random sample of 199 auditors, 104 indicated some measure of agreement with this statement: Cash flow is an important indication of profitability. Test at the 10% significance level against a twosided alternative the null hypothesis that one-half of the members of this population would agree with this statement. Also find and interpret the p-value of this test.

Answer: 3 3/4s' carpets

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Given that:

Cost of purchase and installation = 5323.50

Cost per window = 230.25

Cost of installation = 2100

Hence,

Total purchase cost of windows alone :

5323.50 - 2100 = 3,223.50

Therefore, the number of windows purchased is :

(Total purchase cost of windows alone / price per window)

(3,223.50 / 230.25)

= 14

Hence, 14 windows was purchased

The numbers from the given options that rounds to the nearest tenth would be 5.04. That is options D

When a number is given to be rounded up to the nearest tenth some rules needs to be obeyed.

That is;

The number that is in the hundredth place when more than five or equal to five should be added as one to the number in the tenth position.

Therefore,

For 4.95 = 5.0

4.87 = 4.90

4.93 = 4.93

5.04 = 5.04

4.97 = 5.00

Therefore, the number that rounds up to the nearest tenth would be = 5.04.

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Answer: 11

Step-by-step explanation: It takes ten scoops for 60 so divide 60 by ten to get the amount of flour per cookie, which is 1 scoop per six cookies. 60 cookies is ten scoops, and 66 is 6 additional cookies. Six cookies is one scoop of flour so 10 scoops + 1 scoop is 11 scoops

Step-by-step explanation:

60 cookies need 10 scoops of flour.

how many cookies can be made with 1 scoop of flour ?

60/10 = 6 cookies can be made with 1 scoop of flour.

how many scoops of flour do we need then for 66 cookies ?

66 / 6 = 11 scoops of flour.

Answer:

No

Step-by-step explanation:

It is already simplified to its simplest form.

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

The mean of the uncertainty distribution is 3.7

The probability distribution of a random event describes the likelihood of each possible outcome of that event.

In the case of the modified die at Pharaoh's Palace, the management has changed the standard probability distribution so that the probability of each side is proportional to the number of spots on the side.

The possible outcomes are 1, 2, 3, 4, 5, and 6, and their probabilities can be calculated by summing up the probabilities of each side and ensuring that they add up to 1.

The mean of the uncertainty distribution is calculated by taking the sum of each possible outcome multiplied by its probability and dividing by the number of possible outcomes.

In this case, the mean is approximately 3.7.

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The given functions f(x) = 2x + 2 & g(x) = (x - 2) / 2 are the inverses of each other.

From the given functions, f(x) = 2x + 2, g(x) = (x - 2) / 2

To find f(g(x)):

Substitute the expression for g(x) into f(x):

f(g(x)) = f((x - 2) / 2)

Replace x in f(x) with (x - 2) / 2:

f(g(x)) = 2 * ((x - 2) / 2) + 2

Simplify the expression:

f(g(x)) = (x - 2) + 2

f(g(x)) = x

Therefore, f(g(x)) = x.

To find g(f(x)):

Substitute the expression for f(x) into g(x):

g(f(x)) = g(2x + 2)

Substitute 2x + 2 into g(x):

g(f(x)) = ((2x + 2) - 2) / 2

Simplify the expression:

g(f(x)) = (2x) / 2

g(f(x)) = x

Therefore, g(f(x)) = x.

Since f(g(x)) = x and g(f(x)) = x, we can conclude that the pair of functions f and g are inverses of each other.

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Answer:

slope = 5

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (- 3, 2) ← 2 points on the line

m = \(\frac{2-(-3)}{-3-(-4)}\) = \(\frac{2+3}{-3+4}\) = \(\frac{5}{1}\) = 5

Based on the triangle midsegment theorem, the true statements are:

DE║AC

2DE = AC

If a line segment joins two sides of triangle and divides them at their midpoint, the divided segments will be congruent, and thus, the line segment joining the two sides is a midsegment of the triangle. According to the triangle midsegment theorem, the midsegment will be parallel to the third side that is not divided and also would be 1/2 its length. That is, the third side is twice the midsegment of that triangle.

In the image given, considering triangle ABC, we can make the following conclusions based on the triangle midsegment theorem:

D and E are midpoints of sides AB and BC respectively because they are divided by segment DE equally.

The midsegment is DE.

DE would be parallel to the third side, line segment AC.

Length of AC would be twice the length of DE

In conclusion, the true statements based on the triangle midsegment theorem are:

DE║AC

2DE = AC

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Triangles equal 180°. The bottom left corner is 90° in this triangle. Add the angles together set equal to 180°.

x= unknown angle

90° + 67° + x= 180°

157 + x= 180

subtract 157 from both sides

x= 23°

ANSWER: x=23°

Hope this helps! :)

Answer: 63

Step-by-step explanation: YOU NEED TO ADD 84+33 AND THEN THE ANSWER YOU GET YOU NEED TO SUBTRACT FROM 180

Answer:190000

Step-by-step explanation: To find the half of a number, You divide the number by 2, so it will be 380000/2 =190000

By using the quadratic formula, the solution to this quadratic equation is equal to -0.5251 or -3.8081.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)

From the information provided, we have the following values;

3x² + 13x + 4 = 0

Where:

a = 3

b = 13

c = 4

Substituting the values into the quadratic formula, we have the following;

\(x = \frac{-(13)\; \pm \;\sqrt{(13)^2 - 4(3)(13)}}{2(3)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 72}}{6}\)

x = (-13 + √97)/6

x = -0.5251 or -3.8081.

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Answer:

Scatter plot because, A simply X-Y axis line graph is a good choice for this. I hope I could help.

The scatter plot display should used to records the height of a plant every day for a month.

Scatter plot is a "set of points plotted on a horizontal and vertical axes"

According to the question,

A graph to show how the plant's height changed over the month. A

scatter plots contain 'x' axis used to represent the heights of the plants and 'y' axis used to represent every day of a month  .

Hence, scatter plot display should used to records the height of a plant evert day for a month.

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Answer:

y=18(1.15)^x

Step-by-step explanation:

The general formula is

y=a(b)^x, where

a is the initial amount and

b is the growth (1+.15 in our case "an increase of 15%) or

            decay rate (1 -.15 would be if the problem have said it decreased ).

x is the amount of time

y is the amount of money

20.70 = 18 (1.15)^1

The equation is:

y= 18(1.15)^x

The actual roots of the function \(f(x)=10x^{3}+29x^{2} -66x+27\) are -9/2, 3/5 and 1.

Given  function \(f(x)=10x^{3}+29x^{2} -66x+27\).

Function is a relationship between two or more variables expressed in equal to form.

The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.

The polynomial function is given as:

\(f(x)=10x^{3}+29x^{2} -66x+27\)

factorize the above function

\(f(x)=(2x+9)(5x-3)(x-1)\)

Now put the function f(x) equal to zero.

f(x)=(2x+9)(5x-3)(x-1)

split the function means put all the expressions equal to zero as under:

(2x+9)(5x-3)(x-1)=0

solve each for the value of x

x=-9/2,x=3/5,x=1

Hence the roots of the function \(f(x)=10x^{3} +29x^{2} -66x+27\) are which are also the values of x are -9/2,3/5,1.

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Answer:

Step-by-step explanation:

The side lengths x and y of the right triangle are (5√2)/2 and (5√2)/2.

The figure in the image is a right triangle.

To solve for the values of x and y, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Plug in the values

sin( 45 ) = x / 5

x = sin( 45 ) × 5

x = (√2)/2 × 5

x =  (5√2)/2

Next, we solve for y.

Cosine = Adjacent / Hypotenuse

cos( 45 ) = y / 5

y = cos( 45 ) × 5

y = (√2)/2 × 5

y =  (5√2)/2

Therefore, the value of x is (5√2)/2 and y is (5√2)/2.

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The slope of the line passing through any two of the points is the same, the points are collinear & the line that fits the given points is y = 3x + 2.

The given points are (0, 2), (1, 5), (2, 8).

To determine whether the points are collinear,

we can find the slope of the line passing through any two of the points and then check if the slope is the same for all the pairs of points.

Let's take (0, 2) and (1, 5) to find the slope of the line passing through them:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

                = (5 - 2) / (1 - 0)

                 = 3 / 1

                 = 3Now

Let's take (1, 5) and (2, 8) to find the slope of the line passing through them:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

               = (8 - 5) / (2 - 1)

                = 3 / 1

                = 3

Since the slope of the line passing through any two of the points is the same, the points are collinear.

To find the line y = c₀ + c₁x that fits the points,

we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

We can use any of the points and the slope found above.

Let's use (0, 2):

y - 2 = 3(x - 0)

y - 2 = 3x + 0

      y = 3x + 2

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Answer:

Step-by-step explanation:

If we input 4 into g(x), we get:

g(4) = 3(4/2) = 3(2) = 6

Therefore, the output of g(x) when we input 4 is 6.

Answer:

P=RS1000

R=10%

T=?

COMPOUND AMOUNT=RS 1200

I=1200-1000=RS200

IF IT IS SIMPLE INTEREST

T={I×100}/(P×R)=(200×100)/(1000×10)=20000/10000=2YEARS=2×12=24MONTHS

Answer:

\(E(evens) = E(odds)\) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.

Step-by-step explanation:

Jessica is challenged to a game of sums.

Which means,

\(E(Dice 1) + E(Dice 2)\)

Let's first check the sum of all possible numbers of the two dice.

We have:

\((1+1 = 2); (1+2=3); (1+3=4); (1+4+5); (1+5=6); (1+6=7); (2+1=3); (2+2=4); (2+3=5); (2+4=6); (2+5=7); (2+6=8); (3+1=4); (3+2=5); (3+3=6); (3+4=7); (3+5=8); (3+6=9); (4+1=5); (4+2=6); (4+3=7); (4+4=8); (4+5=9); (4+6=10); (5+1=6); (6+1=7); (6+2=8);*(6+3=9); (6+4=10); (6+5=11); (6+6+12);\)

Total possible outcome = 36 results.

\((2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12)\)

Probability of even numbers =

\(E(even) =\frac{18}{36}\)

Probability of odd numbers =

\(E(odd) = \frac{18}{36}\)

Since they are equal,

\(E(even) = E(odd)\)

Therefore, the correct choice for Jessica is:

\(E(evens) = E(odds)\) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.

The Accurate statement is

E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

The table of the probability of rolling the sums is

Roll      2       3      4        5       6       7      8        9      10      11       12

Prob   1/36  2/36 3/36  4/36 5/36  6/36 5/36  4/36 3/36  2/36  1/36

So, P(an even sum)

=  1/36 + 3/36 + 5/36 + 5/36 + 3 /36 + 1/36

= 18/36

Thus, E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.

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Answer:

(-2 x5y3 )( 3x2y )= -180 x2 y2

Answer:

.68 Centiseconds

Step-by-step explanation:

A microsecond is exactly 1 x 10-6 seconds. 1 µs = 0.000,001 s. One millionth of a second.

and a centisecond is exactly 0.01 seconds. One hundredth of a second.

Im not really sure how to explain it. But I hope that I helped.

There are 0.68 Centiseconds in 6800 microseconds.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometres, or feet, or any other measure of length.

Given that, Convert 6800 microseconds to centiseconds

We know that 1 centisecond = 10000 microseconds

Thereforre, 6800 microseconds = 6800/10000 centiseconds

= 0.68 Centiseconds

Hence, There are 0.68 Centiseconds in 6800 microseconds.

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Answer:

It's because you are multiplying the wrong variables.

Step-by-step explanation:

Answer:

j = 9, b = 5

Step-by-step explanation:

The first equation must be

\(j+b=14\)

Multiplying by -130 result

\(-130j-130b=-1820\)

we add the equations to eliminate the variable "j"

\(20b=100\)

\(b=100/20=5\)

Now we calculate "j"

\(j+b=14\)

\(j=14-b=14-5=9\)

Hope this helps

Answer:

Ok, so we have a square with sides of 14 inches. :)

The diagonal splits the square into two by the corners, so it forms two right triangles!

We can use the Pythagorean theorem on the right triangle to get:

14^2 + 14^2 = x^2

BTW, x is the length of the diagonal :)

So, 196 + 196 = x^2 = 392

Sooo, x is just the square root of 392 :)

\(\sqrt{392}\\\) = 19.7989898732, which rounds to 20

The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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The factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

To answer the question, w e need to know what factorization is

Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.

So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have

[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Factorizing out the denominator, we have

= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Cancelling out the denominator, we have

= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

So, the factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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508 nanometers is a specific wavelength of light that corresponds to the color green, and it can be converted to centimeters using the conversion factor of 1 nanometer equaling 1 × 10^-7 centimetres.

To convert nanometers to centimetres, we can use the conversion factor:

1 nanometer = 1 × 10^-7 centimetres

So to convert 508 nanometers to centimeters, we can multiply 508 by this conversion factor:

508 nanometers * (1 × 10^-7 centimeters/nanometer) = 0.0000508 centimetres.

To provide some context, the visible spectrum of light that we can see with our eyes ranges from about 400 to 700 nanometers. In particular, light with a wavelength of 508 nanometers appears as a bright green color to our eyes. This is the peak sensitivity of the human eye's color response curve, meaning that our eyes are most sensitive to this wavelength and can detect even very small amounts of it.

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