Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043 Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.39 or 1.43 or 2.88 or 0.70

Answer:

At first, we have 3 expressions that are equal.

[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]

[tex]6+21 - 63= 3+32 - 4[/tex]

[tex]-36=31[/tex]

[tex]-36\neq 31[/tex]

This is not true.

Answer:

Step-by-step explanation:

a) The sample space, n(S) = 6^6 = 46656

Let the number fair dice toss that show 6 = n(A)

Hence, the probability of getting, P(A) = n(A)/n(S)

b) Sample space, n(S) = 6^42

n(A) = 6^9

∴ P(A) = n(A)/n(S) = 6^9/6^42 = 1/(6^33) = 2.09 X 10^(-26)

c) No

Answer:

4

Step-by-step explanation:

If 1/20 of the metal is lost during casting. Calculate the number of complete slabs casted. (4mks)

Answer:

4.2

Step-by-step explanation:

f varies inversly with L can be translated matimatically as:

● f = k/L

It takes 7 pounds of pressure to break a 3 feet long board.

Replace f by 7 and L by 3.

● 7 = k/3 => k=7×3=21

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find tge length of a board that takes 5 pounds of pressure to be broken.

● 5 = k/L

● 5 = 21/L

● L = 21/5 = 4.2

So the board is 4.2 feet long

[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]

Answer:

[tex]\huge \boxed{{x=-10}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{5} =-2[/tex]

We need the x variable to be isolated on one side of the equation, so we can find the value of x.

Multiply both sides of the equation by 5.

[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]

Simplify the equation.

[tex]x=-10[/tex]

The value of x that makes the equation true is -10.

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

The probability that the selected adult has liver problems is 0.08

Step-by-step explanation:

In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.

Let E(L) be the event that an adult has liver problems.

The probability is directly obtainable from the question and it is given as 8%

Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08

Answer:

Selling price=rs.600.

Profit of rs=100.

Step-by-step explanation:

C.P=500; profit%=20%

S.P.=100+profit%×C.P/100

S.P=120×500/100

=rs.600

S.P>C.P

Profit S.P-C.P

600-500=100

he gained for rs.100.

Answer:

Hello,

Answer

[tex]\sigma=457,95...[/tex]

Step-by-step explanation:

p(z<a)=0.9

p(z<1.29)=0.9015

p(z<1.28)=0.8997

using linear interpolation: with 4 decimals

p(z<1.282)<0.9

[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]

Answer:

P(C|Y) = 0.5.

Step-by-step explanation:

We are given the following table below;

               X             Y               Z             Total

A             32           10             28              70

B              6             5              25              36

C             18            15              7                40

Total       56           30            60              146

Now, we have to find the probability of P(C/Y).

As we know that the conditional probability formula of P(A/B) is given by;

                    P(A/B) =  [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]

So, according to our question;

P(C/Y) =  [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]

Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) =  [tex]\frac{15}{146}[/tex]  {by seeing third row and second column}

Hence, P(C/Y) =  [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]

                       =  [tex]\frac{15}{30}[/tex]  = 0.5.

Answer: 0.5

Step-by-step explanation:

edge

Answer:

try 91.78, 91.58, 91.26, 363.4

Step-by-step explanation:

Here, we are required to find the area of the paper board given after the semicircle is cut out of it

Area of the paper board that remains is 423 in²

Length = 29 in

Width = 20 in

Area of a rectangle = length × width

= 29 in × 20 in

= 580 in²

Area of a semi circle = πr²/2

π = 3.14

r = diameter / 2 = 20 in / 2 = 10 in

Area of a semi circle = πr²/2

= 3.14 × (10 in)² / 2

= 3.14 × 100 in² / 2

= 314 in²/2

= 157 in²

The semicircle is cut out of the rectangle

Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle

Area of the paper board that remains = Area of a rectangle - Area of a semi circle

= 580 in² - 157 in²

= 423 in²

Read more:

https://brainly.com/question/16994941

9514 1404 393

Answer:

  A. 281,634

Step-by-step explanation:

You can identify the number after the first two "rules".

Choices A and C have 3 in the tens place.

Choice A has 6 in the hundreds place.

Answer:

Hey there!

The area of a rectangle is the length times width.

Thus, we can write the equation, 600=30w.

Solving for the width, we get that the width is equal to 20 ft.

Let me know if this helps :)

Answer:

20 feet across.

Step-by-step explanation:

You will have to do a simple equation solve.

x is how many feet across the court is.

* could be our multiplying sign

600 = 30*x

Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.

That leaves 20 = x.

So it is 20 feet across.

[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]

Answer:

y = 1        m = -3       b = 1

Step-by-step explanation:

y = mx + b                          y = -3x + 1

y = 1

m = -3

b = 1

Answer:

True

Step-by-step explanation:

The normal form of equation of a line is the radius of p. Tangent to a circle is the line that touches one point on the circle. The radius is the circumference of the circle. The tangent line on the circle is always perpendicular to the radius. The statement is correct.

Answer:

-5/8

Step-by-step explanation:

13/ -56   -x = 11/28

Add 13/56 to each side

13/ -56   + 13/56  -x = 11/28+ 13/56

-x = 11/28 + 13/56

Get a common denominator

-x = 11/28 *2/2 +13/56

-x = 22/56 + 13/56

-x = 35/56

Divide top and bottom by 7

-x = 5/8

Multiply both side by -1

x = -5/8

Answer:

-4x - 3.

Step-by-step explanation:

f(x) = -4x + 5.

f(x + 2) = -4(x + 2) + 5

= -4x - 8 + 5

= -4x - 3.

Hope this helps!

Answer:

f(x+2)=-4x-3

Step-by-step explanation:

We are given:

[tex]f(x)= -4x+5[/tex]

and asked to find f(x+2). Therefore, we must substitute x+2 for each x in the function.

[tex]f(x+2)=-4(x+2)+5[/tex]

Now, simplify. First, distribute the -4. Multiply each term inside the parentheses by -4.

[tex]f(x+2)=(-4*x)+(-4*2)+5\\f(x+2)=-4x+(-4*2)+5\\f(x+2)=-4x-8+5[/tex]

Next, combine like terms. There are 2 constants (terms without a variable) that can be added. Add -8 and 5.

[tex]f(x+2)=-4x(-8+5)\\f(x+2)=-4x-3[/tex]

f(x+2) is -4x-3.

Answer:

(x − 7)2 + (y − 8)2 = 11

Step-by-step explanation:

I took the test

The equation of the circle with center at (7, 8) and radius of 11 is

(x - 7)²  +  (y - 8)²  =121

The equation of a circle with center at (a, b) and radius of r is:

(x - a)²  +  (y - b)²  =  r²

The center of the circle, (a, b)  =  (7, 8)

That is, a = 7, b = 8

The radius, r = 11

Substitute a = 7, b = 8, and r = 11 into the equation (x - a)²  +  (y - b)²  =  r²:

(x - 7)²  +  (y - 8)²  =  11²

(x - 7)²  +  (y - 8)²  = 121

Therefore, the equation of the circle with center at (7, 8) and radius of 11 is

(x - 7)²  +  (y - 8)²  =121

Learn more here: https://brainly.com/question/23226948

Sol-1

[tex]\\ \sf\longmapsto |y-12|=21[/tex]

[tex]\\ \sf\longmapsto y+12=21[/tex]

[tex]\\ \sf\longmapsto y=21-12[/tex]

[tex]\\ \sf\longmapsto y=9[/tex]

Sol:-2

[tex]\\ \sf\longmapsto y-12=21[/tex]

[tex]\\ \sf\longmapsto y=21+12[/tex]

[tex]\\ \sf\longmapsto y=33[/tex]

Answer:

[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus

Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]

Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]

[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]

∴ we have evaluated the line integral using Green's Theorem.

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Learn more about multivariable calculus: https://brainly.com/question/14502499

---

Topic: Multivariable Calculus

Unit: Green's Theorem and Surfaces

Answer: 3 pounds.

Step-by-step explanation:

We have two metals:

One that contains 20% nickel, let's call it metal A.

One that contains 80% nickel, let's call it metal B.

We have 6 pounds of metal B, in those 6 punds we have:

0.80*6lb = 4.8lb of nickel.

Now, if we add X pounds of metal A, then we will have:

X + 6lb in total weight.

4.8lb + 0.2*X of nickel.

And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6

(4.8lb + 0.2*X)/(6lb + X) = 0.6

now we solve it for X:

(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X

4.8lb - 3.6lb = 0.6*X - 0.2*X

1.2lb = 0.4*X

1.2lb/0.4 = 3lb = X

We should use 3 pounds of the metal with 20% of nickel.

9514 1404 393

Answer:

  (x, y) = (4, -4)

Step-by-step explanation:

A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).

__

The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.

The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.

The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.

The point of intersection of the lines, (4, -4), is the solution to the system of equations.

Answer:

B. j(kl)

Step-by-step explanation:

(jk)l

We can change the order we multiply and still get the same result

j(kl)

Answer:

Step-by-step explanation:

its B i did it

Answer:

Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Step-by-step explanation:

Given the equation of regression analysis is given as:

[tex]y= 30,000 + 4x[/tex]

where [tex]x[/tex] is the cost on advertising in Dollars.

and [tex]y[/tex] is the sales in Thousand Dollars.

To find:

The correct increase in sales when there is increase in the advertising cost.

Solution:

Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.

Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].

Initial sales

[tex]y= 30,000 + 4x[/tex] ....... (1)

After increase of $1 in advertising cost, final cost:

[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]

Subtracting (2) from (1) to find the increase in the sales:

[tex]y'-y=30004+4x-30000-4x = 4[/tex]

The units of sales is Thousand Dollars ($1000).

So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]

So, correct answer is:

d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Answer:

In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.

We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.

To multiply two 2-digit numbers, using the area model, follow the given steps:

Write the multiplicands in expanded form as tens and ones.

For example, 27 as 20 and 7, and 35 as 30 and 5.

Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.

Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.

On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.

Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.

write the product in the cell

Finally, add all the partial products to get the final product.

Here, for example, the area model has been used to multiply 27 and 35.

area model multiplication

Let us see how to find the product of 3-digit number by a 2-digit number using the area model.

Find the Product using Area Model

Let us now use the area model for the division. Here, we divide 825 by 5.

Area Model Division 1

Area Model Division 2

Fun Facts

The area model is also known as the box model.

The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.

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Answer:

0.07047

Step-by-step explanation:

at least 4 people survive is

4 people survive and 2 don't +

5 people survive and 1 doesn't +

all 6 people survive

the probability of 4 people to survive is the product of the individual probabilities :

0.3×0.3×0.3×0.3 = 0.3⁴ = 0.0081

times the probability 2 don't survive

0.7×0.7 = 0.49

0.0081×0.49 = 0.003969

now, the chance that 4 out of 6 survive is that probabilty times how many times we can select 4 out of 6.

to select 4 out of 6 is

[tex] \binom{6}{4} [/tex]

= 6! / (4! × (6-4)!) = 6! / (4! × 2!) = 6×5/2 = 30/2 = 15

so, the probability of having 4 survivors is

15×0.003969 = 0.059535

the probability of 5 people surviving is 0.3⁵ times one not

0.3⁵×0.7 = 0.001701

we have 6 over 5 combinations to pick 5 out of 6 = 6.

so, in total for 5 survivors we get

6×0.001701 = 0.010206

and the probabilty of all 6 surviving is

0.3⁶ = 0.000729

so, the probability of at least 4 out of 6 surviving is

0.059535 +

0.010206 +

0.000729

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

0.070470

Answer:

The critical value for two tailed test at alpha=0.1 is ± 1.645

The calculated  z= 9.406

Step-by-step explanation:

Formulate the hypotheses as

H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods

Ha : p1≠ p2

Choose the significance level ∝= 0.1

The critical value for two tailed test at alpha=0.1 is ± 1.645

The test statistic is

Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]

p1= scrap rate of old method = 62/200=0.31

p2= scrap rate of new method = 36/400= 0.09

p = an estimate of the common scrap rate on the assumption that the two rates are same.

p = n1p1+ n2p2/ n1 + n2

p =200 (0.31) + 400 (0.09) / 600

p= 62+ 36/600= 98/600 =0.1633

now q = 1-p= 1- 0.1633= 0.8367

Thus

z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)

z= 0.301/√ 0.13663( 3/400)

z= 0.301/0.0320

z= 9.406

The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.

Answer:

-2x -8

Step-by-step explanation: