A certain brand of fishing line claims to have an average breaking strength of 30 pounds. A group of fishermen become angry because this brand of line seems to break so easily and test 25 randomly selected lines of this brand. The mean breaking strength is 27.994 pounds with a standard deviation of 0.846 pounds. A plot of the data follows. Do these data provide sufficient evidence for the fishermen to conclude that the average breaking strength is less than claimed? What procedure should we use?

If the flow of one of the branches of the main pipe is 04 gallons per minutes and the second branch of the main pipe will floe 6 gallons per minute.

Since the water is not leaking, the amount of water flowing in through the larger pipe should be equal to the amount of water flowing out through the smaller pipe.

So, if r₁ is the flow rate in bigger pipe and r₂ and r₃ are the flow rate in smaller pipe, then we must have

           r₁ = r₂ + r₃

⇒       r₃ = r₂ - r₁

In the given problem we have,

r₁ = 10 gallons per minute

r₂ = 4 gallons per minute

So, using the above formula we have,

r₃ = 10 gallons per minute - 4 gallons per minute

   = 6 gallons per minute.

Therefore, the water flow in the other branch will be 6 gallon per minute.

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Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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According to the Triangle Inequality Theorem, the sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.

In this case, you know the lengths of two sides of the triangle, and you also know that "x" represents the length of the third side. Then, you can set up the following:

Solving the inequality, you get:

You can rewrite it as:

Hence, the answer is:

The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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Answer:

11 1/4

Hope I helped

The correlation coefficient of the security X and Y returns is closest to 0.67, indicating a moderate positive correlation between the two securities.

The correlation coefficient of the security X and Y returns is closest to 0.67. This can be calculated by dividing the covariance of the returns by the square root of the product of the variances of X and Y.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, with values close to 1 indicating a strong positive correlation, values close to -1 indicating a strong negative correlation, and values close to 0 indicating a weak or no correlation.

In this case, the given covariance is 10, the variance of Security X's returns is 13%, and the variance of Security Y's returns is 17%. To calculate the correlation coefficient, we use the formula:

Correlation coefficient = Covariance / (\(\sqrt{}\)(Variance_X) * \(\sqrt\)(Variance_Y))

Plugging in the values, we get:

Correlation coefficient = 10 / (\(\sqrt\)(13%) * \(\sqrt\)(17%)) ≈ 0.67

Therefore, the closest option is 0.67, indicating a moderately strong positive correlation between the returns of Security X and Security Y.

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The required measure of the angle x is 72° in the triangle.

Given that,
The value of x in the triangle at 36°, x°, and x° is to be determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
For the triangle sum of the internal angle is 180°,
36 + x + x = 180
2x = 144
x = 72°

Thus, the required measure of the angle x is 72° in the triangle.  

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Answer:

3(3+7)

Step-by-step explanation: you factor out the greatest common multiple. 3 times 3 is 9 and 3 times 7 is 21

The required answers are 6) 150 degree 8) 215 degree.

If the terminal edge of an angle in standard position is on the x- or y-axis, the angle is referred to as a quadrantal angle. Quadrantal angles include 0, 90, 180, 270, and 360 degrees, among others. The images below show examples of some of these angles.

To convert radian to degree just multiply 180/π to radian.

6) 5π/6

= \($\frac{5\pi}{6}\times\frac{180}{\pi}\)

= 150 degree

8) to lie 35 degree in third quadrant add 180 degree to it

= 180 + 35

= 215 degree

Thus, required answers are 6) 150 degree 8) 215 degree.

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Answer:

the answers should be the first, third, and fourth ones

Step-by-step explanation:

Answer:

first third fourth

Step-by-step explanation:

I think

The answer should be 240

Answer:

There is 240 servings in 40 pizzas.

Step-by-step explanation:

You have to start by finding how many servings are just in 1 pizza and that is 6 and then multiple 40 by 6 and you get 240.

The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective. However, if there are several broken eggs, the package design may need to be improved to provide better protection.

When testing a new package design, it is important to simulate real-world conditions as much as possible. In this case, dropping a carton of a dozen eggs from a height of 1 foot is a good way to simulate the types of impacts that the package may experience during shipping and handling.

To conduct the test, you will need to follow these steps:

The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective.

However, if there are several broken eggs, the package design may need to be improved to provide better protection.

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Answer:

A and D

Step-by-step explanation:

B and C are not functions because some inputs have multiple outputs

Answer:

The cost of the printer is x=288 and cost of computer is 3x=864

Step-by-step explanation:

Let the cost of the printer be x and cost of computer be 3x

ATQ, x+3x=1152, x=288.

The cost of the printer is x=288 and cost of computer is 3x=864

Answer:

I think the answer is D

Step-by-step explanation:

If the observed t-value exceeds the critical t-value, then the difference between the sample means is most likely statistically significant.

In other words, the difference between the sample means is unlikely to have occurred by chance and is likely due to a real difference in the population means. The direction and magnitude of the difference must be further examined using effect size measures and confidence intervals.

Therefore, the most suitable value to be fit in the blank space of the given incomplete statement is, statistically significant.

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Answer:

3/19

Step-by-step explanation:

No. of people who ordered the small lemon yogurt divided by total no. of people

= 9/57

= 3/19

The net electric field at (a) \(x=0 cm\) is -1.20 × 10^5 N/C to the left direction and (b) \(x=+6.00\) cm is 2.08 × 10^5 N/C to the right direction.

(a): The electric field due to both charges at point A (x = 0 cm) is \( E = kq1/r1² - kq2/r2²\)

The distance between two charges \((r) = 3.0 + 9.0 = 12.0 cm = 0.12 m\)

∴ The net electric field at \(x=0\) cm is given as; \(E = kq1/r1² - kq2/r2²E = 9 × 10^9 Nm^2/C^2 × (6.14 × 10^-6 C) / (0.12 m)² - 9 × 10^9 Nm^2/C^2 × (23.9 × 10^-6 C) / (0.12 m)²= - 1.20 × 10^5 N/C\).

So, the net electric field magnitude at \(x=0\) cm is 1.20 × 10^5 N/C to the left direction. The direction is indicated by the negative sign.

(b): The electric field due to both charges at point B (\(x= +6.00\) cm) is \(E = kq1/r1² + kq2/r2²\).

The distance between charge 1 and point B, \(r1= 6.0 - 3.0 = 3.0 cm = 0.03 m\)

The distance between charge 2 and point B, \(r2= 9.0 - 6.0 = 3.0 cm = 0.03 m\)

∴ The net electric field at x=+6.00 cm is given as; \(E = kq1/r1² + kq2/r2²E = 9 × 10^9 Nm^2/C^2 × (6.14 × 10^-6 C) / (0.03 m)² + 9 × 10^9 Nm^2/C^2 × (23.9 × 10^-6 C) / (0.03 m)²= 2.08 × 10^5 N/C\)

So, the net electric field magnitude at \(x=+6.00\) cm is 2.08 × 10^5 N/C to the right direction. The direction is indicated by the positive sign. Thus, the net electric field (magnitude and direction given as a plus or minus sign) at (a) \(x=0 cm\) is -1.20 × 10^5 N/C to the left direction and (b) \(x=+6.00 cm\) is 2.08 × 10^5 N/C to the right direction.

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Answer:

answer = 7.5

Step-by-step explanation:

PG = 2 PR ( by Parallelogram law)

4x - 5 = 2 (x + 5)

4x - 5 = 2x + 10

4x - 2x = 10 + 5

2x = 15

x = 15/2

x = 7.5

Answer:

48

Step-by-step explanation:

9,18

6,12,18,24,30

18 + 30 = 48

Answer:

Last option e : X=0

Step-by-step explanation:

X=0

Answer:

x = 0

Step-by-step explanation:

I got it correct on Odyssey.   : )

y is sufficient for β

The probability density function (pdf) of an exponential distribution with mean β is given by:

f(y | β) = (1/β)exp(-y/β), for y ≥ 0

To show that f(y | β) is in the exponential family, we need to write it in the form:

f(y | β) = h(y)exp{θT(y) - A(θ)}

where h(y), θ, and A(θ) are functions that depend only on y, θ, and do not depend on β.

First, we can rewrite the pdf as:

f(y | β) = (1/β)exp(-y/β)

= (1/β)exp{(-1/β)y}

= (1/β)exp{(-1/β)yx}

where x = 1.

Next, we can identify the functions h(y), θ, and A(θ):

h(y) = 1

θ = -1/β

A(θ) = -log(-θ)

= -log(1/β)

= log(β)

Substituting these values, we get:

f(y | β) = exp{(-1/β)y}exp{-log(β)}

= exp{(-1/β)y - log(β)}

Therefore, f(y | β) is in the exponential family.

To show that y is sufficient for β, we can use the factorization theorem.

The joint pdf of the sample y1, y2, ..., yn is:

f(y1, y2, ..., yn | β) = (1/β)^n exp{- (y1 + y2 + ... + yn)/β}

= (1/β)^n exp{-n(ybar)/β}

where ybar is the sample mean.

Using the factorization theorem, we can write:

f(y1, y2, ..., yn | β) = h(y)g(T(y), β)

where T(y) = ∑ yi and h(y) does not depend on β.

Therefore, y is sufficient for β.

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Answer:

The total length of the fox is 30 3/5 inches

Step-by-step explanation:

Here, we are interested in calculating the total length of a fox, given the length of its head and body and also the length of its tail.

Mathematically, the total length of the fox = length of its head and body + length of its tail

length of the head and body = 19 4/5

length of its tail = 10 4/5

Plugging these values into the equation, we have;

19 4/5 + 10 4/5

99/5 + 54/5 = (99 + 54)/5 = 153/5 = 30 3/5 inches

Answer:

4

Step-by-step explanation:

A stock will pay constant dividends of 6 every year. Its required rate of return (a.k.a., cost of capital, discount rate) is 23%. The value of the stock is 26.09.

The value of a stock that pays constant dividends of 6 every year and its required rate of return (a.k.a., cost of capital, discount rate) is 23% is 26.09. To calculate the value of the stock, we will use the Gordon Growth Model or the Dividend Discount Model.

The formula for Gordon Growth Model is as follows:
P0 = D1 / (r - g)
Where P0 is the price of the stock today, D1 is the dividend expected to be paid next year, r is the required rate of return, and g is the expected growth rate of dividends.

Here, the expected growth rate of dividends is zero, which means the dividends will remain constant.
P0 = D1 / (r - g)
P0 = 6 / (23% - 0)
P0 = 6 / 0.23
P0 = 26.09
Therefore, the value of the stock is 26.09.

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The weight of food packed in certain containers is a random variable with a mean of 16 0z. and a standard deviation of 0.6 oz. If 36 packages are randomly selected, the probability that the mean will be greater than 16.2 oz is 2.28%.

Given that the weight of food packed in containers is a random variable with a mean (µ) of 16 oz. and a standard deviation (σ) of 0.6 oz, we want to find the probability that the mean weight of a sample of 36 packages (n) will be greater than 16.2 oz.
Step 1: Calculate the standard error (SE) of the sample mean.
SE = σ / √n = 0.6 / √36 = 0.6 / 6 = 0.1
Step 2: Calculate the z-score for 16.2 oz.
z = (sample mean - population mean) / SE = (16.2 - 16) / 0.1 = 2
Step 3: Find the probability that the mean weight will be greater than 16.2 oz.
To find the probability for a z-score of 2, we can look it up in a standard normal (z) table or use a calculator that provides the area to the left of the z-score.
Using the table or calculator, we find the area to the left of the z-score 2 is approximately 0.9772. Since we are looking for the probability of the mean weight being greater than 16.2 oz, we want the area to the right of the z-score. To find this, subtract the area to the left from 1:
1 - 0.9772 = 0.0228
So, the probability that the mean weight of the 36 packages will be greater than 16.2 oz is approximately 0.0228 or 2.28%.

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The Discriminant of the quadratic equation "2x + 5x² = 1" is 24  .

The Discriminant(D) of the Quadratic Equation ax² + bx + c can be calculated using the formula ; D = b² - 4ac .

the quadratic equation is given as 2x + 5x² = 1 ;

after rearranging the terms ,

the equation can be written as :

⇒ 5x² \(+\) 2x - 1 = 0  ;

Substituting the values in the discriminant formula ,

we get ;

D = (2)² - 4×5×(-1)

Simplifying further ,

we get ;

D = 4 + 20

D = 24 .

Therefore , the value of the Discriminant is 24 .

The given question is incomplete , the complete question is  

What is the discriminant of the quadratic equation 2x + 5x² = 1  ?

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Answer:

See attached image.

Step-by-step explanation:

See the attached image.

Use Microsoft Excel to produce a scatter chart.

The correlation coefficient is -0.12 and the line of the best fit is y = -0.11x + 385.50

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

\(\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}\)

From the table, the value of r:

r = -0.12

The negative correlation exist between year and time.

Since the value of r is not near the -1 or -1 we can say the relation is very weak.

The line of best fit:

y = mx + c

m = -0.11

c = 385.50

y = -0.11x + 385.50

Thus, the correlation coefficient is -0.12 and the line of the best fit is y = -0.11x + 385.50

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Answer:

length = 15 feet.

Step-by-step explanation:

This paper is 15 feet across on any side. Who will deliver this monster?

Area = s^2 where s is the length of 1 side.

Area = 225 feet^2  (You sure this isn't inches).

s^2 = area

s^2 = 225        Take the square root of both sides of the equation.

sqrt(s^2) = sqrt(225)

s = 15