find the area of the shaded region

Answer:

I think it is C

Step-by-step explanation:

Answer:

Value of x --> 15°

Step-by-step explanation:

(2x + 60°) and 6x lie on a straight line. So, they form a linear pair. Their sum gives 180°.

---> (2x + 60°) + 6x = 180°

     2x + 60° + 6x = 180°

     8x + 60° = 180°

     8x = 180°- 60°

     8x = 120

      x = \(\frac{120}{8}\)

Answer:

8

Step-by-step explanation:

Make a ratio

2:9 = 11

In total there will be 11 cups of solution.

2:9 = 11

?:36 = ?

Divide

36 / 9 = 4

Now that you have found the scale factor, multiply

2 × 4 = 8

So, you will need 8 cups of shampoo concentrate.

Answer:

77 degrees

Step-by-step explanation:

The diagram is drawn and attached below.

m∠3= (3x + 4)°

m∠5 = (2x + 11)°

Angles 3 and 5 are co-interior angles and are therefore supplementary (add up to 180 degrees).

(3x + 4)°+(2x + 11)°=180°

5x+15=180

5x=180-15

5x=165

x=33

Therefore, the measure of angle 5

m∠5 = (2x + 11)°

= (2(33) + 11)°

=66+11

=77°

The measure of angle 5 is 77 degrees.

Answer:

-4 ≤ x <7

x is greater than or equal to -4, and x is less than 7

Step-by-step explanation:

Take each side and solve

-12 ≤ 2x -4

subtract 4 on both sides

-8 ≤ 2x

divide by 2 on both sides

-4 ≤ x

2x -4 < 10

add 4 on both sides

2x < 14

divide by two on both sides

x < 7

Final answer:

-4 ≤ x <7

Answer:

-4 ≤ x < 7

Step-by-step explanation:

Method 1: Split the inequality into two parts,

-12 ≤ 2x-4

and

2x -4 < 10

Solve.

-8 ≤ 2x

2x ≥ -8

x ≥ -4

and

2x < 14

x < 7

So, x is greater than (or equal to) -4, but less than 7.

-4 ≤ x < 7

Method 2:

-12 ≤ 2x - 4 < 10

Add 4 to both sides.

-8 ≤ 2x < 14

Divide both sides by 2.

-4 ≤ x < 7

The value of the unknown variable in the ordered pair is 8

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

(r, 3), (5, 9)

Also, we have

m = 2

The meaning of the above notations are

Ordered pairs (x, y) = (r, 3), (5, 9)

Slope, m = 2

The slope of points is calculated using the following slope equation

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (r, 3), (5, 9) and m = 2

Substitute the known values in the above equation, so, we have the following representation

(9 - 3)/(r - 5) = 2

Evaluate the difference

This gives

6/(r - 5) = 2

Divide both sides by 2

So, we have

3/(r - 5) = 1

Cross multiply

r - 5 = 3

So, we have

r = 3 + 5

Evaluate the sum

r = 8

Hence, the value of r is 8

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Possible question

What is the value of r using the following points and slope

(r, 3), (5, 9), m=2

The absolute maximum value is 4.5, which occurs at x = sqrt(81/2), and the absolute minimum value is -4.5, which occurs at x = -sqrt(81/2).

To find the absolute maximum and minimum values of the function f(x) = x * e^(-x²/162) on the interval [-5, 18], we need to evaluate the function at its critical points and endpoints.

To find the critical points, we need to find where the derivative of the function is equal to zero or undefined.

f'(x) = e^(-x²/162) - (2x²/162) * e^(-x²/162)

Setting f'(x) equal to zero and solving for x:

e^(-x²/162) - (2x²/162) * e^(-x²/162) = 0

e^(-x²/162) * (1 - 2x²/162) = 0

Since e^(-x²/162) is always positive and nonzero, the critical points occur when 1 - 2x²/162 = 0.

1 - 2x²/162 = 0

2x²/162 = 1

x²/81 = 1/2

x = 81/2

x = ±\(\sqrt{\frac{81}{2} }\)

Therefore, the critical points are x =    \(\sqrt{\frac{81}{2} }\)    and x = -\(\sqrt{\frac{81}{2} }\).

We also need to evaluate the function at the endpoints of the interval [-5, 18], which are x = -5 and x = 18.

Now, let's evaluate the function at the critical points and endpoints:

f(-5) = -5 * e^((-5)/162)

f(\(\sqrt{\frac{81}{2} }\)) = \(\sqrt{\frac{81}{2} }\) * e^(\(\sqrt{\frac{81}{2} }\))²/162)

f(-\(\sqrt{\frac{81}{2} }\)) = -\(\sqrt{\frac{81}{2} }\) * e^((-\(\sqrt{\frac{81}{2} }\))²)/162)

f(18) = 18 * e^((18²)/162)

To determine the absolute maximum and absolute minimum values, we compare the function values at these points:

f(-5) = -0.144

f(\(\sqrt{\frac{81}{2} }\)) =4.5

f(-\(\sqrt{\frac{81}{2} }\))) = -4.5

f(18) = 0.144

The absolute maximum value is approximately 4.5, which occurs at x = \(\sqrt{\frac{81}{2} }\), and the absolute minimum value is approximately -4.5, which occurs at x = -\(\sqrt{\frac{81}{2} }\).

Therefore, on the interval [-5, 18], the absolute maximum value of f(x) is approximately 4.5, and the absolute minimum value is approximately -4.5.

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Answer:

Step-by-step explanation:

We are given that the factory produces  42,000  computer monitors per day

And the claim is of this amount produces fewer than 660 are defective.

a random sample shows that of 240 monitors 2 are defective

to verify the factory managers claim we need to know how many 240s are there in 42000

=42000/240= 175

Since each 240 will give 2 defective monitors

175 will give= 175*2= 350

350 is less than 660 hence the managers claim is correct

Answer:

Step-by-step explanation:

Find the distance between the given points: (-7, 5) and (-8, 4)

Find the distance between the given points: (-7, 5) and (-8, 4)

Answer:

x = -3

Step-by-step explanation:

9(2x + 1) < 9x -18

= 18x +9 < 9x - 18

= 18x -9x < -18 -9

= 9x = - 27

x = - 27/9

x= - 3

Taking the quotient between the total amount and the amount needed for each serving, we can see that she can make 12 servings.

To see how many individual servings can Keisha make, we need to take the quotient between the total amount of nuts that she has and the amount that she needs for each serving.

The total amount she has is:

T = (4 + 1/2) cups.

Each serving needs:

S = (3/8) cups.

Taking the quotient we will get:

N = (4 + 1/2)/(3/8)

N = (4.5)/(3/8) = 12

She can make 12 individual servings.

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Answer:

3/8

Step-by-step explanation:

To solve this problem, we need to perform division. We can convert the mixed fraction 4 1/2 into an improper fraction: 4 1/2 = (4 x 2 + 1)/2 = 9/2. Then we can divide 9/2 by 3/8:

(9/2) ÷ (3/8) = (9/2) x (8/3) = 12

Therefore, Keisha can make 12 individual servings of nuts by dividing 4 1/2 cups of nuts into 3/8 cup servings.

The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer:

45⁰

Step-by-step explanation:

use TanB=(3/3)

B=Tan-¹(3/3)

B=45⁰

Let's denote the length of one side of the rectangle as L and the width as W. Given that the area of the rectangle is 36 m², we have the equation:

Area = Length × Width

36 = L × W

To express the perimeter of the rectangle as a function of the length (L), we need to find the relationship between the length and the width.

Solving the equation for W, we get:

W = 36 / L

The perimeter (P) of the rectangle is given by the formula:

P = 2L + 2W

Substituting the value of W, we have:

P(L) = 2L + 2(36 / L)

Simplifying further:

P(L) = 2L + 72 / L

Therefore, the perimeter of the rectangle, expressed as a function of the length (L) of one of its sides, is given by P(L) = 2L + 72 / L.

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we can use Heron's formula to find the area of the triangle. The area of the triangle is 6 square centimeters.

To find the area of a triangle given its side lengths, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by the formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are a = 3 cm, b = 4 cm, and c = 5 cm. We can calculate the semi-perimeter as:

s = (3 + 4 + 5) / 2 = 6 cm

Now, we can substitute the values of s, a, b, and c into Heron's formula:

Area = √(6(6-3)(6-4)(6-5))

= √(6(3)(2)(1))

= √(36)

= 6 cm²

Therefore, the area of the triangle is 6 square centimeters.

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The difference between the amount of saturated fat and protein can be calculated using the subtraction operation. Hence, the difference is 0.59 grams.

Given the Parameters :

Using the subtraction operation :

Hence, the amount of saturated fat is 0.59 grams more than Protein.

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The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.

In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:

Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.

Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.

The objective function we want to minimize is:

Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)

Subject to the following constraints:

1. Initial inventory: y1 = 15 (given)

2. Production capacity constraints:

  x1 <= 90 (month 1 capacity)

  x2 <= 75 (month 2 capacity)

  x3 <= 80 (month 3 capacity)

  x4 <= 50 (month 4 capacity)

3. Inventory balance equations:

  y1 + x1 - 50 = y2 (month 1)

  y2 + x2 - 65 = y3 (month 2)

  y3 + x3 - 100 = y4 (month 3)

  y4 + x4 - 70 = 0 (month 4, no carryover inventory)

4. Non-negativity constraints:

  x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0

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6(x-2) > 15

6x - 12 > 15

6x > 27

x > 27/6

Hope it helps!

Answer:

x>4.5

Step-by-step explanation:

6(x-2)>15

We do this is as if it were an equation:

6(x-2)>15

Expand the brackets:

6x-12>15

Add 12 to both sides:

6x-12+12>15+12

Simplify:

6x>37

Now we divide both sides by 6:

6x÷6>37÷6

x > 4.5

If we put 5 into the original equation as it is more than 4.5, we get:

6(5-2)>15

We can simplify the brackets or expand first:

Simplifying the brackets first:

6(3)>15

18>15 ✅

Expanding first:

6(5-2)>15

30-12>15

18>15 ✅

The volume of the cylinder to the nearest whole number is 274 cubic inches

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

Substitute the given parameters:

V = 3.14 * 3.75² * 6.21

V = 274.21

Hence the volume of the cylinder to the nearest whole number is 274 cubic inches

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To calculate the p-value, we have to follow the following steps:

To calculate the p-value, we need

p = sample proportion

p' = assumed population proportion in the null hypothesis

n = sample size

Example

Given, n =40, σ = 32.17 and X = 105.37. calculate p-value.

σₓ = σ/ √n

σₓ = 32.17 / √40

    = 5.0865

Now, by applying the test static formula, we get

t = (105.37 – 120) / 5.0865

t = -2.8762

Using the table, we find the value of P(t>-2.8762)

From the table, we get

P (t<-2.8762) = P(t>2.8762) = 0.003

If P(t>-2.8762) = 1- 0.003 = 0.997

P- value = 0.997 > 0.05

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Answer:

Step-by-step explanation:

F(x)=4x-6

It will start at -6C and every hour we will be going up by 4

To study the behavior of the neuron, one can analyze the solution of this differential equation or study its phase portrait to understand the different states and dynamics of the neuron's spiking activity.

The given differential equation represents the spiking behavior of a neuron. It can be written as:

dθ/dt = 1 - cos(θ)

This equation describes the rate of change of the membrane potential (θ) of the neuron over time (t). The right-hand side of the equation represents the input current to the neuron, which is influenced by the difference between the resting potential and the current potential.

The equation shows that the rate of change of θ with respect to time is proportional to 1 minus the cosine of θ. The cosine term represents the influence of the current potential on the spiking behavior of the neuron.

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Step-by-step explanation:

x/3+x/6=7/2

We simplify the equation to the form, which is simple to understand

x/3+x/6=7/2

Simplifying:

+ 0.333333333333x+x/6=7/2

Simplifying:

+ 0.333333333333x + 0.166666666667x=7/2

Simplifying:

+ 0.333333333333x + 0.166666666667x=+3.5

We move all terms containing x to the left and all other terms to the right.

+ 0.333333333333x + 0.166666666667x=+3.5

We simplify left and right side of the equation.

+ 0.5x=+3.5

We divide both sides of the equation by 0.5 to get x.

x=7

take l.c .m of 3 and 6 then

2x+x/6 = 7/2

3x = 7/2*3

x = 21/2/3

x = 21/2 * 1/3

x = 7/2

The value of A that makes the function a continuous function on (−∞, ∞) is A = -1. However, there are no values of A and B that make the function differentiable at x = 0.

To determine the values of A and B that make the given piecewise function continuous on the interval (−∞, ∞), we need to evaluate the conditions at the point where the two pieces of the function meet, which is x = 0.

(a) For the function to be a continuous function at x = 0, the limit of f(x) as x approaches 0 from the left (x < 0) must be equal to the limit of f(x) as x approaches 0 from the right (x ≥ 0). In other words, the left-hand and right-hand limits of the function should be equal at x = 0.

Let's evaluate the left-hand limit first:

lim(x→0-) f(x) = lim(x→0-) (A cos x + 2) = A cos(0) + 2 = A + 2.

Now, let's evaluate the right-hand limit:

lim(x→0+) f(x) = lim(x→0+) (\(e^{(3x)}\) + Ax²) = e⁰ + A(0)² = 1.

To ensure continuity, we set A + 2 = 1 and solve for A:

A + 2 = 1

A = -1.

Therefore, the value of A that makes the function continuous on (−∞, ∞) is A = -1. The value of B is not relevant to the continuity of the function since it does not appear in the definition.

(b) To find the values of A and B such that the function is differentiable, we need to check if the derivatives of the two pieces of the function match at x = 0.

Differentiating the left-hand piece, we have:

f'(x) = d/dx(A cos x + 2) = -A sin x.

Differentiating the right-hand piece, we have:

f'(x) = d/dx(\(e^{(3x)}\) + Ax²) = 3\(e^{(3x)}\) + 2Ax.

For the function to be differentiable at x = 0, the derivatives from the left and right must be equal.

Let's evaluate the derivatives at x = 0:

f'(0-) = -A sin(0) = 0,

f'(0+) = \(3e^{(3(0))} + 2A(0)\) = 3 + 0 = 3.

To ensure differentiability, we set -A sin(0) = 3 and solve for A:

-A sin(0) = 3,

0 = 3.

Since the equation is not satisfied, there are no values of A and B that make the function differentiable at x = 0.

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The p-value from the appropriate resources to determine the final conclusion in this case.

To determine the p-value for the given sample, we need to perform a one-sample t-test.

Given:

Null hypothesis (H₀): μ = 64.9

Alternative hypothesis (H₁): μ < 64.9

Sample mean (M) = 59.7

Sample standard deviation (SD) = 6.3

Sample size (n) = 17

Significance level (α) = 0.01

To calculate the p-value, we can use the t-distribution and the test statistic formula:

t = (M - μ) / (SD / √n)

Substituting the given values, we get:

t = (59.7 - 64.9) / (6.3 / √17)

Now we can calculate the test statistic:

t = -5.2 / (6.3 / √17)

Next, we can calculate the degrees of freedom (df) using the sample size (n - 1):

df = 17 - 1 = 16

Using the t-distribution table or a statistical software, we can find the p-value corresponding to the calculated test statistic and degrees of freedom.

However, since the p-value is not provided in the question, I cannot provide the exact value. You would need to consult a t-distribution table or use statistical software to obtain the p-value.

Once you have the p-value, compare it to the significance level (α = 0.01) to make a decision:

If the p-value is less than or equal to α, reject the null hypothesis.

If the p-value is greater than α, fail to reject the null hypothesis.

Finally, based on the decision made, you can draw a conclusion:

If the null hypothesis is rejected, the conclusion would be: "There is sufficient evidence to warrant rejection of the claim that the population mean is less than 64.9."

If the null hypothesis is not rejected, the conclusion would be: "There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 64.9."

Please obtain the p-value from the appropriate resources to determine the final conclusion in this case.

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There are at least two solutions to the equation (c + 1)cos(πc) = 1/π in the interval (0, 2), and the answer is (C) Two.

f'(c) = (f(2) - f(0))/(2 - 0)

f'(c) = 1/(π)

Substituting the given expression for f'(x) gives:

(c + 1)cos(πc) = 1/(π)

The graph of (c + 1)cos(πc) is a smooth, continuous curve that starts at (0, 1) and ends at (2, -1). The graph of 1/π is a horizontal line at y = 1/π.

Since the cosine function oscillates between -1 and 1, the graph of (c + 1)cos(πc) must cross the graph of 1/π at least twice in the interval (0, 2).

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Let f be the function with f(0)=1π2,f(2)=1π2, and derivative given by f'(x)=(x+1)cos(πx). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the function f on the closed interval [0, 2] ?

A. None

B. One

C. Two

D. More than two

Answer:

2200-1700=500

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Express with positive exponent:

(6^2/z^4)^3

Evaluate:

6^6/z^12

The probability of finding 0 contaminated pieces in  225 g of chocolate is 5.57 X 10⁻⁷.

Here the number of contaminated fragments follows a Poisson process. Hence, let the distribution for the same be X.

Hence we get X ~ Poi(λt)

where λ is the mean no. of contaminated pieces and t is the no. of bars consumed.

For P(X = x) we get [(λt)ˣ  e^(-λt)]/x!

Here λ = 14.4 and t = 1 Hence we will get

P(X = x) = [(14.4)ˣ e⁻¹⁴°⁴]/x!

Here we need to find the probability of the no. of contaminated pieces = 0

Therefore

P(X = 0) = [(14.4)⁰ e⁻¹⁴°⁴]/0!

Hence the probability of finding 0 contaminated pieces in a bar of chocolate is

P(X = 0) =  e⁻¹⁴°⁴

= 5.57 X 10⁻⁷

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