the area of trapezoid $abcd$ is $60$. one base is $4$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.

Answer:

take any point on the triangle and any point on the image: for now let's take point A(-3,4) A`(-0.6

Step-by-step explanation:

sf =3/4

scale factor=5

Answer:

(- 1, - 1 )

Step-by-step explanation:

2x + 5y = - 7 → (1)

7x + y = - 8 → (2)

multiplying (2) by - 5 and adding to (1) will eliminate y

- 35x - 5y = 40 → (3)

add (1) and (3) term by term to eliminate y

(- 35x + 2y) + (5y - 5y) = - 7 + 40

- 33x + 0 = 33

- 33x = 33 ( divide both sides by - 33 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (1)

2(- 1) + 5y = - 7

- 2 + 5y = - 7 ( add 2 to both sides )

5y = - 5 ( divide both sides by 5 )

y = - 1

solution is (- 1, - 1 )

Answer: 9

Step-by-step explanation:

If a rancher has 80 feet of fencing with which to enclose two adjacent rectangular corrals, then for the maximum area the dimensions will be 10 feet and 40/3 feet

From the given figure

4x + 3y = 80 feet

3y = 80 - 4x

y = (80 - 4x) / 3

The area of the rectangle

A = length × width

A = 2x × y

= 2x × (80 - 4x) / 3

Apply distributive property

= (160/3)x - (8/3)x^2

For the maximum area differentiate the values

0 = 160/3 - 16/3x

16/3x = 160/3

x = 160/3 ÷ 16/3

x = 160/3 × 3/16

x = 10 feet

The value of y = (80 - 4x) / 3

y = (80 - 4(10))/3

y = (80-40) / 3

y = 40/3 feet

Therefore, the dimensions are 10 feet and 40/3 feet

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The answer is (a) Zimbardo did not use a control group.

The stanford prison experiment was a two week simulation of a prison environment that examined the effect of situational variables on participants reactions and behaviors.

The Stanford prison experiment, one of the most famous and compelling psychological studies of all time.

The major flaw in the research design of the Stanford prison experiment was that the Zimbardo did not use a control group.

A control group is used to establish a cause-and-effect relationship by isolating the effect of an independent variable. A control group was necessary to study a particular variable in prison. He had no alternative group to compare to measure the results of the experiment.

A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments.

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Answer: $16 dollars

Step-by-step explanation: 40% of 40 is 16 so you save $16. Game would now cost $24.

The equation that can be solve to know the amount of tights needed is c = 20p.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the teacher orders 20 tights for the dance class and she buys as many as p tights as there are students.

The equation will be illustrated thus:

Let total amount be c

c = 20 × p

c = 20p

The equation is c = 20p.

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Complete question

A teacher orders 20 tights for the dance class. She buys as many as p tights as there are students. What equation can solve the amount of tights needed?

[tex]\frac{10 +3b}{a} =x[/tex]

By manipulating equations, we can solve for different variables.

Error

The error in the equation is in the factoring. In the second line, the x is factored out of the expression; however, this cannot be factored. Factoring is like dividing. When you factor x out you divide the terms by x. Since there is not an x in 3b, x cannot be factored out.

A correct version of factoring looks like:

Correction

Now, we can go back to the beginning and solve for x correctly using the properties of equality. First, rewrite the equation.

Then, add 3b to both sides.

Finally, divide by a.

This is the final, correct equation solved for x.

Answer:09.8990

Step-by-step explanation: take one and add

The factors by applying distributive property out the greatest common factor is 20(3 - 2y).

For the stated equation;

= 60 − 40 y

Do the prime factorization of the both numbers-

60 = 2×2×3×5

40 = 2×2×2×5

Thus, the greatest common factor from both numbers is-

2×2×5 = 20

Taking 20 common from both terms in equation-

Using distribute property;

= 20(3 - 2y)

Thus, factors by applying distributive property out the greatest common factor is 20(3 - 2y).

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a) The coefficients of the regression equation are given as follows:

b) The regression equation is defined as follows: y = 0.9x + 7.6.

c) The estimate of y when x = 6 is given as follows: y = 13.

The slope-intercept definition of the regression equation is given as follows:

y = b1x + b0.

In which the parameters are given as follows:

The points from the table in this problem are given as follows:

(2,7), (6, 18), (9,9), (13, 26), (20,23).

Inserting these points into a linear regression calculator, the equation is given as follows:

y = 0.9x + 7.6.

Then the estimate of the value of y when x = 6 is obtained as follows:

y = 0.9(6) + 7.6 = 13.

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The equation of the ellipse with given foci (2,4) and (2,-8) and co-vertices (10, -2) and ( -6 , -2) is equal to (x - 2)²/40 + ( y + 2)²/36 = 1.

As given in the question,

Given foci of the ellipse :

( 2,4) and ( 2, -8)

Co-vertices of the ellipse :

( 10,-2) and (-6 , -2)

From the given foci and vertices ,

Centre 'c' = 2

b = 6

( h, k) = (2, -2)

a² = c² + b²

⇒a² = 4 + 36

⇒a = √40

⇒a = 2√10

Equation of the ellipse is given by:

( x - h)²/ a² + (y - k)²/b² =1

⇒( x - 2)²/ (2√10)² + (y + 2)²/6² = 1

⇒( x - 2)²/ 40 + (y + 2)²/36 = 1

Therefore, equation of the ellipse is equal to (x - 2)²/ 40 + (y +2)²/36 = 1.

The complete question is:

Determine the equation of the ellipse with foci (2,4) and (2,−8), and co-vertices (10,−2) and(−6,−2).

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The probability for sample mean tax is less than $7,900 is 0.1894.

μ = population mean = 8,040

σ = standard deviation = 5,000

n = amount of sample = 1,000

[tex]\bar x[/tex] = sample mean = 7,900

The probability for sample mean tax can be calculated using z test formula.

P(x < 7,900) = P(z < [tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] )

= P(z < [tex]\frac{7,900 - 8,040}{\frac{5,000}{\sqrt{1,000}}}[/tex])

= P(z < [tex]\frac{-140}{\frac{5,000}{31.622}}[/tex])

= P(z < -0.88)

Using z table for P(z < -0.88). So,

= 0.1894

Thus, the probability is 0.1894 for sample tax mean is less than $7,900.

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Answer:

276 inches

Step-by-step explanation:

︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

Answer:

d= 24 + 9a

Step-by-step explanation:

– 9a – 12 = 12 – d

by collecting like terms

–9a +d = 12 +12

–9a +d = 24

d= 24 + 9a

Answer:

Step-by-step explanation:

-9a-12=12-d

d=9a+24

Can 'r' be 0? No, because a cylinder wouldn't exist otherwise. Because a radius on Earth cannot be endlessly vast, the highest limit would be constrained. But it is hard to say what is excessive, so I'd probably just say that the domain is r > 0.

What do you mean by a domain?

The set of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this set. The collection of values that the function assumes is known as its range. Following the insertion of an x value, the function outputs this set of values. The domains of f(x)=x2 and g(x)=1/x, respectively, are all real numbers with the exception of x=0.

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Answer:

17 degrees

Step-by-step explanation:

<ABD = 25. We know that ABD has a right triangle included. Therefore we know that 25 + 90 + <A = 180.

Therefore 115 + <A = 180.

<A = 65 degrees.

This means that part of <A = 65 degrees. The other part of <A is 44 degrees, add the two to find the whole of angle A.

65 + 44 = 109.

Angle CAD would be congruent to angle C due to alternate interior angles. meaning <C is 44 degrees. Since the angles in a triangle add up to 180 you can write the equation:

109 + 44 + <B = 180.

Combine the like terms.

163 + <B = 180.

Subtract to find angle B.

<B = 17

The measure of angle QOB is  75°.

What is right angle?

90 degrees is the angle of a right.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol stands for a right angle.

Given:

Point O is the incenter of triangle ABC.

Lines are drawn from the points of the triangle to point O.

Lines are drawn from point O to the sides of the triangle to form right angles and line segments OQ, OR, and OS.

Angle OBC is 15 degrees. Angle OCR is 30 degrees.

OBC= 15

OCR =30

In OBQ

OBQ + QOB + OQB = 180

OBQ= OBC=15

OQB= 90

So,

QOB = 180- OBQ- OQB

= 180-15 -90

= 75

Hence, the measure of angle QOB is  75°.

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The probability that the coin will come up heads on the fourth try is 1/2.

Given,

If a fair coin were tossed three times and each time it landed on its head.

We have to find the probability that it will come up heads on the fourth try;

Here,

Coming up short in the first three of four attempts.

The probability will not depend on the first three occurrences in the fourth try.

Consequently, the likelihood of winning the fourth time will be as follows:

Desired outputs as a percentage of overall output

=> 1 / 2

Hence,

The probability of the coming head in the fourth time is 1/2 because the coming head in the fourth time is independent of the coming head in the first three times.

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Multipluy the equations i think...

By identifying all possible outcomes and the probability of each outcome the negotiation used here is Game theory.

The study of mathematical models of strategic interactions between rational beings is known as game theory and it has uses in computer science, logic, systems science, and all branches of social science.

The most well-known application of game theory is The Prisoner's Dilemma for instance take two offenders who were detained following an arrest as an example. The prosecution lacks concrete proof to prove their guilt. Officials, however, take the inmates out of their isolation cells and question each one separately in order to extract a confession.

The area of mathematics known as "game theory" is concerned with the analysis of such games. Classical game theory and combinatorial game theory are the two primary subfields of game theory. Traditional game theory examines games where participants can move, wager, or strategize all at once.

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The number of white roses left in each bouquet is 5.

You must identify the most prevalent common factor for this task (GCF).

The actions are:

The florist's stock of 72 red roses with 40 white roses reveals what the most common factor is, which is:

72 = 2×2×2×3×3 = 2³×3²

40 = 2×2×2×5 = 2³×5

GCF = 2³

Divide this number of white roses in the first bouquet (40 roses) first by Greatest Common Factor to get how many white roses are in each arrangement.

The result is:

= 40 white roses / 8

= 5 white roses

Thus, number of white roses left in each bouquet is 5.

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The probability that the marksman will hit the target 13 times is 0.279.

Here, we are given that the probability that a marksman will hit a target each time he shoots is 0.89.

Thus, the probability that he will not hit the target = 1 - 0.89 = 0.11

Here, we can use the concept of binomial distribution to find the probability.

There are a total number of 15 trials, thus, n = 15

Success ⇒ marksman hits the target

Probability of success ⇒ p = 0.89

Failure ⇒ marksman fails to hit the target

Probability of failure ⇒ q = 0.11

Number of successful outcomes required ⇒ x = 13

Now, according to the formula for calculating binomial probability-

P(x) = [tex]nCx *p^{x} *q^{n-x}[/tex]

P(x) = [tex]15!/(13!*2!) *(0.89)^{13} *(0.11)^{2}[/tex]

P(x) = (15*14/2) (0.2198) (0.0121)

P(x) = 105* 0.0026

P(x) = 0.279

Thus, the probability that the marksman will hit the target 13 times is 0.279.

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Answer: $22.40

Step-by-step explanation:

30% of 32, or 0.3(32) is equal to 9.6. Then you have to subtract that amount, which is 32 - 9.6, which then gets us to 22.40.

Answer:

This equation represents Plan 1, since it shows that the cost to join the plan is $30 and the cost for each bowling visit is $3.

Step-by-step explanation:

Answer: 3x + 30

Step-by-step explanation: the $3 fee depends on how many times joey goes bowling so it will be 3x + the flat $30 per month

Answer:

C≈31.9

Step-by-step explanation:

Answer:

[tex]\textsf{D)} \quad 27x^3+33x^2-x -8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x+8)(3x^2+x-1)[/tex]

Distribute the parentheses:

[tex]\implies 9x \cdot 3x^2+9x \cdot x+ 9x \cdot (-1) + 8 \cdot 3x^2 + 8 \cdot x +8 \cdot(-1)[/tex]

Simplify:

[tex]\implies 27x^3+9x^2-9x + 24x^2 + 8x -8[/tex]

Collect like terms:

[tex]\implies 27x^3+9x^2+ 24x^2-9x + 8x -8[/tex]

Combine like terms:

[tex]\implies 27x^3+33x^2-x -8[/tex]

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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Answer:

  [-2, 2/5] ∪ [2, ∞)

Step-by-step explanation:

You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.

The inequality can be rewritten to a comparison with zero by subtracting the right-side expression.

  7x³ -20x +11 -(2x³ +2x² +3) ≥ 0

  5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify

  x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms

  (x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor

  (x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares

The values of x that make this product equal to zero are

  x -2 = 0   ⇒   x = 2

  5x -2 = 0   ⇒   x = 2/5

  x +2 = 0   ⇒   x = -2

These x-intercepts divide the domain into 4 intervals where we need to check the sign.

From left to right:

(-∞, -2)

  Using x = -3, we find the product to be ...

  (-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0

[-2, 2/5]

  Using x = 0, we find the product to be ...

  (0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution

(2/5, 2)

  Using x = 1, we find the product to be ...

  (1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0

[2, ∞)

  Using x = 3, we find the product to be ...

  (3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution

The solution to the inequality is [-2, 2/5] ∪ [2, ∞).

__

Additional comment

The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.

The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.