The ratio of ages of kissi and esinam is 3:5 and esinam is 3:5 The sum of ages of all 3 is 147 years.whats the age difference between oldest and youngest ?

The total volume of the solid = 1,035,000 cm³

Volume of a Pyramid = 1/3(length)(width)(height).

Volume of a cuboid = (length)(width)(height).

Volume of the Pyramid = 1/3(length)(width)(height)

Volume of the Pyramid = 1/3(90)(50)(240 - 225)

Volume of the Pyramid = 1/3(90)(50)(15)

Volume of the Pyramid = 22,500 cm³

Volume of the cuboid = (length)(width)(height)

Volume of the cuboid = (90)(50)(225)

Volume of the cuboid = 1,012,500 cm³

The total volume of the solid = 22,500 + 1,012,500

The total volume of the solid = 1,035,000 cm³

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Answer:

x = 5 (Amount of problems each student got equally)

Equation - "5x + 2 =27"

Working out:

The story focuses on the problems, so the equation will link to the output of the problem.

The story starts with 5 students, so 5 will be a coefficient of x.

The story has a total of 27 problems given to the 5 students, so this will be solving a linear equation.

There are +2 problems added individually to a student, so this will be a constant itself.

Putting all this together gives us:

5x + 2 = 27

x = Number of problems each student got equally.

Solving it:

5x + 2 =27

5x = 25

x = 5

Each student got 5 problems equally, and one individual student got 2 extra (wohoo).

Hope this has helped! ^^

Answer:

it c

Step-by-step explanation:

the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0. The given function is f(x, y, z) = (x - y + 2z) / (2x + y - z). We are asked to find an equation for the level surface passing through the point (3, 0, 1).

To find the equation for the level surface, we need to set the function equal to a constant value and solve for z.

Let's start by substituting the coordinates of the given point into the function:

f(3, 0, 1) = (3 - 0 + 2(1)) / (2(3) + 0 - 1)
           = 5 / 5
           = 1

So, the constant value for the level surface passing through (3, 0, 1) is 1.

Now, let's set the function equal to 1 and solve for z:

1 = (x - y + 2z) / (2x + y - z)

Cross-multiplying, we get:

2x + y - z = x - y + 2z

Rearranging the terms, we have:

x + 2y - 3z = 0

Therefore, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

In summary, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

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The sum of the series is 7 / (1 - (-2z)), and the domain for which the series converges is (-1/2, 1/2).

The given series is a geometric series with the first term, a = 7, and the common ratio, r = -2z.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

sum = a / (1 - r)

sum = 7 / (1 - (-2z))

To find the domain for which the series converges, we need the absolute value of the common ratio to be less than 1:

| -2z | < 1

-1 < 2z < 1

-1/2 < z < 1/2

So, the sum of the series is 7 / (1 - (-2z)), and the domain for which the series converges is (-1/2, 1/2).

In a bundle of 50 kg of cloth, the weight of each material is:

Cotton: 12.5 kg

Nylon: 7.5 kg

Polyester: 20 kg

Others: 10 kg

To calculate the percentage of each material found in the cloth, we need to convert the given angles in the pie chart into percentages.

i) Calculating the percentage of each material:

Cotton: 90° / 360° * 100% = 25%

Nylon: 54° / 360° * 100% = 15%

Polyester: 144° / 360° * 100% = 40%

Others: 72° / 360° * 100% = 20%

Therefore, the percentage of each material found in the cloth is:

Cotton: 25%

Nylon: 15%

Polyester: 40%

Others: 20%

ii) To calculate the weight of each material contained in a bundle of 50 kg of cloth, we need to multiply the percentage of each material by the total weight.

Weight of Cotton = 25% * 50 kg = 0.25 * 50 kg = 12.5 kg

Weight of Nylon = 15% * 50 kg = 0.15 * 50 kg = 7.5 kg

Weight of Polyester = 40% * 50 kg = 0.40 * 50 kg = 20 kg

Weight of Others = 20% * 50 kg = 0.20 * 50 kg = 10 kg

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Answer:

Step-by-step explanation:

(2x^2 + 10x + 7x + 35) - (x^2 - 3x + 5x - 15)

x^2 + 15x + 50

(x + 5)(x + 10)

x = -10

Step-by-step explanation:

a

(x+5)(2x+7)-(x+5)(x-3)

factorize (x+5) out

(x+5)[(2x+7)-(x-3)]

(x+5)(2x+7-x+3)

(x+5)(2x-x+7+3)

(x+5)(x+10)

b. to get the zeros of the equation,

(x+5)(x+10)=0

x+10=0

x=-10

since the other one has been found already

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer: .775 lbs

Step-by-step explanation:

7 3/4 _> 7.75

7.75 / 10 = .775

a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

The 'x' and 'y' variables and the 4 angles are highlighted in the boxes

Answer:

standard

Step-by-step explanation:

The growth of yeast cultures in a medium typically exhibits logarithmic growth.

In logarithmic growth, the population size increases exponentially over time, meaning that the growth rate is proportional to the current population size.

This results in a characteristic J-shaped curve when the population size is plotted against time.

During the early stages of yeast culture growth, there is a lag phase where the population adjusts to the new environment and begins to adapt and reproduce.

Following this phase, yeast cells enter the exponential or logarithmic growth phase, where the population size increases rapidly.

The growth rate is high during this phase as each yeast cell divides and produces new cells, leading to a doubling of the population within a specific time frame.

Logarithmic growth eventually reaches a stationary phase, where the growth rate slows down, and the population stabilizes.

This occurs when the available nutrients in the medium start to become limited or when waste products accumulate, creating an unfavorable environment for further growth.

Therefore, the growth of yeast cultures in a medium shows logarithmic growth.

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Answer: 1. 3(17-y)

Step-by-step explanation: multiply 3 to 17 and y, which you get (51) and (3). Subtract it to get 48, which is equivalent to 60 - 3y - 9 = 48

if it's wrong, i'm sorry

hope this helps!!

Answer: 10

Step-by-step explanation:

Answer:

(-8, 10)

Step-by-step explanation:

A P E X

Answer: The filled out chart is shown below.

===========================================================

Explanation:

For each row, we divide the number of locations over the population count. Treat the population values in millions. Something like 35.2 million means 35,200,000 which is the same as writing 35.2*10^6 when using scientific notation. I prefer to stick to scientific notation.

In the first row, they computed 1460/(35.2*10^6) = 0.0000415 = 4.15*10^(-5); the last entry of 4.15 for this row represents having 4.15 stores for 100,000 people. In other words, we chop off the 10^(-5) portion in 4.15*10^(-5). This is because the 10^(-5) portion represents "1 out of 100,000".

The other remaining rows are handled the same way. I'll show the steps for the second row

Like the previous row, each value is approximate.

Check out the table below. The stuff in gray represents the new entries that were previously blank.

False. The angle associated with the total impedance is the angle by which the source current leads the applied voltage.

Angle is defined as the space or area between two lines or surfaces that meet at a certain point. It is measured in degrees, and can be categorized by its size (acute, right, obtuse, and reflex) or by its type (straight, reflex, complementary, supplementary, and vertical). Angle is an important concept in mathematics, geometry, physics, and engineering, and is used to describe the size of a turn, the shape of an object, and the directions of movements.

This is because the total impedance is defined as the ratio of the applied voltage to the source current. Since the applied voltage is divided by the source current, the source current will lead the applied voltage. This is due to the fact that the total impedance is a complex quantity, with both a real and imaginary component. If the total impedance only had a real component, then the angle associated with the total impedance would be zero, meaning the applied voltage and source current would be in phase. However, since the total impedance is complex, the angle associated with the total impedance is the angle by which the source current leads the applied voltage.

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The first moment about the x-axis (Mx) of the steel plate is given by Mx = density * (4√2/3), where "density" represents the uniform density of the steel plate.

To find the first moment about the x-axis (Mx) of the steel plate with a uniform density, we need to integrate the product of the density and the distance from the x-axis.

Given that the plate is bounded by x = 0 and y = 2 - x^2, let's plot these two functions to visualize the region and find the intersection points:

The equation x = 0 represents the y-axis, and the equation y = 2 - x^2 represents a downward-opening parabola.

Let's draw the graph:

```

      |

   2  |                   *

      |                *

      |              *

      |           *

      |      *

-------|------------------

      | 0

```

The intersection points occur when y = 2 - x^2 intersects with the y-axis (x = 0).

To find the intersection points:

y = 2 - x^2

0 = 2 - x^2

x^2 = 2

x = ±√2

So, the intersection points are (√2, 0) and (-√2, 0).

Now, let's find the first moment about the x-axis, Mx:

Mx = ∫[a,b] (density * distance from x-axis) dA

In this case, the density is uniform, so it can be taken outside the integral. The distance from the x-axis is simply y.

Mx = ∫[a,b] (density * y) dA

To find the limits of integration, we need to determine the region bounded by the curves.

Since x = 0 is the y-axis and y = 2 - x^2 is the parabola, we integrate from the y-axis (x = 0) to the intersection points (√2, 0) and (-√2, 0).

Mx = ∫[0, √2] (density * y) dx + ∫[0, -√2] (density * y) dx

Since the density is uniform, we can take it outside the integrals.

Mx = density * ∫[0, √2] y dx + density * ∫[0, -√2] y dx

The integral of y with respect to x is the same as finding the area under the curve y = 2 - x^2.

Let's calculate the area under the curve from x = 0 to x = √2:

Area = ∫[0, √2] (2 - x^2) dx

Using the integral properties, we can split this integral into two parts:

Area = ∫[0, √2] 2 dx - ∫[0, √2] x^2 dx

Evaluating these integrals:

Area = [2x] [0, √2] - [(x^3)/3] [0, √2]

    = 2(√2) - (√2)^3/3

    = 2√2 - 2√2/3

    = 4√2/3

Now, substituting the area back into the equation for Mx:

Mx = density * (4√2/3)

Since the density is not specified, we cannot calculate the exact value for Mx without the density information.

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The Taylor series for f(x)=ex about x=2 is given by ∑n=0[infinity]cn(x−2)n where cn = fⁿ(2)/n! = e²/2! e²/3! ... e²/n!.

The Taylor series is a way to represent a function as an infinite sum of terms that involve the function's derivatives evaluated at a specific point.

In this case, we want to find the Taylor series for f(x)=ex about x=2. To do this, we first need to find the derivatives of f(x) at x=2.

We have fⁿ(x) = ex for all n, so fⁿ(2) = e² for all n. We can then use this to find the coefficients cn in the Taylor series.

We have cn = fⁿ(2)/n! = e²/2! e²/3! ... e²/n!.

We can then substitute these coefficients into the Taylor series to get ∑n=0[infinity]cn(x−2)n = ∑n=0[infinity] e²/2! e²/3! ... e²/n!(x−2)n, which is the Taylor series for f(x)=ex about x=2.

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Answer:

to hard.

Step-by-step explanation:

Answer:

The three numbers are:

4.62,

23.1, and

462.2

Step-by-step explanation:

Let X be the "first number."

B = What number is five times the first number:  5X

C = third number is 100 more than the first number:  100X

The sum of all three is 490:  X + B + C = 490

----

X + B + C = 490

X + 5X + 100X = 490

106X = 490

X = 4.622

Check:

X = 4.622

B = 5X = 23.11

C = 100X = 462.2

Check:

Sum (4.622 + 23.11 + 462.2) = 490

Answer:

\( = { \tt{ \frac{30}{120} + \frac{40}{120} }} \\ = \frac{7}{12} \)

Answer: not enough to answer

The new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

(a) The values of E(θ^1) and E(θ^2) are unknown without further information. Being unbiased estimators means that, on average, they provide estimates that are equal to the true population parameter θ. Therefore, we have:

E(θ^1) = θ

E(θ^2) = θ

(b) To find the expectation E(θ^3), we can use the linearity property of expectations:

E(θ^3) = E(aθ^1 + (1 - a)θ^2)

Since θ^1 and θ^2 are unbiased estimators, their expectations are equal to θ:

E(θ^3) = E(aθ^1 + (1 - a)θ^2) = aE(θ^1) + (1 - a)E(θ^2)

Using the values from part (a), we have:

E(θ^3) = aθ + (1 - a)θ = θ(a + 1 - a) = θ

Therefore, the new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

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