Which expression is equivalent to the following complex fraction? 2 minus startfraction 1 over y endfraction divided by 3 + startfraction 1 over y endfraction startfraction 3 y + 1 over 2 y minus 1 endfraction startfraction (2 y minus 1) (3 y + 1) over y squared endfraction startfraction y squared over (2 y minus 1) (3 y + 1) endfraction startfraction 2 y minus 1 over 3 y + 1 endfraction.

Answer:

42

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

hope this helps!

You know that this equation represents the boundary line:

You can solve for "y" in order to write the equation in Slope-Intercept Form:

Where "m" is the slope of the line and "b" is the y-intercept.

Then:

By definition, when the line is dashed the inequality symbol could be:

To determine the symbol, you can observe the graph. Notice that the shaded region is below the line. Then, you can determine that the inequality represented by the graph is:

Hence, the answer is:

The measurements of its short leg and hypotenuse are 4.1 and 14√3 respectively.

We have,

The measurement of the long leg of 30-60-90 right triangle is 14√3.

Now, Apply sine rule,

⇒ sin 90° / 14√3 = sin 60° / a = sin 30° / b  .. (i)

Where, a and b are the measurements of its short legs.

Solve for a and b,

from (i);

⇒ sin 90° / 14√3 = sin 60° / a

⇒ 1 / 14√3 = (√3/2) / a

⇒ a = (√3/2) × 14/√3

⇒ a = 7

From (i);

⇒ sin 90° / 14√3 = sin 30° / b

⇒ 1 / 14√3 = (1/2) / b

⇒ b = (1/2) × 14/√3

⇒ a = 7/√3

⇒ a = 4.1

Thus, The measurements of its short leg and hypotenuse are 4.1 and 14√3 respectively.

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Answer:

\(here \: given \: that \: wy = yx \\ so \: wy + yx = 8.8 \\ 2yx = 8.8 \\ yx = 4.4\)

\(here \: given \: that \: wy = yx \\ so \: wy + yx = 8.8 \\ 2yx = 8.8 \\ yx = 4.4mm \\ thank \: you\)

Answer:

Step-by-step explanation:

(23,0)

23 computers

the they make 0 dollars

Nine hundred Fifty-Six and three hundreths

900 + 50 + 6 + 3/100

956.03

900+ 50+ 6+ .03

Answer:

12x⁴ - 15x³ + 18x²

Step-by-step explanation:

1. distribute -3x²

-3x² • 5x = -15x³

-3x² • -4x² = 12x⁴

-3x² • -6 = 18x²

2. combine terms and put in descending order (standard form)

12x⁴ - 15x³ + 18x²

Answer:

12x⁴ - 15x³ + 18x²

Step-by-step explanation:

1. distribute -3x²

-3x² • 5x = -15x³

-3x² • -4x² = 12x⁴

-3x² • -6 = 18x²

2. combine terms and put in descending order (standard form)

12x⁴ - 15x³ + 18x² correct answer would be this

In conclusion, the expected running time for generating random numbers p and g can be expressed as a function of m and t as follows:

\(O((1/(m ln(2))) * (m^3t)) = O(m^2t/ln(2))\)

The expected time for generating the prime number p depends on the probability of q being prime and the number of iterations required to find a Sophie Germain prime. Since q is an m-bit integer, the probability of q being prime is approximately \(1/ln(2^m) = 1/(m ln(2)).\)

The cost of performing Miller-Rabin primality testing on a composite number N is O(\(m^3t\)) time, as stated in the problem. Therefore, the expected time to find a prime q is proportional to the number of iterations required, which is 1/(m ln(2)).

Finding a primitive element g within the range 1 ≤ g ≤ p-1 involves randomly selecting integers and checking if they satisfy the condition. Since this step is independent of the primality testing, its time complexity is not affected by the value of t. Therefore, the expected time to find a primitive element g is not directly influenced by t.

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The expression is simplified to  give answers with no negative indices to c¹⁴/d¹⁰

Index forms are defined as mathematical models or expressions that are used to represent numbers that are too small or too large in a more proper way.

They are also referred to as;

Some rules for index forms are;

We have;

(c7d-5)2

expand the bracket

c¹⁴d⁻¹⁰

Take the inverse of the form

c¹⁴/d¹⁰

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0.64 or 64% of the variance for the y scores is predicted by its relationship with x.

The percentage of the variation in the dependent variable that can be predicted from the independent variable is known as the coefficient of determination, abbreviated R2 or r2, in statistics.

given that

A set of n = 25 pairs of scores (x and y values) has a pearson correlation of r = 0.80.

now we have to find the variance for the y scores.

here, r=0.80 then \( {r}^{2} = 0.64\)

which means 0.64 or 64% of the variance for the y scores is predicted by its relationship with x.

\(r = \sqrt{ {r}^{2}} \: or \: \sqrt{ {r}^{2}} \\ 0.80 = \sqrt{ {0.80}^{2} } \\ 0.80 = 0.80\)

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The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.

What is an extraneous solution?

An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

We are given two equations as f(x) = \(\frac{-1}{2}\)x + 6 and f(x) = √x - 4.

Now, on equating both the equations, we get

⇒ \(\frac{-1}{2}\)x + 6 = √x - 4

On squaring both sides, we get,

⇒ \((\frac{-1}{2}x + 6)^{2}\)= x - 4

⇒ \(\frac{1}{4}x^{2}\) + 36 - 6x = x - 4

⇒ \(\frac{1}{4}x^{2}\) + 40 = 7x

⇒ \(\frac{1}{4}x^{2}\) -7x + 40 = 0

⇒ \(x^{2}\) -28x + 160 = 0

⇒ x = 20 , 8

For point of intersection, we will substitute x = 20 in both the equations.

So, we get

⇒ f(x) = \(\frac{-1}{2}\) (20) + 6

⇒ f(x) = -10 + 6

⇒ f(x) = -4

Similarly,

⇒ f(x) = √20 - 4

⇒ f(x) = √16

⇒ f(x) = 4

Since both the solutions are not same so this is an extraneous solution.

Hence, the extraneous solution which arises is 10.

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The system of equations is 3x + y = 360 and y = 2x and the angles are 72, 72, 72, and 144 degrees.

It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

As we know, the sum of the angles in a quadrilateral is 360 degree

Let's suppose the one angle is x degrees, so the angles will be also x and x degrees and the fourth angle is y

x + x + x + y = 360

3x + y = 360 ..(1)

The fourth angle has twice the measure of each of the other angles.

y = 2x ...(2)

Equations (1) and equation (2) are the systems of the equation that can be used to find the measure of the angles.

After solving, the measures of the angles will be:

x = 72 degree

y = 144 degree

Thus, the system of equations is 3x + y = 360 and y = 2x and the angles are 72, 72, 72, and 144 degrees.

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If the average velocity is doubled in turbulent flow through a square channel with smooth surfaces, the change in the head loss of the fluid can be determined by considering the relationship between the head loss and the friction factor. The correct answer is: The head loss decreases by a factor of 3.48.

The head loss in a fluid flow is proportional to the friction factor, and the friction factor is dependent on the average velocity. When the average velocity is doubled, the friction factor can be calculated using the given equation. By substituting the new velocity into the equation, we find that the new friction factor is approximately 0.184 * (2)^(-0.2) = 0.116.

Since the head loss is proportional to the friction factor, when the friction factor decreases from 0.184 to 0.116, the head loss decreases by a factor of 0.116/0.184 ≈ 0.631 or approximately 3.48. Therefore, the head loss decreases by a factor of 3.48.

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If the average velocity is doubled in turbulent flow through a square channel with smooth surfaces, the change in the head loss of the fluid can be determined by considering the relationship between the head loss and the friction factor. The correct answer is: The head loss decreases by a factor of 3.48.

The head loss in a fluid flow is proportional to the friction factor, and the friction factor is dependent on the average velocity. When the average velocity is doubled, the friction factor can be calculated using the given equation. By substituting the new velocity into the equation, we find that the new friction factor is approximately 0.184 * (2)^(-0.2) = 0.116.

Since the head loss is proportional to the friction factor, when the friction factor decreases from 0.184 to 0.116, the head loss decreases by a factor of 0.116/0.184 ≈ 0.631 or approximately 3.48. Therefore, the head loss decreases by a factor of 3.48.

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The function that lets you test if something is true or false and then do different things depending on which result you get is called an "if statement".

In programming, an if statement is a conditional statement that allows you to execute certain code if a specified condition is true, and a different set of code if the condition is false. The syntax for an if statement typically involves the use of a comparison operator (such as "==" for equality or ">" for greater than) to compare a variable or expression to a specific value or set of values. If the comparison evaluates to true, the code inside the if statement is executed. If the comparison evaluates to false, the code inside the if statement is skipped and the program moves on to the next line of code. If statements can also be combined with other statements, such as else statements or nested if statements, to create more complex logic in a program.

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Answer:

$237.30

Step-by-step explanation:

14 ( 12.00 + 4.95)

14 × 12 14 × 4.95

168.00 + 69.30 = 237.30

To find the exact length of the curve given by x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3, we can use the arc length formula:
L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the given values, we get:
L = ∫(0 to 3) √[e^t - 9]^2 + [6e^(t/2)]^2 dt
Simplifying the expression under the square root, we get:
L = ∫(0 to 3) √(e^(2t) - 18e^t + 81 + 36e^t) dt
L = ∫(0 to 3) √(e^(2t) + 18e^t + 81) dt
L = ∫(0 to 3) (e^t + 9) dt
L = [e^t + 9t] from 0 to 3
L = [e^3 + 9(3)] - [e^0 + 9(0)]
L = e^3 + 27 - 10.99
L ≈ 25.5
Therefore, the exact length of the curve is approximately 25.5 units.

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Answer: Choose A my smart self just knew

Answer:

KM = 34

Step-by-step explanation:

Since L is the midpoint of KM that makes KL and LM equal. If LM and KL are congruent that means that the measure of KL is also 17. Therefore KM is just double 17 therefore being 34.

The correct answer is that the k population's variance would be small. In the one-way ANOVA F test, if the null hypothesis was true, the variance of the k population means would be small.

The null hypothesis in ANOVA is that there is no significant difference between the means of the populations from which the samples are drawn. If this hypothesis is true, the differences between the sample and overall mean are due to random sampling variability.

In this case, the variance of the population means is expected to be small, because the samples are expected to be representative of their respective populations, and any differences observed between the sample means are due to chance.

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Answer:

The given lengths do not make a right triangle

Step-by-step explanation:

A right triangle has the sum of the squares of the side lengths equal to the square of the hypotenuse, per the Pythagorean Theorem:

\(a^2+b^2=c^2\\\\12^2+16^2\stackrel{?}{=}25^2\\\\144+256\stackrel{?}{=}625\\\\400\stackrel{?}{=}625\\\\400\neq625\)

Since the sum of the squares of the side lengths are not equal to the square of the hypotenuse, then the lengths of the triangle don't make a right triangle.

The difference between strength and fit in regression equations lies in their focus.

Strength refers to the degree of association between the independent and dependent variables. It is determined by the correlation coefficient, which ranges from -1 to +1.

A correlation coefficient of +1 indicates a perfect positive relationship, while a coefficient of -1 indicates a perfect negative relationship.

The strength of a regression equation is usually expressed as an R-squared value, which ranges from 0 to 1. An R-squared value of 1 indicates a perfect fit while a value of 0 indicates no correlation.

Fit, on the other hand, refers to the accuracy of the regression model in predicting the dependent variable. It is determined by the residual sum of squares, which is a measure of the difference between the actual values and the predicted values.

A smaller residual sum of squares indicates a better fit between the model and the data. It is important to report both the strength and fit of the regression equation when interpreting it.

This is because the strength of the association between the variables does not necessarily imply a good fit, and vice versa. Therefore, it is necessary to discuss both to get a clear understanding of the regression model.

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The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9

A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.

The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.

Complete Question:

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

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Answer:

$1.46

Step-by-step explanation:

Required cards for winning :

1's, 2's and 3's

There are 4 cards of each in a total of 52 cards ;

Therefore, number of winning cards ;

(4 * 3) = 12 cards

Hence,

P(winning) = 12 / 52 = 3 / 13

P(not winning) = 1 - 3 /13 = (13 - 3) / 13 = 10/13

Earning (X)

Amount earned for winning = $43

Amount lost for not winning = $11

X ___ $43 ______ - $11

P(X) _ 3/13 _______ 10/13

Expected value, E(X) = ΣX*P(X)

Σ(X) = (43 * 3/13) + (-11 * 10/13)

E(X) = 9.9230769 - 8.4615384

E(X) = 1.4615385

E(X) = $1.46

C. 1/4

There is a table with 36 possible outcomes. 9 of them are desired outcomes because they have an even number rolled first and then an odd number rolled second (a few random examples from the table would be 2,1, 2,3, 4,1, 4,5, 6,3 etc.)

All we have to do is make a fraction of the desired outcomes over the total number of possible outcomes. 9/36. That can be simplified into 1/4 and voilà, there is your answer.

Hope this helped ッ

My Answer:

The of getting an even number in first and an odd number second is 1/4.

That would be option C.

I just took the quiz in math on edge 2020/2021

I hope this helps!

:)

The IRA (individual retirement account) of a 22-year-old college student, who deposits $55 into the account each month, will have a total balance at retirement. To calculate this, we need to consider the time period, the monthly deposit, and the annual percentage rate (APR).

The student plans on retiring at age 65, which means the IRA will have 65 - 22 = 43 years to grow. Since the student deposits $55 each month, we can calculate the total number of deposits over the 43-year period: 43 years * 12 months/year = 516 deposits.

To calculate the total balance at retirement, we need to consider the growth of the account due to the APR. The annual growth rate is 6%, which can be expressed as 0.06 in decimal form. To calculate the monthly growth rate, we divide the annual growth rate by 12: 0.06/12 = 0.005.

Using the formula for the future value of an ordinary annuity, we can calculate the total balance at retirement:
FV = PMT * [(1 + r)^n - 1] / r

Where:
FV = future value (total balance at retirement)
PMT = monthly deposit ($55)
r = monthly interest rate (0.005)
n = number of deposits (516)

Plugging in these values into the formula:
FV = 55 * [(1 + 0.005)^516 - 1] / 0.005

Calculating this equation, the IRA will contain $287,740.73 at retirement.

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Answer:

1. = station A

because 15 gallons = 0.75 discount at B but station A has a 1.50 discount at 15 gallons

Step-by-step explanation:

2. for satation B you have to read the graph

but for station A it is unclear on the graph

a way to work it out is that you know that 10= 1.00 so 12 = 1.2

( divide 12 by 10 )

station B = discount for 12 gallons = 0.6

but Station A = discount for 12 gallons = 1.2

the difference is

1.2 - 0.6 = 0.6 discount

A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

Here,

radius=10 cm

r²+h²/4=10²

r²=10²-h²/4

volume=πr²h

=π(10²-h²/4).h

V=π(10²h-h³/4)

dV/dh=π(10²-3h²/4)

dV/dh=0

10²=3h²/4

10²*2²/3=h²

20/√3=h

h=11.55 cm

r²=10²-h²/4

=10²-(10²*2²/3)/4

r²=(100-400/12)

r²=100-33.33

r²=66.67

r=√66.67

r=8.165 cm

volume=πr²h

=3.14*8.165*8.165*11.55

volume=2417.82 cm³

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.

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Answer:

I think 25.5 degrees may be right answer

The present worth of all costs for a newly acquired machine with an initial cost of $34,000, annual operating costs of $17,000 for the first 4 years, increasing by 10% per year thereafter, a life of 13 years, and an interest rate of 10% per year is $222,543.

To calculate the present worth of all costs, we need to consider the initial cost, operating costs, and the time value of money. The initial cost of $34,000 is already in the present, so it remains unchanged. For the annual operating costs, we calculate the present worth for each year using the shifted gradient formula. The present worth of the operating costs for the first four years is $52,032, considering the increasing rate of 10% per year.

For the remaining nine years, we calculate the present worth of the increased operating costs and sum them up, resulting in $136,511. Adding the initial cost and the present worth of operating costs, we obtain the final answer of $222,543. This represents the total present worth of all costs for the newly acquired machine over its 13-year life span, taking into account the 10% interest rate per year.

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