The U.S. Federal Seed Act establishes germination rates for various fruit and vegetable seeds. Watermelon seeds are to meet a 70% germination standard. A skeptical gardener who has not had very good luck planting watermelons believes that the seed company he purchases seeds from is not adhering to the 70% federal mandate. Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%. Compute a 98% confidence interval to estimate the proportion of watermelon seeds that germinate. Be sure to interpret your interval in the context of the problem.

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:

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:

2806

Step-by-step explanation:

→ First complete the multiplication

456 × 6 = 2736 and 35 × 2 = 70

→ Add the totals

2736 + 70 = 2806

Answer:2806

Step-by-step explanation:

^﹏^

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:

The formula to find the nth term of the given sequence is 54 · [tex]\frac{2}{3} ^{n}[/tex]

Step-by-step explanation:

The formula for nth term of an geometric progression is :

[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex]

In this example, we have [tex]a_{1}[/tex] = 36 (the first term in the sequence) and

r = [tex]\frac{2}{3}[/tex] (the rate in which the sequence is changing).

Knowing what the values for r and [tex]a_{1}[/tex] are, now we can solve.

[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex] = [tex]\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }[/tex] = 54 · [tex]\frac{2}{3} ^{n}[/tex]

Therefore, the formula to find the nth term of the given sequence is

54 · [tex]\frac{2}{3} ^{n}[/tex]

Answer:

1460

Step-by-step explanation:

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:

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:

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:

2.52m³

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

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:

A, L, F

Step-by-step explanation:

Quadrant ll (2) is the top left one so points A, L, F are in it. Hope this is correct!

Answer: AL

Step-by-step explanation: THE OTHER ARE ON THE AXIS AND NOT NEITHER QUADRANTS

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:

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:

h = 30°

Step-by-step explanation:

All angles in a triangle add up to 180°, so:

60° + 90° + h° = 180°

Solving for h, we should get 30 as our answer.

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:

1800 ml of oil

Step-by-step explanation:

300*6

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:

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:

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.

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] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]

Step-by-step explanation:

Since, given is a 30°-60°-90° triangle.

[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]

[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]

[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]

[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]

[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]

Answer:

[tex](g + f)(8) =133[/tex]

Step-by-step explanation:

Given

[tex]g(n) = 3n - 5[/tex]

[tex]f(n) = n^2 + 50[/tex]

Required

[tex](g + f)(8)[/tex]

This is calculated as:

[tex](g + f)(n) =g(n) + f(n)[/tex]

So, we have:

[tex](g + f)(n) =3n - 5 + n^2 +50[/tex]

[tex]Substitute[/tex] 8 for n

[tex](g + f)(8) =3*8 - 5 + 8^2 +50[/tex]

[tex](g + f)(8) =24 - 5 + 64 +50[/tex]

[tex](g + f)(8) =133[/tex]

Answer:

Graph A (first graph from top to bottom)

Step-by-step explanation:

Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.

Factoring the polynomial:

[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]

Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).

The graph that corresponds with this is graph A.

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:

[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:

2

Step-by-step explanation:

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.

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

Answer:

yeet

Step-by-step explanation: