please help 20 points!!!!!

hree students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. Sample Backpack weight (in pounds) Sample mean 1 3, 7, 8, 3, 7, 9, 6, 8 2 8, 6, 4, 7, 9, 4, 6, 7 3 9, 4, 5, 8, 7, 5, 9, 6
(b)Use the table to calculate the range of the sample means. Rangeofsamplemeans:
(c)The students are going to use the sample means to estimate the mean backpack weight of their schoolmates. Select all the true statements below.

A single sample mean will tend to be a worse estimate than the mean of the sample means.

The mean of the sample means will tend to be a worse estimate than a single sample mean.

The closer the range of the sample means is to 0, the less confident they can be in their estimate.

The farther the range of the sample means is from 0, the less confident they can be in their estimate.

The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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The area of the trapezoidal tarp in the hotel is 47.3 square inches.

How do determine the area of the trapezoid?

From the complete question, the parallel sides are 10ft and 12ft.

Evaluate,

The height (h) is computed using the cosine function shown below:

This gives

Make h the subject:

Evaluate:

So, we get:

Evaluate:

Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.

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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.

Answer:

Step-by-step explanation:

base=b=7.2yd

height =h=7yd

area of parallelogram = b x h

.                                    =7.2yd x 7yd

                                     =50.49[tex]yd^{2}[/tex]

Answer:

23.6

Step-by-step explanation:

→ Identify length not given

Opposite

→ Find a formula without opposite

Cos = Adjacent ÷ Hypotenuse

→ Rearrange

Adjacent = Cos × Hypotenuse

→ Substitute

cos 38 × 30 = 23.6

Answer:

[tex]x = 23.6[/tex]

Step-by-step explanation:

To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.

In this case:

• The side adjacent to the given 38° angle is [tex]x[/tex] (required).

• The hypotenuse is 30 units.

The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:

[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].

Substituting into the formula:

[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]

⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]

⇒ [tex]x = 23.6[/tex]

Part 1

[tex]m\angle AOB=m\angle BOC[/tex]

Part 2

Since [tex]m\angle AOB=m\angle BOC[/tex] from part 1, we know that since [tex]m\angle AOB=53^{\circ}[/tex], by the transitive property of equality, [tex]m\angle BOC=53^{\circ}[/tex].

Part 3

[tex]m\angle AOC=m\angle AOB+m\angle BOC=53^{\circ}+53^{\circ}=106^{\circ}[/tex]

Answer:

3.11%

Step-by-step explanation:

4/128.6=0.0311

multiply by 100

3.11%

Answer:

Step-by-step explanation:

A. a = $1350 b. b= 89%

B. 1350(.89)^t = 675

    t = 5.9 years

Answer:

Even

Step-by-step explanation:

Answer:

[tex]\frac{263}{999}[/tex]

Step-by-step explanation:

The solution to this problem is (s2+1)Y(s)−2s−1=2s2+4 .

We let  L[y(t)]=Y(s) . With that, tabular Laplace-transform laws entail

L[y′]=sY(s)−y(0)=sY(s)−2

L[y′′]=s2Y(s)−sy(0)−y′(0)=s2Y(s)−2s−1

∴L[y′′+y]=(s2+1)Y(s)−2s−1 .

Since the Laplace transform of  sin(kt)  is  ks2+k2 , we have

(s2+1)Y(s)−2s−1=2s2+4 .

This equation readily solves to  Y(s)=2s3+s2+8s+6(s2+1)(s2+4) . We compute its partial fraction decomposition as  Y(s)=2s+53s2+1+−23s2+4 .

Our final step is to use tabular Laplace-transform laws ( sin(kt)↦ks2+k2 , and  cos(kt)↦ss2+k2 ) to get  y(t)=2cost+53sint−13sin(2t) . One can check that this indeed satisfies the initial value problem.

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Answer:

334 in^2.

Step-by-step explanation:

The surface area = area of the top prism + area of the bottom - 2 * area of the base of the  top smaller prism

= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) -  2* 3*5

= 2* 39 + 2*143 - 30

= 334

The amount of money that you will have to save to buy a car at the $9,500 price is $556.11 ($9,500 - $8,943.89).

The amount of money needed can be determined by calculating the future value of $7,500 invested at 4.5% for 4 years.

Then, the result, which is the future value, $8,943.89, is deducted from the $9,500 price, to determine the additional savings required.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value can also be determined using an online finance calculator, as follows.

N (# of periods) = 4 years

I/Y (Interest per year) = 4.5%

PV (Present Value) = $7,500

PMT (Periodic Payment) = $0

Results:

FV = $8,943.89

Total Interest = $1,443.89

Thus, the amount of money that you will have to save to buy a car at the $9,500 price is $556.11.

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Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,

[tex]a_2 = a_1 + 2[/tex]

[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]

[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]

[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]

and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,

[tex]b_2 = 2b_1[/tex]

[tex]b_3=2b_2 = 2^2 b_1[/tex]

[tex]b_4=2b_3=2^3b_1[/tex]

[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

It follows that

[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)[/tex]

so the left side is

[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]

Also recall that

[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]

so that the right side is

[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]

Solve for [tex]c[/tex].

[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]

Now, the numerator increases more slowly than the denominator, since

[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]

[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]

and for [tex]n\ge5[/tex],

[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]

This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].

[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].

If [tex]n=2[/tex], then

[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]

If [tex]n=3[/tex], then

[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]

If [tex]n=4[/tex], then

[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]

There is only one value for which the claim is true, [tex]c=12[/tex].

Answer:

K(6, 9)

Step-by-step explanation:

Let the K coordinates be (x, y)

Mid-point formula:

[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Applying formula:

[tex]\sf (-3,\:-1) = (\:\dfrac{-12+x}{2} ,\: \dfrac{-11+y}{2} )[/tex]

Comparing expression:

[tex]\sf \dfrac{-12+x}{2} = -3 \quad and \quad \dfrac{-11+y}{2} = -1[/tex]

[tex]\sf -12+x = 2(-3) \quad and \quad -11+y = 2(-1)[/tex]

[tex]\sf x = -6 + 12 \quad and \quad y = -2 + 11[/tex]

[tex]\sf x = 6 \quad and \quad y = 9[/tex]

So, coordinates of K is (6, 9)

The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

Linear equations are equations that have constant average rates of change, slope or gradient

From the table of values, we have the following points

(x, y) = (5, 5.5) and (10, 5)

The slope of the table of values is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (5 - 5.5)/(10 -5)

Evaluate the difference

m = -0.5/5

Evaluate the quotient

m = -0.1

This means that the slope is -0.1

From the table of values, we have

x represents the elapsed time and y represents the volume of helium

So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

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The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

From the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point

Lines that are parallel to each other will have the same slope.

First, we will determine the slope of the line in the given equation.

The given equation of the line is

8x − 3y = 1

Express the equation in the slope-intercept form of a line, y = mx + b

Where m is the slope and

b is the y-intercept

That is,

8x − 3y = 1

8x -1 = 3y

3y = 8x - 1

y = 8/3(x) - 1/3

By comparing,

∴ The slope of the line is 8/3

Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3

Now, find the equation of a line containing the point (-2, 0) and that has  a slope of 8/3

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -2

and y₁ = 0

∴ y - 0 = 8/3(x - -2)

y = 8/3(x +2)

3y = 8(x +2)

3y = 8x + 16

8x -3y = -16

Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

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Step-by-step explanation:

8x+6y=24

6y=24-8x

y=24/6 - 8/6x

y=4-4/3x

Answer:

Step-by-step explanation:

Equation

f(x) = (8x + 1) / (2x + 9)

Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.

Behavior

The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for  this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.

So you want to know the behavior.

Right Curve

Crosses the x axis at (-0.125, 0)

Crosses the y axis at (0,0,111)

The right curve has a domain of -∞ < x < ∞

The  right curve has a range of -∞ < x < ∞

The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.

Left Curve.

The right hand curve never crosses either the x or y axis.  Nor does it just touch the x or y axis.

The domain is -∞ <x < 0

The range is 0<x<∞

Answer:

Step-by-step explanation: I did the test and the answer should be A

hope this helps :)

The answer is g'(x) = 4x² - 72x + 307.

If shifted 9 units right, substitute (x - 9) in place of x.

If shifted 1 unit down afterwards, subtract 1.

Answer:

h(x)=4(x-9)^2-17

Step-by-step explanation:

The original price of the laptop is calculated as $545

We are given;

Sales Price of Laptop = $299.75

Now, the laptop is on sale for 45% off regular price.

If original price is x, then we can express that;

(100% - 45%) * x = 299.75

Thus;

55%x = 299.75

0.55x = 299.75

x = 299.75/0.55

x = $545

Thus, the original price of the laptop is calculated as $545

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The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

According to the statement

We have given that the sin(x) = 5/13 , x in quadrant iii

And we have to Find the value of cos x using the following:

So, For this purpose, we know that the trigonometry terms are:

sin2(x) + cos2(x) = 1;  

or cos2(x) = 1-sin2(x)

And

cos2(x) = 1-(-5/13)2 =

cos2(x) = 144/169;  

We know that the

In quadrant III both the sin and cos are negative so

cos(x) = -12/13 (after taking square roots).

And

Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.

Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).

Now

sin(x + x) = sinx * cosx + cosx * sinx

              = (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169

And

cos(x + x) = cosX * cos(x) - sinx*sinx

               = (-12/13)(-12/13) - (-5/13)(-5/13)

               =  119/169

So,

You could use the tan double angle formula, but it is easiest to use  

tan(2x) = sin(2x)/cos(2x)  = (120/169) / (119/169)

          = 120/119.

So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

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The experimental probability the placebo pill induced better concentration on the student exams is 0.64

The question has to do with probability.

Probability is the likelihood of an event occurring.

The probability of an event A is given by

P(A) = number of occurrences of event A/total number of occurrences of all events.

Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.

The event A = students performing better.

Since 64 students performed better, the number of occurrences of event A = 64.

Since there were 100 students, the total number of occurrences = 100.

So, P(A) = P(students perform better)

= number of occurrences of event A/total number of occurrences of all events.

= 64/100

= 0.64

So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64

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Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, the proportion of books with major damage is:

43/(716 + 68 + 43) = 0.051995.

Hence, out of 36,500 books, the expected amount of books with major damage is:

0.051995 x 36,500 = 1898.

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Answer:

the greatest 7 digit no.is = 999,99,99 the smallest 6 digit no.is= 1,00,000

Step-by-step explanation:

Sorry if I'm wrong I tried.

Answer:

Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.

Step-by-step explanation:

3/5 = 0.6

The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6

This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.

Hope this helps!

The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

-t² + 7t = 0

Comparing with the standard form.

We substitute into the quadratic formula.

x = (-b±√(b² - 4ac)) / (2a)

x = (-7±√( (7)² - ( 4 × -1 × 0) ) / (2 × -1)

x = (-7±√( 49 - 0) ) / (-2)

x = (-7±√49 ) / (-2)

x = (-7±7 ) / (-2)

x = (-7-7 ) / (-2), (-7+7 ) / (-2)

x = -14/(-2), 0/(-2)

x = 7, 0

The solutions to the quadratic equation -t² + 7t = 0 are 7 and 0.

Hence, x = 7, 0.

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