_n\rightarrow N(\mu, \sigma^2)[/tex]

[tex]\mu = 40n[/tex]

[tex]\sigma^2=100n[/tex]

[tex]n=20[/tex]

then,

The required probability will be:

= [tex]P(Y_{20}>1000)[/tex]

= [tex]P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )[/tex]

= [tex]P(Z>\frac{1000-800}{44.7214} )[/tex]

= [tex]P(Z>\frac{200}{44.7214} )[/tex]

= [tex]P(Z>4.47)[/tex]

By using the table, we get

= [tex]0.0000039110[/tex]

Answer:

(-6,2)

Step-by-step explanation:

when it asks for the scale factor all you do is take your coordinates and multiply it by whatever the question gives you. Like in this question you would multiply -3 and 1 by 2 and whatever the number comes out to be then thats your answers.

Sorry if the explanation isnt very good!

Answer:

Distance in ft = 597.57 feet

Step-by-step explanation:

As per the

First equation of motion

84 mph = 37.5514 m/s

45 mph = 20.1168 m/s

v-u = a* t

Substituting the given values, we get -

37.5514 m/s - 20.1168 m/s = a * 6.3

a = 2.76 m/s^2

Now as per Newton's third law of motion

v^2-u^2 = 2 *a*S

Substituting the given values, we get -

37.5514^2 - 20.1168^2 = 2 * 2.76 m/s^2 * S

S = 182.142 Meters

Distance in ft = 597.57 feet

Answer:

Growth.

Step-by-step explanation:

y = 2(1/2)x is the same as y = x. as it multiplies and divides x by 2. y = x is exponential growth.

Hope that this helps!

Answer:

13.5 inches

Step-by-step explanation:

11.5 x 2.25 x 4

I could be wrong

Answer:

13.5 inches is correct :)

[tex]\sf\purple{The\:value\:of\:x\:is\:10.4.}[/tex]✅

Step-by-step explanation:

[tex] \frac{(10x - 4)}{5} = 20 \\ ✒ \: 10x - 4 = 20 \times 5 \\ ✒ \: 10x = 100 + 4 \\ ✒10x = 104 \\ ✒ \: x = \frac{104}{10} \\ ✒ \: x = 10.4[/tex]

[tex]\sf\red{Therefore,\:the\:value\:of\:x\:is\:10.4.}[/tex]

To verify:-

[tex] \frac{(10x - 4)}{5} = 20 \\ ✒ \: \frac{10 \times 10.4 - 4}{5} = 20 \\ ✒ \: \frac{104 - 4}{5} = 20 \\ ✒ \: \frac{100}{5} = 20 \\ ✒ \: 20 = 20 \\ ✒ \: L.H.S.=R. H. S[/tex]

Hence verified. ✔

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

Step-by-step explanation:

From the question we are told that:

Null Hypothesis [tex]H_0: 50[/tex]

Alternative Hypothesis [tex]H_a: > 50[/tex]

Sample size [tex]n=50[/tex]

standard deviation[tex]\sigma=6[/tex]

Significance level [tex]\alpha=0.05[/tex]

a)

Sample mean [tex]\=x=52.5[/tex]

Generally the equation for Test statistics is mathematically given by

[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]t=\frac{52.5-50}{\frac{6}{\sqrt{50} } }[/tex]

[tex]t=2.95[/tex]

Therefore from table

[tex]Critical\ value=1.645[/tex]

We conclude The value of test statistics is greater than critical value.

Therefore we Reject the Null hypothesis [tex]H_0[/tex]

b)

Sample mean [tex]\=x=51[/tex]

Generally the equation for Test statistics is mathematically given by

[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]t=\frac{51-50}{\frac{6}{\sqrt{50} } }[/tex]

[tex]t=1.18[/tex]

Therefore from table

[tex]Critical\ value=1.645[/tex]

We conclude,The value of test statistics is less than critical value.

Therefore we Fail to Reject the Null hypothesis [tex]H_0[/tex]

c)

Sample mean [tex]\=x=51[/tex]

Generally the equation for Test statistics is mathematically given by

[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]t=\frac{51.8-50}{\frac{6}{\sqrt{50} } }[/tex]

[tex]t=2.12[/tex]

Therefore from table

[tex]Critical\ value=1.645[/tex]

We conclude The value of test statistics is greater than critical value.

Therefore we Fail to Reject the Null hypothesis [tex]H_0[/tex]

Answer:

circumference = 2πr

diameter = 3ft, so radius =3/2 =1.5

                       =2π ×1.5=3π= 9.42ft

Answer:

here diameter =3 ft

radius=diameter/2

=3/2

=1.5 ft

now use formula 2 pie r where pie =3.14

=2*3.14*1.5 ft

=9.42 ft

Step-by-step explanation:

Hope this helps u!!

Answer: $2

Step-by-step explanation:

Answer:

∠S = 151

Step-by-step explanation:

The figure shown is a pentagon

The angles in a pentagon add up to equal 540

Thus, ∠Q + ∠P + ∠T + ∠S + ∠R = 540

Or 10x - 3 + 5x + 2 + 7x - 11  + 13x - 31 + 8x - 19 = 540

This is the equation we will use to solve for x

Step 1 combine like terms

10x = 5x + 7x + 13x + 8x = 43x

-3 + 2 - 11 - 31 - 19 = -62

We now have 540 = 43x - 62

Step 2 add 62 to each side

-62 + 62 cancels out

540 + 62 = 602

we now have 602 = 43x

Step 3 divide each side by 43

43x / 43 = x

602 / 43 = 14

we're left with x = 14

Finally we plug in 14 for x in the given expression for ∠S

∠S = 13x - 31

* substitute 14 for x *

∠S = 13 ( 14 ) - 31

∠S = 13 * 14 = 182

182 - 21 = 151

Thus, ∠S = 151

The measure of ∠S is equal to 151°.

In mathematics, shapes define the perimeters or contours of an object. The forms can be categorized into numerous groups according to their individual traits. A border or outline made up of points, lines, curves, etc. frequently surrounds the forms.

As per the given data:

We are given the diagram of a shape and all its internal angles.

As the given shape is having 5 sides, it will be a pentagon.

The sum of all internal angles in a pentagon is equal to 540°.

∴ ∠P + ∠Q + ∠R + ∠S + ∠T = 540°

⇒ 10x - 3 + 5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 = 540

= 43x - 62 = 540

= 43x = 602

x = 14

To find the measure of ∠S.

∠S = 13x - 31

∠S = 13(14) - 31

∠S = 151°

The measure of ∠S is equal to 151°.

To learn more about shape, click:

brainly.com/question/28978432

#SPJ2

Answer:

10.5

Step-by-step explanation:

Answer:

tenths.........

Step-by-step explanation:

.....is the answer

(Hypotenuse)² = (Base)²+ (Perpendicular)²

Taking, Hypotenuse As H

Base As B

Perpendicular As P

_________________________

H²= B²+ P²

[tex](9 \sqrt{2} ) {}^{2} = x {}^{2} + {x}^{2} \\ \\ \implies \: 81 \times 2 = 2x {}^{2} \\ \\ \implies162 = 2x {}^{2} \\ \\ \implies \frac{162}{2} = x {}^{2} \\ \\ \implies \cancel\frac{162}{2} = x {}^{2} \\ \\ \implies81 = {x}^{2} \\ \\ \implies x = \sqrt{81} \\ \\ \implies \: x = 9[/tex]

i dont know this questions

Answer:

For a data set of N elements:

{x₁, x₂, ..., xₙ}

The median is the middle value (or the average of the two middle values)

The average or mean is:

[tex]m = \frac{x_1 + ... + x_n}{N}[/tex]

The mode is the value that is more repeated.

The range is the difference between the largest value and the smallest value.

Now, let's try to construct two sets A and B that meet the required conditions:

Let's suppose two sets of 5 values each:

A = {2, 2, 3, 4, 5}

The median of A is 3.

The range of A is = 5 - 2 = 3

The average of A is: (2 + 2 +3 +4 +5)/5 = 16/5

And the value "2" appears two times, so the mode is 2.

Now, let's try to find a data set B such that:

The mode is smaller than 2  (so for example, we can have a "1" that repeats two times)

The median is smaller than 3 (let's have a median equal to 2)

The average is larger than 16/5

The range is larger than 3

This is ratter simple:

B = {1, 1, 2, 6, 9}

The median of B is 2.

The mode of B is 1

The range of B is: 9 - 1 = 8

The average of B is: (1 + 1 + 2 + 6 + 9)/5 = 19/5

So, we just found an example for two data sets A and B such that A has a greater median and mode, while B has a greater average and range.

So the answer is yes, it is possible.

Answer:

[tex]P(t) = 1460(1.06)^t[/tex]

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for a population after t years is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

Currently, there are 1,460 wolves in Scataway National Park.

This means that [tex]P(0) = 1460[/tex]

Growing at a rate of 6% every year:

This means that [tex]r = 0.06[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 1460(1+0.06)^t[/tex]

[tex]P(t) = 1460(1.06)^t[/tex]

Answer:

Step-by-step explanation:

Answer:

347,392

Step-by-step explanation:

yes

Step-by-step explanation:

the rectangle area=L*W

(5x+2)(2x-1)

10x^2-5x+4x-2

10x^2-x-2

Answer:

44.4 units

Step-by-step explanation:

Recall: 2 tangents drawn from an external point from a circle are congruent

Perimeter of the quadrilateral = AB + BC + CD + AD

AB = 3.1 + 8 = 11.1

BC = 3.1 + 8 = 11.1

CD = 11.1 (given)

AD = 8 + 3.1 = 11.1

Perimeter = 11.1 + 11.1 + 11.1 + 11.1

= 44.4 units

Answer:

if you want to find perimeter you must do addition for the corners. For example on long side in the regtangle the number is 4. And the short side is 6. The one thing we must do is addition. Than the answer will be 10. You're welcome.

if you meant to put a link there is none

Step-by-step explanation:

Total time taken=(30/24+12/8)

=(1.25+1.5)

=2.75 hrs

=165 minutes

=2 hrs and 45 minutes

formula used: v=d/t

or,d=v×t

or,t=d/v which is the master formula used in the solution of this problem.

If you are satisfied with my answer then please, give brainliest.