Arthur and Bradley can complete a job in 12 minutes if they work together. By himself, Bradley would take 36 minutes to do the same job. How long would Arthur take working alone?

The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

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Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

The volume of the cone is (100)π cubic centimeters.

Given that the slant height (l) of the cone is 13 cm, and the height from the vertex to the center of the base (h) is 12 cm, we need to find the volume (V) of the cone.

To do this, we'll first need to find the radius (r) of the cone's base.
We can use the Pythagorean theorem to find the radius, since the slant height, height, and radius form a right triangle:
l² = h² + r²
Plugging in the given values:
13² = 12² + r²
169 = 144 + r²
r² = 25
r = 5 cm
Now that we have the radius, we can find the volume of the cone using the following formula:
V = (1/3)πr²h
Substitute the known values:
V = (1/3)π(5²)(12)
V = (1/3)π(25)(12)
V = (1/3)π(300).

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Answer:

2/4-1/3= 6/12-4/12

=2/12

=1/6

Answer:

Step-by-step explanation:

Yes plzz give me brainliest

The area of triangle ΔAFD found using trigonometric ratios to find the leg lengths FD and FA is 24.5·√3 square units

Trigonometric ratios expresses the relationship between two sides of a right triangle and an interior angle of the right triangle.

The specified parameters are;

m∠F in ΔAFD = 90°

The length of the hypotenuse side, AD = 14

The measure of angle ∠D, m∠D = 30°

The area of a triangle = Half base length × Height

The area of the triangle ΔAFD = (1/2) × FD × FA

The trigonometric ratios for cosines, indicates that we get;

cos(∠D) = FD/AD

Therefore;

FD = AD × cos(∠D)

Plugging in the values, we get;

FD = 14 × cos(30°)

FD = 14 × (√3)/2 = 7·√3

FD = 7·√3

The trigonometric ratios for sines indicates that we get;

sin(∠D) = FA/AD

Therefore; FA = AD × sin(∠D)

FA = 14 × sin(30°) = 7

FA = 7

ΔAFD = (1/2) × 7·√3 × 7 = (49·√3)/2

The area of triangle ΔAFD, A = 24.5·√3 square units

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Answer:

Five and twenty six twenty eighths.

Step-by-step explanation:

Start with writing the fractions in numbers:

\(2\frac{3}{7} +3\frac{2}{4}\)

The 2 next to the first fraction is considered a whole number therefore we can say:

\(\frac{2}{1} *\frac{7}{7} =\frac{14}{7}\) then,  \(\frac{14}{7} + \frac{3}{7} =\frac{17}{7}\)

\(2\frac{3}{7} =\frac{17}{7}\)

The 3 is also considered a whole number therefore:

\(\frac{3}{1} *\frac{4}{4} =\frac{12}{4}\) then, \(\frac{12}{4} +\frac{2}{4} =\frac{14}{4}\)

\(3\frac{2}{4} =\frac{14}{4}\)

We got our 2 fractions without whole numbers now which makes it easier to add them up however they have different denominators meaning we can't add them.

\(\frac{17}{7} +\frac{14}{4}\) not possible to add up.

We have to find a common factor, we will do this by looking at our times tables and realizing that 7x4= 28 and 4*7= 28. This will ensure both dominators are the same.

\(\frac{17}{7} *\frac{4}{4} =\frac{68}{28}\)

\(\frac{14}{4} *\frac{7}{7} =\frac{98}{28}\)

Now we got both fractions with equal denominators which means we can add them up as you would with normal numbers:

\(\frac{68}{28} +\frac{98}{28} =\frac{166}{28}\)

We need to make sure to simplify the resultant fraction now, we know that 28*5= 140 and 28*6= 168, we will use 5 as our whole unit since it fits (168 is greater than 166 therefore we can't use that):

\(\frac{166}{28} =5\frac{26}{28}\) (this is the answer on the answer choices)

Now just simplify 26 over 28:

\(5\frac{26}{28}=5\frac{13}{14}\)

This gives us our final answer of 5 and thirteen fourteenths however judging from the answer choices our answer will be five and twenty six twenty eighths.

*see attachment for the diagrambifbthe mapping

Answer:

{x | x = –5, –3, 1, 2, 6}

Step-by-step explanation:

The domain of a function includes all input values entered in the oval for input, while the range includes all the values in the output oval.

From the mapping given in the attachment, we have the following possible values of the function in the input oval as: -5, -3, 1, 2, 6.

These x-values make up the domain of the function, and represented as: {x | x = –5, –3, 1, 2, 6}

Answer:

2x+15=5y

y=(2x+15)/5

hope this helps

Answer:

\(y = \frac{2}{5} x + 3\)

Step-by-step explanation:

2x - 5y = -15

Firstly, you will need to isolate the variable you are solving for, in this case, y.

2x - 2x - 5y = -15 - 2x

-5y = -15 - 2x

-5y/-5 = -15/-5 - 2x/-5

A negative divided or multiplied by a negative is positive.

\(y = 3 + \frac{2}{5} x\)

Rearrange.

\(y = \frac{2}{5} x +3\)

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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14/85 is the probability that one of each color is drawn.

How does probability explain work?

Red balls = 2

black balls = 7

white balls = 8

total balls  = 2 + 7 + 8 = 17

p( one ball from each color = ²C₁ * ⁷C₁ * ⁸C₁/ ¹⁷C₃

                                              = 2 * 7 * 8//680

                                              = 14/85

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The square MATH has equal side lengths MA, TH, AT and HM

Hanna's claim is correct because

The coordinate points are given as:

M(1, 2), A(-5, 3), T(-6,-3), and H(0,- 4).

Calculate the side lengths of the square using the following distance formula

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

MA = √[(1 + 5)^2 + (2 - 3)^2] = √37

AT = √[(-5 + 6)^2 + (3 + 3)^2] = √37

TH = √[(-6 + 0)^2 + (-3 + 4)^2] = √37

HM = √[(0 - 1)^2 + (-4 - 2)^2] = √37

The side lengths are equal.

Next, we calculate the slopes using:

m =(y2 - y1)/(x2 - x1)

So, we have:

MA = (2-3)/(1+5) = -1/6

AT = (3+3)/(-5+6) = 6

TH = (-3+4)/(-6+0) = -1/6

HM = (-4-2)/(0-1) = 6

See that opposite sides have the same slope

i.e MA = TH and AT = HM

And adjacent sides have their slopes to be opposite reciprocals

i.e. MA = -1/AT and TH = -1/HM

The calculated distances and slopes implies that Hanna's claim is correct

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Answer:

Step-by-step explanation:

BP ^2 = AP*PC

AP = 5

PC = 8

BP^2 = 5 * 8

BP^2 = 40

Don't bother taking it down any further. We are going to need it as it is.

BP^2 + PC^2 = x^2

BP^ = 40

PC^2 = 8^2 = 64

40 + 64 = x^2

104 = x^2

sqrt(x^2) = sqrt(104)

x = 2 sqrt(26)  or

x = 10.198

Answer:

Ling should atleast work 15 hours a week to earn $120.

Step-by-step explanation:

Ling earn per hour = $8

Let the number of hours she worked to be x.

Now, inequality =  

\(8x \geq 120\)

Dividing both side by 8.

\(\dfrac{8x}{8} \geq \dfrac{120}{8}\)

\(x \geq 15\)

Hence, Ling should atleast work 15 hours a week to earn $120.

Answer:

10.875 total, 1.5 times each are below.

Step-by-step explanation:

1.5 (1 1/2) x 1.5 = 2.25

0.5 (2/4) x 1.5 = 0.75

0.125 (1/8) x 1.5 = 1.875

4 x 1.5 = 6

2.25 + 0.75 + 1.875 + 6 = 10.875 total

The net represents a cube.

The net shows a cube with a side length of 12 cm, meaning its surface area is \(6(12)^{2}=\boxed{864 \text{ cm}^{3}}\)

Answer:

Step-by-step explanation:

The Platonic solid with six (6) square faces is the cube. Its surface area is the sum of the areas of the square faces. Each of those is the square of its edge length.

__

The 3-dimensional shape represented by the net is a cube.

The area of the cube is ...

  6 × (12 cm)² = 6 × (144 cm²) = 864 cm²

Answer:

6

Step-by-step explanation:

You know DF = 6 and EB = 6 too. Since E is the mid-point of AEB, EB and AB are equal.

DF = EB

     = AB

     = 6

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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To determine which proposal(s) to select, we need to compare the present worth or net present value (NPV) of each proposal. The NPV represents the difference between the present value of cash inflows and outflows for each proposal.

For independent proposals at MARR = 15.5% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 15.5%.

Select the proposal(s) with a positive NPV. Positive NPV indicates that the project's expected cash inflows exceed the initial investment and the MARR.

For mutually exclusive proposals at MARR = 10% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 10%.

Select the proposal with the highest positive NPV. The proposal with the highest positive NPV indicates the project that generates the highest expected return or value relative to the MARR.

For mutually exclusive proposals at MARR = 14% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 14%.

Select the proposal with the highest positive NPV. The proposal with the highest positive NPV indicates the project that generates the highest expected return or value relative to the MARR.

It's important to note that the specific details of the proposals, including cash inflows, outflows, and timing, are needed to calculate the NPV accurately. Without this information, it is not possible to provide a definitive answer.

Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:

Horizontal asymptote at y = 0.

They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.

Researching this problem on the internet, the functions are given as follows:

The limits are given as follows:

\(\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0\)

\(\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty\)

Hence, the correct statement is:

Horizontal asymptote at y = 0.

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Answer:

Yes.

Step-by-step explanation:

To find if a triangle is a right triangle or not, we use the Pythagorean theorem. The Pythagorean theorem states that \(a^{2} + b^{2} = c^{2}\).

a and b are the triangle legs. The c is the hypotenuse of the triangle.

Now, to find if a triangle is a right triangle, we plug in 9 for a and b and 9root2 for c.

\(9^{2} + 9^{2} = (9\sqrt{2})^{2}\)

81 + 81 = 81 * 2

162 = 162

So the given triangle, is indeed a right triangle.

The graph that shows the most reliable results is given as follows:

Option C.

The correlation coefficient between two variables is an index that measures correlation between these variables, assuming values between -1 and 1.

If it is positive, the relation is direct proportional, and if it is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is strong.

From this description, we get that the most accurate graph is the one with the higher correlation coefficient, hence Option C is correct.

This problem gives two options, as follows:

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The probability of selecting a heart and then a star with replacement is approximately 0.1875 or 18.75%.

Assuming that a standard deck of 52 playing cards is used, with 13 cards of each suit (including hearts) and 4 suits in total, the probability of selecting a heart on the first draw and then selecting a star (presumably meaning a card from a different suit) on the second draw with replacement is

P (heart than star)

= P (heart) × P (star)

= 13/52 × 39/52

= 507/2704

= 0.1875

where P (heart) is 13/52 is the probability of selecting a heart on the first draw (since there are 13 hearts in the deck), and P (star) is the probability of selecting a card that is not a heart on the second draw (since there are 39 non-heart cards left in the deck after the heart is replaced).

Therefore, the probability of selecting a heart and then a star with replacement is approximately 0.1875 or 18.75%.

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-- The given question is incomplete, the complete question

"What is the probability of selecting a heart and then a star with replacement?" --

Answer:

66r+77   |    -14k+9

Step-by-step explanation:

i gotchu big daddy

Answer:

Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.

Step-by-step explanation:

You can add or subtract mixed numbers by turning them to improper fractions first. Improper fractions are fractions where the numerator is greater than the denominator.

Answer:98

Step-by-step explanation:

Ap3x

Answer:

its 270, just for clarification.

Step-by-step explanation:

The quotient of 874 and 23 is 38.

To get the quotient of 874 and 23 using an area model, create a rectangle with an area of 874 and divide it into 23 equal parts.

Each part would depict the value of one of the 23 groups that 874 is divided into. Then count how many of these equal parts fit into the rectangle and this would give the answer to the division problem.

The rectangle can be divided into 23 equal parts horizontally, and then count how many of these parts fit into the rectangle vertically. Start with one part and see how many times we can fit it into the rectangle vertically before reaching a total of 874.

874 ÷ 23 = ( 1 x 23) + ( 7 x 23)

874 ÷ 23 = 23 + 161

874 ÷ 23 = 38

So the quotient of 874 and 23 is 38.

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Thus, the probability that the focus group will have two males and two females is 0.3.

To determine the total number of possible ways to select four members from a department of 10. This is known as the sample space and is calculated using the combination formula, which is:
n C r = n! / r! (n - r)!

where n is the total number of individuals (in this case, 10) and r is the number of individuals being selected (in this case, 4).

So, the sample space for selecting four members from a department of 10 is:
10 C 4 = 10! / 4! (10 - 4)! = 210

Next, we need to determine the number of ways to select two males and two females from a department with 7 males and 3 females.

This is calculated using the multiplication principle, which states that the total number of ways to perform a sequence of events is equal to the product of the number of ways to perform each individual event.

So, the number of ways to select two males and two females from a department with 7 males and 3 females is:
(7 C 2) x (3 C 2) = 21 x 3 = 63

Finally, we can calculate the probability of selecting a focus group with two males and two females by dividing the number of ways to select two males and two females by the total number of possible ways to select four members:
63 / 210 = 0.3

Therefore, the probability that the focus group will have two males and two females is 0.3. The answer is d.

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Answer:

x= -11

Step-by-step explanation:

hope this helps you!

Answer:

x = -11

Step-by-step explanation: