"Find an equation of the sphere containing all surface pointsP = (x, y, z)such that the distance from P toA(−2, 4, 4)is twice the distance from P toB(5, 2, −2).Find its center and radius.

Let a represent the volume of solution A. If it contains 2% of alcohol, then the amount of alcohol that A contains is 2/100 * a = 0.02a

If A = 200, then the amount of alcohol in A is 0.02 * 200 = 4

Let b represent the volume of solution B. If it contains 7% of alcohol, then the amount of alcohol that B contains is 7/100 * a = 0.07b

The total volume of solution A and B is (a + b)

If the volume of A = 200, then the total volume or resulting mixture is 200 + b

If the mixture contains 5% alcohol, the the amount of alcohol in the mixture is

5/100 * (200 + b)

0.05(200 + b)

By equating the concentrations, we have

4 + 0.07b = 0.05(200 + b)

4 + 0.07b = 10 + 0.05b

0.07b - 0.05b = 10 - 4

0.02b = 6

b = 6/0.02

b = 300

She needs to use 300 milliliters of solution B

Answer:

588.6

Step-by-step explanation:

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the total amount of oil that leaks out over the entire time interval [0, 120].

integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.

To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:

Σᵢ r(tᵢ) Δt

where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:

∫₀¹₂₀ r(t) dt

which represents the total amount of oil that leaks out over the entire time interval [0, 120].

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The level of measurement used in the operationalization of extracurricular participation is categorical/nominal.

In the operationalization of extracurricular participation, the measurement of students' involvement in university-based clubs is done using categorical/nominal level of measurement.

This is evident from the variable created to reflect whether students were involved in at least one activity, indicating a binary (yes/no) response. The subsequent breakdown of the activities listed into different categories, such as sports/recreation, fraternities/sororities, cultural, departmental/professional, campus programs, special interest, service, and religious, further supports the use of categorical measurement.

Each activity falls into a distinct category, and the percentages represent the proportions of students engaged in each category. Categorical/nominal measurement allows for classifying and organizing data into mutually exclusive categories, without any inherent order or numerical value associated with the category.

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The slope of the line that models this situation is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Answer:

\(l = \frac{1}{2} w\)

\(l = \frac{1}{2} ( \frac{b}{2} + 1) = \frac{b}{4} + \frac{1}{2} \)

\(p = 2( \frac{b}{4} + \frac{1}{2} + \frac{b}{2} + 1) \)

\(p = 2( \frac{3b}{4} + \frac{3}{2} )\)

\(p = \frac{3b}{2} + 3\)

Answer:

add the like terms if there's no like the answer will be 3x+2y-3z=-1

To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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Answer:

(-2,-2)

Step-by-step explanation:

use midpoint formula:  (average of two x-values, average of two y-values)

(-7 + 3)/2 = -4/2 = -2

(1 + -5)/2 = -4/2 = -2

Answer:

\(let \: m \: be \: the \: mid \: point \\ m = (( \frac{( {x}^{1} + {x}^{o})}{2}) \: \: \: ( \frac{ ({y}^{1} + {y}^{o}) }{2} )) \\ m = (( \frac{( - 7 + 3)}{2} ) \: \: \: ( \frac{(1 + - 5)}{2} ) \\ m = ( \frac{ - 4}{2} \: \: \: \frac{ - 4}{2} ) \\ m = ( - 2 \: \: \: - 2) \\ mid \: point \: = \: \binom{ - 2}{ - 2} \)

Answer:

Find the perimeter of the rectangle. Then we have the length of the other side is 12 cm 12 \ \text{cm} 12 cm.

Answer:

12cm

15

\(15 \times15 - 9 \times 9 = \sqrt{144 = 1} } \)

Answer:

-4 and +4

Step-by-step explanation:

(- - - -) = -4

(+ + + +) = 4 or +4

Answer:

f(x) = 3(x+1)^2 +3

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Step-by-step explanation:

\( \sqrt{16} \times \frac{1}{8} = \frac{1}{2} answer\)

Answer:

x = 25

Step-by-step explanation:

you need x on its own, so just divide both sides by 3, and you get 25.

Answer:  7.5 E 0

This is the same as saying 7.5 * 10^0

Both of these values convert to the number 7.5; meaning that the population of the US is about 7.5 times greater than the population of CA.

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

Work Shown:

40,000,000 = 40 million

40,000,000 = 4.0 * 10^7

Note how we move the decimal 7 spots to the right to go from 4.0 to 40,000,000

so the 7 in 10^7 tells us how many spots to move the decimal point in the base number 4.0

The number 4.0*10^7 can be condensed to 4E7. The "E" represents "times 10 to the"

As another example, "3E8" means "3 times 10 to the 8th power" which becomes 3.0*10^8 = 300,000,000 = 300 million

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

We have these two facts

We'll divide the two populations to get

y/x = (3E8)/(4E7)

y/x = (3*10^8)/(4*10^7)

y/x = (3/4)*10^(8-7)

y/x = 0.75*10^1

y/x = 7.5

We can see that the population of the US is roughly 7.5 times greater compared to the population of CA.

Convert 7.5 to scientific notation, and we get

7.5 = 7.5*1 = 7.5 * 10^0 = 7.5 E 0

Keep in mind that these are population estimates, and populations change over time.

Answer

divide 880 with 8 so the correct answer would be 110

Step-by-step explanation:

hope this helps :)

Answer:

65

Step-by-step explanation:

<S = <t

x + 50 = 3x + 20

2x = 30, x = 15

. <t = <v

3x + 20 = 45 + 20 =  65

Answer:

b.  65 degrees.

Step-by-step explanation:

m < RST = m < STU (alternate angles), so

x + 50 = 3x + 20

50 - 20 = 3x - x

2x = 30

x = 15.

Now m < RVT = m < RST  ( opposite sides of a parallelogram are equal).

So m < RVT = x + 50 = 15 + 50 = 65.

Answer:

1

Step-by-step explanation:

It is 1 because the laws of exponents state that anything raised to the power of 0 is 1.

After 39 years, the value of this quantity is 1,023.35

Here we know that:

Then the exponential equation is:

\(A(t) = 570*(1 + 0.35)^{t/20}\)

Where t is the time in years.

So, after 39 years, the value of this quantity is given by:

\(A(39) = 570*(1 + 0.35)^{39/20} = 1,023.35\)

After 39 years, the value of this quantity is 1,023.35

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This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

What is Taylor Series?

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the derivative of the function at a single point. For most common functions, the function and the sum of its Taylor series near this point are the same.

To find the Taylor series for the function f(x) = x⁴ - 6x² + 1 centered at a = 2, we can use the formula for the Taylor series expansion:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

First, let's find the values of f(a) and its derivatives at x = a = 2:

f(2) = (2)⁴ - 6(2)² + 1 = 16 - 24 + 1 = -7

f'(x) = 4x³ - 12x

f'(2) = 4(2)³ - 12(2) = 32 - 24 = 8

f''(x) = 12x² - 12

f''(2) = 12(2)² - 12 = 48 - 12 = 36

f'''(x) = 24x

f'''(2) = 24(2) = 48

Now, we can substitute these values into the Taylor series formula:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

f(x) = -7 + 8(x - 2)/1! + 36(x - 2)²/2! + 48(x - 2)³/3! + ...

Simplifying the terms:

f(x) = -7 + 8(x - 2) + 18(x - 2)² + 8(x - 2)³ + ...

This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

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Answer:

Step-by-step explanation:

First, we'll write the cost equations for each house, using the number of months since the initial purchase as the independent variable X:

For the house on Main Street:

Cost = 900X + 10,000

For the house on Empire Road:

Cost = 1050X + 4000

Next, we'll find the rate of change for each house by finding the slope of the respective cost equation:

The slope of the cost equation for the house on Main Street is 900. This means that for every month that passes, the cost of the house will increase by $900.

The slope of the cost equation for the house on Empire Road is 1050. This means that for every month that passes, the cost of the house will increase by $1050.

Now that we have found the rate of change for each house, we can compare them to determine which house has the greater rate of change:

Since the slope of the cost equation for the house on Empire Road is greater than the slope of the cost equation for the house on Main Street (1050 > 900), the house on Empire Road has a greater rate of change.

Finally, we can compare the initial values of each house by comparing the y-intercepts of the respective cost equations:

The y-intercept of the cost equation for the house on Main Street is 10,000, which means that the initial cost of the house is $10,000.

The y-intercept of the cost equation for the house on Empire Road is 4000, which means that the initial cost of the house is $4,000.

Since the y-intercept of the cost equation for the house on Main Street is greater than the y-intercept of the cost equation for the house on Empire Road (10,000 > 4,000), the house on Main Street has a greater initial value.

Answer:

27

Step-by-step explanation:

Area of Triangle x 2 = 3 * 3

The reason I did not divide it by 2 is because of how the other triangle is bound to have the same area. Just leave it as it is because later you're going to reach the same answer.

3 * 3 = 9

Rectangle Area = 6 * 3 = 18

18 + 9 = 27

Answer:

The answers are in the image attached to this response.

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Answer:

answer to question 1. Triangle Sum Theorem

answer to question 2. Exterior Angle Theorem

answer to question 3. Transversal

answer to question 4. SAS Similarity Theorem

Step-by-step explanation:

there is not much of an explanation but uh there the answers lol

Answer:

The simplified value of the expression m/n if m=4/5 and n= −0.25 is -16.

Step-by-step explanation:

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Answer:

\(D = 900\ miles\) --- nearest 100 miles

\(D = 930\ miles\) --- nearest 10 miles

Step-by-step explanation:

Missing Information

\(Austin\ to\ Fort\ Worth: 189.9\ miles\)

\(Austin\ to\ Jackson: 552.7\ miles\)

On Monday, the total distance is:

\(D_1 =Austin\ to\ Fort\ Worth + Fort\ Worth\ to\ Austin\)

\(D_1 = 189.90\ miles + 189.90\ miles\)

\(D_1 = 379.80\ miles\)

On Tuesday, the total distance is:

\(D_2 = Austin\ to\ Jackson\)

\(D_2 = 552.70\ miles\)

So, the total distance (D) is:

\(D = D_1 + D_2\)

\(D = 379.80\ miles + 552.70\ miles\)

\(D = 932.50\ miles\)

To the nearest 100 miles, the total distance is:

\(D = 900\ miles\)

To the nearest 10 miles, the total distance is:

\(D = 930\ miles\)

Answer:

Rounding to the Nearest Integer

The most common type of rounding is to round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth's place (the first digit to the right of the decimal point).

Answer:

Step-by-step explanation:

We know that a day contains 24 hours in total.

The time already passed will be represented by \(x\).

The remaining time would be \(\frac{x}{2}\), becasye half of what has already passed remains until the end of the day.

Basically, the sum of these two expression gives 24 hours in total.

\(x + \frac{x}{2} =24\\\frac{3x}{2}=24\\ x=16\)

Therefore, the actual time is 4 p.m.