❗️❗️❗️Find the length of side x in simplest radical form with a rational denominator.❗️❗️❗️
Plzzz helppppp

Answer: Pat caught 9 basses and 3 trouts

Let:

x = number of basses

y = number of trouts

Since Pat caught a total and 30 pounds, and each bass weighed 3 pounds while trouts weighed 1 pound, we can write this equation as:

Then, it was stated that he got 5 points for each bass and lost 1 point for each trout. He then scored a total of 42 points. We can write this equation as:

We now have the equations:

3x + y = 30.........Equation 1

5x - y = 42..........Equation 2

We can solve this system of equations by elimination. Since we can see that we have a positive and a negative y, we can cancel this and solve for x.

Canceling y, we now have:

3x = 30

5x = 42

Add these two equations:

Then, we will substitute the value of x to any of the equations that we had to solve for y.

With these, we now know that Pat caught 9 basses and 3 trouts.

The equivalent expression would be \($\frac{1}{\sqrt[7]{12^4}}$\).

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It may also include functions, parentheses, brackets, and other symbols.

We know that \($12^{-\frac{4}{7}}$\) means the reciprocal of the seventh root of 12raised to the fourth power. Therefore, we can simplify this expression as follows:

\($12^{-\frac{4}{7}}=\frac{1}{\sqrt[7]{12^4}}$\)

Therefore, the expression that is equivalent to \($12^{-\frac{4}{7}}$\) is:

\($\frac{1}{\sqrt[7]{12^4}}$\)

So, the correct answer is:

\($\frac{1}{\sqrt[7]{12^4}}$\)

Hence, the equivalent expression would be \($\frac{1}{\sqrt[7]{12^4}}$\).

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The expression that is equivalent to \(12^{(-\frac{4}{7}) }\) is \(\frac{1}{\sqrt[7]{12^{4} } }\)

An exponential expression is a mathematical expression in which a number (called the base) is raised to a power (called the exponent or index). The general form of an exponential expression is:

aˣ

Where a is the base, x is the exponent or index, and the result of the expression is a multiplied by itself x times. Exponential expressions can also be written in different forms, such as:

aⁿ: This represents the product of n copies of the base a, where n is a positive integer.

a⁻ⁿ: This represents the reciprocal of the product of n copies of the base a, where n is a positive integer.

a^(1/n): This represents the nth root of the base a, where n is a positive integer.

Exponential expressions have many important properties and applications in mathematics, science, engineering, and finance. Some of these properties include:

The product of exponential expressions with the same base is equal to the base raised to the sum of their exponents.

The quotient of exponential expressions with the same base is equal to the base raised to the difference of their exponents.

The power of an exponential expression is equal to the base raised to the product of the exponent and the power.

Exponential functions have a special property called exponential growth or decay, which describes how quickly a quantity increases or decreases over time.

The expression that is equivalent to \(12^{(-\frac{4}{7}) }\) is \(\frac{1}{\sqrt[7]{12^{4} } }\)

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The Gini coefficient is 2(−13/30) = -13/15.

The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).

In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.

The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.

The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.

The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=

∫[0,1](p^4/3−p)dp

=(1/15)−(1/2)

= -13/30

The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.

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Answer:

a) P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = \(\frac{1}{9}\)

b) P( the sum of both dice adding up to 4) = \(\frac{5}{54}\)

Step-by-step explanation:

Given - You roll two six-sided dice. Die 1 is fair. Die 2 is unfair such that the probability of rolling an odd number is  and the probability of rolling an even number is  , though the probability rolling of each odd number is the same, and the probability of rolling each even number is the same.

To find - What is the probability of:

                a) rolling a number less than 4 on Die 1 and rolling a 5 on Die 2.

                b) the sum of both dice adding up to 4.

Proof -

The sample space , S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

                                          (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

                                          (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

                                           (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

                                           (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

                                            (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

Now,

Given that , Dice 1 is fair

⇒P₁(1) = P₁(2) = P₁(3) = P₁(4) = P₁(5) = P₁(6) = \(\frac{1}{6}\)

Also,

Given Dice 2 is unfair

⇒P₂(1) = P₂(3) = P₂(5) = \(\frac{2}{3}.\frac{1}{3} = \frac{2}{9}\)

    P₂(2) = P₂(4) = P₂(6) = \(\frac{1}{3}.\frac{1}{3} = \frac{1}{9}\)

Now,

a)

P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = P₁(1)P₂(5) + P₁(2)P₂(5) + P₁(3)P₂(5)

= P₂(5) [ P₁(1) + P₁(2) + P₁(3) ]

= \(\frac{2}{9}\) [ \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) ] =  \(\frac{2}{9}\)\([\frac{3}{6} ]\) = \(\frac{1}{9}\)

⇒P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = \(\frac{1}{9}\)

b)

P( the sum of both dice adding up to 4) = P₁(1)P₂(3) + P₁(2)P₂(2) + P₁(3)P₂(1)

                                                                   = \(\frac{1}{6}\) × \(\frac{2}{9}\)  + \(\frac{1}{6}\) × \(\frac{1}{9}\) + \(\frac{1}{6}\) × \(\frac{2}{9}\)   =  \(\frac{5}{54}\)

⇒P( the sum of both dice adding up to 4) = \(\frac{5}{54}\)

We are 99% confident that the true proportion of employed individuals working at home at least once per week is between 11.8% and 21.8%.

The formula for a confidence interval for a proportion is

p ± Z(α/2) * \(\sqrt[(p(1-p))/n],\)

where p is the sample proportion and

n is the sample size.

Given n=250 and 42 individuals working from home, we find

p=42/250

= 0.168.

For a 99% confidence level, Z(α/2) is approximately 2.58.

Plugging in these values, we get 0.168 ± 2.58 * \(\sqrt{[(0.168*(1-0.168))/250]. }\)

This results in an interval (0.118, 0.218).

Therefore, we are 99% confident that the true proportion of employed individuals working at home at least once per week is between 11.8% and 21.8%.

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Where is the given proof

Answer:

a= 4

Step-by-step explanation:

Rearrange terms

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

Multiply the numbers

than subastraract form both by 25

Simplify the expression

Subtract the numbers

Subtract the numbers

You will find the solution

Answer:12/3=4

ratio 4:1

Step-by-step explanation:

Answer:

12:3 is the ratio of ana's age and Joe's age

Answer:

6

Step-by-step explanation:

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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Answer:

the equation is (2x^9y^n)(4x^2y^10)=8x^11y^20

Step-by-step explanation:

,

If 7 in every 9 packets of crisps in a box are salt and vinegar, then 9-7 = 2 packets of crisps in a box are plain.

If there are 63 packets of salt and vinegar in the box, then 63 packets / 7 = 9 groups of 9 packets in the box.

So, 9 groups * 2 plain crisps = 18 packets of plain crisps in the box.

Your Welcome :) Hope you have a great day!

Answer:

14

Step-by-step explanation:

9/9 - 7/9 = 2/9

2 in every 9 packets of ceisps in a box are plain crisps.

Then:

63*2/9 = 126/9

= 14

x=45°

angle 1=45°

angle 2= 135°

ps are you sure you've written the question properly??

Answer:  x = -3/2

Step-by-step explanation:

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

a(A) = 0

Step-by-step explanation:

Answer:

1 and 3,  if im wrong i am sorry I have not don this in a long time

Step-by-step explanation:

Answer:

I can't read the numbers correctly but a supplementary angles are angle that equal 180*

Hope this helped a little :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use long multiplication to evaluate.

576

Answer:

x = 120°

Step-by-step explanation:

Since there are parallel lines, we have congruent alternate interior angles.

\(20 + x + 40 = 180\)

\(60 + x = 180\)

\(x = 120\)

Answer:

Step-by-step explanation:

In both the point, y-coordinates are same. So, the line is parallel to x-axis

Slope of the line parallel to x-axis =0

m = 0

Equation : y =6.7

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Step-by-step explanation:

It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other .   Opposite angles are equal and adjacen angles sum to 180 degrees .

Then remember alternate angles are equal  and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)

Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.

y = 3/4|x-6|-8

y = 3/4(-(x-6))-8

y= 3/4( -x + 6) -8

y = 3(-x + 6 - 32)/4

4y = -3x - 24

y = -3(x + 24)/4

For another function of y

y = 3/4|x-6|-8

y= 3/4( x - 6) -8

y = 3(x - 6 - 32)/4

4y = 3(x - 38)

y = 3(x - 38)/4

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

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Answer: x = 70

Step-by-step explanation:

You can simply solve for x by simplifying both sides of the equation, then isolating the variable

Solve, x/7 - 2 = 8, for x.

x/7 = 10, added the value of 2 to both sides of the equation.

x=70, multiplied the value of 7 to both sides of the equation.

Thus the value of x is equal to 70.