Use calculator to find the values of the following,correct to 3decimal places:

1. Cot 61,4

Answer:

First answer = -22/15

Second answer= -10/81  

Third answer= -8/21

Step-by-step explanation:

Heyaa!!! :)))

 Answers:

- 4/5 - 2/3 = 2/5

-5/9 x 2/9 = 10/81

-1/3 divided by 7/8 = 8/21

Step-by-step explanation:

For... - 4/5 - 2/3 You Have To... To subtract fractions, find the LCD and then combine.

For... - 5/9 x 2/9 You Have To... Simplify the expression.

For... - 1/3 divided by 7/8 You Have To... Reduce the expression, if possible, by cancelling the common factors.

Hopefully this helps you!

\(Matthew\)

The probability that both customers say that the service is poor is 0.0588 or 5.88%.

To determine the probability that both customers say the service is poor, use the binomial distribution and the following formula:P(X = k) = (nCk) * p^k * (1 - p)^(n - k)Where:P(X = k) represents the probability that k successes occurn is the sample sizep is the probability of successk is the number of successes requested(1 - p) represents the probability of failure.Substitute the given values and calculate:P(X = 2) = (2C2) * (140/500)^2 * (1 - 140/500)^(2 - 2) = 0.0588 or 5.88%

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The completed table with the corresponding values of y for each given value of x is as shown above.

To complete the table using the given rule y = (1/7)^x, we can substitute the values of x into the equation and calculate the corresponding values of y.

Let's calculate the values of y for each given value of x:

For x = -2:

y = (1/7)^(-2)

= 1 / (1/7)^2

= 1 / (1/49)

= 49

For x = -1:

y = (1/7)^(-1)

= 1 / (1/7)^1

= 1 / (1/7)

= 7

For x = 0:

y = (1/7)^0

= 1

For x = 1:

y = (1/7)^1

= 1/7

For x = 2:

y = (1/7)^2

= 1 / (1/7)^2

= 1 / (1/49)

= 49

For x = 3:

y = (1/7)^3

= 1 / (1/7)^3

= 1 / (1/343)

= 343

Completing the table:

x -2 -1 0 1 2 3

y 49 7 1 1/7 49 343

Therefore, the completed table with the corresponding values of y for each given value of x is as shown above.

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A skewed distribution is neither symmetrical nor normal as the data values trail off more sharply on one side than on the other. It occurs due to the lower or upper bounds on data. In symmetric distribution left and right sides mirror each other.

a. The given data distribution is skewed as the data is not even on either side.

b. The median is defined as the middle value of a data set. Here 20 is the median as it is the mid point.

c. The average of the given numbers is known as mean and it is obtained by dividing sum of numbers divided by total numbers.

Mean = 207 / 11 = 18.81

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Answer:

First choice, 25

Step-by-step explanation:

200 times 1/8 = 200/8 = 25

Given the exponential model:

Where A is the initial condition, b is the growth factor and x is a time-like variable.

We know that the growth factor is 1.9 and that 1500 people died of AIDS in 1983. If we make x to be the years passed since 1983, then 1500 is our initial condition (because 0 years passed). In our model:

For 2005, x = 22:

Answer:

all we need to do is keep on adding 1/4 until you get to 1 1/2 its lik dividing to how muc times con 1/4 go into 1 1/2. so you run 7 laps

this is you answer

Step-by-step explanation:

example: at home you walk around your yard and you walked 4 1/2 miles. and yard is 1/2 of a mile. 1/2+1/2+1/2+1/2+1/2+1/2+1/2+1/2+1/2=4 1/2

so 1/2 can go into 4 1/2 9 times.

The probability that the obstetrician has delivered no child with polydactyly is 0.8187.

To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:

P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)

First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.

Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.

Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):

P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187

So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.

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Answer:

1.   5 in.

2.   12 in.

3.   3.5 in.

4.   30 ft

5.   4 m

6.   32 mm

7.   53.41 m

8.   18.85 ft

9.   87.96 in

10.  56.56 mm

11.   20.57 in

12.  25.71 yd

Step-by-step explanation:

Answer:

the answer is B on edge

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

good luck! :)

(a) g'(π/3)  = 12. This can be found using the product rule, which states that the derivative of f(x) g(x) is f'(x) g(x) + f(x) g'(x). In this case, f(x) = sin x and g(x) = f(x), so the product rule gives us: g'(x) = f'(x) g(x) + f(x) g'(x)

Plugging in x = π/3 and using the fact that f(π/3) = 4 and f'(π/3) = −3, we get g'(π/3) = (-3) 4 + 4 g'(π/3)

Solving for g'(π/3), we get g'(π/3) = 12.

(b) h'(π/3)

The h'(π/3) = −3/4, this can be found using the quotient rule, which states that the derivative of f(x)/g(x) is (g'(x) f(x) - f'(x) g(x)) / [g(x)]^2. In this case, f(x) = cos x and g(x) = f(x), so the quotient rule gives us h'(x) = (f'(x) g(x) - f(x) g'(x)) / [g(x)]^2

Plugging in x = π/3 and using the fact that f(π/3) = 4 and f'(π/3) = −3, we get: h'(π/3) = ((-3) 4 - 4 (-3)) / (4)^2 = -3/4

The product rule and quotient rule are two important differentiation rules that can be used to find the derivatives of composite functions. The product rule states that the derivative of f(x) g(x) is f'(x) g(x) + f(x) g'(x). The quotient rule states that the derivative of f(x)/g(x) is (g'(x) f(x) - f'(x) g(x)) / [g(x)]^2.

In this problem, we were given that f(π/3) = 4 and f'(π/3) = −3. We were then asked to find g'(π/3) and h'(π/3). To find g'(π/3), we used the product rule. To find h'(π/3), we used the quotient rule.

The product rule and quotient rule are powerful tools that can be used to find the derivatives of a wide variety of functions. They are essential for anyone who wants to understand calculus.

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                                       "complete question"

Suppose f(π/3) = 4 and f '(π/3) = −3, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following.

(a) g'(π/3)

(b) h'(π/3)

a.  2 + 3πi  in polar form is approximately 5.79(cos(1.48 + kπ) + i sin(1.48 + kπ)).

To convert 2 + 3πi to polar form, we need to find the magnitude r and the argument θ. We have:

r = |2 + 3πi| = √(2^2 + (3π)^2) ≈ 5.79

θ = arg(2 + 3πi) = arctan(3π/2) + kπ ≈ 1.48 + kπ, where k is an integer.

Therefore, 2 + 3πi in polar form is approximately 5.79(cos(1.48 + kπ) + i sin(1.48 + kπ)).

b. To convert 1 + i to polar form, we need to find the magnitude r and the argument θ. We have:

r = |1 + i| = √2

θ = arg(1 + i) = arctan(1/1) + kπ/2 = π/4 + kπ/2, where k is an integer.

Therefore, 1 + i in polar form is √2(cos(π/4 + kπ/2) + i sin(π/4 + kπ/2)).

c. To convert 2π(1 + i) to polar form, we first need to multiply 2π by the complex number (1 + i). We have:

2π(1 + i) = 2π + 2πi

To convert 2π + 2πi to polar form, we need to find the magnitude r and the argument θ. We have:

r = |2π + 2πi| = 2π√2 ≈ 8.89

θ = arg(2π + 2πi) = arctan(1) + kπ = π/4 + kπ, where k is an integer.

Therefore, 2π(1 + i) in polar form is approximately 8.89(cos(π/4 + kπ) + i sin(π/4 + kπ)).

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Answer:

105

Step-by-step explanation:

0 (104) is equal to 0, so let's cross that out. 103 times 102 is definitely not equal to 105. The third one is 105. The fourth one is not 105. The last one is not 105 either.

The simplified form of 3√2 + 4³√2 is 11√2.

To simplify 3√2+4³√2 we will use the formula for combining like radicals, which is a√m + b√m = (a+b)√m.

So, 3√2 + 4³√2 = 3√2 + 4√8

Now, we will try to simplify the √8.

So, we will divide 8 by its largest perfect square factor. The largest perfect square factor of 8 is 4, as 4*2=8.√8 = √(4*2) = √4 * √2 = 2√2

We substitute this in 3√2 + 4√8 = 3√2 + 4*2√2 = 3√2 + 8√2 = (3+8)√2 = 11√2

Therefore, the simplified form of 3√2 + 4³√2 is 11√2.

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Notice that the intersecton of both inequality is located approximately at the point (150,50). This means that there are at least 100 more feet of quarter inch pipe than half inch pipe, and since the combined cost is represented by the inequality

then, it must not cost more than 800. Therefore, the correct option is a)

Assuming the distribution of property crime rates is normal, percentage of the states had property crime rates between 2360 and 4055 is 0.67. Therefore, the correct option is option 2.

To find the percentage of states with property crime rates between 2360 and 4055, we will use the mean, standard deviation, and the z-scores. The given data are:

Mean (μ) = 3377.2
Standard Deviation (σ) = 847.4
Lower limit (X₁) = 2360
Upper limit (X₂) = 4055

The z-score for a property crime rate of 2360 is:

z₁ = (X₁ - μ) / σ = (2360 - 3377.2) / 847.4 = -1.207

The z-score for a property crime rate of 4055 is:

z₂ = (X₂ - μ) / σ = (4055 - 3377.2) / 847.4 = 0.801

Using a standard normal distribution table, we can find the percentage of states that had property crime rates between these two values:

P(-1.207 < Z < 0.801) = P(Z < 0.801) - P(Z < -1.207)

= 0.7881 - 0.1131

= 0.6750

So, approximately 0.6750 or 67.50% of the states had property crime rates between 2360 and 4055 which corresponds to option 2.

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The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

The quadratic approximation was found to be f(x, y) ≈ 4xy, while the cubic approximation was f(x, y) ≈ f(0, 0) + 4xy + 4e²ˣxy.

To find the quadratic and cubic approximations of f(x, y), we'll start by finding the first and second partial derivatives of the function at the origin. Then, we'll use these derivatives to construct the polynomial approximations using Taylor's formula.

The partial derivative of f(x, y) with respect to x, denoted as fₐ, can be found by treating y as a constant and differentiating f(x, y) with respect to x: fₐ = ∂f/∂x = 2e²ˣ

Similarly, the partial derivative of f(x, y) with respect to y, denoted as fₓ, can be found by treating x as a constant and differentiating f(x, y) with respect to y: fₓ = ∂f/∂y = 4xe²ˣ

Now, let's find the second partial derivatives:

The second partial derivative of f(x, y) with respect to x, denoted as fₐx, can be found by differentiating fₐ with respect to x: fₐx = ∂²f/∂x² = 0 (since the derivative of 2e²ˣ with respect to x is 0)

Similarly, the second partial derivative of f(x, y) with respect to y, denoted as fₓy, can be found by differentiating fₓ with respect to y: fₓy = ∂²f/∂y² = 8xe²ˣ

The mixed partial derivative of f(x, y) with respect to x and y, denoted as fₐy, can be found by differentiating fₐ with respect to y or fₓ with respect to x: fₐy = ∂²f/∂x∂y = 8e²ˣ

The quadratic approximation involves the first partial derivatives and the second partial derivatives:

f(x, y) ≈ f(0, 0) + fₐ(0, 0)x + fₓ(0, 0)y + (1/2)fₐx(0, 0)x² + (1/2)fₓy(0, 0)y² + fₐy(0, 0)xy

Since we are approximating near the origin (x = 0, y = 0), we substitute these values into the formula:

f(x, y) ≈ f(0, 0) + fₐ(0, 0)x + fₓ(0, 0)y + (1/2)fₐx(0, 0)x² + (1/2)fₓy(0, 0)y² + fₐy(0, 0)xy

Substituting the derivative values we calculated earlier:

f(x, y) ≈ f(0, 0) + 0 + 0 + (1/2) * 0 * x² + (1/2) * 8xe⁰ * y² + 8e⁰ * x * y

Simplifying further:

f(x, y) ≈ f(0, 0) + 4xy

So, the quadratic approximation of f(x, y) near the origin is f(x, y) ≈ 4xy.

The cubic approximation involves the first partial derivatives and the second partial derivatives:

f(x, y) ≈ f(0, 0) + fₐ(0, 0)x + fₓ(0, 0)y + (1/2)fₐx(0, 0)x² + (1/2)fₓy(0, 0)y² + fₐy(0, 0)xy + (1/6)fₐxx(0, 0)x³ + (1/6)fₓyy(0, 0)y³ + (1/2)fₐxy(0, 0)x²y + (1/2)fₐyy(0, 0)xy²

Since the second partial derivative fₐx(0, 0) is zero, and fₐxx(0, 0) is also zero, the cubic approximation simplifies to:

f(x, y) ≈ f(0, 0) + fₐ(0, 0)x + fₓ(0, 0)y + (1/2)fₓy(0, 0)y² + fₐy(0, 0)xy + (1/6)fₓyy(0, 0)y³ + (1/2)fₐyy(0, 0)xy²

Substituting the derivative values we calculated earlier:

f(x, y) ≈ f(0, 0) + 0 + 0 + (1/2) * 8xe⁰ * y² + 8e⁰ * x * y + (1/6) * 0 * y³ + (1/2) * 0 * xy²

Simplifying further:

f(x, y) ≈ f(0, 0) + 4xy + 4e²ˣxy

So, the cubic approximation of f(x, y) near the origin is f(x, y) ≈ f(0, 0) + 4xy + 4e²ˣxy.

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Answer:

6.

x = 13   isosceles

7.

x= 60 equilateral

Step-by-step explanation:

6.

154 + 13 = 167

180 - 167 = 13

x = 13 degrees

7. 180 / 3 = 60

Answer:

see explanation

Step-by-step explanation:

\(\frac{2}{3}\) x - 5 < 11 ( multiply through by 3 to clear the fraction )

2x - 15 < 33 ← equivalent inequality

to solve add 15 to both sides

2x < 48 ( divide both sides by 2 )

x < 24

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

The trees.

Step-by-step explanation:

IXL huh? just get it wrong, it doesn't matter. Also read the question more carefully. He's using white for the bushes, so it is going to be lighter

Answer:

125 questions

Answer:

125 questions

Step-by-step explanation:

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

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

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

1.366

Step-by-step explanation:

The answer is 5.5 inches, expressed as a decimal to the nearest tenth.

The longest side of the paper immediately after the second fold is 5.5 inches. To calculate this, the 8.5-by-11 inch piece of paper was folded in half, repeatedly (never being unfolded), each time shortening the longer side. This results in the longest side of the paper being 4.25 inches after the first fold, and 5.5 inches after the second fold. Therefore, the answer is 5.5 inches, expressed as a decimal to the nearest tenth.

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Sam will earn $99 for 12 hours of babysitting.

Two or more expressions with an equal sign are defined as an equation.

Given that, Sam earns $33 for babysitting for 4 hours.

4 hours = $33

4 ×3 hours = $33×3

12 hours = $99

Hence, Sam will earn $99 for 12 hours of babysitting.

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Answer:

x = 3

Step-by-step explanation:

Given the linear function, f(x) = -4x + 2, for which we must determine the integer value of x that will provide an output of f(x) = -10:

The first step is to substitute the output value, f(x) = -10, into the given function, and solve for its corresponding input value, x:

f(x) = -4x + 2

-10 = -4x + 2

Subtract 2 from both sides:

-10 - 2 = -4x + 2 - 2

-12 = -4x

Divide both sides by -4 to solve for x:

\(\displaystyle\mathsf{\frac{-12}{-4}\:=\:\frac{-4x}{-4} }\)

x = 3

Hence, when x = 3, f(x) = -10.  

Substitute the value of x = 3 into the original function:

f(x) = -4x + 2

f(3) = -4(3) + 2

f(3) = -12 + 2

f(3) = -10  ⇒  f(x) = -10.

Therefore, the input value of x = 3 gives an output value of f(x) = -10.