What is the area of the trapezoid? Show your work and leave your answer in exact form.

If f(x, y, z) = xyzi + yj + zk, the divergence of the curl of the vector field f is zero.

To find the divergence of the curl of the vector field f(x,y,z) = xyzi + yj + zk, we first need to compute the curl of f, which is given by:

curl f = (∇ × f) = ∂(zk)/∂y - ∂(yj)/∂z + (∂(yj)/∂x - ∂(xyzi)/∂y)k + (∂(xyzi)/∂z - ∂(zk)/∂x)j + (∂(zk)/∂x - ∂(yj)/∂y) i

Simplifying this expression, we get:

curl f = (-z)i + xj + yk

Next, we need to find the divergence of the curl of f, which is given by:

div(curl f) = ∇ · (∇ × f) = ∂(∂(zk)/∂y - ∂(yj)/∂z)/∂x + ∂(∂(yj)/∂x - ∂(xyzi)/∂y)/∂y + ∂(∂(xyzi)/∂z - ∂(zk)/∂x)/∂z

Substituting the values from the curl f expression, we get:

div(curl f) = ∂(-z)/∂x + ∂(x)/∂y + ∂(y)/∂z

Simplifying this expression, we get:

div(curl f) = 0

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She would need approximately 12.91 ounces of water should be added to the mixture to make it 45.5% water.

To make the mixture 45.5% water, you need to determine how much water should be added to the gallon bottle containing 60% bleach and 40% water.

Step 1: Calculate the initial amount of water in the bottle. A gallon is 128 ounces. Multiply 128 ounces by 40% (0.4) to get the initial water content: 128 * 0.4 = 51.2 ounces.

Step 2: Let x be the amount of water to be added. The new mixture will have (51.2 + x) ounces of water and (128 + x) ounces in total.

Step 3: Set up the equation for the desired percentage of water: (51.2 + x) / (128 + x) = 0.455.

Step 4: Solve for x. Multiply both sides by (128 + x) to get rid of the denominator: 51.2 + x = 0.455 * (128 + x).

Step 5: Simplify and solve for x: 51.2 + x = 58.24 + 0.455x. Rearrange the equation: 0.545x = 7.04. Now, divide by 0.545 to get x: x ≈ 12.91 ounces.

Therefore, approximately 12.91 ounces of water should be added to the mixture to make it 45.5% water.

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9514 1404 393

Answer:

  cos(θ) = (5√74)/74

Step-by-step explanation:

The length of the hypotenuse is given by the Pythagorean theorem:

  h = √(5² +7²) = √74

The cosine of the angle is the ratio of the adjacent leg to the hypotenuse:

  cos(θ) = 5/√74 = (5√74)/74

Answer:

60$ is the normal price.

Why:

Because if 45$ is 75%, then 30$ is 50%, 15 is 25%, and 0 is 0%. 50% + 50% = 100%. (That's how I did this one, anyway. This works on any 25%, 50%, or 75% problem.)

Answer:2250

Step-by-step explanation:

All we need to do is multiply 15,000 by 15% also known as 0.15 as a decimal.

15,000 X 0.15 = 2250

Answer: 2250

Answer:

81

Step-by-step explanation:

81

Answer:

6+3=9x9=81 final answer 81.

Step-by-step explanation:

Answer:

5) 3(2+3x)+4(y+2x)-6

Step-by-step explanation: its gone be -6 either way

The association as shown in the scatter plot is

Negative association

One outlier

In statistics, a negative association between two variables means that when the value of one variable increases, the value of the other variable decreases, and vice versa. In other words, there is an inverse relationship between the two variables.

Negative association is often represented graphically with a downward-sloping line on a scatter plot, which shows the negative correlation between the two variables.

While, an outlier is an observation or data point that is significantly different from other observations in a dataset.

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The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34

Answer:

P=26 cm A=40 cm^2

Step-by-step explanation:

Perimeter:

5+5+8+8=26

Area:

8x5=40

Answer:

This is a false statement

Step-by-step explanation:

75.7-9=66.7

7-4=3

66.7 is not equal yo three therefor it is false

Step-by-step explanation:

so when we have 25> w -7 we must move the

-7 to the 25 for the w to stand on it own so

25+7 > w

32 > w

Their present age are:

Vikas 's age = 15 years, Mother's age = 42 years  and

Grandmother's age = 64 years.

Let that present age of Vikash is x yrs.

So, his Mother's age= (x+27) yrs

Grandmother's age = (x+27+22) i.e., (x+49) yrs.

According to question,

   x+ (x+27)+ (x+49) = 121

⇒ 3x+ 76 = 121

⇒ 3x = 121-76

⇒ x= 45/3

⇒ x = 15

Therefore,

x = 15

Which means the age of Vikas is 15 years.

Now

So, mother's age will be = 15+27

                                        = 42 years.

And,

Grandmother's age = 15+49

                                = 64 years.

Hence, age of Vikash, his Mother and his Grandmother are 15 yrs, 42 yrs, and 64 yrs respectively.

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The square root of 1 has two solutions: 1 and -1, then

Answer:

b = 21

Step-by-step explanation:

If there are 5 arithmetic means between 5 and b and the last term is 25, then we can find the value of b by using the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.

We know that there are 5 arithmetic means between 5 and b. Therefore, there are 7 terms in total (including 5 and b). We also know that the last term is 25. So we have:

a_7 = 25 a_1 = 5 n = 7

We can use these values to solve for d:

a_n = a_1 + (n - 1)d 25 = 5 + (7 - 1)d d = 4

Now that we know d, we can find b by using the formula for the fifth term:

a_5 = a_1 + (5 - 1)d a_5 = 5 + (4)(4) a_5 = 21

Therefore, b = 21.

Answer:

it is the second choice, because if you read the questions out loud then the second one is the way you would read it.

Answer:

n = 3

Step-by-step explanation:

\(3(4 + n) = n + 18 \\ 12 + 3n = n + 18 \\ 2n = 6 \\ n = 3\)

The population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.

To find the population of the city after a certain number of years with a 3% annual growth rate, we can use the formula:

P = P₀(1 + r)ⁿ

where:

P₀ = initial population

r = annual growth rate (as a decimal)

n = number of years

P = population after n years

In this case, we have:

P₀ = 350,000

r = 0.03 (since the annual growth rate is 3 percent, or 0.03 as a decimal)

n = the number of years we want to find the population for

Substituting these values into the formula, we get:

P = 350,000(1 + 0.03)ⁿ

Simplifying:

P = 350,000(1.03)ⁿ

If we want to find the population after, say, 5 years, we can substitute n = 5 into the formula:

P = 350,000(1.03)⁵

P ≈ 408,022

Therefore, the population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.

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Answer:

735 students

Step-by-step explanation:

create a proportion of students to teachers

let 's' = # of students

\(\frac{15}{1}\) = \(\frac{s}{49}\)

cross-multiply to get:

s = 735

The solution of the inequality 2(4x - 3) ≥ -3(3x) + 5x is true for all x such that its a real number bigger or equal to 0.5 (Option A: x ≥ 0.5)

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

The considered inequality is:

\(2(4x - 3) \geq -3(3x) + 5x\)

Simplifying its both sides, we get:

\(2(4x - 3) \geq -3(3x) + 5x\\8x-6\geq -9x + 5x\\8x-6 \geq -4x\)

Adding 4x on both the sides, we get:

\(8x-6+4x \geq -4x + 4x\\(8+4)x - 6 \geq 0\\12x -6 \geq 0\\\)

Adding 6 on both the sides, and dividing by 12, we get:

\(12x-6 +6 \geq 0+6\\12x \geq 6\\12x/12 \geq 6/12\\x \geq 0.5\)

(some operations like addition, subtraction, multiplication by positive real number or division by positive real number keeps the inequality relation unaltered. With the use of such operations, here we tried to get x on one side, and constants on other side).

Thus, the considered inequality is true for all the values of x which are real numbers bigger or equal to 0.5 (Option A: x ≥ 0.5)

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The answer of the given question based on the sequence is , the sum of the first 50 terms in the sequence is approximately 4.5036 × 10¹⁵.

In mathematics, an explicit formula is a formula that defines a specific term or element of a sequence or function, in terms of the preceding terms or elements or some other input. Explicit formulas are also sometimes called closed-form formulas.

To find the sum of the first 50 terms in the sequence, we need to use the explicit formula:

aᵢ = aᵢ₋₁ × 2

where a₁ = -4.

Using the formula repeatedly, we can find the values of the first few terms:

a₂ = a₁ × 2 = -4 × 2 = -8

a₃ = a₂ × 2 = -8 × 2 = -16

a₄ = a₃ × 2 = -16 × 2 = -32

and so on.

We can see that the sequence is a geometric sequence with a common ratio of 2 and a first term of -4. So we  use  formula for sum of geometric sequence:

S₅₀ = a₁(1 - rⁿ) / (1 - r)

where a₁ = -4, r = 2, and n = 50.

Plugging in these values, we get:

S₅₀ = (-4)(1 - 2⁵⁰) / (1 - 2)

= (-4)(1 - 1,125,899,906,842,624) / (-1)

= (4)(1,125,899,906,842,623)

= 4.503599627370494e+15

Therefore, the sum of the first 50 terms in the sequence is approximately 4.5036 × 10¹⁵.

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Answer:

I promise you the app Math. way will save you it will do it for u and show you where to put it on the graph just download it

Answer:

B. Negative

Step-by-step explanation:

A slope of zero would cause the red line (the slope) to be horizontal/sideways

A negative slope goes down

A positive slope goes up

An undefined slope is vertical/up and down

Hope this helps!

Answer:

Hi there!

The answer is:

B. Negative

Step-by-step explanation:

Slopes that increase to the left and decrease to the right are negative! Think about is as rise/run (which determines slope). It rises 4 for every -2 units (or units to the left!)

Hope this makes sense!

The detail from “The Gold Coin” that best supports the inference that Juan is beginning to enjoy reconnecting with people is when he helps the old woman carry her basket of fruit.

Juan is a thief, and he has been for many years. He has no friends, and he doesn't care about anyone but himself. But when he sees the old woman struggling with her groceries, he stops and helps her.

This act of kindness shows that Juan is beginning to change. He is starting to care about other people, and he is starting to understand that there is more to life than just stealing. This is a significant development in Juan's character, and it suggests that he is on the road to redemption.

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Answer:

15.9

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

you know what to do with a different person and you know what to do with a different person and you know what to