Simplify: −12 • −4

A. −4,816
B. −16
C. 16
D. 48

Finding the area of the circle of spilled juice as a function of time is: j(t) = πr(t)²

An equation is mathematical statement that asserts  equality of two expressions. It contains one or more variables, and typically consists of terms on either side of equals sign.

Part A:

Let the radius of the circular pattern be r at time t. Then, we have:

j = πr²

Taking the derivative of both sides with respect to time, we get:

dj/dt = 2πr(dr/dt)

Since the rate of change of the radius is unknown, we can express it in terms of the rate of change of j:

dr/dt = (1/2πr)(dj/dt)

Substituting this expression for dr/dt back into our original equation, we get:

j = πr²

dj/dt = π(2r)(dr/dt)

dj/dt = 2πr(dr/dt)

dj/dt = 2πr(1/2πr)(dj/dt)

dj/dt = dj/dt

Therefore, the area of the spilled juice as a function of time is:

j(t) = πr(t)²

Part B:

If we assume that the rate of change of the radius is constant over the first 2 minutes, we can use the formula for the area of a circle to find the area of the spilled juice after 2 minutes:

j(2) = πr(2)²

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The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

Here, we have,

Given ,

the circle with radius 8 and center (1, 3).

so, we have,

the center of circle (h,k) = (1,3) and radius, r = 8

we know that,

Equation of the circle = (x-h)² + (y-k)² = r²

so, we get,

⇒ (x - 1)² + (y - 3)² = 64

⇒ x² - 2x + 1 + y² - 6y + 9 = 64

⇒ x² + y² - 2x - 6y - 54 = 0 (on simplification)

Hence, The solution is: the equation of the circle with radius 8 and center (1, 3) is: x² + y² - 2x - 6y - 54 = 0.

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Answer:

$23

Step-by-step

Johns debt is 70.00 dollars in 3 months. 70 divided by 3 is 23.

Answer:

2.5 cups

Step-by-step explanation:

\(\frac{2}{12} =\frac{x}{15}\) (x is the amount of cups of zucchini you will need to feed 15 people)

This proportion is showing that 2 cups of zucchini can feed 12 people, and we will use it to find how much zucchini we will need to feed 15 people.

Cross multiply

30 = 12x

divide both sides by 12 to isolate x

\(\frac{30}{12}\) = x

2.5 = x

That is your answer

- Kan Academy Advance

Step-by-step explanation:

ASA IS ANSWER

By ''ASA congruence theorems'', both triangles CDE and OPQ are congruent.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find the correct congruence theorems or postulates could be given as reasons for both triangles CDE and OPQ are congruent.

Here, By both triangles CDE and OPQ;

CE = OQ

∠CDE = ∠OPQ = 90°

∠ DCE = POQ

Hence, By ASA congruence theorems, both triangles CDE and OPQ are congruent.

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Given that v0 = (2, 1, -2), v1 = (-2, 1, 1), and v2 = (1, 2, 2), we can find the orthonormal basis that should be parallel to v0, and w0 and w1 should span the same subspace as v0 and v1.To find the orthonormal basis that should be parallel to v0.

we need to follow these steps:

Let v0 be a vector in Rn with nonzero norm ||v0||, and let V be the subspace of Rn that is perpendicular to v0 (so if y is in V, then y·v0 = 0).

Then, we can construct an orthonormal basis {v1, . . . , vp} for V, and {v0/v0, v1, . . . , vp} will be an orthonormal basis for Rn.

To find {v1, . . . , vp}, we apply Gram-Schmidt to the basis {v0, v1, . . . , vp}.

Specifically, we compute vi' = vi - projv0vi for i = 1, . . . , p.

This ensures that {v1, . . . , vp} are all in V and that {v0/v0, v1, . . . , vp} is an orthonormal basis for Rn that is parallel to v0.

So, in this case, we can take v0 = (2, 1, -2), which has norm ||v0|| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9) = 3.

Now, we need to find w0 and w1 that span the same subspace as v0 and v1. Since {v0, v1} is a basis for this subspace, any two linearly independent vectors in this subspace will span the same subspace. So, we can just pick any two such vectors. Let w0 = (2, 1, -2) and w1 = (-2, 5, 1).

We claim that {w0, w1} is linearly independent and spans the same subspace as {v0, v1}.To show that {w0, w1} is linearly independent, suppose that aw0 + bw1 = 0 for some scalars a and b. Then, we have(2a - 2b, a + 5b, -2a + b) = (0, 0, 0).This gives us two equations:2a - 2b = 0a + 5b = 0

Solving for a and b, we geta = 5/7 and b = -2/7.

Since a and b are not both zero, this shows that {w0, w1} is linearly independent.

To show that {w0, w1} spans the same subspace as {v0, v1}, we need to show that every vector in this subspace can be written as a linear combination of w0 and w1. Let (x, y, z) be any vector in this subspace.

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\(\huge\color{skyblue}\boxed{\colorbox{black}{Answer♡}}\)

\(a \: number \: x \: is \: reduced \: by \: 25\%\)

\(25\% \: of \: x \: means \: ( \frac{25}{100} )(x) = 0.25x \\ \\=> x - 0.25x \\ = > 0.75x\)

hope helpful~

The reduced quantity if x is reduced by 25% is 0.75x.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

x is reduced by 25%,

Calculate the 25% of x as shown below,

25 / 100 × x

0.25x

Calculate the reduced quantity,

Reduced quantity = x - 0.25x

Reduced quantity = x(1 - 0.25)

Reduced quantity = 0.75x

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n should be a whole number, we round up to the nearest integer, giving n = 540. Therefore, if Russel wants 0.99 certainty, n should be at least 540.

To determine how large n should be in order to have a certain level of certainty about the true probability p, we can use the concept of confidence intervals.

For a binomial distribution, the estimate of the probability p is X/n, where X is the number of successes (in this case, the number of times tails is obtained) and n is the number of trials (the number of times the coin is flipped).

To find the confidence interval, we need to consider the standard error of the estimate. For a binomial distribution, the standard error is given by:

SE = sqrt(p(1-p)/n)

Since p is unknown, we can use a conservative estimate by assuming p = 0.5, which gives us the maximum standard error. So, SE = sqrt(0.5(1-0.5)/n) = sqrt(0.25/n) = 0.5/sqrt(n).

To ensure that the true p is within 0.1 of the estimate X/n with at least 0.95 certainty, we can set up the following inequality:

|p - X/n| ≤ 0.1

This inequality represents the desired margin of error. Rearranging the inequality, we have:

-0.1 ≤ p - X/n ≤ 0.1

Since p is unknown, we can replace it with X/n to get:

-0.1 ≤ X/n - X/n ≤ 0.1

Simplifying, we have:

-0.1 ≤ 0 ≤ 0.1

Since 0 is within the range [-0.1, 0.1], we can say that the estimate X/n with a margin of error of 0.1 includes the true probability p with at least 0.95 certainty.

To find the value of n, we can set the margin of error equal to the standard error and solve for n:

0.1 = 0.5/sqrt(n)

Squaring both sides and rearranging, we get:

n = (0.5/0.1)^2 = 25

Therefore, n should be at least 25 to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n.

If Russel wants 0.99 certainty, we need to find the value of n such that the margin of error is within 0.1:

0.1 = 2.33/sqrt(n)

Squaring both sides and rearranging, we get:

n = (2.33/0.1)^2 = 539.99

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3230 Kilograms of the soil supplement are required for the entire Vineyard.

Some units that need to be recalled are as follows:

1 km = 1000 m

1 km^2 = 1000000 m^2

1 km^2 = 247 acres

1 kg = 1000 g

Let's tackle the problem now:

A vineyard has 145 acres of Chardonnay grapes.

145 acres = \(\frac{145}{247}\)× 1 km^2

145 acres = 145/247 km^2

145 acres ~ 0.587 km^2

A particular soil supplement requires 5.50 grams for every square meter of vineyard

1m^2 → 5.50 gram

1 km^2 = 10^6 →5.50 x 10^6 gram

1 km^2 →5.50 x 10^6 x 10^-3 kg

1 km^2 →5.50 x 10^3 kg

145 acres = 145/247 km^2 →145/247 x 5.50 x 10^3 kg

145 acres → 797500/247 kg

145 acres → 3230 kg

It required 797500/247 kg ~ 3230 kg of the soil supplement for the entire Vineyard.

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Answer:

son = 10 , father = 40

Step-by-step explanation:

Let Five years ago the age of son be x years and age of father be 7x years

Present age of son =x+5

Present age of father =7x+5

5 years later their age will (x+10) and (7x+10)

∴7x+10=3(x+10)

7x−3x=20

4x=20

x=5

So, the present age of son=x+5=5+5=10years

and the present age of father=7x+5=35+5=40years

hope it helps you

Answer:

The answer is A.

Step-by-step explanation:

As you multiply first equation by -5, you will get the coefficient of x is -5. So when both equations add up, you will eliminate x variable as -5 + 5 = 0, leaving y variable for the solutions.

Answer:

A.

Step-by-step explanation:

If we multiply the first equation by -5 we'll get -5x.

Then on adding the x terms are eliminated.

The type of savings institution that offers a range of services described in the question is commercial bank.

option D.

A commercial bank is a kind of financial institution that carries all the operations related to deposit and withdrawal of money for the general public, government and others.

commercial bank banks offers wide range of services including;

So the type of savings institution that offers a range of services to its customers, including savings accounts, checking accounts, and money market accounts, and also makes loans and investments and buys government bonds is commercial bank.

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Answer:

Both solutions are correct

Step-by-step explanation:

Given

Expression:

\(14x - 2x +3 = 3(5x + 9)\)

See attachment for Clare and Lins' solution

Required

Determine if they are correct or not

\(14x - 2x +3 = 3(5x + 9)\)

Open bracket

\(14x - 2x + 3 = 15x + 27\)

Collect like terms

\(14x - 2x -15x = -3 + 27\)

\(-3x = 24\)

Divide by -3

\(x = \frac{24}{-3}\)

\(x = -8\)

Both solutions are correct

Answer:

5(5x-t)

=13×5

25x - 5t

=65

25x -5t + 4x +5t

=65 + 22

29x

= 87

x

= 87÷29

x =3

substituting x=3 in 5x-t=13

15- t

=13

15 - 13

= t

t = 2

Step-by-step explanation:

As per unitary method, the height of the light pole is 3 feet.

The unitary method involves finding the value of one unit and then using it to find the value of another unit. In this problem, we can use the height of Jenny as one unit and her shadow length as another unit. Let's assume that Jenny's height is 1 unit and her shadow length is x units.

Now, we need to find the value of one unit in terms of the height of the light pole. To do this, we can use the fact that the lengths of the two shadows are proportional to the heights of the objects casting the shadows. That is, if the height of the light pole is h units, then we have:

Jenny's height / Jenny's shadow length = Light pole's height / Light pole's shadow length

Substituting the values, we get:

1 / x = h / y

where y is the length of the shadow of the light pole.

We can rearrange this equation to find the value of h in terms of x and y:

h = (x * y) / 1

Now, we can substitute the given values of x and y to find the height of the light pole. If Jenny's shadow is 10 feet long and the shadow of the light pole is 30 feet long, then we have:

h = (1 * 30) / 10 = 3 feet

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Answer:

A and C

Step-by-step explanation:

Answer:

a and c are right

Step-by-step explanation:

the base must be the number and the exponent is how many times it is multiplied

a. A graph of the functions f(x) and g(x) is shown in the image attached below.

b. A function that could be described as exponential is f(x).

c. The value of x for which the function values are equal is -2.678.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

In this scenario, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

Part b.

By critically observing the graph of the functions f(x) and g(x), we can logically deduce that only f(x) represent an exponential function.

Part c.

For the value of x for which the function values are equal, we have:

\(0.3333x + 7 = 1.1487e^{-0.624x}\\\\7 = 1.1487e^{-0.624x}-0.3333x\)

x = -2.678.

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Answer:

Answer:

9 11

But are you okay? It spells 9-1-1.

Answer:

800,000+90,000+4,000+200+10+17= 894,217

Eight Hundred thousand+ Ninety thousand+ Four thousand+ Two hundred+ Ten+ Seven= 894,217      

Step-by-step explanation:

The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

Answer:

C. \(x^{3}\) - 4\(x^{3}\) - 24x + 21

Step-by-step explanation:

(x - 7)(\(x^{2}\) + 3x - 3)

x(\(x^{2}\) + 3x - 3) + -7(\(x^{2}\) + 3x - 3)

(\(x^{3}\) + 3\(x^{2}\) - 3x) + (-7\(x^{2}\) + -21x + 21)

\(x^{3}\) - 4\(x^{3}\) - 24x + 21

Answer:

The interval estimate is:

41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45

or

38.05 ≤ true average time ≤ 44.95

Inequality notation:

[38.05, 44.95]

The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.

Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:

(sample mean) ± (margin of error)

Substituting the given values, we get:

41.5 ± 2.45

Simplifying, we get:

[39.05, 43.95]

Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.

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The area of the triangle in the diagram is one square foot.

We know that the area of a triangle of base B and height H is given by the formula:

Area = B*H/2

On the diagram we can se that the measure of the base is 3 ft, and the height is 2/3 ft, then the area of that triangle will be:

Area = (3 ft)*(2/3 ft)/2 = 1 ft²

The area of the triangle is one square foot.

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Answer:

angle y = 60

Step-by-step explanation:

They are equal due to the rule that vertical angles are always equal

"A pair of vertically opposite angles are always equal to each other."

hope this helps

Answer:

hope that helps :))

Step-by-step explanation:

Step 1: Subtract 12c from both sides.

12c+12−12c=12c+9−12c

12=9

Step 2: Subtract 12 from both sides.

12−12=9−12

0=−3

Answer:

6

Step-by-step explanation:

Let x be the vertical height

area of triangle=1/2×6×6=18

1/2×3×x=18/2

1.5x=9

x=6

Answer:

your not showing the whole thing

Step-by-step explanation:

Centering x values before squaring eliminates the correlation between x and its square term, reducing multicollinearity. This helps to determine independent effects of predictor variables, and can also straighten the curve of a scatterplot.

Centering the x values before squaring is important because it helps to eliminate the correlation between the x variable and its square term. When we square a variable without centering it, we are essentially capturing the effect of both the linear and the quadratic terms.

This can lead to multicollinearity, which occurs when two or more predictor variables are highly correlated with each other.

Multicollinearity can create problems in statistical analyses because it can make it difficult to determine the independent effects of each predictor variable on the outcome variable. Centering the x values before squaring helps to reduce the effects of multicollinearity by eliminating the correlation between the x variable and its square term.

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