The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

Answer:

3 boxes of candy will cost $12 and 4 bags of popcorn will cost $28, adding the two gives us $40. They are only allowed to spend 42 dollars

Step-by-step explanation:

Answer: im on the same question

Step-by-step explanation:

sorry

The probability is the ratio of the favorable event to the total number of events. Then the probability of the elk caught in the park being unmarked will be 92.44%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The total number of elk is 5,625.

The number of elk that were marked is 225.

Then the number of elk that were unmarked will be

→ 5625 - 225 = 5,200

Then the probability of the elk caught in the park being unmarked will be

\(\rm P = \dfrac{5200}{5625}\\\\P = 0.9244 \ or \ 92.44\%\)

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The size P of a certain insect population at time t (in days) is given by the function P(t) = 900e^(0.04t), where e is Euler's number (approximately 2.71828).

The function P(t) = 900e^(0.04t) represents an exponential growth model for the insect population. The size of the population is determined by the time t in days.

In this equation, e is the base of the natural logarithm, approximately equal to 2.71828. The term e^(0.04t) represents the exponential growth factor, where 0.04 is the growth rate per day.

As time t increases, the exponent 0.04t becomes larger, resulting in exponential growth. The constant 900 represents the initial population size at t = 0.

By substituting different values of t into the function, we can calculate the size of the insect population at specific points in time.

For example, if we substitute t = 10 into the function, we find:

P(10) = 900e^(0.04*10)

= 900e^(0.4)

≈ 900 * 1.49182

≈ 1342.64

Therefore, at t = 10 days, the estimated size of the insect population is approximately 1342.64. The population size will continue to grow exponentially as time progresses, following the pattern described by the function P(t).

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Answer:

Step 1: multiply

10*10=100*10=1000*10=10000

Step 2: write 1st one out.

(8*10000)

Step 3: multiply

8*10000=80000

________________-

Step 1: multiply

10*10=100*10=1000*10=10000*10=100000*10=1000000*10=10000000*10=100000000*10=1000000000*10=10000000000*10=100000000000*10=1000000000000

step2: multiply

2*100000000000=200000000000

step 3: write it out

80000*200000000000

step 4: solve

80000*200000000000=1.6 to the power of 17

Step-by-step explanation:

so your answer is

1.6 to the power of 17

that was a lot yw

The jumbo gumball's will fit in the machine is 1000.

According to the statement

we have given that the A gumball machine is in the shape of a sphere with a radius of 6 inches. A store manager wants to fill up the machine with jumbo gumballs, which have a radius of 0.6in.

And we have to find that the How many jumbo gumball's will fit in the machine.

So, For this purpose, we know that the

the volume of the minature and the machine should be calculated. Volume of sphere:

V = (4/3) pi* r^3

Volume of the machine r = 6 in

V = (4/3) pi* 6^3 = 904.77 in^3

Volume of the miniature gumballs

V = (4/3) pi* (0.6)^3 = 0.90432 in^3

Divide the two volume to get the number of gumballs that can fill the machine

904.77 in^3/ 0.90432 in^3 = 1000.

So, The jumbo gumball's will fit in the machine is 1000.

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Answer:

70%

Step-by-step explanation:

5/10. 50%

6/10. 60%

8/10. 80%

9/10. 90%

Answer:

70%

Step-by-step explanation:

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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Answer:

y= -3x+1

Step-by-step explanation:

y=mx+b

find m: (y2-y1)/(x2-x1)

pick any two points: (-1,4) and (0,1)

plug them in: (4-1)/(-1-0)= -3=m

b is the y intercept which is 1=b

plug these into the equation for a line y=mx+b

y=-3x+1

Answer: Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Step-by-step explanation:

Given that;

U = 75

X = 78

standard deviation α = 10

sample size n = 20

population is normally distributed

PROBLEM is to test

H₀ : U = 75

H₁ : U ≠ 75

TEST STATISTIC

since we know the standard deviation

Z =  (X - U) / ( α /√n)

Z = ( 78 - 75 ) / ( 10 / √20)

Z = 1.3416 ≈ 1.342

Now suppose we need to test at ∝ = 0.05 level of significance,

Then Rejection region for the two tailed test is Zc = 1.96

∴ Reject H₀ if Z > Zc

and we know that Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

At the null hypothesis, we test if the mean is of 75, that is:

\(H_0: \mu = 75\)

At the alternative hypothesis, we test if the mean is different of 75, that is:

\(H_1: \mu \neq 75\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which:

For this problem, we have that:

\(X = 78, \mu = 75, \sigma = 10, n = 20\)

The value of the test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}\)

\(z = 1.34\)

Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.

Looking at the z-table, z = -1.34 has a p-value of 0.0901.

2(0.0901) = 0.1802

The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

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The critical numbers of the function f(x) = (x^3/5)(4 - x) are x = 0 and x = 3.

To find the critical numbers of the function f(x) = (x^3/5)(4 - x), we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.

Let's first find the derivative of f(x):

f'(x) = d/dx[(x^3/5)(4 - x)]

Using the product rule, we can differentiate the function:

f'(x) = [(3/5)x^(3/5-1)(4 - x)] + [(x^3/5)(-1)]

Simplifying further:

f'(x) = [(3/5)x^(3/5-1)(4 - x)] - (x^3/5)

f'(x) = (3/5)x^(3/5-1)(4 - x) - (x^3/5)

Now, let's find the critical numbers by setting the derivative equal to zero and solving for x:

0 = (3/5)x^(3/5-1)(4 - x) - (x^3/5)

0 = (3/5)x^(-2/5)(4 - x) - (x^3/5)

Multiply through by 5x^2 to get rid of the fractions:

0 = 3(4 - x)x^2 - x^3

0 = 12x^2 - 3x^3 - 3x^2

0 = -3x^3 + 9x^2

0 = x^2(-3x + 9)

From this equation, we can see that x^2 = 0 or -3x + 9 = 0.

For x^2 = 0, we have x = 0.

For -3x + 9 = 0, we solve for x:

-3x = -9

x = 3

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non-linear functions

Average Rate of Change is used primarily with non-linear functions, since all linear functions have a constant rate of change.

Answer:

x = -36

hope it helps

Answer:36

Step-by-step explanation:

-1/6x=23-17

-1/6x=-6

1/6x=6

x=36

Answer:

The answer is C

Step-by-step explanation:

2x + 4y

2 x 3 = 6

4 x 6 = 24

24 + 6 = 30

Answer:

30

Step-by-step explanation:

2x+4y

Let x=3 and y=6

2*3 +4*6

Multiply

6+24

Add

30

Answer:

Step-by-step explanation:

To get the length of segment HJ if H lies at (-1,7) and J lies at (8,-5)​, we will use the formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²+(y₂-y₁)²

From the coordinates x₁ = -1, y₁ = 7, x₂ = 8, y₂ = -5

HJ = √(8-(-1))²+(-5-7)²

HJ = √(8+1)²+(-12)²

HJ = √81+144

HJ = √225

HJ = 15

Hence the length of segment HJ is 15 units

Answer:

7250

Step-by-step explanation:

145,000

x

0.05

145000 / 100 = 1450.

1450 x 5 = 7250

Using the given function V(x) = 15,000(0.87)^x , the value of Mr.Dulaney's car 5 years after its purchase will be approximately equal to given option $7500.

A mathematical phrase, rule, or law that establishes the relation between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A mathematical function is a rule that assigns a unique output, also called the function value, to each input value within a certain set called the domain. The output is determined by the instructions, also called the function rule, that defines the relationship between the input and output values. It can be represented by an equation, such as y = f(x), where x is the input, y is the output, and f is the function symbol. The graph of a function is a set of points, where each input in the domain corresponds to a unique output. It helps to express the relationship between two variables and allows to make predictions and analyze patterns in mathematical problems.

Given,

V(x) = 15,000(0.87)^x where x denotes number of years after its purchase.

So, to find the value of Mr. Dulaney's car 5 years after its purchase,

let x =5

so V(x) = 15,000(0.87)^5 = $7476.31

Which is approximately equal to given option , $7,500

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Answer:

The area of the shaded region is \(49.5 cm^{2}\) to 3. significant figures

Step-by-step explanation:

Step one: find the two diagonals of the kite.

The Horizontal diagonal can be obtained using the cosine rule:

\(AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)\)

\(AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm\)

The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:

Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.

This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.

\(cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm\)

Step two: Use the dimensions of the two diagonals of the Kite to find the area:

The area of a Kite is obtained using this formula:

\(Area = \frac{pq}{2}\), where p and q are the two diagonals.

hence,

\(Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}\)

Step three: Calculate the area of the sector of the circle.

Area of the sector is obtained using this formula

\(Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}\)

Step Four: Subtract the area of the sector from the area of the kite:

Area of the shaded region will be \(116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}\)

This will be\(49.5 cm^{2}\) to 3. significant figures

Answer:

43.8 cm²

Step-by-step explanation:

1. Split the kite in two and find the length of OB

When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.

Then, use the sine rule we can find out the length of OB. It goes like this:

\(\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm\)

2. Calculate the area of the kite

Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of \(area of triangle=\frac{1}{2}absinc\).

\(\frac{1}{2}\)×8×16×sin60 = \(32\sqrt{3}\)

But as there are two triangles, we duplicate the answer.

2×\(32\sqrt{2}\) = \(64\sqrt{3}\)

2. Calculate the area of the sector

area of sector =\(\frac{angle of sector}{360} \\\)×πr²

\(\frac{120}{360}\)×8²π = \(\frac{64}{3}\)π

3. Subtract the area of the sector from the area of the kite

\(64\sqrt{3}\) - \(\frac{64}{3}\)π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)

HOPE THIS WILL HELP YOU :)

The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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Answer:

\( (2m - 7)(4 {m}^{2} + 3)\)

Step-by-step explanation:

\(8m^3 - 28m^2 + 6m - 21 \\ = 4 {m}^{2} (2 {m} - 7) + 3(2m - 7) \\ = (2m - 7)(4 {m}^{2} + 3)\)

Option:-

\( \: \)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

Answer:

a) 3x + 2

Step-by-step explanation:

Now we have to,

→ Find the quotient of the following.

Given problem,

→ (9x + 6) ÷ 3

Let's find the required quotient,

→ (9x + 6) ÷ 3

→ (9x + 6)/3

→ (9x/3) + (6/3)

→ (3x) + (2)

→ 3x + 2

Hence, the option (a) is correct.

If the function is continuous function and ∫0 to 8 f(u) du = 6, the value of ∫ 1 to 3 xf(x² - 1) dx is B) 3.

Given ∫0 to 8 f(u) du = 6 and we need to find the value of ∫ 1 to 3 xf(x² - 1) dx

We can say, u = x² - 1

Differentiating both sides

du = 2x dx

dx = du/2x

When x = 1,

         u = 1² - 1 = 0

and when x = 3

         u = 3² - 1 = 8

So, ∫ 1 to 3 xf(x² - 1) dx can be written as

           ∫ 1 to 3 xf(x² - 1) dx = ∫ 0 to 8 xf(u)  du/2x

                                          = 1/2∫ 0 to 8 f(u) du

It is given that ∫0 to 8 f(u) du = 6

So, ∫ 1 to 3 xf(x² - 1) dx = 1/2 x 6 = 3

Hence, the value of ∫ 1 to 3 xf(x² - 1) dx is 3.

The question is incomplete. The complete question is

" The function f is continuous and ∫0 to 8 f(u) du=6. What is the value ∫ 1 to 3 xf(x² - 1) dx? (A) 3/2 (B) 3 (C) 6 (D) 12 (E) 24 "

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Answer: 56% of them

Step-by-step explanation:

Answer:

25151/100000

Step-by-step explanation:

To arrive at the objective function, we must make the main assumption that the returns are normally distributed

The objective function is a mathematical expression used to represent the goal of a problem in terms of one or more variables. In finance, the objective function is used to represent the goal of maximizing returns.

The distribution of returns is an important factor to consider when creating an objective function for an investment portfolio. Returns are the gains or losses an investor makes on his investments. The distribution of returns refers to the way in which these returns are distributed in the portfolio.

To arrive at the objective function, we must make the main assumption that the returns are normally distributed. A normal distribution is a bell-shaped curve that represents the distribution of data in a population. In finance, normal distributions are used to model portfolio returns because they ensure a good approximation of how returns are distributed across a wide range of investments.

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Answer:

Step-by-step explanation:

The given rate, in words per minute, is ...

  (190 words)/(5 min) = 38 words/min

The offered ratios are ...

  38/1 = 38 . . . . proportional

  74/2 = 37 . . . . NOT proportional

  230/45 ≈ 5.11 . . . NOT proportional

  290/105 ≈ 2.76 . . . NOT proportional

  570/15 = 38 . . . . proportional

  950/25 = 38 . . . . proportional