a large University with over 40,000 took a recent survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. b = the proportion of students in the sample who claimed to work out 3 at least 3 times a week. What is the standard deviation of the sampling??

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let's think of the boat and wind as vectors:

Boat Vector --> [tex]\langle28cos36^\circ,28sin36^\circ\rangle[/tex]

Wind Vector --> [tex]\langle10cos22^\circ,10sin22^\circ\rangle[/tex]

Now, let's add the vectors:

[tex]\langle28cos36^\circ+10cos22^\circ,28sin36^\circ+10sin22^\circ\rangle[/tex]

Find the magnitude (the true velocity):

[tex]\sqrt{(28cos36^\circ+10cos22^\circ)^2+(28sin36^\circ+10sin22^\circ)}\approx37.78\approx38[/tex]

Find the direction (angle):

[tex]\theta=tan^{-1}(\frac{28sin36^\circ+10sin22^\circ}{28cos36^\circ+10cos22^\circ})\approx32.32^\circ\approx32^\circ[/tex]

Thus, D is the best answer

Problem 2

Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of the vectors and [tex]||u||*||v||[/tex] is the product of each vector's magnitude:

[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{\langle-82,47\rangle\cdot\langle92,80\rangle}{\sqrt{(-82)^2+(47)^2}*\sqrt{(92)^2+(80)^2}})\\\\\theta=cos^{-1}(\frac{(-82)(92)+(47)(80)}{\sqrt{6724+2209}*\sqrt{8464+6400}})\\\\\theta=cos^{-1}(\frac{(-7544)+3760}{\sqrt{8933}*\sqrt{14864}})\\\\\theta=cos^{-1}(\frac{-3784}{\sqrt{132780112}})\\\\\theta\approx109.17^\circ\approx109^\circ[/tex]

Therefore, C is the best answer

Answer:

15

Step-by-step explanation:

15 is the answer

If you need solution do let me know in the comments

Answer:

28.42 feet

Step-by-step explanation:

Given

To Find

Solving

Answer:

28.4 feet

Step-by-step explanation:

The question can be solved by using Pythagoras Theorem.

Given:-

Height of tree :- 18 feet (Perpendicular)

length of shadow :- 22 feet (Base)

To find:-

Distance of shadow from the end to the top of the tree

Solution:-

We know the Pythagoras theorem,

Which is , H² = P² + B²

So putting the given value , we get

H² = 18²+22²

H² = 324 + 484

H = √ 808 feet

H = 28.4 feet

Answer:

8a + 24

Step-by-step explanation:

Use Distributive property: a(b +c) = a*b + a*c

Here a = 8 ;  b= a & c = 3

8(a + 3) = 8*a + 8*3

            = 8a + 24

Answer:

38.5 cm²

Find area of the full rectangle:

Length * Width

6 * 7

42 cm²

Find area of the missing triangle

1/2 * base * height

1/2 * 7 * 1

3.5 cm²

Area of the figure:

42 - 3.5

38.5 cm²

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Probability is the likelihood of occurrance of an event. It is given by:

Probability = number of occurrence / total number of possible occurence

A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.

Probability of using coupon = 32/40 = 0.8

Hence if 750 people go to this store each day, number of people sampled = 75.

Number of people expected to use the coupon = 75 * 0.8 = 60

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Find out more on probability at: https://brainly.com/question/24756209

Answer:

4/9 is left over.

Step-by-step explanation:

First make the denominators the same. 2/3=6/9. 6/9-2/9=4/9.

Answer:

The second option, 1,008 cm²

Step-by-step explanation:

   This shape has 5 sides to solve for with reguards to surface area.

   Let us solve for them all.

[1 & 2 - the triangles]

12 * 9 = 108 cm²

-> I am not going to divide since we have 2 congruent triangles

[3 - the bottom side]

25 * 12 = 300 cm²

[4 - the side facing away]

25 * 9 = 225 cm²

[5 - the side facing up]

25 * 15 = 375 cm²

   Now we will add them together for the total.

108 + 300 + 225 + 375 = 1,008 cm²

             The surface area for the triangular prism shown is 1,008 cm².

Answer:

Your answer would be:
C.) 1,350 cm2

Volume = 0.5 x b x h x length

0.5 x (25 x 12) x 9 =
0.5 x 300 x 9 =
= 1,350 cm2

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

[tex]\textbf{Solve for u:}\\\\u(wf+v)=m+j\\\\\implies u = \dfrac{m+j}{wf+v}\\\\\textbf{Solve for f:}\\\\u(wf+v) = m+j\\\\\implies uwf+uv = m+j\\\\\implies uwf = m+j-uv\\\\\implies f=\dfrac{m+j-uv}{uw}[/tex]

Answer:

0.1 percent

Step-by-step explanation:

sorry I don't have an explanation. sorry if it's wrong, at least I tried

Answer:

0.1

Explanation:

It's right

Answer:

325/377×100= 116% it means they completed 116%of the trip

Answer: x=20

Step-by-step explanation:

(6x-10)=(3x+50) (subtract both sides by 3x)

3x-10=50(add ten to both sides)

3x=60(divide both sides by 3)

x=20

Answer:

3 units

Step-by-step explanation:

you count how many blocks they are from each other

Answer:

24 per bag

Step-by-step explanation:

18x8=144 then divide by 6= 144÷6=24

Answer:

Y-Intercept: (0, -5)

Slope: 1/2

Explanation:

The y-int is when x = 0. The slope formula is (y2 - y1)/(x2 - x1) in which you use 2 points on the line.

It's a trapezoid

Now

Area:-

Answer:

£78

Step-by-step explanation:

65 divided by 5= £13

13+65=£78

Answer:

£78

Step-by-step explanation:

Let the total value be T.

go into settings and click on subscription

Step-by-step explanation:

this is very simple.

you can compare this to the question "in my bag are 70 pieces of fruit. 30 of them are apples. how many pieces of other fruit are there ?"

well, it is 70 - 30 = 40 !

that's it ! that is all there is to it.

so, q = 40°

what is still unclear, please ?

Answer:

20%

Step-by-step explanation:

A=R^2

120/100

=1.2

1.2R= new value of R

original of R=R

A^1/2=R

change/origionalx100%

(1.2A^1/2-A^1/2)

-------------------- x 100%

A^1/2

A^1/2 (1.2-1)

--------------- x100%

A^1/2

0.2

---- x100

1

0.2x100

=20%

Answer:

You didn't attach a picture of the pentagon, but the perimiter can easily be found using one of the following formulae:

Step-by-step explanation:

P = 5s, where s is the length of a side

P = 2r × Sin(180/5), where r is the radius

Answer:

11/2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

This is because each dot represents one plot, and the only number with one plot above it is 1 and 1/2, aka D

Answer:

[tex]y < -8[/tex]

[tex]y > 4[/tex]

Step-by-step explanation:

Absolute Value Inequality entered :

     |y+2|>6

Step by step solution :
Step 1: Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

     |y+2| > 6

Step 2: Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |y+2|

For the Negative case we'll use -(y+2)

For the Positive case we'll use (y+2)

Step 3: Solve the Negative Case

     -(y+2) > 6

    Multiply

     -y-2 > 6

    Rearrange and Add up

     -y > 8

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     y < -8

    Which is the solution for the Negative Case

Step 4: Solve the Positive Case

     (y+2) > 6

    Rearrange and Add up

     y > 4

    Which is the solution for the Positive Case

Step 5:

Wrap up the solution

 y < -8

 y > 4

Solutions in Interval Notation

   (-∞,-8)

   (4,+∞)

Solutions on the Number Line

Two solutions were found :

 y > 4

 y < -8

The value of  a and b in the product of 4+3i  and its conjugate in the format a + bi are 25 and 0.

The conjugate is where we change the sign in the middle of two terms. For example:

3y + 1

conjugate of 3y + 1 is 3y - 1.

Therefore, the conjugate of 4 + 3i is 4 - 3i.

The product of 4 + 3i and its conjugate is as follows:

(4 + 3i)(4 - 3i) = 16 - 12i + 12i - 9(i)²

Therefore,

16 - 9i²

i² = -1

Hence,

16 - 9(-1) = 25

It can be written in the form a complex form → (25 + 0.i)

Therefore, a = 25 and b = 0.

learn more on conjugate here: https://brainly.com/question/20757260

[tex] \mathsf\red{♧ANSWER♧}[/tex]

[tex] \mathsf \blue{5 \frac{2}{5} - 3 \frac{7}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{27}{5} - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{2( \frac{27}{5} ) - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{54}{10} - \frac{37}{10} }[/tex]

[tex] \blue \implies \mathsf \green{ \frac{17}{10} = 1 \frac{7}{10} = 1.7}[/tex]

#1

Paved area:-

#b

Let's see

Answer:

(a)  121 miles

(b)  7 days

Step-by-step explanation:

Given function:

[tex]\sf L(d)=205-7d[/tex]

Question (a)

When d = 12:

[tex]\sf \implies L(12)=205-7(12)[/tex]

                [tex]\sf =205-84[/tex]

                [tex]\sf =121 \ miles[/tex]

Therefore, the crew has 121 miles left to pave after 12 days.

Question (b)

When L(d) = 156

[tex]\sf \implies 156=205-7d[/tex]

[tex]\sf \implies 7d=205-156[/tex]

[tex]\sf \implies 7d=49[/tex]

[tex]\sf \implies d=\pm\sqrt{49}[/tex]

[tex]\sf \implies d=\pm7[/tex]

As distance is positive, [tex]\sf d=7[/tex] only

Therefore, the crew has been paving the the road for 7 days.

Answer:

Acute angle

Step-by-step explanation:

Acute angle = less than 90 degrees

Answer:

acute angles

Step-by-step explanation:

Angles between 0 and 90 degrees (0°< θ <90°) are called acute angles. Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles. Angles that are 90 degrees (θ = 90°) are right angles.