Which expression is equivalent to 12x + 36y

Approximately 44.1% of randomly selected females purchased a compact fuel-powered vehicle, while approximately 26.7% of randomly selected customers purchased an electric vehicle.

a) To compute the probability that a randomly selected female purchased a compact-fuel powered vehicle, we divide the number of females who purchased a compact-fuel powered vehicle (45) by the total number of females (102).

The probability is 45/102, which simplifies to approximately 0.441.

b) To compute the probability that a randomly selected customer purchased an electric vehicle, we divide the number of customers who purchased an electric vehicle (55) by the total number of customers (206).

The probability is 55/206, which simplifies to approximately 0.267.

Therefore, the probability that a randomly selected female purchased a compact-fuel powered vehicle is approximately 0.441, and the probability that a randomly selected customer purchased an electric vehicle is approximately 0.267.

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The Probability of a pregnancy lasting less than 250 days is 0.1151.

Probability: - It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed  from 0 to 1.

Let the length of human pregnancy be denoted by X. We obtain the probability associated with this value by converting it to be standard normal ( z) score and then consulting a Z- table to find the corresponding probability.

P(x< 250) = P( x-μ /σ < 250 - 268 /15)

                = P( z < -1.2)

                = 0.1151

∴ The probability of a pregnancy lasting less than 250 days is 0.1151.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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To approximate Ppk for the given binomial distribution X~Bin(n=50, p=0.4), we can use the Normal distribution with mean µ = n*p and variance σ² = n*p*(1-p).

The mean µ = 50 * 0.4 = 20.
The variance σ² = 50 * 0.4 * (1-0.4) = 12.

Using the Normal approximation, we have approximated the binomial distribution X~Bin(50, 0.4) with a Normal distribution with mean µ = 20 and variance σ² = 12.

For a more detailed explanation, when the sample size (n) is large, and the probability (p) is not too close to 0 or 1, the binomial distribution can be approximated by a normal distribution. In this case, the normal approximation simplifies calculations and provides a good estimate for the binomial probability P(pk).

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(a) The margin of error at 95% confidence is approximately 1.68 ounces.

(b) The 95% confidence interval for the population mean weight of bags of sugar is approximately (1 lb 13.32 oz, 2 lb 8.68 oz).

(a) To compute the margin of error at 95% confidence, we need to determine the critical value corresponding to a 95% confidence level. Since the sample size is large (n = 121) and the population standard deviation is unknown, we can use the t-distribution.

With 120 degrees of freedom (121 - 1), the critical value at 95% confidence is approximately 1.98. The margin of error is then calculated as 1.98 * (standard deviation / square root of sample size), which gives us 1.98 * (7 oz / √121) ≈ 1.68 oz.

(b) To determine the 95% confidence interval for the population mean weight, we use the formula: sample mean ± margin of error. From part (a), the margin of error is approximately 1.68 ounces. The sample mean is 2 lb 3 oz, which can be converted to 35 ounces.

Thus, the 95% confidence interval is (35 oz - 1.68 oz, 35 oz + 1.68 oz), which simplifies to (33.32 oz, 36.68 oz). Converting back to pounds and ounces, we have approximately (1 lb 13.32 oz, 2 lb 8.68 oz) as the confidence interval for the population mean weight of bags of sugar.

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Answer:

The height of the window = x + 2 = 4.23 + 2= 6.23m

Step-by-step explanation:

The angle of elevation of the top of the house and the window is 60 and 45 degree.

We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.

we don't know the distance between man and the building let it be 'b'

\(\frac{x}{b}=tan 45\) =1

x=b .............(1)

total height of the building is given as 12m

  x + y + 2=12

x + y = 10 .....................(2)

\(\frac{x+y}{b} =\frac{x+y}{x }\)  = tan 60

\(\frac{10}{x} = \sqrt{3}\)

x = \(\frac{10}{\sqrt{3} }\)  ≈ 5.77m

y = 10 -   \(\frac{10}{\sqrt{3} }\)

y= 10(1-\(\frac{1}{\sqrt{3} }\) ) ≈ 4.23m

The height of the window = x + 2 = 4.23 + 2= 6.23m

There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

What is permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.

So, the number of desired cases are,

= \(\frac{7_P_3(24)^4}{2} = 34836480\)

Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

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Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

Answer:

Step-by-step explanation:

Greatest number that divides 300, 560 and 500 is 20 .

Given numbers : 300, 560 and 500

First let’s find prime factors of 300,560 and 500

300 = 2^2 *3^1 *5^2

560= 2^4 * 7^1 *5^1

500 = 2^2 * 5^3

So,

Here highest common power of 2 is 2

Here highest common power of 3 is 0

Here highest common power of 5 is 1

Here highest common power of 7 is 0

Thus HCF (300, 560 and 500) = 2^2 * 5^1 * 3 ^0 * 7 ^0

=4*5*1*1

= 20

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Answer:

1/21

Step-by-step explanation:

hope this helps

Answer:

1/21

Step-by-step explanation:

7x6=42

5x6=30

6x7=42

4x7=28

30-28=2

2/42=1/21

so ur answer would be 1/21

Answer: D. The range stays the same, but the domain changes.

Step-by-step explanation: A function can be reflected over or across an axis. When the function is reflected in the y-axis, it means:

g(x) = f(-x)

i.e, the x-values are opposite to the original function.

In the image below, when we reflected the function across the y-axis, the new one will be drawn at the positive x-axis but still at the negative y-axis as shown in red at the second attachment.

Domain of a function is all the values x can assume. Range of a function is all the results the variable y assume.

According to the new graph, y-values didn't change, so Range stays the same. However, x-values changed their signal. Therefore, domain changes.

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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In the expression for calculating binomial probabilities, term n tells the number of trials, P tells the probability of success and K represents number of success desired.

The binomial probabilities is the experimental probability in which the total number of output values is 2, therefore it is known as binomial probabilities.

The number of independence variable in case of binomial experiments is fixed.Both the two output has the 1/2 chances to occur.

The binomial probability distribution can be given as,

\(P(x)=_{n}^{}\textrm{C}_kp^k(1-p)^{n-k}\)

Here, (C) is the number of ways to choose and (x) is the number of success desired.

Other terms in the formula are,

Thus for the expression for calculating binomial probabilities the term n represents the number of trials, P represents the probability of success and K represents number of success desired.

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Answer:

1st question

n represents the number of trials

p represents the probability of success

k represents the number of successes

2nd question

n= 10

p= 0.5

k= 5

Step-by-step explanation:

edge 2022

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

Answer:

um.. as many needed lol

Step-by-step explanation:

The right answer is option D. 36−180/√(0.45/80 + 0.25/72). It represents the test statistic for investigating the difference in population proportions between High School F and High School G.

The appropriate test statistic for investigating whether there is a difference in population proportions (High School F minus High School G) is calculated using the formula: (p1 - p2) / √[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2).

Here, p1 and p2 represent the proportions of interest and n1 and n2 represent the sample sizes for High School F and High School G, respectively.

Among the options provided, the correct test statistic can be found in option D: (36 - 180) / √[(0.45/80) + (0.25/72)].

Therefore, option D correctly represents the test statistic for investigating the difference in population proportions between High School F and High School G.

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Answer:

Step-by-step explanation:

boody boody

For given division,

                                  416 is dividend

                                   8 is divisor

                                   0 is remainder   and

                                   52 is quotient

Long division:

                       long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand.

                       In the case of long division of numbers, the remainder is always smaller than the divisor. We can verify the quotient and the remainder of the division using the division formula,

                 Dividend = (Divisor × Quotient) + Remainder.

The above formula is also known as division algorithm.

Example:

                       a ÷ b

a is called dividend and b is called divisor

For given question,

                   416 ÷ 8

      that is,

                                      8 )  416  ( 52

                                            40

                                               16

                                               16

                                                0

416 is dividend

8 is divisor

0 is remainder

and 52 is quotient

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Answer: N=6

Step-by-step explanation:

Add 34 degrees with the 90 degree angle and you get 124

Then add 124 to your other equation (9n +2)

Make that equation equal to your straight angle 180 and solve.

9n + 126 = 180

9n = 54

n= 6

Answer:

116 degrees

Step-by-step explanation:

180 - (26 + 90)

180 - 116 = 64 degrees

180 - 64 degrees = 116 degrees

Angle 1 = 116 degrees

Hope that helps!

Answer:

<1 = 116

Step-by-step explanation:

90 + 26 + x = 180

116 + x = 180

x = 64

<1 + 64 = 180

<1 = 116

The given function, after applying the series of transformations, results in the following equation:

y = -3 * f(3(x + 1)) - 2 * f(2(x - 2)) - 2 - 3 * f(x + 1) + 3 - 3 * |f(x + 2)| - 1 * |f(x)| / 2 - 3

The series of transformations can be summarized as follows:

(1) Compress horizontally by a factor of 3 and translate left 1 unit: f(3(x + 1)).

(2) Compress horizontally by a factor of 2 and translate right 2 units: f(2(x - 2)).

(3) Translate left 2 units and translate down 2 units: f(x + 1) - 2.

(4) Translate right 1 unit and translate up 3 units: -3 * f(x + 2) + 3.

(5) Expand vertically by a factor of 3 and reflect across the x-axis: -3 * |f(x + 2)|.

(6) Translate left 2 units and translate down 3 units: -3 * |f(x + 2)| - 1.

(7) Reflect across the x-axis and translate left 1 unit: -1 * |f(x)| / 2.

(8) Compress vertically by a factor of 2 and translate down 3 units: -1 * |f(x)| / 2 - 3.

The resulting equation combines all these transformations to describe the final function.

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The correct model the equation 5x+6= 4x+(-3) is 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.

What is the model equation?

The model equation is a representation of an equation using tiles.

Given equation is 5x+6= 4x+(-3).

1 is represented by a positive tile.

-1 is represented by a negative tile.

We can rewrite the given equation as:

5×(x)+6× (1)= 4×(x)+(3×(-1))

The model of 5×(x)+6× (1) is 5 positive x-tiles and 6 positive unit tiles.

The model of 4×(x)+(3×(-1)) is 4 positive x-tiles and 3 negative unit tiles.

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A countable set is the union of two countable sets. for each kN. Now that AB=cn:nN, it may be counted because it is an infinite set.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

Hence, A countable set is the union of two countable sets. for each kN. Now that AB=cn:nN, it may be counted because it is an infinite set.

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Answer:

11 1/2 miles per hour is the answer I believe

The frequency-domain equivalent circuit equation obtained using phasor methods can be used to analyze the behavior of the circuit at different frequencies, and to predict the performance of the circuit under various operating conditions.  

To transform a circuit from the time domain to the frequency domain using phasor methods, follow these steps:

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Answer:

9

Step-by-step explanation:

r+8r+11=29

9r+11=29

9r=29-11

9r=18

r=18-9

r=9

HOPE IT HELPS YOU

STAY SAFE AND ENJOY YOUR DAY

hello there I can help you

\( = \: \: \: \: r = 2\)

hope it helps

#carry on learning

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The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics.

Standard form of the equation of an ellipse is given by:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h,k) represents the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis.

To find the standard form of the equation, you need the coordinates of the center and the lengths of the semi-major and semi-minor axes. Let's assume the center of the ellipse is (h,k), the length of the semi-major axis is 'a', and the length of the semi-minor axis is 'b'. Then the standard form equation becomes:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics. By knowing the center and the lengths of the semi-major and semi-minor axes, you can easily write the equation in standard form, allowing for further analysis and calculations.

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Answer:

m<J = 83

m<L = 97

m<M = 97

Step-by-step explanation:

The corners across (left to right/right to left) from each other of a trapezoid are always equal.

So, it would be like this:

Angle J is equal to angle K

Angle M is equal to angle L

See how they are across from each other?

Therefore, Angle J will be 83 degrees.

To find the other 2 angles subtract 83 from 180

180 - 83 = 97

So, Angle L and M are 97 degrees.

To check your answer you can add up all the corners and they should equal 360 degrees:

83 + 83 + 97 + 97 = 360

360 = 360

Hope this helps!!

- Kay :)

The surface area of rectangular prism is 346 square meters.

Given the figure is rectangular prism.

We know that the surface area of rectangular prism with length L, width W and height H is = 2(LW+WH+LH)

Given that the length of prism = 5 m

Width of prism = 17 m

Height of prism = 4 m

So the total surface area of the rectangular prism is given by,

= 2 [5*17 + 17*4 + 4*5]

= 2 [85 + 68 + 20]

= 2*173

= 346 square meters

Hence the surface area of rectangular prism is 346 square meters.

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