Mr. Smith wants to know if he can fit 4 trapezoid tables like the one shown below into a room. What is the total area of 4 trapezoid tables? Answer without units. NUMBER ONLY!

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is

W = F • r cos(θ)

The cosine of the angle between the vectors can be obtained from the dot product identity,

a • b = ||a|| ||b|| cos(θ)   ==>   cos(θ) = (a • b) / (||a|| ||b||)

so that

W = (F • r)² / (||F|| ||r||)

For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is

W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   W ≈ 5.12 J

(assuming F and r are measured in Newtons (N) and meters (m), respectively).

Answer: [tex]\dfrac{7}{132}[/tex]

Step-by-step explanation:

Total marbles in the jar =  8+25 = 33

Using combinations, the number of ways of choosing two marbles out of 33=  [tex]\dfrac{33!}{2!(33-2)!}\\\\=\dfrac{33!}{2\times31!}\\\\=\dfrac{33\times32}{2}=528[/tex]  (total outcomes)

Similarly, the number of ways of choosing two red marbles =

[tex]\dfrac{8!}{2!6!}\\\\=\dfrac{8\times7}{2}=28[/tex](favorable outcomes)

Required probability = [tex]\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]

[tex]=\dfrac{28}{528}\\\\=\dfrac{7}{132}[/tex]

hence, required probability = [tex]\dfrac{7}{132}[/tex]

Answer:

2657205.

Step-by-step explanation:

This is a Geometric Sequence with common ratio 3.

13th term = 5*(3)^(13-1)

=5(3)^12

= 2657205.

Answer:

2657205.

Step-by-step explanation:

Answer:

1460

Step-by-step explanation:

Answer:

Equation is C = 4P

Graph is shown below

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Explanation:

The equation is C = 4P since it costs $4 per person. We just multiply 4 with the number of people (P) to get the cost (C).

Let's say 0 people show up, so that means C = 4*P = 4*0 = 0

The input P = 0 leads to the output C = 0. This is basically the same as saying x = 0 leads to y = 0. The point (0,0) is on the graph.

Repeat for P = 1 and you'll find that C = 4. This is the same as x = 1 leading to y = 4. The point (1,4) is on the graph.

If you keep going for various values of P, you'll get corresponding values of C. It turns out that all you need are 2 points to graph this line. Plot (0,0) and (1,4) on the same xy grid. Draw a line through them to complete the graph.

The graph is shown below.

Answer:

Step-by-step explanation:

Answer:

[tex]L =21.945[/tex] --- Length

[tex]W = 7.9725[/tex] --- Width

Step-by-step explanation:

Given

Let

[tex]L \to Length[/tex]

[tex]W \to Width[/tex]

So:

[tex]Area = 175[/tex]

[tex]L = 6 + 2W[/tex]

Required

The dimension of the rectangle

The area is calculated as:

[tex]Area =L*W[/tex]

This gives:

[tex]175 =L*W[/tex]

Substitute: [tex]L = 6 + 2W[/tex]

[tex]175 =(6 + 2W)*W[/tex]

Open bracket

[tex]175 =6W + 2W^2[/tex]

Rewrite as:

[tex]2W^2+ 6W -175 = 0[/tex]

Using quadratic formula:

[tex]W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

This gives:

[tex]W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}[/tex]

[tex]W = \frac{-6 \± \sqrt{1436}}{2*2}[/tex]

[tex]W = \frac{-6 \± 37.89}{4}[/tex]

Split

[tex]W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}[/tex]

[tex]W = \frac{31.89}{4}, W = \frac{-43.89}{4}[/tex]

The width cannot be negative;

So:

[tex]W = \frac{31.89}{4}[/tex]

[tex]W = 7.9725[/tex]

Recall that:

[tex]L = 6 + 2W[/tex]

[tex]L =6 + 2 * 7.9725[/tex]

[tex]L =21.945[/tex]

Answer:

d = 52°

Step-by-step explanation:

The two sides with little marks are congruent.

That means that the opposite angles are congruent.

One angle measures 76°.

The other to angles measure d each.

d + d + 76 = 180

2d + 76 = 180

2d = 104

d = 52

Answer:

Mean = 19.84

Standard deviation = 11.12

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.

The explanation of the answer is now given as follows:

Note: See the attached excel file for the calculation of the total of fx and total of f*x^2.

N = Number of individuals sampled = 200

From the attached excel file, we have:

Total of fx = 3,967

Total of f*x^2 = 103,425.50

Therefore, we have:

Mean = Total of fx / N = 3,967 / 200 = 19.84

Variance = (Total of f*x^2 / N) - Mean^2 = (103,425.50 / 200) - 19.84^2 = 517.13 - 393.43 = 123.70

Standard deviation = Variance^0.5 = 123.70^0.5 = 11.12

Answer:

2

Step-by-step explanation:

Answer:  a+b+c/3

Step-by-step explanation:

mean= sum of all values/number of values

Answer:

it would be 32

Step-by-step explanation:

you would add them all up then divide it by five

Answer: The answer is 32

Answer:

Step-by-step explanation:

Let the amount Emily started with be 100x

Amount spent at grocery 1/2 of the money:

                                                                 [tex]\frac{1}{2} \ of \ 100x = 50x[/tex]

Remaining amount  

                         [tex]=100 x - 50x = 50x[/tex]

Amount spent at the Bakery 1/2 of what is left :

                                                                      [tex]\frac{1}{2} \ of \ 50x = 25x[/tex]

Remaining amount

                      [tex]= 50x - 25x = 25x[/tex]

Amount spent on CD , 1/2 of what is left :

                                                               [tex]=\frac{1}{2} \ of \ 25x = \frac{1}{2} \times 25x = 12.5x[/tex]

Remaining amount

                     [tex]= 25x - 12.5x = 12.5x[/tex]

But given the amount left is $6

That is  ,

                [tex]12.5x = 6\\\\x = \frac{6}{12.5} = 0.48[/tex]

Therefore amount Emily had in beginning = 100 x  = 100( 0.48) = $48

Answer:

2.52m³

Step-by-step explanation:

volume=L x W x H

V=2 x 1.4 x 1.8

V=5.04

WE DIVIDE 5.04m³ by 2 to get 2.52m³

Have a nice day

Step-by-step explanation:

[tex]f(x) = g(x)h(x)[/tex]

Taking the derivative of f(x), we get

[tex]f'(x) = g'(x)h(x) + g(x)h'(x)[/tex]

Then [tex]f'(1)[/tex] becomes

[tex]f'(1) = (-1)(-2) + (1)(3) = 5[/tex]

Answer:

[tex]m =-4[/tex]

Step-by-step explanation:

Given

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

Required

Find m

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

By comparison:

[tex]m-3 = -7[/tex]

Add 3 to both sides

[tex]m = -7+3[/tex]

[tex]m =-4[/tex]

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]

Answer:

b. S = AUB

Step-by-step explanation:

Since the coins are tossed  3 times and each coin has head, H and tail, T(2 sides), the sample space is S = 2 × 2 × 2 = 2³ = 8

All the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH,THT and TTT

Since S denote the sample space

S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}

Since A denote the event that at least 1 of the coins comes to rest with its heads side upwards, the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH and THT

So, A = {HTT, HHT, HHH, THH, TTH, HTH,THT}

Also B denote the event that none of the coins comes to rest with its heads side upwards, that is no heads. The possible outcome is TTT

So, B = {TTT}

Since S denote the sample space

S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}

So, A ∪ B = {HTT, HHT, HHH, THH, TTH, HTH,THT} ∪  {TTT} = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT} = S

So, S = A ∪ B

So, S = A ∪ B does not denote an abuse of notation.

The answer is b.

Answer:

yeet

Step-by-step explanation:

Answer:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

Step-by-step explanation:

Given

[tex]Cups = 5[/tex]

[tex]Ball=1[/tex]

[tex]Trials = 20[/tex]

See attachment

Required

Simulate the above experiment (fill in the gaps)

The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:

[tex]P(Correct) = \frac{Ball}{Cups}[/tex]

This gives:

[tex]P(Correct) = \frac{1}{5}[/tex]

The number of times (i.e. 6) he chose correctly is not a factor in his simulation

So, a correct simulation of the experiment is as follows:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

The selected ball represents the number of balls hidden (i.e. 1 ball).

The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)

The 20 times represent the number of times the experiment is repeated.

Answer:

y = -7

Step-by-step explanation:

Slope: 0

y-intercept: (0,−7)

Since the line doesn't change up, down, right, or left, and it stays on the y-axis, that's how u get y = . The straight line runs along -7 . That's how u get -7 . so when u put it all together u get: y = -7 .

Hope that helps. Tried to explain the best I could :)

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

Answer:

90 kilometers

Step-by-step explanation:

https://www.bing.com/search?q=kilometers+are+there+in+9000000cm

Answer:

368.47

1686.56

Step-by-step explanation:

effective rate: .05/12=.00416666667

payment=x

[tex]16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47[/tex]

Interest:

368.47*48-16000=1686.56

Answer:

Answer:

368.47

1686.56

Step-by-step explanation:

effective rate: .05/12=.00416666667

payment=x

\begin{gathered}16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47\end{gathered}

16000=x

.00416666667

1−(1+.00416666667)

−48

x=368.47

Interest:

368.47*48-16000=1686.56

Answer:

y = -2+1/3x

Step-by-step explanation:

Slope = -2

x - intercept = -3

To make the x-intercept positive you make it 1/3.  

y = -2 +1/3x

9514 1404 393

Answer:

  -3840t^4

Step-by-step explanation:

The k-th term, counting from k=0, is ...

  C(5, k)·(4t)^(5-k)·(-3)^k

Here, we want k=1, so the term is ...

  C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4

__

The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.

Answer:

Step-by-step explanation:

(2d + 1)(3d - 1)

2d(3d - 1) + 1(3d - 1)

6d^2 - 2 + 3d + 1

6d^2 - 1 + 3d

6d^2 + 3d - 1 (after arranging in standard form)

Answer:

7d/(2d+1)(3d-1)=6d^2 + 3d - 1

Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered.

Answer:

The 30 minutes that she is changing the flat

Step-by-step explanation:

Answer:

a) Z = 2.575.

b) Z = 2.327.

c) Z = 1.96.

d) Z = 1.645.

e) Z = 1.88.

Step-by-step explanation:

Question a:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Question b:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Question c:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Question d:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Question e:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.94}{2} = 0.03[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.03 = 0.97[/tex], so Z = 1.88.

Answer:

Step-by-step explanation:

The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.