Adam and Mags win £2400. They split the money in the ratio 1:5. How much does Adam get?

In the given situation, the required value of x for the given pair of adjacent angles is 30°.

When two angles have a similar vertex and side, they are referred to as neighboring angles.

The vertex of an angle is the point at which the rays that make up its sides come to an end.

When adjacent angles have the same vertex and side, they can be a complimentary angle or supplemental angle.

The definition of adjacent is next to or nearby.

Two next-door residences are an illustration of proximity.

Typically, we think of those who live on our street as neighbors.

So, we have:

x + x + 30 = 90

Now, solve for x as follows:

x + x + 30 = 90

2x + 30 = 90

2x = 90 - 30

2x = 60

x = 60/2

x = 30

Therefore, in the given situation, the required value of x for the given pair of adjacent angles is 30°.

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The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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The value of the sample proportionThe sample proportion is the percentage of individuals in a sample who have the attribute of interest. As a result, the sample proportion is computed by dividing the number of students who answered "yes" by the total number of students surveyed.

Here's the computation:Sample proportion= 220/400= 0.55Therefore, the sample proportion is 0.55.b. The standard error of the sample proportionThe standard error of the sample proportion can be determined using the following formula:Standard error of Standard error of the sample proportion= √[(0.55 * 0.45)/400]= √(0.00061875)= 0.0249Therefore, the standard error of the sample proportion is 0.0249.c. Constructing an approximate 95% confidence interval for the true proportion

A confidence interval is a range of values around a sample statistic, such as the sample proportion, that is expected to contain the true value of the population parameter with a certain degree of confidence. A 95 percent confidence interval implies that we are 95 percent certain that the true population parameter is within the specified interval.Let's first compute the margin of error:Margin of error= z* √[(p*q)/n]wherez= critical value of the standard normal distribution for a 95% confidence level= 1.96Margin of error= 1.96* √[(0.55*0.45)/400]= 0.0487Therefore, the margin of error is 0.0487. Now that we have the margin of error, we can construct the confidence interval using the following formula:Confidence interval= sample proportion ± margin of error= 0.55 ± 0.0487= (0.5013, 0.5987)Therefore, an approximate 95 percent confidence interval for the true proportion is (0.5013, 0.5987).

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Answer: Caitlyn’s chocolate milk is stronger.

Step-by-step explanation:

Rachel = 60/400
= 3/20 or 15%

Caitlyn = 40/250

= 4/25 or 16%

Answer:

2 nickels and 21 dimes

Step-by-step explanation:

0.05N + 0.1D = 2.2

N + D = 23

Let's use the substitution method. Solve the second equation for N.

N = 23 - D

Now where you see N in the first equation substitute N with 23 - D.

0.05(23 - D) + 0.1D = 2.2

1.15 - 0.05D + 0.1D = 2.2

0.05D = 1.05

D = 1.05/0.05

D = 21

Now substitute 21 for D in the second original equation and solve for N.

N + 21 = 23

N = 2

Answer: 2 nickels and 21 dimes

Answer:

10 levels

Step-by-step explanation:

Ralph is on level 7

Mike level 5

Don level 10 and is playing the last one of game

The game has 10 levels

Leo is playing the first level and Ralph is sex levels above Leo. This means that Ralph is playing level:

= 1 + 6

= 7

Mike is two levels below Ralph which means that Mike is playing level:

= 7 - 2

= 5

Don is playing the last level and is five levels above Mike which means that Don is playing level:

= 5 + 5

= 10

Don is playing level 10 which is the last level so the game has 10 levels.

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The length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

1. Let's start by finding the measure of angles x and y. We know that the area of the circle is \(\(81\pi\)\), and since the area of a circle is given by the formula \(\(A = \pi r^2\\)), we can equate it to find the value of \(\(r\). So, \(81\pi = \pi r^2\).\)

  Solving this equation, we get \(\(r^2 = 81\)\), which gives us \(\(r = 9\)\).

2. Since points A, B, C, and D are on the circle, we can consider the angles formed by the lines connecting these points to the center of the circle.

3. Let's assume that the measure of angle x is \(\(a\)\) radians. As per the given information, the measure of angle y is \(\( \frac{5\pi}{9} \)\) radians greater than angle x. So, the measure of angle y is \(\(a + \frac{5\pi}{9}\)\) radians.

4. Since angles x and y are formed by lines from the center of the circle, the sum of their measures should be equal to \(\(2\pi\)\) radians. So we can write the equation \(\(a + (a + \frac{5\pi}{9}) = 2\pi\).\)

5. Simplifying the equation, we get \(\(2a + \frac{5\pi}{9} = 2\pi\).\)

6. Solving for \(\(a\)\), we find \(\(a = \frac{4\pi}{9}\).\)

7. Now that we have the value of angle x, we can find the measure of angle z. Again, since the sum of angles formed by lines from the center of the circle is \(\(2\pi\)\), we can write the equation \(\(a + (a + \frac{5\pi}{9}) + z = 2\pi\)\).

8. Substituting the known values, we have \(\( \frac{4\pi}{9} + (\frac{4\pi}{9} + \frac{5\pi}{9}) + z = 2\pi\)\).

9. Simplifying the equation, we get \(\( \frac{13\pi}{9} + z = 2\pi\)\).

10. Solving for \(\(z\)\), we find \(\(z = \frac{5\pi}{9}\)\).

11. Angle z represents the measure of the central angle that corresponds to minor arc CD.

12. The length of a minor arc in a circle is given by the formula \(\(s = r\theta\)\), where \(\(r\)\) is the radius of the circle and \(\(\theta\)\) is the central angle in radians.

13. Substituting the known values, we have \(\(s = 9 \cdot \frac{5\pi}{9} = \frac{5\pi}{3}\)\).

14. Therefore, the length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

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The required local linear approximation of 4 at xy 4 1 is y = 4x + 8.

Given, x0 = -1 And, the formula to obtain the local linear approximation (y) of 4 at xy 4 1 is f(c)f() + f'(x0)(x - 30)

where,f(c) is a function of x;f() is the constant function;and f'(x0) is the first derivative of the function f(x) evaluated at x = x0 = -1.

The derivative of a function f(x) is defined as the slope of the tangent line at any given point x on the graph of the function f(x).

Here, f(x) = y = 4x and x = 1.So, y = 4(1) = 4 and y is given as 4.The first derivative of the function f(x) is obtained as;f'(x) = dy/dx = 4And, f'(x0) = f'(-1) = 4Given the value of x0, and substituting the values in the formula,y = f(c)f() + f'(x0)(x - 30) y = 4 + 4(x - (-1))y = 4 + 4(x + 1) y = 4 + 4x + 4y = 4x + 8.

Hence, the required local linear approximation of 4 at xy 4 1 is y = 4x + 8. Therefore, the required local linear approximation of 4 at xy 4 1 is y = 4x + 8.

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Answer: 2

Step-by-step explanation:

because e=mc

Answer:

190

Step-by-step explanation:

30x6=180+10=190

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To provide the final numerical answer, the exact values of f(x1), f(x2), f(x3), and f(x4) need to be calculated using a calculator or numerical approximation techniques.

To approximate the integral of the function f(x) = x · 2^x over the interval [0, 4], we can use the midpoint rule with four equal-width subintervals. The midpoint rule estimates the integral by evaluating the function at the midpoint of each subinterval and multiplying it by the width of the subinterval.

To apply the midpoint rule, we divide the interval [0, 4] into four equal-width subintervals. The width of each subinterval is (4-0)/4 = 1.

The midpoints of the subintervals are located at x = 0.5, 1.5, 2.5, and 3.5. Let's denote these midpoints as x1, x2, x3, and x4, respectively.

For each subinterval, we evaluate the function f(x) = x · 2^x at the corresponding midpoint and multiply it by the width of the subinterval:

I ≈ Δx [f(x1) + f(x2) + f(x3) + f(x4)]

Now, let's calculate the values of f(x) at each midpoint:

f(x1) = 0.5 · 2^(0.5) = 0.5 · sqrt(2)

f(x2) = 1.5 · 2^(1.5)

f(x3) = 2.5 · 2^(2.5)

f(x4) = 3.5 · 2^(3.5)

Finally, we substitute these values into the midpoint rule formula:

I ≈ 1 [f(x1) + f(x2) + f(x3) + f(x4)]

Replace the values of f(x) at each midpoint and simplify to find the approximate value of the integral.

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The stretch of an exponential decay function is y = 2(1/5)ˣ

From the question, we have the following parameters that can be used in our computation:

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

Answer:

8.63 square units

Step-by-step explanation:

you must set up a proportion.

3 x

- = -

8 23

after you set up that proportion, cross multiply to find x.

8x = 69

divide by 8

x = 8.625, rounded to 8.63

The graph represents the unregulated market for uranium, where the mines dump their waste in a river that passes through a small town.

The marginal external cost (MEC) of the dumped waste is equal to the marginal private cost (MPC) of producing uranium, and the marginal social cost (MSC) is double the MPC. The government imposes a pollution tax to internalize the externality. The question asks to draw the MSC curve at a production level of 200 tons and indicate the efficient quantity that reflects the marginal external cost.

It also seeks to determine the tax per ton of uranium needed to achieve the efficient quantity of pollution. In the graph, draw the MSC curve above the supply (S) curve, representing the doubled marginal private cost due to the marginal external cost. At a production level of 200 tons, mark a point on the MSC curve. This point represents the marginal social cost at that quantity. To indicate the efficient quantity, draw an arrow pointing to the point on the MSC curve that aligns with the intersection of the demand (D) curve and the original supply curve (MPC).

To achieve the efficient quantity of pollution, the government imposes a tax per ton of uranium. The tax should be equal to the marginal external cost at the efficient quantity. Mark the tax per ton of uranium (S) on the graph, which aligns with the efficient quantity point. This tax internalizes the externality by adjusting the private cost of production to reflect the true social cost, leading to the efficient level of pollution.

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Answer:

145 degrees

Step-by-step explanation:

The largest exterior angle would be the one with the smallest interior angle, which is 35 And exterior and interior angles is always 180.

180 - 35 = 145 degrees

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Answer:

145 degrees

Step-by-step explanation:

I don't want the brainleist.

The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ .

In the question it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ.

In the question, it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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Answer: The answer is x = 6.5

Answer:

The mean is 5.33

Step-by-step-Explanation:

'Mean' means the sum of all the observations divided by the number of observations.

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Hi, there!

 _____

» Multiply every term by 3.

\(\boldsymbol{3b+11=-6}\)

Now we can subtract 11 from both sides.

\(\boldsymbol{3b=-17}\)

Now we can divide by 3 both sides.

\(\boldsymbol{b=-\dfrac{17}{3}}\)

Hope the answer - and explanation - made sense,

happy studying!!

Answer:

35

Step-by-step explanation:

18+17=35

Answer:

216\(\pi\)

Step-by-step explanation:

Given the figure.

And the perimeter in the ratio 4: 2: 1.

Perimeter of smallest circle = \(8\pi\)

To find:

Area of shaded region.

Solution:

To find the area, we need to have radius first.

And radius can be calculated by the given perimeter.

Formula for Perimeter is given as:

Perimeter = \(2\pi r\)

\(8\pi = 2\pi r\\\Rightarrow r = 4\ cm\)

Radius of smallest circle = 4 cm

Ratio of perimeter is equal to the ratio of the radii.

Radius of 2nd smallest circle by the given ratio = 8 cm

Radius of largest circle = 16 cm

Area of a circle is given the formula:

\(A = \pi r^2\)

Area of the smallest circle = \(\pi 4^2 = 16\pi\ cm^2\)

Area of the 2nd smallest circle = \(\pi 8^2 = 64\pi\ cm^2\)

Area of the largest circle = \(\pi 16^2 = 256\pi\ cm^2\)

Area of the shaded region = Area of largest circle + 2 \(\times\) Area of 2nd smallest circle + 3 \(\times\) Area of smallest circle - 2 \(\times\) Area of smallest circle - 3 \(\times\) Area of 2nd smallest circle

Area of the shaded region = Area of largest circle - Area of 2nd smallest circle + Area of smallest circle = \(256\pi - 64\pi +16\pi = 216\pi\)

Answer:

5.25 inches after 5 wks

7 inches after 12 wks

Step-by-step explanation:

after 5 weeks:  y = .25(5) + 4 which is 5.25 inches

after 12 weeks:  y = .25(12) + 4 which is 7 inches

The maximum dimensions  6 Centimeters for the side length and 12 centimeters for the height.For square base dimensional is 7 and hexagonal base dimension is 6

1. Square Base:

Let's assume the side length of the square base is x centimeters. Since the height is double the side length, the height of the pyramid will be 2x centimeters.

The surface area of the four triangular sides of the pyramid is given by:

Surface Area of Triangular Sides = 4 * (1/2 * x * 2x) = 4x^2

The surface area of the square base is given by:

Surface Area of Square Base = x^2

To find the maximum dimensions, we need to maximize the surface area while keeping it under 250 square centimeters. Therefore, we have the equation:

Surface Area of Triangular Sides + Surface Area of Square Base ≤ 250

4x^2 + x^2 ≤ 250

5x^2 ≤ 250

x^2 ≤ 50

x ≤ √50

Rounding √50 to the nearest whole number, we get x ≈ 7. So, the maximum side length for the square base is approximately 7 centimeters. The height will be double the side length, so the maximum height will be approximately 14 centimeters.

2. Hexagonal Base:

Let's assume the side length of the hexagonal base is y centimeters. Again, the height of the pyramid will be 2y centimeters.

The surface area of the six triangular sides of the pyramid is given by:

Surface Area of Triangular Sides = 6 * (1/2 * y * 2y) = 6y^2

The surface area of the hexagonal base is given by:

Surface Area of Hexagonal Base = (3√3 / 2) * y^2

To find the maximum dimensions, we have the equation:

Surface Area of Triangular Sides + Surface Area of Hexagonal Base ≤ 250

6y^2 + (3√3 / 2) * y^2 ≤ 250

Simplifying and solving the inequality, we find that y ≤ √(250 / (6 + 3√3 / 2)). Rounding this value to the nearest whole number, we get y ≈ 6.

So, the maximum side length for the hexagonal base is approximately 6 centimeters.

The height will be double the side length, so the maximum height will be approximately 12 centimeters.

For a square base, the maximum dimensions are approximately 7 centimeters for the side length and 14 centimeters for the height.

For a hexagonal base, the maximum dimensions are approximately 6 centimeters for the side length and 12 centimeters for the height.

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Answer:

34.71%

Step-by-step explanation:

1112-100 percent

386-x percent

x=386*100/1112≈34.71

The percentage of students living with their parents is 34.44%. The correct option is B.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that after a study was completed at a local college, it was found that 386 in 1,112 students live with their parents.

The percentage of the students who live with their parents will be calculated as,

Percentage = ( 386 / 1120 ) x 100

Percentage = 0.3471 x 100

Percentage = 34.71%

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The parametric equation of the line which is the intersection of the planes - x+3y+z=7 and x+y=1 is-  x= 1- t,  y= t,  z= 8- 4t.

Given:  -x+3y+z=7      - (i)

            x+y=1            - (ii)

Rearrange the equation (i) and (ii),

we get,   -x+3y+z-7=0   -(iii)

               x+y-1=0       -(iv)

To find the parametric equation of the line, solve the equation (iii) and (iv) simultaneously,

On solving the equation simultaneously we get,

4y+z-8=0

arrange this equation,  z=8-4y   -(v)

Let y=t     -(vi)

putting the value of y in equation (v)

so we get,  z=8-4t     -(vii)

putting the value of y and z in equations (iii) or (iv)

-x+3t+8-4t-7=0

x=1 -t

Therefore the parametric equation of the line which is the intersection of the planes -x+3y+z=7 and x+y=1  are x = 1 - t, y = t, z = 8 - 4t.

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Answer:

there is not enough info to answer this

Step-by-step explanation:

Answer: There is not enough information given to answer. You need to include how fast Jose and Edwin were jogging/walking.

Answer:

\(3\frac{11}{12}\) cups

Step-by-step explanation:

\(2\frac{1}{2} = \frac{5}{2}\) of pears

\(\frac{2}{3}\) of grapes

\(\frac{1}{4}\) of apples

\(\frac{1}{2}\) of orange

when adding fractions, make sure all denominators are the same:

\(\frac{5}{2} = \frac{30}{12}\) of pears

\(\frac{2}{3} = \frac{8}{12}\) of grapes

\(\frac{1}{4} = \frac{3}{12}\) of apples

\(\frac{1}{2} = \frac{6}{12}\) of orange

add all of the fractions:

\(\frac{30}{12} + \frac{8}{12} + \frac{3}{12} + \frac{6}{12} = \frac{47}{12}\)

convert to mixed fraction:

\(\frac{47}{12} = 3\frac{11}{12}\)

Look at the other guys

Answer:

C

Step-by-step explanation:

I think, I’m not so sure.. But if I am correct, the table shows capable coordinates.

The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let \(Wi\) and \(Li\) denote whether the game '\(i\)' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [\(W1W2\)] + P [\(W1L2W3\)] + P [\(L1W2W3\)]

        = \(p(1-p)\) + \(p3\) + \(p(1-p){2}\)

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.