Find the surface area of the rectangular prism.

Answer: 60

Step-by-step explanation:

To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.

There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.

5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60

There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.

The probability that exactly two balls are of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 4/16 or 1/4.

There are three ways to draw two balls of the same color: two green balls and one of any other color, two red balls and one of any other color, or two yellow balls and one of any other color. Each of these ways can occur in 4 different orders (e.g. GGR, GRG, RGG, etc.) for a total of 12 possible outcomes. The probability of each of these outcomes is (1/4)^3 = 1/64. Therefore, the probability of exactly two balls being of the same color is 12/64 or simplified to 3/16, which is equivalent to 1/4.

Therefore, the probability of exactly two balls being of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 1/4.

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Answer:

A

Step-by-step explanation:

If bottles of soda are marked S, and one bottle costs $1,75

And slices of pizza - P, and one slice costs $3,5

Then the equation would be:

3,50p + 1,75s = 35,00

To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.

Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.

To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.

Area of first quadrilateral A1  = [tex]16^{2}[/tex] = 256

Area of first quadrilateral A2  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A3  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A4  = [tex]19^{2}[/tex] = 361

To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1  + Area of first quadrilateral A2 + Area of first quadrilateral A3)

= 361 - (9 + 9 + 256)

=87

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Answer:

Step-by-step explanation:(10,4)=10.9.8.7/4.3.2.1=210

The number of different samples of size 4 that can be taken from a finite population of size 10, without replacement, is 210.

The formula for calculating the number of different samples of size r that can be taken from a finite population of size n without replacement is given by the combination formula: nCr = n! / (r! * (n-r)!), where n! denotes n factorial (n × (n-1) × (n-2) × … × 1).

In this case, we want to find the number of different samples of size 4 that can be taken from a population of size 10, so we use the combination formula with n=10 and r=4:

10C4 = 10! / (4! × (10-4)!) = (10987) / (4321) = 210

Therefore, there are 210 different samples of size 4 that can be taken from a population of size 10 without replacement.

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According to the solution we have come to find that, The equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

What is radius?

Radius is a straight line segment that joins the center of a circle to any point on its circumference. It is half of the diameter of the circle. The length of the radius is denoted by the letter "r".

The equation of a circle with center (a,b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Substituting the given values, we have:

[tex](x - (-2))^2 + (y - 9)^2 = 8^2[/tex]

Simplifying, we get:

[tex](x + 2)^2 + (y - 9)^2 = 64[/tex]

Therefore, the equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

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The cost of  each piece of trim is $1.63

To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula

Cost of one piece of trim = Total cost / Number of pieces

We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula

Cost of one piece of trim = $6.52 / 4

Simplifying this expression, we get

Cost of one piece of trim = $ 1.63

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We are given that the quadratic function has the equation:

y = a(x + 6)(x - 2)

To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:

36 = a(3 + 6)(3 - 2)

36 = 9a

a = 4

Therefore, the value of a is 4.

The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.

We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:

R(x) = (1200 - 50x)(7.75 + x)

Expanding this expression, we get:

R(x) = 9300 + 650x - 50x^2

To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:

R'(x) = 650 - 100x = 0

Solving for x, we get:

x = 6.5

This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:

7.75 + 6.50 = $14.25

So, the musical theater group should charge $14.25 per ticket to maximize revenue.

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Answer:

A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 4.25%, which

results in a monthly payment of $206.05 How much more is paid over the life of the loan versus paying in cash?

O $1,000 25

O $11,000 25

O $12,363 00

Step-by-step explanation:

You're welcome.

The probability that he will reach out into his pocket and pull out a $10 bill each time is 1/7. The correct option is the second option 1/7

From the question, we are to determine the probability of William pulling out a $10 bill twice without replacement

The probability of pulling out a $10 bill on the first draw is 3/7, since William has three $10 bills out of a total of seven bills in his wallet.

Since William does not replace the first bill when he pulls out the second one, there will be one less bill in the wallet for the second draw. Therefore,

The probability of pulling out another $10 bill on the second draw is 2/6 (since there will be two $10 bills left out of six bills in the wallet).

Thus,

The probability that he will reach out into his pocket and pull out a $10 bill each time is

P(two $10 bill) = 3/7 × 2/6

P(two $10 bill) = 3/7 × 1/3

P(two $10 bill) = 1/7

Hence, the probability is 1/7

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Answer:

She was supposed to DIVIDE the amount of money by the amount of eggs in the carton.

Step-by-step explanation:

12 egg carton = $2.40, 1 egg = $2.40 ÷ 12 = 0.2c
18 egg carton = $3.40, 1 egg = $3.40 ÷ 18 = 0.188 (1.9)

The 18 egg carton was more affordable by about 1.22 cents. Nikki was supposed to divide the amount of money it was worth by the quantity in it.

The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.

What is dice?

Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.

Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.

When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.

To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.

So, the probability of rolling a 5 and a 6 is

P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes

= 1 / 36

Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.

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The name of a function identifies it and must be used when the function is called - True

A function serves as its unique identifier and must be used when calling the function. A function in a computer language is given a name when it is created so that the user can invoke it later on in their particular code. The function is identified by its name which also serves to set it apart from similar functions with potentially different titles.

Depending on its definition, the parentheses that come after the function name may or may not contain arguments or parameters when calling a function. A function is called, executed, and its outcomes are returned to the caller code. Due to the reason that it is a crucial part of the function's definition, its name must always be employed when a function is called.

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Answer:

25°, 65°, and 90°

Step-by-step explanation:

To form a triangle the 3 angles must sum to 180 degrees.

The composite functions  are (A + B)(x) = x² + 2x + 4. and (AB)(x) = 2x³ - x² + 10x - 5.

To find (A + B)(x), we add the two functions A(x) and B(x):

(A + B)(x) = A(x) + B(x)

So, we have

= x² + 5 + 2x - 1 (substituting the given expressions for A(x) and B(x))

= x² + 2x + 4

Therefore, (A + B)(x) = x² + 2x + 4.

To find (AB)(x), we multiply the two functions A(x) and B(x):

(AB)(x) = A(x)B(x)

= (x² + 5)(2x - 1) (substituting the given expressions for A(x) and B(x))

= 2x³ - x² + 10x - 5

Therefore, (AB)(x) = 2x³ - x² + 10x - 5.

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Answer:

The ladder is approximately 9.75ft from the building

Step-by-step explanation:

We can use Pythagoras theorem:

[tex]c^2=a^2+b^2[/tex]

where:

[tex]c =[/tex] it's the size of the ladder, 12ft

[tex]b=[/tex] it's the top of the ladder above the ground, 7ft

so:

[tex]c^2-b^2=a^2\\\implies a=\sqrt{c^2-b^2}\\ a=\sqrt{(12)^2-(7)^2}\\a=\sqrt{95}\\ a\approx 9.75ft[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:

Step-by-step explanation:

When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis.

What is a hypothesis?

A hypothesis is a statement that proposes a potential relationship between two variables. It's a conjecture about the nature of the relationship between the two variables that a researcher might test.In hypothesis testing, the null hypothesis is always the hypothesis being tested. A null hypothesis is a statement that assumes there is no relationship between the variables being studied. It is denoted by H0.The alternative hypothesis is a statement that negates the null hypothesis. It suggests that there is a relationship between the variables being studied. It is denoted by Ha.When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis. As a result, the researcher may conclude that the alternative hypothesis is true with a certain level of confidence.If the null hypothesis is not rejected in a hypothesis test, it means that there is insufficient evidence to support the alternative hypothesis. As a result, the researcher cannot conclude that the alternative hypothesis is true with a certain level of confidence.

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Answer:

90.6°

Step-by-step explanation:

It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:

[tex]y = 8.2x + 25\\y = 8.2(8) + 25[/tex]

Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, multiply 8.2 with 8:

[tex]y = (8.2 * 8) + 25\\y = (65.6) + 25\\[/tex]

Next, add:

[tex]y = 65.6 + 25\\y = 90.6[/tex]

90.6 is your answer.

~

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The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

Finding the height of the stack :

To form the equation assume the number of bowls and height increased by stacking one into another with variables x and y and form the equation according to the given condition. Now use the resultant equation to find the number of bowls in the given stack.

Here we have

The diagram below shows 5 identical nesting bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of a stack of 5 bowls is 5 inches.

Part (A)

Let 'y' be the increase in the height of the stack and 'x' be the number of bowls stacked

Hence, Height of stack  = 2 + xy  

Therefore,

The equation that can be used to find the height of a stack is 2 + xy

From the given data,

Height of 5 bowls = 5 inches

=> 2 + xy = 5

=> xy = 3

Leaving the first bowl number bowls stacked = 4

=> x(4) = 3

=> x = 3/4

=> x = 0.75 inches

Part (B)

Given that height of the stack is 14 inches

Using the above equation

=> Height of stack, 2 + xy = 14

=> 2 + (0.75)y = 14

=> (0.75)y = 12

=>  y = 16

Therefore,

The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

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Answer:

A=240 P=64

Step-by-step explanation:

A=240 because you take lxw and that gives you the answer

P=64 because you just add 12+12+10+10

Answer: The area is 240 and the perimeter is 64

Step-by-step explanation:

To get the area you need to do 20 x 12 = 240

And to get the perimeter you need to add up all the sides;

20 + 20 + 12 + 12 = 64

Answer:

The probability that she has breast cancer if she gives a positive test result is P=0.16

Step-by-step explanation:

And according to the Bayes theorem I got 0.16

The probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

Let A denote the event that the woman has breast cancer, and let B denote the event that she has a positive test result. Then we need to find P(A|B), the probability that A occurs given that B has occurred. By Bayes' theorem, we have:

P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)]

where P(not A) = 1 - P(A) is the probability that the woman does not have breast cancer.

From the problem statement, we have:

P(A) = 1/101, P(B|A) = 0.8, and P(B|not A) = 0.05.

Therefore,

P(not A) = 100/101,

and

P(A|B) = (0.8 x 1/101) / [(0.8 x 1/101) + (0.05 x 100/101)] = 0.017 (to three decimal places).

Therefore, the probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

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Answer:

x ≈ 19,47°

Step-by-step explanation:

Use trigonometry:

[tex] \sin(∠cab) = \frac{cb}{ab} [/tex]

[tex] \sin(x°) = \frac{2}{6} [/tex]

[tex]x ≈19.47°[/tex]

Answer:

Step-by-step explanation:

x = 9

The distance around the equator is 40,820 km, when the Earth's diameter is approximately 13000km. The distance around the Earth is the circumference.

The Earth is nearly a perfect sphere, but not quite. Astronomers utilized the diameter of the Earth as their primary measuring tool to gauge the extent of the solar system during the 18th and 19th centuries. Today's astronomers typically don't need to be aware of the Earth's size for their regular research tasks.

Nonetheless, the Earth's diameter continues to be the starting point for us, the inhabitants of this planet, in our quest to comprehend the cosmic distance scale. Eratosthenes measured the polar radius, and the number he obtained using the conversion of 0.15 km/stadium sits halfway between the polar and equatorial values.

Given:

Diameter = 13,000 km

Circumference = pi x diameter

Circumference = 3.14 x 13,000 = 40,820 km

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Step-by-step explanation:

Question 6,

x+3=2x-23

x- 2x=-23-3

-1x=-26

x=26

The following are answers to the probability questions;

1. 2/3 or 0.67 or 0.7 chances

2. 2/3 or 0.67 or 0.7 chances

3. No probability is greater than the other. They are both 2/3.

4.  There are 36 possible outcomes

5. 3/36 or 1/12

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

To  calculate the probability of choosing a password with no Y's and With no O's we need to consider all the combinations that do not have Y and O. There are 20 combinations with no Y's and 20 combinations with no O.

Therefore, the probability of choosing a password with no Y's or O's are 20 each. When then calculate by sating

20/30, which simplifies to 2/3 or 0.67.

The number of possible outcomes for a single number cube is as follows;

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,3 3,4 3,5 3,6

4 4,1 4,2 4,3 4,4 4,5 4,6

5 5,1 5,2 5,3 5,4 5,5 5,6

6 6,1 6,2 6,3 6,4 6,5 6,6

In total, there are 36 combinations.

! There are three ways to obtain a sum of 10: rolling a 4 and a 6, rolling a 6 and a 4, or rolling two 5's. Since there are 36 possible outcomes in total (as we determined earlier), the probability of rolling two numbers that have a sum equal to 10 is:

P(sum of 10) = number of outcomes that add up to 10 / total number of possible outcomes

P(sum of 10) = 3 / 36

P(sum of 10) = 1/12

So the probability of rolling two numbers that add up to 10 is 1/12.

The answers provided is based on the full questions below as seen in the picture;

12. Higher Order Thinking The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y's? With no O's? Is one probability greater than the other? Explain.

Possible Combinations

Y, B          B, R            R, O          O, G       G, P            P. Y

Y, R          B, O           R, G           O, P       G, Y            P, B

Y, O         B, G            R, P           O, Y       G, B            P, R

Y, G         B, P            R, Y           O, B        G, R            P, O

Y, P         B, Y            R, B           O, R         G, O           P,G

13. A single number cube is rolled twice.

PART A

Determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.

PART B

Find the probability of rolling two numbers that have a sum equal to 10.

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Answer:

Independent: the number of cups, c, that he sells

Dependent: the amount of money, m, that he makes each day

Step-by-step explanation:

* The independent variable determines the value of the dependent variable. The number of cups of frozen juice that Richard sells each day determines the amount of money that he makes each day.

* Side note: For your information, the linear equation that models this relationship would be m = 1.25 c. You would graph that as y = 1.25 x, and since x is independent while y is dependent, you know that c is independent and m is dependent.

* Good luck completing the table! I would help out with that if I could see it!