Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {2, 4, 6, 8}. What is P' ?
{2, 4, 6, 8}
{1, 2, 3, 4, 5, 6, 7, 8}
{1, 3, 5, 7}
{1, 3, 5, 7, 8}

Assume grapes cost $2.35 per pound, oranges cost $0.99 per pound, and apples cost $1.65 per pound in exercise 13. Adrian paid a total of $5 for the fruits.

Therefore,

The cost of Grapes = $2.35 per pound

The cost of Oranges = $0.99 per pound

The cost of Apples = $1.65 per pound

If Adrian purchased one pound of each fruit,

He paid:

$2.35 + $0.99 + $1.65 = $4.99 = $5 (Approx.)

So, Adrian paid $5 in total for the fruits.

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Analyze each plan according to the given specifications.

Plan A:

The basic fee must be added to the product of 0.13 and the average messages sent.

Plan B:

It already includes the cost for unlimited messages.

Plan C:

The plan costs the product of 0.28 and the average messages sent.

When comparing these plans, the cheapest one is Plan B, which only costs $53.00.

Answer:

12 m

Step-by-step explanation:

area = (side)²

(side)² = area

√(side)² = √(area)

side = √(area)

side = √(144 m²)

side = 12 m

The total distance of the trip is 50 miles

From the question, we have the following parameters

Distance completed = 40%

Distance travelled = 20 miles

Represent the total distance with x

So, we have the following equation

Distance travelled = Distance completed  *Total distance

This gives

Distance travelled = Distance completed  * x

So, we have

20 miles = 40% * x

Divide both sides by 40%

x = 50 miles

Hence. the length of the trip is 50 miles

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The intervals to the given function are as follows:

This function is defined(values of x) for all real values and also assumes all real values(values of y), hence both the domain and the range are of the function are given by the interval (-∞,∞).

From the graph, the function is classified as decreasing or increasing according to the direction of movement in the graph, as follows:

Hence the intervals are given as follows:

The relative minimum is when the graph of the function changes from decreasing to increasing, hence it is at these two following points:

(-0.366, -5.848) and (2,-1).

The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:

(1.366, -0.652).

The end behavior of the function is given by the limits of the function when x go to infinity, looking to the left and to the right of the graph of the function, hence:

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Answer:

b > 6, b < -6

Step-by-step explanation:

Hello!

Using absolute value rules:

The compound inequality is as follows: b > 6, b < -6

This makes sense because all values turn positive in the asbolute value. So a number that is negative and less than -6 (say -7), would turn positive to be 7, which is greater than 6.

And any number already greater than 6 will always be greater than 6.

ANSWERS

a) 58

b) 62.2

EXPLANATION

a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:

The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.

The first 4 values are 44,49,53,54, so the median is 58.

b) The mean is the sum of all values of the data set divided by the amount of data:

Rounded to one decimal place, the mean is 62.2

Answer:

[tex]\dfrac{3}{2\cos\theta - r\sin\theta}[/tex]

Step-by-step explanation:

The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ  the angle which the which the radius makes relative to the x=axis

The following equations are used to convert from cartesian coordinate to polar coordinates

[tex]r = \sqrt{x^2 + y^2}\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\[/tex]

Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives

[tex]2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = \dfrac{3}{2\cos\theta - r\sin\theta}[/tex]

So we want to find the vertical asymptotes of the function:

Remember that there's a vertical asymptote at points of x where the denominator of the rational function is 0.

So, equal the denominator to zero:

And solve this equation for x as follows:

We could factor

Now, notice that any of both factors could be zero, so:

Therefore, the function has vertical asymptotes at x=6 and x=3.

Jerry burger replicated milgram's experiment in 2009, he found that 70% of participants were still obeying, a from milgram's result is slight reduction .slight reduction means small in quantity or extent. 2 of small importance; trifling. slim and delicate.  lacking in strength or substance.

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Answer:

y= 1 800- 150x

Step-by-step explanation:

y= 1 800- 150x



Answer:

The area is 196π, or 615.752160 when evaluated to 6 decimal places.

Step-by-step explanation:

There is an equation for the area of a circle:

A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:

A=π([tex]14^{2}[/tex])

A=196π

If we write out π and evaluate with an (un)reasonable amount of decimal places:

π≅3.1415926536

A=196×(3.1415926536)

A≅615.752160

Answer:

A = [tex]\pi ^{2}[/tex]

Step-by-step explanation:

A≈615.75

Answer:

[tex]a_{n}[/tex] = 2n - 6

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 2 - (- 4) = 0 - (- 2) = 2 - 0 = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 4 and d = 2 , then

[tex]a_{n}[/tex] = - 4 + 2(n - 1) = - 4 + 2n - 2 = 2n - 6

the rule is then 2n - 6

The probability that Robert picks a black marble is 3/8. The result is obtained from the ratio of the number of black marble to all marbles.

Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

In case Robert has 3 black marbles and 5 marbles of other colors, then he picks a marble randomly, what is the probability of picking black marble?

Total number of marbles is 3 + 5 = 8.

n(S) = 8

Number of black marble is 3.

n(A) = 3

The probability of picking black marble is

P(A) = n(A) / n(S)

P(A) = 3/8

Hence, the probability that Robert picks a black marble is 3/8.

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The temperature change from a 5 - kilometer altitude increase is 35 degrees.

It is given in the question that for every 1-kilometer increase in altitude, the temperature drops 7 degrees Celsius.

We have to find the temperature change from a 5-kilometer altitude increase.

As, for 1 km altitude increase, the temperature drops by 7 degrees, hence by using unitary method, we can say that,

For 5 km altitude increase, the temperature will decrease by 7*5 = 35 degrees.

Unitary Method

The unitary method is generally a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

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Answer:

A. 2.25 feet.

Explanation:

We know the following equation:

Where v is the speed, g is the gravity and h is the height. So, replacing v by 12 feet per second and g by 32 feet per second square, we get:

So, solving for h, we get:

Therefore, the answer is A. 2.25 feet.

Answer:

Step-by-step explanation:

We will follow the same steps as in the previous question. First, we can start by leaving the variable [tex]y[/tex] alone.

In this step, let's be careful to give the variable [tex]x[/tex] odd numbers. The rational expression will then be an integer.

Finally, connect these three points. You can see the connected version in the photo. Good luck!

The equation to find the cost of the shirt is s = 5h and the cost is 30.

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

Cost of the hat = 6

The shirt costs 5 times as much as the hat. Therefore, this will be:

s = 5h

where s = cost of shirt

h = cost of hat

The cost will be:

s = 5h

s = 5 × 6

s = 30.

The cost is 30.

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Answer:

11

Step-by-step explanation:

You will just add 6+5=11

72.1232 rounded to the nearest thousandth is 72.123.

The term "rounding to the nearest thousandth" refers to the practice of rounding any decimal number to the next thousandth value. Thousandth in the decimal system signifies (1/1000) or 0.001. 3.125, for example, is the number 3.1249 rounded to the closest thousandth.

To round it to the closest thousandth, we must focus on the number following this spot - tens of thousandths. This figure will determine whether we round up or round down. "Five and above go up like a bird," as the phrase goes. Therefore, this will give a value of 72.123.

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x=3

Answer:

no solutions

Step-by-step explanation:

2x - y = 3 → (1)

- 4x + 2y = 5 → (2)

multiply (1) by 2 and add to (2)

4x - 2y = 6 → (3)

add (2) and (3) term by term

0 + 0 = 11

0 = 11 ← not possible

this indicates the system has no solution

The multiplicative inverse property of the questions that we have here are:

This is the term that is used in Mathematics to show that we are to multiply a fraction by the inverse of that fraction.

A good example of this would be the form that is written as:

1/a would have the inverse property written as a/1

such that 1/a *a/1 = 1

In the same way,

we have

9/7 * 7 / 9 = 1

4/3 * 3/4 = 1

5 1/3 = 16 / 3 * 3/ 16 = 1

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The unit rate of Ben is 8.5 minutes.

For this problem, we are looking for how many miles Ben walked per minute — so the goal is miles per minute

So, calculate:

Therefore, the unit rate for Ben is 8.5 minutes.

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Complete question:

Ben walked 3/4 of a mile in 8 1/2 minutes. Find the Unit Rate.

The amount of paint that must be used from can A and can B is 3.86 liters and 5.14 liters respectively to obtain 9 liters of paint which is half blue and half yellow.

Can A has 9 parts of blue paint and 1 part of yellow paint, this can be expressed in percentage as;

Can A = 90% blue, 10% yellow

Similarly,

Can B = 20% blue, 80% yellow

Now consider an algebraic expression as follows;

A + B = 9 liters

90% A + 20% B = 50% [Blue]

10% A + 80% B = 50% [Yellow]

Resolving;

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Solving the equation, A + B = 9, for one variable;

A + B = 9

B = 9 - A

80% A = 60% (9 - A)

80% A = 540% - 60% A

140% A = 540%

A = 3.86 Liters

Now solving for B;

B = 9 - A

B = 9 - 3.85

B = 5.14 Liters

Therefore 3.86 liters should be used from can A and 5.14 liters should be used from can B.

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The expression for a linear equation in thee slope-intercept form is ,

y = mx + b

the slope = m= (y2-y1)/ (x2-x1)

y-intercept is (0, b)

___________________

Rearreging tha expresion

y = 3x + 4

The rate is the slope (m) = 3

__________________________

Answer

the constant, in this case, is 3

The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Sarah has 85 and 89 on her first two math 23 tests.

Let the third test be represented as x. This will be illustrated as:

(85 + 89 + x) / 3 ≥ 90

Cross multiply

85 + 89 + x ≥ 90 × 3

174 + x ≥ 270

Collect like terms

x ≥ 270 - 174

x ≥ 96

The value is x ≥ 96.

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