The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to test H0: μ = 100 versus H1: μ ≠ 100 with a sample of n = 9 specimens.
A. If the acceptance region is defined as 98.5 le x- 101.5, find the type I error probability alpha.
B. Find beta for the case where the true mean heat evolved is 103.
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

Answer:

A

Step-by-step explanation:

● first one:

The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.

STP is one of them so this statement is true.

● second one:

If ST and PT were equal this would be a square not a rhombus.

● third one:

If SPQ was a right angle, this woukd be a square.

● fourth one:

Again if the diagonals SQ and PR were equal, this would be a square.

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

Find out more at: https://brainly.com/question/18880408

The area is given by the integral

[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]

where C is the curve and [tex]dS[/tex] is the line element,

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]

[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]

[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]

So the area is

[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]

Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:

[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

Step-by-step explanation:

positive integer divisible by 3 includes

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...

less than highest possible value is 42

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

Answer:

b . sphere

Step-by-step explanation:

Answer:

X+9=24

Or,x=24-9

:.x=15

Step-by-step explanation:

Answer:

B. x=15

Step-by-step explanation:

To find the solution to the equation, we must get x by itself on one side of the equation.

[tex]x+9=24[/tex]

9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.

[tex]x+9-9=24-9[/tex]

[tex]x=24-9[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]x+9=24 (x=15)[/tex]

[tex]15+9=24[/tex]

[tex]24=24[/tex]

This checks out, so we know our solution is correct. The answer is B. x=15

Answer:

Step-by-step explanation:

Initial population in 2018 = 25,000

Annual growth rate (in %) = 4%

Yearly Increment in population = 4% of 25000

= 4/100 * 25000

= 250*4

= 1000

This means that the population increases by 1000 on yearly basis.

To determine what the  population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.

Amount of years we have between 2018 and 2033 = 2033-2018

= 15 years

After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.

Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

3 hours

Step-by-step explanation:

Downstream, the speeds add up:

It will take:

To ride 87 km.

Answer:

a) 40 dollars

b) 480 dollars

Step-by-step explanation:

Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0

T'(x) = 2(20)x¹ + 40x° + 0

T'(x) = 40x+40

At x = 0,

T'(0) = 40(0)+40

T'(0) = 40

Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).

b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)

Given T(x) =20x²+40x+600

T(4) =20(4)²+40(4)+600

T(4) = 320+160+600

T(4) = 1080 dollars

Also T(0) =20(0)²+40(0)+600

T(0) = 0+0+600

T(0)= 600 dollars

T(4) - T(0) = 1080 - 600

T(4) - T(0) = 480 dollars

Hence, the tax has changed by $480 between 2008 and 2012

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

A. a line segment

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C: 512 = 2w2

Step-by-step explanation:

on edge

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

The answer is $12792

Explanation:

It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:

1. Write the values you know and use x to represent the value you need to find

108 = 18        

  x =   82      

3. Cross multiply

x 18 = 8856

4. Find  the value of x by solving this simple equation

x = 8856 ÷ 18

x = 492 - Amount the employer pays every two weeks for Tessa's family coverage

Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.

1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks

52 ÷ 2 = 26

2. Finally, multiply the money paid by the employer every two weeks by 26

26 weeks x $492 = $12792- This is the total the employer pays annually

Answer:

26.75 units²

Step-by-step explanation:

Cube Area: A = l²

Triangle Area: A = 1/2bh

Step 1: Find area of biggest triangle

A = 1/2(3.5)(2 + 2 + 5)

A = 1.75(9)

A = 15.75

Step 2: Find area of 2nd biggest triangle

A = 1/2(5)(2)

A = 1/2(10)

A = 5

Step 3: Find area of smallest triangle

A = 1/2(2)(2)

A = 1/2(4)

A = 2

Step 4: Find area of cube

A = 2²

A = 4

Step 5: Add all the values together

A = 15.75 + 5 + 2 + 4

A = 20.75 + 2 + 4

A = 22.75 + 4

A = 26.75

Answer:

x=9.6

Step-by-step explanation:

The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.

The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.

Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:

[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]

Work Shown:

T = average Celsius temperature two Sundays ago

8% = 8/100 = 0.08

8% of T = 0.08T

L = average Celsius temperature last sunday

L = 8% higher than T

L = T + (8% of T)

L = T + 0.08T

L = 1.00T + 0.08T

L = (1.00 + 0.08)T

L = 1.08T

The 1.08 refers to the idea that L is 108% of T

Answer:

b and d

Step-by-step explanation:

khan

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

(-8, -2)

Step-by-step explanation:

y-x = 6

y + x = -10

Add the two equations together to eliminate x

y-x = 6

y + x = -10

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

2y = -4

Divide by 2

2y/2 = -4/2

y = -2

Now find x

y+x = -10

-2+x = -10

x = -8

Answer:

Step-by-step explanation:

1. 4/4+4-4=1

2. 4/4+4/4=2

3. 4+4/4-4=3

4. 4 × (4 − 4) + 4=4

5. (4 × 4 + 4) / 4=5

6. 44 / 4 − 4=6

7. 4+4-4/4=7

8. 4+4+4-4=8

9. 4+4+4/9=9

10. 44 / 4.4=10

Answer:

1 = (4 x 4)/(4 x 4) or  (4 + 4)/(4 + 4) or  (4 / 4) x (4 / 4) or  (4 / 4)/(4 / 4)  

2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)

3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4

4 = 4 - (4 - 4)/4

5 = (4 x 4 + 4)/4

6 = 4 + (4 + 4)/4

7 = 4 - (4/4) + 4

8 = 4 + (4 x 4)/4

9 = 4 + 4 + (4/4)

10 - I tried the best. You might need ! or sqrt operator to get 4.

Updated:

I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:

10 = (44 - 4)/4

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16