Abstract art. A painter has four different jars of paint colors available, exactly one of which is purple. She wants to paint something abstract, so she blindfolds herself, randomly dips her brush, and paints on the canvas. She continues trying paint jars until she finally gets some purple onto the canvas (her assistant will tell her when this happens). Assume that she does not repeat any of the jars because her assistant removes a jar once it has been used.


Required:

a. How many outcomes are in the sample space? What are they?

b. How many different events are there?

c. Another painter borrows the four jars of paint and performs the same experiment; i.e., selects paint at random, but she allows the jars to be reused, perhaps over and over many times (assume each contains an unlimited amount of paint). List a few of the outcomes in the sample space, when repetitions are allowed.

d. In the scenario from part c, write an expression for the sample space.

The equation is 25x + 8 = 183

The value of x is 7

The group of friends have $183 to spend

The cost of parking is $8

The tickets cost $25 per person

The equation can be written as follows

25x + 8 = 183

Collect the like terms

25x= 175

Divide by the coefficient of x which is 25

x= 175/25

x= 7

Hence the value of x is 7 and the equation is written as 25x + 8 = 183

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Answer:

B:1

Step-by-step explanation:

the values are the same, so we know the scale is 1:1

hope this helps

Answer:

b)1

Step-by-step explanation:

The dropping degree temperature will be  -12°.

A drop of 17 degrees means subtract 17  from given temperature

∴5°-17°=-12°

so, the Temperature drop will be -12°

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Answer:

4 or |4| (Absolute value of 4)

Answer:

\((8x - 14) + (2x + 54) = 180 \\ 8x + 2x - 14 + 54 = 180 \\ 10x - 14 + 54 = 180 \\ 10x + 40 = 180 \\ 10x = 180 - 40 \\ 10x = 140 \\ x = \frac{140}{10} \\ x = 14\)

The zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π) are: x = π/4, 3π/4.

To find the zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π), we need to solve the equation f(x) = 0.

We know that the cosine function has zeros at x = π/2, 3π/2, 5π/2, etc. So we need to find all values of x in the interval (-2π, 2π) that satisfy the equation cos(2x) = 0.

Using the double angle formula for cosine, we have:

cos(2x) = 2cos²(x) - 1 = 0

Solving for cos(x), we get:

cos(x) = ±sqrt(1/2)

So the solutions for cos(2x) = 0 are:

x = π/4, 3π/4, 5π/4, 7π/4

However, we need to check which of these solutions are within the interval (-2π, 2π).

Since π/4 and 3π/4 are both between -2π and 2π, they are valid solutions. But 5π/4 and 7π/4 are not within the interval, so we can discard them.

Therefore, the zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π) are: x = π/4, 3π/4.

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Answer:

\(-x^{3}+x^{2} +x-3\)

Step-by-step explanation:

Remove Parentheses

Subtract  3x^3-4x^3

Leave x^2

Subtract 2x-x

Leave the 3

This can be rewritten as `(y - 3) = 5/3 (x - 2)`, which is answer C.

An equation is a mathematical statement that expresses the equality of two expressions. It is an expression that states the equality between two values, which may be numbers, variables, functions, or other mathematical objects. Equations are used to describe relationships among variables, to solve problems, and to model physical systems. Equations are also used to make predictions and to analyze data. Equations are an important tool in mathematics, science, and engineering.

The point-slope form of a line is given by the equation `y - y_1 = m(x - x_1)` where `(x_1, y_1)` is any point on the line and `m` is the slope of the line. In this case, the point `(x_1, y_1)` is `(2, 3)` and the slope of the line is `m = (0 - 3)/(3 - 2) = -3/5`. Thus, the point-slope form of the line is `(y - 3) = -(3/5)(x - 2)`. This can be rewritten as `(y - 3) = 5/3 (x - 2)`, which is answer C.

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The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

If i am correct the area should 337inches..........

Step-by-step explanation:

my reason is becuase if you multiply these numbers

13* 6 = 78       and   8 * 8 = 64     and   10 * 17 + 170   and  last 5 * 5 = 25

they you add    170+ 78 + 64 + 25 =  337inches          so means the answer is 337 Your Welcome :D

Answer:

$1,194

Step-by-step explanation:

The area of the parking lot is 253.5(176.5) which equals 44,472.75. You then divide 44,472.75 by 4000 to see how many gallons you need to cover the parking lot. The answer to that was about 11.2 and since you can only purchase full drums you have to round it up to 12 to have enough. Finally, you multiply 12 by 99.50 and get your answer.

Dave's savings is -$290, which means he spent more than his total monthly earnings.

To determine how much of Dave's monthly earnings were used for savings, we need to subtract the expenses (food, car, rent) from his total monthly earnings.

Total Monthly Earnings = $520

Expenses:

Food = $300

Car = $180

Rent = $330

Savings = Total Monthly Earnings - (Food + Car + Rent)

Savings = $520 - ($300 + $180 + $330)

Savings = $520 - $810

Savings = -$290

Based on the given information, Dave's savings is -$290, which means he spent more than his total monthly earnings.

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Answer: 14

Step-by-step explanation:

The s is equal to the change of y/change of x. That means you have to subtract 4 and -10, and the denominator is 9 minus 8. It looks like this:

m=4-(-10)/9-8

m=4+10/9-8

m=14/1

m= 14

Step-by-step explanation:

(3⁵×2^-5×5^-5×2×3²)/(5⁵×3^-2×2^-2)

[3^(5+2+2)][2^(-5+1+2)][5^(-5-5)]

3⁹×2^-2×5^-10.

hope this helps you.

Answer:

D: 7c + 9t

Step-by-step explanation:

I assume c = car and t = truck

Since it costs 7 dollards PER car and 9 dollars PER truck, you would use 7c+9c as the equation.

The probability that a score will have a value between X = 100 and X = 130 is 0.4332. (option b)

To find the probability of a score being between 100 and 130, we need to calculate the area under the normal curve between those two values. Since we know the mean and standard deviation of the distribution, we can standardize the values of 100 and 130 using the z-score formula:

z = (X - μ) / σ

Where X is the score we are interested in, μ is the mean of the distribution, and σ is the standard deviation.

For X = 100, the z-score is:

z = (100 - 100) / 20 = 0

For X = 130, the z-score is:

z = (130 - 100) / 20 = 1.5

Now, we need to find the probability of a z-score being between 0 and 1.5. We can use a standard normal distribution table or calculator to look up this probability. The table or calculator will give us the probability of a z-score being less than 1.5, which we can then subtract from the probability of a z-score being less than 0 to get the probability of a z-score being between 0 and 1.5.

Using a standard normal distribution table or calculator, we find that the probability of a z-score being less than 0 is 0.5. The probability of a z-score being less than 1.5 is 0.9332. Therefore, the probability of a z-score being between 0 and 1.5 is:

P(0 ≤ z ≤ 1.5) = P(z ≤ 1.5) - P(z < 0) = 0.9332 - 0.5 = 0.4332

Therefore, the answer choice that best matches this probability is p = 0.4332.

Hence the correct option is (b).

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The area of triangle will be 12x and perimeter of triangle will be 5x + 14.

The sides of a triangle which is divided into two parts i.e., a right angle triangle and a non-right angle triangle is given in figure.

We have to find area and perimeter of triangle using the data given.

What are the area and perimeter of a triangle ?

The area of triangle is A = \(\frac{1}{2}\) × b × h and perimeter is sum of all sides i.e.,  P = a + b + c.

As per the fig. given in question ;

h = 3x

b = 8

The area of the given triangle will be ;

A = \(\frac{1}{2}\) × b × h

A =  \(\frac{1}{2}\) × 8 × 3x

A = 24x ÷ 2

A = 12x

The perimeter of triangle will be sum of all sides i.e.,

P = x + 9 + 4x - 3 + 8

P = 5x + 17 - 3

P = 5x + 14

Thus , the area of triangle will be 12x and perimeter of triangle will be 5x + 14.

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Answer:

a^3 + b^3 + ab^2 + a^2b

Step-by-step explanation:

Here, we want to find a product

we proceed as follows;

(a + b)(a^2 + b^2)

= a(a^2 + b^2) + b(a^2 + b^2)

= a^3 + ab^2 + a^2b + b^3

= a^3 + b^3 + ab^2 + a^2b

\(\cfrac{AC}{BC}\implies \cfrac{\stackrel{AC=3+9}{3~~ + ~~9}}{\underset{BC=9}{9}}\implies \cfrac{\stackrel{4}{~~\begin{matrix} 12 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{4}{3}\implies 4~:~3\)

Based on the scatter plot of the population of the town in thousands, the applicable statements are:

The horizontal axis has years listed on it and the difference between these years is 1 which makes one a reasonable interval for the scale.

For the vertical axis, the distance between corresponding points is low so an interval scale of 2/10 is good as it would take the population amounts well into account.

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Answer:

79 cm

Step-by-step explanation:

area = length x width

7505 = 95 x width

7505/95 = width

Answer:

1499

5

(Decimal: 299.8)

Step-by-step explanation: =

300

1

−

20

100

=

300

1

+

−20

100

=

300

1

+

−1

5

=

1500

5

+

−1

5

=

1500+−1

5

Answer:

The answer would be C. An obtuse equilateral triangle :)

Given that c = 25, a = 7.391812, and b = ? The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Thus, we can use this theorem to find the length of the unknown side. This can be written as a² + b² = c², where a and b are the legs and c is the hypotenuse of the right triangle.Substituting the given values, we get:

7.391812² + b² = 25².

Simplifying, we get:

b² = 625 - 54.54545424= 570.45454545.

Taking the square root of both sides, we get: b ≈ 23.901. We have been given a right triangle, where one of the legs has a length of 7.391812 units and the hypotenuse has a length of 25 units. We are required to find the length of the unknown side. To solve this problem, we can use the Pythagorean theorem. This theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. Thus, we can write the equation as a² + b² = c², where a and b are the legs and c is the hypotenuse of the right triangle.Substituting the given values, we get:

7.391812² + b² = 25²

Simplifying, we get:

b² = 625 - 54.54545424= 570.45454545

Taking the square root of both sides, we get:b ≈ 23.901Therefore, the length of the unknown side is approximately equal to 23.901 units.

Thus, the length of the unknown side is approximately equal to 23.901 units.

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:6

Step-by-step explanation: The rules of exponential says (a^x)^y=a^xy.

Therefore you will multiply 1/4 with 4 to get an exponent of 1. So the answer is 6^1 which is also written as 6

Answer:

1 : 4

Step-by-step explanation:

12c : 48c ( divide both parts by 12c )

= 1 : 4

Answer:

1 and 4 so it would be 1:4

To construct the exponential function that contains the points (0,-2) and (3,-128), we can use the general form of an exponential function:

y = a * b^x

where y is the function value, x is the input value, b is the base of the exponential function, and a is a constant representing the y-intercept. To find the specific exponential function that contains the two given points, we need to solve for a and b using the given coordinates.

First, we can use the point (0,-2) to find the value of a:

-2 = a * b^0
-2 = a * 1
a = -2

Next, we can use the point (3,-128) to find the value of b:

-128 = -2 * b^3
64 = b^3
b = 4

Now that we know the values of a and b, we can write the exponential function:

y = -2 * 4^x

Therefore, the exponential function that contains the points (0,-2) and (3,-128) is y = -2 * 4^x.

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Answer:

Step-by-step explanation:

finding the first term by putting n=1

t(1)=4.\((1)^{2}\) +2 = 4.1 +2 = 4+2 = 6

finding the second term by putting n=2

t(2)=4.\((2)^{2}\) +2 = 4.4 +2 = 16+2 = 18

finding the third term by putting n=3

t(3)=4.\((3)^{2}\) +2 = 4.9 +2 = 36+2 = 38

hence first three terms are:

               6,18,38,......,4\(n^{2}\) +2