A particular moth can infest avocado trees and potentially damage the avocado fruit. A farmer plans to investigate the number of damaged avocado fruit on moth-infested avocado trees of a certain variety. A recent article states that the population distribution of the number of damaged avocado fruit on moth-infested avocado trees of this variety is symmetric with mean of 6.4 and standard deviation of 1.9.


Required:

Compare the shapes of the sampling distributions of the sample mean number of damaged avocado fruit for random samples of 6 moth-infested trees and for random samples of 90 moth-infested trees from the population. Explain your answer.

The fraction 13/7 lies between the fractions 6/6 and 6/7.

We have,

Between the fractions 6/6 and 6/7, there are infinitely many fractions.

To find a fraction that lies between these two fractions, we can take their average.

The fraction 6/6 simplifies to 1, and the fraction 6/7 cannot be simplified further.

To find the average, we add the two fractions and divide the sum by 2:

(6/6 + 6/7) / 2

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 6 and 7, which is 42.

Converting the fractions to have a common denominator:

(6/6) x (7/7) + (6/7) x (6/6) / 2

Simplifying the expression:

(42/42 + 36/42) / 2

Combining the numerators:

(78/42) / 2

Dividing:

78/42 = 13/7

Thus,

The fraction 13/7 lies between the fractions 6/6 and 6/7.

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Answer:

make a proportion:

                        90% - 76.50$

original price is 100% - x$

x=76.50$*100%/90%=85$

Answer: original price is 85$

Step-by-step explanation:

The minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.

The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of prism.

Total surface area of the rectangular prism is calculated with the following formula.

\(A=2(lb+bh+lh)\)

Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.

The minimum amount of wrapping paper required to cover the gift is equal to the surface area of the figure.

The figure is made with different sides, The area of all the sides is equal to the surface area of the figure. The surface area of it is,

\(A=2(5\times8)+(15\times8)+(15\times10)+2(\dfrac{1}{2}3\times8)+(15\times5)+(15\times11)\\A=614\rm\;in^2\)

Thus, the minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.

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Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

4.01

Step-by-step explanation:

The quotient of the expressions −48.132 and −0.84 will be 57.30. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Given −48.132 ÷ −0.84.

Then the value of the expression will be

⇒ −48.132 / −0.84

If in the numerator and the denomination, the negative sign is present, then both will cancel out each other.

⇒ 48.132 / 0.84

⇒ 57.30

The quotient of the expressions −48.132 and −0.84 will be 57.30.

Then the correct option is C.

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The value of K = 0.044999999 and the initial value of Machine Vo = 949999.9952

The value of a machine is depreciating using the exponential function = 0 − where k is a constant, 0 is initial value of the machine and t is time in years. The value of the machine after 5 years is Sh. 758,590.4078 and its value after 8 years is Sh. 662,792.5098.

According to Exponential function

\(V = Voe^-Kt\)

where K = constant

Vo = Initial value

At = t = 5

V = 758590.4078

At = t = 8

V = 662792.5098

\(V_{Q} = Voe^{-Kt}\)

758590.4078 = \(Voe^-5t\)   --- equation 1

662792.5098 = \(Voe^{-8k}\)   --- equation 2

Dividing equation 1 by 2

1.144536784 = \(e^{3k}\)

Taking log on both the sides

3k = 0.134999999

K = 0.044999999

At t = 5 years

\(V = Voe^{-5k}\)

758590.4078 = \(Voe^{-5k}\)

\(Vo = \frac{758590.4078}{e^{-5(0.044999999)}}\)

Vo = 949999.9952

Hence the answer is the value of K = 0.044999999 and the initial value of Machine Vo = 949999.9952

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

Pizzas will be ordered by the two classes

Answer:

x=-8, 8.

Step-by-step explanation:

–|x| = –8. To solve this absolute value inequality we remove the negative sign on the left hand side

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

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

Collinear points are the points on the same line.

There are two lines in the diagram.

The collinear points:

The points that are collinear are  D,G and E  and another set of points which are collinear are L,G and J.

The points which lie on the same straight line are known as collinear points.

Similarly, if three or more number of points are collinear then they form a straight line.

If we observe the figure, the points D,G and E are collinear points as they are on same line.

Similarly the points L, G and H are in the straight line which makes them collinear.

Therefore , the points L,G and J are collinear points.

Hence, the points that are collinear are  D,G and E and another set of points which are collinear are L,G and J

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Answer:

x=5

Step-by-step explanation:

.

Answer:

C) -4,4,-6

Step-by-step explanation:

domain is x so plug the domain numbers into the function

4-2(-4)=12

4-2(0)=4

4-2(5)=-6

Therefore Range is (-4,4,-6)

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

Answer:

It does not represent a proportional relationship

Step-by-step explanation:

Answer:

It does not represent a proportional relationship

Step-by-step explanation For a line, the constant of proportionality is a fancy way to say the slope. It makes more sense without the intercept: y=2xclearly, the constant of proportionality is 2.

Answer:

77.47°

75.96°

26.57°

Step-by-step explanation:

Given vertices of the triangle:

Find the vectors from A to B, B to C and A to C:

\(\begin{aligned}AB = B - A &=(x_B-x_A,y_B-y_A) \\&=(-3-(-2), 8-4)\\& = (-1, 4) \end{aligned}\)

\(\begin{aligned}BC=C-B &=(x_C-x_B,y_C-y_B)\\ &=(6-(-3),8-8)\\&=(9,0)\end{aligned}\)

\(\begin{aligned}AC = C - A &=(x_C-x_A,y_C-x_A)\\&= (6-(-2), 8-4) \\&= (8, 4)\end{aligned}\)

Use Pythagoras Theorem to calculate the magnitudes of the vectors:

\(|AB| = \sqrt{(-1)^2+4^2}=\sqrt{17}\)

\(|BC|=\sqrt{9^2+0^2}=9\)

\(|AC| = \sqrt{8^2+4^2}=4\sqrt{5}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}\)

Rearrange the dot product formula to make θ the subject:

\(\implies \theta=\cos^{-1}\left(\dfrac{a \cdot b}{|a||b|}\right)\)

Use the rearranged dot product formula to find the angles between two pairs of vectors.

\(\boxed{\begin{minipage}{4 cm}\underline{Dot Product}\\\\$\textbf{u} \cdot \textbf{v}=u_1v_1+u_2v_2$\\\\where:\\ \phantom{ww}$\bullet$ $\textbf{u}=\left\langle u_1,u_2 \right\rangle$ \\\phantom{ww}$\bullet$ $\textbf{v}= \left\langle v_1,v_2 \right\rangle$ \\ \end{minipage}}\)

Angle A

\(\implies A=\cos^{-1}\left(\dfrac{AB \cdot AC}{|AB||AC|}\right)\)

\(\implies A=\cos^{-1}\left(\dfrac{-1 \cdot 8+4 \cdot4}{\sqrt{17} \cdot 4 \sqrt{5}}\right)\)

\(\implies A=\cos^{-1}\left(\dfrac{8}{4 \sqrt{85}}\right)\)

\(\implies A=77.47^{\circ}\; \sf (2 \; d.p.)\)

Angle C

\(\implies C=\cos^{-1}\left(\dfrac{BC \cdot AC}{|BC||AC|}\right)\)

\(\implies C=\cos^{-1}\left(\dfrac{9 \cdot 8+0 \cdot4}{9 \cdot 4 \sqrt{5}}\right)\)

\(\implies C=\cos^{-1}\left(\dfrac{72}{36 \sqrt{5}}\right)\)

\(\implies C=26.57^{\circ}\; \sf (2 \; d.p.)\)

Interior angles of a triangle sum to 180°.

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-77.47^{\circ}-26.57^{\circ}\)

\(\implies B=75.96^{\circ}\)

Therefore, the interior angles of the triangle with the given vertices are:

Answer:

b

Step-by-step explanation:

Answer: D:  y = 0

Step-by-step explanation: Hope that helped

Answer:

H0 : P = 0.72

H1 : P > 0.72

Step-by-step explanation:

Claim is to test that percentage of customers who leave a review is greater than 72%

From the information given :

P0 = 72/100 = 0.72

The null hypothesis, H0 : P = 0.72

Alternative hypothesis claims the proportion is greater than 0.72 and from the sampling result obtained, phat = 0.90

Hence,

Alternative hypothesis, H1 : P > 0.72

Answer: disagree

Step-by-step explanation:

Caterpillar A is longer, but not because of the decimal places. It is longer because of the place value.

Answer:

Disagreed

Step-by-step explanation:

In order to find the answer to this question you must remember that when dealing with finding the greater decimals you have to look at which have the greater place values in this case...

\(CA=4.125\)

\(CB=4.03\)

\(CC = 4.23\)

Caterpillars 1 place value is already greater then caterpillar B's place value of 0, so it doesn't really matter how many more numbers to add after 1 and 0 because these two place values are already different 1 > 0

Meaning that "although Caterpillar A is greater then Caterpillar B, it is not because it has more digits simply because one is greater then zero." You can prove this by seeing that Caterpillar C is greater then Caterpillar A because two is greater then one.

\(4.125 > 4.03\)

\(4.125 < 4.23\)

Hope this helps.

We make distinct dot plots for every predictor variable.

x₂=6.3368+0.7604×x₄

x₂=6.67+0.04×x₆

x₂=7.718+0.04×x₁₂

Given that,

Refer to Appendix C.1's SENIC data collection. All additional variables in the data set, with the exception of medical school affiliation and area, are included in the list of potential predictor variables for length of stay (Y). It is anticipated that the best model will have logio Y as the response variable, first-order terms for the predictor variables, and no interaction terms. Take examples 57–113 into consideration as the model-building data set for the subsequent studies.

We have to make distinct dot plots for every predictor variable. Do these storylines have any significant elements.

We know that,

Average length of stay = x₂

Infection risk = x₄

X-ray ratio = x₆

Available Services = x₁₂

57–113 into consideration as the model-building data set for the subsequent studies.

By using, regression equation for x₂ as dependent variable and regression equation for x₄ as independent variable..

Then,

x₂=6.3368+0.7604×x₄

x₂=6.67+0.04×x₆

x₂=7.718+0.04×x₁₂

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Answer:

She has 180 stamps in total

Step-by-step explanation:

Answer:

180 stamps

Step-by-step explanation:

if she used 60 stamps and that was only a thrid of it, then all you have to do is multiply by 3

Formula: 60·3=180

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

A square is a type of rectangle, so any square can also be called a rectangle. However, not all rectangles are squares.

A rectangle is a quadrilateral with four right angles, whereas a square is a special type of rectangle with four right angles and four equal sides.

So the shape that is both a rectangle and a square is a square.

Answer: 40

Step-by-step explanation: 40*.7 is 28 so that's the answer. How I got the answer was I did 28/.7 to get 40

Hope this helps and brainliest would be appreciated

Answer:

30% ywww

Step-by-step explanation:

After converting Cartesian into polar form, ∂S = (3cost, 3sint, -3) at t=0→2π. So option d is correct.

In the given question, we have to find a parametrization of the boundary curve as with positive orientation if

1. S is the part of the surface of the paraboloid z = 6-X^2-y^2 above the plane z=-3 with a normal vector pointing upward.

a. (√6 cos(t), √6 sin(t), 0)

b. (√6 cos(t), √6 sin(t), -3)

c. (3 cos(t), – 3 sin(t), -3)

d. (3 cos(t), 3 sin(t), -3)

e. (3 cos(t), 3 sin(t),0)

The given paraboloid is z = 6-X^2-y^2 above the plane z=-3.

Now convert Cartesian form to the polar equation.

In polar form x=rcost, y=rsint z=z and x^2+y^2=r^2

Now z = 6-X^2-y^2

z = 6-(X^2+y^2)

z = 6-r^2

Now put z=-3

-3 = 6-r^2

Subtract 6 on both side, we get

-r^2 = -9Now r^2 = 9

Taking square root on both side, we get

r=3

Now x=3cost, y=3sint, z= -3

So ∂S = (3cost, 3sint, -3) t=0→2π

So option d is correct.

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The answer is: 55 crayons.

Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!