According to a survey, the probability that a randomly selected worker primarily drives a van to work is 0.868. The probability that a randomly selected worker primarily takes public transportation to work is 0.044.

Answer:

y=4x and x+4y=12 are perpendicular because they have opposite reciprocal slopes

Step-by-step explanation:

y=4x slope is 4

x+4y=12 slope is -1/4

Answer:

6+ 2z

Step-by-step explanation:

2(3+z)= 6+ 2z

The construction worker will be able to repaint 6 walls with 4 ½ gallons of paint. Option C

To determine how many walls the construction worker will be able to repaint with 4 ½ gallons of paint, we need to divide the total amount of paint by the amount required per wall.

The worker has 4 ½ gallons of paint, which can be written as 4 + 1/2 gallons.

Each wall requires 3/4 gallon of paint.

To find the number of walls that can be repainted, we divide the total amount of paint by the amount required per wall:

Number of walls = (Total amount of paint) / (Amount required per wall)

Plugging in the values, we have:

Number of walls = (4 + 1/2) gallons / (3/4 gallon)

To simplify the division, we can convert the mixed number 4 1/2 to an improper fraction:

Number of walls = (9/2) gallons / (3/4 gallon)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

Number of walls = (9/2) gallons * (4/3 gallon)

Simplifying the multiplication:

Number of walls = (9 * 4) / (2 * 3) = 36/6 = 6

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The length of the side b is 106. 7 inches

The Pythagorean theorem can be defined as a mathematical theorem stating that the square of the longest side of a given triangle, called the hypotenuse side is equal to the sum of the square values of the other two sides.

This is represented as;

x² = y² + z²

Such that;

Now, substitute the values

121² = 57² + b²

find the squares

b² = 14, 641 - 3249

b = √11392

b = 106. 7 inches

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To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

\(3x(x+6)=-10\)

\(3x^2+18x=-10\)

To create a quadratic equation, add 10 to both sides of the equation:

\(3x^2+18x+10=-10+10\)

\(3x^2+18x+10=0\)

The quadratic formula is defined as:

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

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

\(\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}\)

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

\(\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}\)

Simplify the radicand:

\(\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}\)

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

\(\sqrt{4\times51}\)

Then, using the Product Property of Square Roots, break this into two radicands:

\(\sqrt{4} \times \sqrt{51}\)

Since 4 is a perfect square, it can be evaluated:

\(2 \times \sqrt{51}\)

To simplify further for easier reading, remove the multiplication symbol:

\(2\sqrt{51}\)

Then, substitute for the quadratic formula:

\(\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}\)

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

\(\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}\)

\(\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}\)

Then, simplify the numerator of the roots by factoring 2 out:

\(\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}\)

\(\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}\)

Then, simplify the fraction by reducing 2/6 to 1/3:

\(\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}\)

\(\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}\)

The final answer to this problem is:

\(\displaystyle x=\frac{-9 + \sqrt{51}}{3}\)

\(\displaystyle x=\frac{-9 - \sqrt{51}}{3}\)

Answer:

z= - 5 √ 38

Step-by-step explanation:

take the root of both sides

or

you can factor each set and make them equal to zero

so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.

we have a line passing through (-6,0) and (0,8), side one

we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two

we have a line passing through (0,-4) and (6,4), side three

now, side four is simply the line connecting one and three.

the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?

well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)

\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)

now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to  (-3 , 4).  Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.

now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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Step-by-step explanation:

48 divided by 4, is 12

or 12/1

Answer:

According to my calculations, 1.6 goes into 10.8 a total of 6 times with a remainder of 1.1999999999999993. If you continue the long division beyond the decimal point, the result would be 6.75.

Step-by-step explanation:

Answer:

6.75 miles

Step-by-step explanation:

1.6 km = 1 mile

   1 km = 1/1.6  mile

10.8 km = \(\frac{1}{1.6}*10.8\)

             = 6.75 miles

Answer:

Step-by-step explanation:

Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.

Volume of cylinder up to water level:

Volume of marbles:

Volume of water:

Correct choice is C

Answer:

C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)

Step-by-step explanation:

Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)

Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)

Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)

Correct choice is C

(a) Through the conditional probability formula:\(P(B ∩ A) = P(B | A) P(A),\)

\(P(B / A1) P(A1) = 0.50 x 0.20 = 0.10A2 = 0.30 x 0.30 = 0.09A3= 0.40 x 0.50 = 0.20\)

(b)Bayes' theorem gives

\(P(A2 | B) = p(B | A2) p(A2) / [p(B | A1) P(A1) + p(B | A2) P(A2) + p(B | A3) p(A3)]= 0.26Thus, P(A2 | B) = 0.26.\)

(c)the tabular approach can show us

Events      P(Ai)    P(B | Ai)   P(Ai ∩ B)   P(Ai | B)

A1          0.2     0.5       0.1        0.167

A2          0.3     0.3       0.09      0.307

A3          0.5     0.4       0.2        0.526

Therefore,\(P(A1 | B) = 0.167, p(A2 | B) = 0.307, p(A3 | B) = 0.526.\)

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f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.

The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.

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The longest amount of time that Marco could use his phone without changing the battery is given as follows:

3.3 hours.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In 5 hours, the battery fell from 50% to 20%, hence the slope is given as follows:

-30/5 = -6% an hour.

The battery is currently at 20%, hence the time that Marco could use the phone without charging it is given as follows:

20/6 = 3.3 hours.

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Answer:

  34.43

Step-by-step explanation:

A differential of length in terms of t will be ...

  dL(t) = √(x'(t)^2 +y'(t)^2)

where ...

  x'(t) = 4cos(4t)

  y'(t) = 7cos(7t)

The length of c(t) will be the integral of this differential on the interval [0, 2π].

Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...

  (π/5)(n -1/2), so the area of the piece will be ...

  sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))

It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.

__

The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.

The length of the curve is estimated to be 34.43.

The average rate of change of the function over the interval is -6

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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The answer of the slope or Gradient of the line is 2

Answer:

1,900

Step-by-step explanation:

fixed costs doesn't depend on the value of x in our case they doesn't depend on the value of produced bottles

Given:

Required:

To solve the given equations by using substitution method.

Explanation:

Consider the given two equation

Substitute equation (1) in (2), we get

Put x in (1), we get

Final Answer:

The angle of rotation for the described transformation is

The movement or transformation described is form quadrant 4 to quadrant  2.

The transformation will require 180 degrees transformation.

In this type of transformation, both clockwise and the counter clockwise have similar effects

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The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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the answer would be c because the angles are equal to each other

Answer:

9

Step-by-step explanation:

8x27/9-15

8x27= 216

216/9-15

216/9= 24

24-15=9

=9

Answer:

Your answer is nine

9

Step-by-step explanation:

A strike in bowling meant all 10 pins knocked down.

In this case, there is only 1 strike

its 7y bcs y + 7 is addition,y / 7 is division and y - 7 is subtraction

Answer:

The following are what Roger must calculate and put into consideration when calculating the taxable equivalent yield for a municipal bond:

~The bond has a tax-free yield of 5%.

~Roger’s investment income increases an average of 7% each year.  

~Roger owns stock that pays a 4% dividend.

~Roger is in the 24% tax bracket.

Step-by-step explanation:

Answer:

k = 3

Step-by-step explanation:

Expanding the first term, we find 1/x at 10(kx)²(1/x)³ = 10k²/x

Expanding the first term, we find 1/x at 8*1⁷(-2/x)¹ = -16/x

Then

10k² - 16 = 74

k = 3

Answer:

1) 1050 ft squared

2) 200 yards

Step-by-step explanation:

Hope this helps! Pls give brainliest!