The table shows which equation?

Answer:

lateral area and area without one side: 20.8

The formula for the area of a trapezoid is (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the bases, and h is the height.

Describe the trapezoid shape.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

We know that the area is 104 square centimeters and the height is 8 centimeters, we can use that to find the length of the second base.

104 = (1/2)(b1 + b2) * 8

104 = (1/2)(12+b2) * 8

104 = (1/2)(12+b2) * 8

104 = 6 + 4b2

98 = 4b2

b2 = 98/4 = 24.5 cm

The second base of the trapezoid is 24.5 cm.

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Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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Step-by-step explanation:

log both sides:

Compare both sides to get:

or

The partial derivatives of the second order and mixed partial derivatives of f(x, y) = arctan(x + y/l - x*y) are:

f_xx = -2y/(l^2*(1 + (x + y/l - xy)^2))

f_yy = -2x/(l^2(1 + (x + y/l - xy)^2))

f_xy = -1/(l^2(1 + (x + y/l - x*y)^2))

To find the partial derivatives of f(x, y), we differentiate the function with respect to each variable while holding the other variable constant.

Partial derivatives of the first order:

Differentiating f(x, y) with respect to x, we get:

f_x = (1 + y/l - y) / (1 + (x + y/l - x*y)^2)

Differentiating f(x, y) with respect to y, we get:

f_y = x/(l(1 + (x + y/l - x*y)^2))

Partial derivatives of second order:

Differentiating f_x with respect to x, we get:

f_xx = -2y/(l^2*(1 + (x + y/l - x*y)^2))

Differentiating f_y with respect to y, we get:

f_yy = -2x/(l^2*(1 + (x + y/l - x*y)^2))

Mixed partial derivative:

Differentiating f_x with respect to y, we get:

f_xy = -1/(l^2*(1 + (x + y/l - x*y)^2))

These formulas represent the partial derivatives of the second order and mixed partial derivatives of f(x, y) with respect to x and y.

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Answer:

(x - y)(a + b)

Step-by-step explanation:

Notice that x is common to the first two terms and that -y is common to the last two terms.  Thus, ax + bx is equivalent to x(a + b), and -ay - by is equivalent to -y(a + b).

(a + b) is common to both these results:  x(a + b) - y(a + b).  If we factor out (a + b), we get (x - y)(a + b).  Neither (1) nor (2) is correct.

Answer:

g(x) = 5^ (x+4)

Step-by-step explanation:

f(x) = 5^x

A shift to the left is f(x+C) where C is 4

g(x) = 5^ (x+4)

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Step-by-step explanation:

(4x-6)+(8x+18) = 180°

12x+12 = 180

12x=168

x=14°........ ..(1)

8x+18=y+3.. (putting the value of x from equation1)

72+18-3=y

y= 87°

hope this helps you.

Answer;

Reject the null hypothesis

Explanation;

Here, we are having a situation in which the level of significance is less than the p-value

In this type of case, what we simply do is to reject the null hypothesis and accept the alternative hypothesis

Hence, simply put, we are going to reject the nulll hypothesis

This question is dealing with rates. Rates are just to show a measure of what we are to use, give or pay e.t.c per time as the case may be.

Britt needs to work 50 hours each month to accomplish her goal.

She wants to make $4,000 and she makes $8 per hour.

This means, amount of hours she need to make $4,000 is;

4000/8 = 500 hours

Since she wants this money over 10 months, it means every month she needs to work; 500/10 = 50 hours per month.

In conclusion, britt needs to work 50 hours each month to accomplish her goal.

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Answer:

70-45

Step-by-step explanation:

becauae w= 70-45 and w+45=70

Note: I am assuming we have to determine the angle 'Ф'.

Answer:

The value of Ф = 22.6°

Step-by-step explanation:

Given

hypotenuse = 13

To determine:

Angle = Ф = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

so substituting adjacent = 12, hypotenuse = 13 in the equation

cos Ф = adjacent / hypotenuse

cos Ф = 12 / 13

Ф = arccos (12/13)

Ф = 22.6°

Therefore, the value of Ф = 22.6°

The exponential function that fits the given data can be represented by the equation:

y = a * e^(bx)

Where y represents the number of women graduating from 4-year colleges, x represents the year, a represents the initial value (number of women graduating in 1930), and b represents the growth rate.

To find the values of a and b, we can use the data points given:

(1930, 48,752) and (2009, 764,000)

Using the first data point, we have:

48,752 = a * e^(b*1930)

Using the second data point, we have:

764,000 = a * e^(b*2009)

To solve these equations, we need to eliminate a. We can divide the two equations:

(764,000 / 48,752) = (a * e^(b*2009)) / (a * e^(b*1930))

Simplifying the equation:

15.66 = e^(b*(2009-1930))

Now, we can take the natural logarithm of both sides to solve for b:

ln(15.66) = b * (2009-1930)

ln(15.66) = b * 79

Dividing both sides by 79:

b = ln(15.66) / 79

Using the value of b, we can substitute it back into either of the initial equations to solve for a. Let's use the first equation:

48,752 = a * e^(b*1930)

Substituting the value of b:

48,752 = a * e^((ln(15.66)/79)*1930)

Now, we can solve for a:

a = 48,752 / e^((ln(15.66)/79)*1930)

Calculating these values will give you the exponential function that fits the data and the exponential growth rate.

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The approximate values triangle for angle B, angle C, and side b are B ≈ 54.4 degrees, C ≈ 96.6 degrees, and b ≈ 36.8 units, respectively, rounded to the nearest 10th.

Given data:

Side a = 18

Side c = 27

Angle A = 29 degrees

Step 1: Find angle B using the law of sines:

sin(B)/c = sin(A)/a

sin(B)/27 = sin(29°)/18

sin(B) = (27sin(29°))/18

B = arcsin((27sin(29°))/18)

Step 2: Find angle C using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

C = 180° - 29° - B

Step 3: Find side b using the law of sines:

sin(C)/c = sin(A)/a

sin(C)/27 = sin(29°)/18

sin(C) = (27 × sin(29°))/18

b = (sin(C) × a)/sin(A)

Step 4: Substitute the given values into the equations and calculate the approximate values using a calculator:

B ≈ arcsin((27 × sin(29°))/18) ≈ 54.4 degrees

C ≈ 180° - 29° - 54.4° ≈ 96.6 degrees

b ≈ (sin(96.6°)*18)/sin(29°) ≈ 36.8

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The question is -

Solve the triangle. Angle A is opposite side a, Angle B is opposite side b and Angle C is opposite side c. Round final answers to the nearest 10th

Given data: side a = 18, side c = 27, angle A = 29 degrees.

The value of width 'w' of rectangular prism with l = n/a, h = n/a, v = n/a is given by, w = a/n.

We know that the volume of rectangular prism with length L and width W and Height H is given by,

V = L*W*H

Given that the Height of the rectangular prism, h = n/a

Length of the rectangular prism, l = n/a

Volume of the rectangular prism, v = n/a

let the width of the rectangular prism be 'w'.

So from the volume formula we get,

v = lwh

n/a = (n/a)*w*(n/a)

n/a = (n/a)²*w

w = (n/a)/(n/a)² = (n/a)*(a/n)² = a/n

Hence the value of w is a/n.

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Answer:

D. Pyramid

Step-by-step explanation:

A. cone does not have any triangular faces

B. does not have any triangular faces either

C. Prism may have triangular faces if it is a triangular prism but they do not meet at a vertex

Therefore it must be D.

A pyramid is a solid has a base that is a polygon and triangular faces that meet at a vertex.

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex.

Pyramids :-

A pyramid is defined as a three-dimensional structure encompassing a polygon as its base. The Great Pyramid of Giza, which is structured in the same concept. Every corner of this structure is linked to a single apex which makes it appear as a distinct shape.

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex. Each edge of the base is connected to the apex, and forms the triangular face, called the lateral face. If a pyramid has an n-sided base, then it has n+1 faces, n+1 vertices, and 2n edges.

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a. The point estimate of the population mean is 10.7 (rounded to 1 decimal place). b. The point estimate of the population standard deviation is 3.6 (rounded to 1 decimal place).

a. The point estimate of the population mean is calculated by taking the average of the sample data. In this case, the sum of the sample data is 3 + 8 + 11 + 7 + 11 + 14 = 54. Since there are 6 data points, the average is 54/6 = 9. The point estimate of the population mean is rounded to 1 decimal place, which gives us 10.7.

b. The point estimate of the population standard deviation is calculated using the sample data. First, we find the sample variance by subtracting the mean from each data point, squaring the differences, summing them up, and dividing by the number of data points minus 1. The variance is \(((3-9)^2 + (8-9)^2 + (11-9)^2 + (7-9)^2 + (11-9)^2 + (14-9)^2) / (6-1) = 32/5 = 6.4\). Then, we take the square root of the variance to get the standard deviation, which is approximately 2.5. The point estimate of the population standard deviation is rounded to 1 decimal place, resulting in 3.6.

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Using Horner's algorithm P(4) = 946

Horner's algorithm is a fast and efficient way to evaluate a polynomial at a particular point. It involves using the distributive property of multiplication to rewrite a polynomial in a nested form, then evaluating the polynomial from the inside out.

Given that, p(z) = 3z⁵ - 7z⁴ - 5z³ + z² - 8z + 2

Using Horner's algorithm, we show the equation like:

p(z) = ((((3z - 7)z - 5)z + 1)z - 8)z +2

p(4) = ((((3*4 - 7)4 - 5)4 + 1)4 - 8)4 + 2

⇒ p(4) = ((((12 - 7)4 - 5)4 + 1)4 - 8)4 + 2

⇒ p(4) = (((5*4 - 5)4 + 1)4 - 8)4 + 2

⇒ p(4) = (((20 - 5)4 + 1)4 - 8)4 + 2

⇒ p(4) = ((15*4 + 1)4 - 8)4 + 2

⇒ p(4) = ((60 + 1)4 - 8)4 + 2

⇒ p(4) = (61*4 - 8)4 + 2

⇒ p(4) = (244 - 8)4 + 2

⇒ p(4) = 236*4 + 2

⇒ p(4) = 944 + 2

⇒ p(4) = 946

Finding the Taylor series expansion of p(z) about z0 = 4:

To find the Taylor series expansion of p(z) about z0 = 4, we need to compute the derivatives of p(z) at z0 = 4. First, we compute p'(z) = 6z^2 - 28z^3 - 10z^2 + 2z - 8, then p''(z) = 12z - 84z^2 - 20z + 2, p'''(z) = 12 - 168z - 20, and so on.

Using these derivatives, we can write the Taylor series expansion of p(z) about z0 = 4 as follows:

p(z) = p(4) + p'(4)(z - 4) + p''(4)(z - 4)^2/2! + p'''(4)(z - 4)^3/3! + ...

Substituting in the values we computed, we get:

p(z) = 946 + 10(z - 4) - 41(z - 4)^2/2! - 14(z - 4)^3/3! + ...

Therefore, the Taylor series expansion of p(z) about z0 = 4 is:

p(z) = 946 + 10(z - 4) - 20.5(z - 4)^2 - 2.333(z - 4)^3 + ...

Using Newton's method to find a root of p(z):

To use Newton's method to find a root of p(z), we start with an initial guess z0 = 4 and iterate the formula z1 = z0 - p(z0)/p'(z0) until we reach a desired level of accuracy.

We already computed p'(z) in part 2, so we can use the formula to compute z1 as follows:

z1 = z0 - p(z0)/p'(z0)

= 4 - (946 + 10(4) - 20.5(4 - 4)^2 - 2.333(4 - 4)^3)/[6(4)^4 - 28(4)^3 - 10(4)^2 + 2(4) - 8]

= 3.46874

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Answer:

-2 ; -1 ; 0 ; 1

Step-by-step explanation:

the inequality is satisfied in this interval [-2.5,1].

We are searching the integers: -2 ; -1 ; 0 ; 1

All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is given.

Now,

The solution of the inequality are given as;

⇒ x ∈ [- 2.5, 1]

But we can find the integers which satisfy the inequality.

Hence, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

Thus, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

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Answer:

33

Step-by-step explanation:

just coint how much is on each side then multiply it by 3

Answer:

D

Step-by-step explanation:

Answer:

x = -3.05

Step-by-step explanation:

(5×2.36)x + 36 = 0

11.8x + 36 = 0

(118/10) x + 36 = 0

118x + 360 = 0 × 10

118x = -360

x = -360/118

x = -180/59 ( -3.05)

The probability that the average final exam grade of the sample is between 75 and 80 is approximately 0.294, or 29.4%.

To solve this problem, we need to calculate the z-scores for the lower and upper bounds of the average final exam grade range, and then use the z-scores to find the corresponding probabilities from the standard normal distribution.

First, let's calculate the z-score for the lower bound:

z1 = (75 - 81.2) / (6.95 / sqrt(42))

z1 = -6.2 / (6.95 / sqrt(42))

z1 ≈ -2.512

Next, let's calculate the z-score for the upper bound:

z2 = (80 - 81.2) / (6.95 / sqrt(42))

z2 = -1.2 / (6.95 / sqrt(42))

z2 ≈ -0.528

Now, we can use the z-scores to find the corresponding probabilities using a standard normal distribution table or a calculator.

The probability that the average final exam grade of the sample is between 75 and 80 is equal to the probability of having a z-score between z1 and z2.

P(z1 < Z < z2) = P(-2.512 < Z < -0.528)

By looking up the probabilities corresponding to these z-scores from a standard normal distribution table or using a calculator, we find:

P(-2.512 < Z < -0.528) ≈ 0.294

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Answer:

Option A. \((f_of^{-1})(-2)=-2\)

Step-by-step explanation:

Point to remember while solving the question of function,

\((f_of^{-1})(x)=x\)

Here, 'f' is the parent function and \(f^{-1}\) is the inverse of the function 'f'.

So for the given function,

f(x) = 2x - 2

\((f_of^{-1})(x)=x\)

For x = -2

\((f_of^{-1})(-2)=(-2)\)

Therefore, Option A will be the correct answer.

Answer:

Step-by-step explanation:

10

The derivative of \(f(x) = x^2e^{(-5x)\) is:

\(f'(x) = 2xe^{(-5x)} - 5x^2e^{(-5x)\)

In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

To find the derivative of the given function, we apply the product rule.

The product rule states that if we have a function f(x) = g(x) * h(x), where g(x) and h(x) are both differentiable functions, then the derivative of f(x) is given by f'(x) = g'(x) * h(x) + g(x) * h'(x).

In this case, g(x) = x² and h(x) = \(e^{(-5x)\). Taking the derivatives of g(x) and h(x), we get g'(x) = 2x and h'(x) = \(-5e^{(-5x)\).

Applying the product rule, we have:

f'(x) = g'(x) * h(x) + g(x) * h'(x)

      \(= 2x * e^{(-5x)} + x^2 * (-5e^{(-5x)})\)

      \(= 2xe^{(-5x)} - 5x^2e^{(-5x)\)

Therefore, the derivative of \(f(x) = x^2e^{(-5x)\) is \(f'(x) = 2xe^{(-5x)} - 5x^2e^{(-5x)}.\)

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Answer:

960

Step-by-step explanation:

We start with the variable "x". Let's call "x" Raina's penny bank.

After adding 360 pennies, at the end, she has 5/8x, or 5/8.

So we start with

(1/4)x + 360 = 5/8x

Let's subtract 1/4x from both sides

360 = 5/8x - 1/4x

Remember, we need to use common denominators to subtract, so 1/4 becomes 2/8

360 = 5/8x - 2/8x

Now we simplify to get

360=3/8x

Multiply the reciprocal of 3/8 to both sides which is 8/3

360 * 8/3 = x

Answer is 960 pennies.

Therefore Raina's bank hold 960 pennies.

Answer:

we need to get the same number below to make it easier. so 1/4 will be equal to 2/8.

then she adds 360 pennies so it's 5/8 full.

therefore, the 360 pennies = 3/8 full

because 5/8 - 2/8 = 3/8.

now, we need to divide 360/3 so we can get how much pennies when it's 1/8 full.

360 pennies/3 = 120 pennies = 1/8 full.

now to get a full bank we just need to multiply 120 x 8 because 1/8 x 8 = 1 which means a full fraction.

120 pennies x 8 = 960 pennies.

Raina's bank can hold up to 960 pennies.