A large insurance company claims that 80 percent of their customers are very satisfied with the service they receive. To test this claim, a consumer watchdog group surveyed 100 customers, using simple random sampling. Assuming that a hypothesis test of the claim has been conducted, and that the conclusion is to reject the null hypothesis, state the conclusion. A. There is sufficient evidence to suggest that the proportion of satisfied customers at this insurance company is lower than the company's claimed 80%. B. There is not sufficient evidence to suggest that the proportion of satisfied customers at this insurance company is greater than the company's claimed 80%. C. There is sufficient evidence to suggest that the proportion of satisfied customers at this insurance company is greater than the company's claimed 80%. D. There is not sufficient evidence to suggest that the proportion of satisfied customers at this insurance company is lower than the company's claimed 80%.

The values of the variables are computed below

Find x

This is calculated as

16x + 1 + 35 = 180 ---- sum of adjacent angles in a parallelogram

Evaluate

16x = 144

Divide

x = 9

Find x and y

This is calculated as

3x + 4 = 16

y - 60 = 56

Evaluate

3x = 12 and y = 60 + 56

So, we have

x = 4  and y = 106

Find x

This is calculated as

43x - 1 = 85 ----  opposite angles in a parallelogram

Evaluate

43x = 86

Divide

x = 2

Find m and n

This is calculated as

2n - 1 = 9

m + 8 = 3m

Evaluate

n = 5 and m = 4

Find CBE

This is calculated as

21x - 5 + 4x + 1 + 34 = 180 --- sum of angles in a triangle

Evaluate

25x = 150

So, we have

x = 7

From the figure, we have

CBE = 34 + 4x + 1

CBE = 34 + 4 * 7 + 1

CBE = 63

Find JKL

This is calculated as

10x + 14 + 50 + 36 = 180 --- sum of angles in a triangle

Evaluate

10x = 80

So, we have

x = 8

From the figure, we have

JKL = 10x + 14

JKL = 10 * 8 + 14

JKL = 94

Find x

This is calculated as

2(2x - 13) = 14

So, we have

2x - 13 = 7

This gives

2x = 20

So, we have

x = 10

Find V

This is calculated as

7x  - 2 + 8x + 2 = 180 ---- sum of adjacent angles in a parallelogram

So, we have

15x = 180

This gives

x = 12

So, we have

V = 8x + 2

V = 8 * 12 + 2

V = 98

Find x and y

This is calculated as

y + 10 = 2y - 40

y = 50

Next, we have

4x + y + 10 = 180

4x + 50 + 10 = 180

Evaluate

4x = 120

So, we have

x = 30

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The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

z = -675

Step-by-step explanation:

z : 15 = -45

For that, we can change it into

z/15 = -45

z = -45*15

z = -675

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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Answer:

\(adjacent = \sqrt{ {50}^{2} - {14}^{2} } = 48 \\ \\ \sin(Q) = \frac{14}{50} = \frac{7}{25} \\ \cos(Q) = \frac{48}{50} = \frac{24}{25} \\ \tan(Q) = \frac{14}{48} = \frac{7}{24} \)

\( \sin(R) = \frac{48}{50} = \frac{24}{25} \\ \cos(R) = \frac{14}{50} = \frac{7}{25} \\ \tan(R) = \frac{48}{14} = \frac{24}{7} \)

Base

Now

The given power series is: Σ [(-1)^n * (x-4)²ⁿ * (2n)!] To determine the center of the power series, look at the term (x-4) in the expression. The power series is centered at the value that makes this term equal to zero. (x-4) = 0 Solving for x:

x = 4

So, the power series is centered at x = 4

A more detailed explanation of the answer.

The power series is given as:

∑n=0∞(−1)n(x−4)2n(2n)! .

To state where the power series is centered, we can look at the formula for a power series:

∑n=0∞an(x−c)n,

where a is a constant and c is the center of the power series. Comparing this formula to the given power series, we can see that the center is c = 4. Therefore, the power series is centered at x = 4.

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The number of cakes Jas can make in an hour are 55/12 cakes.

It is given in the question that it takes Jas 2/5 hours to make 11/6 cakes.

We have to find the number of cakes made by Jas in an hour.

All we had to do in this question is multiply the numbers of hours by its reciprocal to get 1 hour.

Hence, according to the data given in the question, we can write,

Number of cakes made by Jas in (2/5)*(5/2) hour = 1 hour = (11/6)*(5/2) = 55/12 cakes.

Hence, the number of cakes made by Jas in an hour is 55/12 cakes.

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Answer: 256.7

Step-by-step explanation: the tenth place, (7) is rounded to 7 because when you round the number after the tenth place (7) the number has to be at 5 or greater inorder to change values.

∫ z / √(z^2 - 4) dz = a / 2 * arcsinh (z/2) + C

Evaluate the integral using trigonometric substitution.(Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.)

∫ z / √(z^2 - 4) dz

The given integral is of the form ∫ z / √(z^2 - a^2) dz which is solvable by using trigonometric substitution.

z^2 - a^2 = x^2;

z = a secx;

dz = a secx tanx dx

So ∫ z / √(z^2 - 4) dz = ∫ a secx . tanx / √(a^2 sec^2 x - 4) dx

Let mu2 = a^2 - 4; b = a / 2

The integral now becomes

∫ a secx . tanx / √[(b^2)sec^2x + mu2] dx

Let y = b secx; dy/dx = b tanx secx;

dx = dy / (b tanx secx) = dy / (b y) = dx

On substituting, we get:∫ dy / √((y^2 - b^2)mu2/b^2) = mu/b * arcsin (y / b) + C

Putting back the values of y and b, we get:

∫ a / 2 √(a^2 - 4) arsinh (z/2) + C

Therefore, ∫ z / √(z^2 - 4) dz = a / 2 * arcsinh (z/2) + C

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Answer:y intercept = 5

Step-by-step explanation:f(x)=5•(1/6)^xThe y intercept is when x =0Let x =0f(0)=5•(1/6)^0      = 5* 1     = 5The y intercept is 5If the question is f(x)=5•(1/6)xalthough I have never seen the question written this wayThe y intercept is when x =0Let x =0f(0)=5•(1/6)0      = 5* 0     = 0The y intercept is 0

Answer:

x=12 and y=31

Step-by-step explanation:

First, ( 5x - 7 ) and ( 3x + 17 ) are alternate interior angles, which means they are congruent, or equal:

5x - 7 = 3x + 17

Add 7 to each side:

5x = 3x + 24

Subtract 3x from both sides:

2x = 24

Divide each side by 2:

x = 12

Now we can see that ( 5x - 7 ) and ( 4y + 3 ) are supplementary angles, which means they will add up to 180 degrees:

5x - 7 + 4y + 3 = 180

Substitute 12 in for x to solve for y:

5 ( 12 ) - 7 + 4y + 3 = 180

60 - 7 + 4y + 3 = 180

combine like terms:

( 60 + ( -7 ) + 3 ) + 4y = 180

56 + 4y = 180

Subtract 56 from each side:

4y = 124

Divide each side by 4:

y = 31

False. Line charts are best suited for representing data that follows a sequential order, such as time series data. Nonsequential data is better represented by other types of charts, like scatter plots or bar graphs.

Line charts are graphical representations of data points connected by lines. They are commonly used to display trends over time or sequential data. For example, they are often used to show the change in stock prices over a period of time or the temperature variations throughout the day. This sequential order is the key feature of line charts.

However, for data that does not follow a sequential order, line charts may not be the best choice. Nonsequential data, such as categorical or unrelated data points, are better represented by other types of charts. Scatter plots, for instance, are useful for showing the relationship between two variables that are not necessarily ordered. Bar graphs can also be used to compare nonsequential data points in different categories.

In summary, line charts are not best suited for representing data that follows a nonsequential order. They are most effective when used to display data that has a clear sequential relationship, allowing for easy interpretation of trends and patterns.

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Answer:

B: 8 7/8 Lbs

Step-by-step explanation:

answer = \(15\frac{1}{8} -3\frac{1}{2} -2\frac{3}{4}\)

step 1 find a common denominator

common denominator - 8

* apply *

\(\frac{1^*^1}{8^*^8} =\frac{1}{8} \\\\\frac{1^*^4}{2^*^4} =\frac{4}{8} \\\\\frac{3^*^2}{4^*^2} =\frac{6}{8}\)

now we have

\(15\frac{1}{8} -3\frac{4}{8} -2\frac{6}{8}\)

step 2 make each fraction a improper fraction

We can do this my multiplying the big number by the denominator and adding that to the numerator.

\(15*8=120\\120+1=121\\\frac{121}{8} \\\\3*8=24\\24+4=28\\\frac{28}{8} \\\\2*8=16\\16+6=22\\\frac{22}{8}\)

now we have

\(\frac{121}{8} -\frac{28}{8} -\frac{22}{8}\)

Now we can subtract

remember when subtracting fractions you only subtract the numerators. ( so we keep the denominator as 8 )

so 121 - 28 - 22 = 71

so the answer is \(\frac{71}{8}\)

finally we want to change the answer back into a mixed fraction

To do this we divided 71 and 8

8 can go into 71 8 times

8 * 8 = 64

71 - 64 = 7

We're left with \(8\frac{7}{8}\)

To find (the derivative of \( y \) with respect to \( x \)) from the given function \( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) \), we can apply the rules of logarithmic differentiation.

First, we can rewrite the function using logarithmic properties:

\(\( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) = \ln(x^2(x+3)) - \ln(2x+1) \).\)

Now, using the rules of logarithmic differentiation, we can differentiate \( y \) with respect to \( x \) as follows:

\( \frac{dy}{dx} = \frac{1}{x^2(x+3)} \cdot (2x(x+3)) - \frac{1}{2x+1} \).

Simplifying further:

\(\( \frac{dy}{dx} = \frac{2x(x+3)}{x^2(x+3)} - \frac{1}{2x+1} \).\( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \).Thus, \( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \) is the derivative of \( y \) with respect to \( x \)\) for the given function.

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Answer: A-(2,-3)

B-(5,-5)

c-(7,-3)

d-(5,-2)

Step-by-step explanation:

over the x axis would make it into quadrant 4. You make them all th e same points away from the x axis and y axis.

Answer:

nice pfp hehe genshin player here >○<

constant is 5

coefficient is 6 7

terms: 5, 6m2, 7m

The required value of UCL \( \left(\mathrm{UCL}_{\bar{x}}\right)\) is 0.292 mL.

Given data For a sample size of 10, the control limits for 3-sigma \( \bar{x} \) chart are: Upper Control Limit \( \left(\mathrm{UCL}_{\bar{x}}\right)=\quad \mathrm{mL} \) (round your response to three decimal)We have to find UCL \( \left(\mathrm{UCL}_{\bar{x}}\right)\).The formula for the Upper Control Limit for an \( \bar{x} \) chart is,\[\mathrm{UCL}_{\bar{x}}=\mathrm{Average\;of\;samples}+A_2 \times \mathrm{Std.\;deviation\;of\;samples}\]Where A2 is a constant value depending on the sample size n. It can be found using the following table:

n A2   3 1.023   4 0.729   5 0.577   6 0.483   7 0.419   8 0.373   9 0.337   10 0.308. We have given sample size of 10; hence the value of A2 is 0.308.The value of Sigma is 3 because the control limits for 3-sigma \( \bar{x} \) chart are given.

Now, UCL \( \left(\mathrm{UCL}_{\bar{x}}\right)\) can be calculated as,\[\mathrm{UCL}_{\bar{x}}=\mathrm{Average\;of\;samples}+A_2 \times \mathrm{Std.\;deviation\;of\;samples}\]Using the given data, the standard deviation of the sample is,\[3 \div \sqrt{10}=\mathrm{0.948}\]UCL \( \left(\mathrm{UCL}_{\bar{x}}\right)\) is,\[\mathrm{UCL}_{\bar{x}}=\mathrm{Average\;of\;samples}+A_2 \times \mathrm{Std.\;deviation\;of\;samples}\]\[\begin{aligned}\mathrm{UCL}_{\bar{x}}&= 0 + 0.308 \times 0.948\\&=0.292\\&=0.292\; mL\end{aligned}\]

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We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Answer:

120 pizzas

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Answer:

False.

Step-by-step explanation:

In truth, an inequality is a statement marked by any of these signs:

< less than

> greater than

\(\leq\) less than or equal to

\(\geq\) greater than or equal to

For example, if I wrote x < y. This means that x must always be less than y. Now, if I wrote c \(\geq\) d, this means that c can be greater than OR equal to d. If you see a line under one of these signs, it means (sign) or equal to. So at times, they can be equal, but not strictly. That would be an equation.

To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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Answer:

181º isnt a triangle.

Step-by-step explanation:

Answer: p = 20

Step-by-step explanation: 5 x 20 = 100

-zomba

Answer: 1) 2

2) 7/10

3) -1/3

Step-by-step explanation:

This is a polynomial so we can use rational roots Theorem to solve the equation.

The rational roots simply states that the roots of a polynomial, in the form of

\(p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} \)

The possible roots of the polynomial are the factors of

p/r.

We say r^0 to represent the constant and p to represent the leading coeffceint.

So the rational roots states the possible roots of a polynomial is

the factors of leading coeffceint/ the factors of the constant.

In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.

The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are

positive or negative (1,1/2, 1/3,1/6, 3, 3/2).

Now, we see which of the following roots will that the polynomial, P will equal zero.

It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.

So our factored version of the polynomial is

\((x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)\)

Now can we continue and factor the right side of the factors.

3 also works so x-3 is a factor as well so

\((3 {x}^{2} - 5x - 2)(x + 1)(x - 3)\)

Now factor the quadratic using factoring by grouping

\(3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) \)

So our factor are

\((3x + 1)(x - 2)\)

So in conclusion our factors are

\((3x + 1)(x - 2)(x + 1)(x - 3)\)

And our x values are -1/3, 2, -1, and 3.

(a) The location of the centroid of the channel's cross-sectional area is 72.4 mm.

(b) The moment of inertia of the area about this axis is 2.9 x 10^8 mm^4.

Given: Length a = 310 mm Width b = 270 mm Thickness c = 40 mm

Formula used: Centroidal distance of area = [(b × t/2) × (2t/3) + (a × t) × (t/2)] / (2bt + at) = [(bt² + 3at²) / 6(a+b+t)]

Moment of Inertia = 1/12 bt³ + (c²/12) + (t/2) (t/2) [(b/2) - c/2]² + 1/12 at³ + (t/2) (t/2) [(a/2) - c/2]²

(a) To determine the location of the centroid of the channel's cross-sectional area, use the given formula.

The given values are: Length a = 310 mm, Width b = 270 mm, Thickness c = 40 mm.1

Substituting the given values in the formula:

Centroidal distance of area = [(b × t/2) × (2t/3) + (a × t) × (t/2)] / (2bt + at) = [(bt² + 3at²) / 6(a+b+t)]

Centroidal distance of area = [(270 x 40² + 3 x 310 x 40²) / 6 (270 + 310 + 40)] = 72.4 mm.

Therefore, the location of the centroid of the channel's cross-sectional area is 72.4 mm.

(b) To determine the moment of inertia of the area about this axis, use the given formula.

The given values are

Length a = 310 mm, Width b = 270 mm, Thickness c = 40 mm.

Substituting the given values in the formula:

Moment of Inertia = 1/12 bt³ + (c²/12) + (t/2) (t/2) [(b/2) - c/2]² + 1/12 at³ + (t/2) (t/2) [(a/2) - c/2]²

Moment of Inertia = (1/12 x 270 x 40³) + (40²/12) + (20²) [(270/2) - 40/2]² + (1/12 x 310 x 40³) + (20²) [(310/2) - 40/2]²

Moment of Inertia = 2.9 x 10^8 mm^4

Therefore, the moment of inertia of the area about this axis is 2.9 x 10^8 mm^4.

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Answer:

Step-by-step explanation:

x=√(5+2√6)/(5-2√6)

x²(x-10)²=1

substitute the value of x in the equation

[√(5+2√6)/(5-2√6)]²(√(5+2√6)/(5-2√6) -10)²=

solve :

(49+20√6)(49-20√6)=1     multiply

1=1 proved