LINES AND ANGLES

Circle the correct answer to each of the following questions. Show your work, if necessary.
1 Which of the following objects is two-dimensional?
a. a pair of dice
b. a basketball
C
tree
d. a circle

The probability that at least one of the three users is more careful is 0.936.

We need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.

The probability that none of the three users are more careful is (0.40)^3 = 0.064.

Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.

Rounding to three decimal places, the answer is 0.936.

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The equation with the following y-intercepts are matched

a) c ⁢ x + b ⁢ y = a: (0, a/b)

b) c ⁢ x + a ⁢ y = b: (0, b/a)

c) b ⁢ x + a ⁢ y = c: (0, c/a)

d) a ⁢ x + b ⁢ y = c: (0, c/b)

Given data ,

Let the set of equations be represented by

c ⁢ x + b ⁢ y = a

c ⁢ x + a ⁢ y = b

b ⁢ x + a ⁢ y = c

a ⁢ x + b ⁢ y = c

Now , the y-intercept of the equation is when the value of x = 0

So , when x = 0

The y intercepts of the equation are

c ⁢ x + b ⁢ y = a: (0, a/b)

c ⁢ x + a ⁢ y = b: (0, b/a)

b ⁢ x + a ⁢ y = c: (0, c/a)

a ⁢ x + b ⁢ y = c: (0, c/b)

Hence , the equations are solved

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Answer:

Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:

2x + 3 > 3x - 2

Solving for x, we get:

x < 5

So the solution set is:

Df = [3, infinity) intersect (-infinity, 5) = [3, 5)

Therefore, the inequality is true for all x in the interval [3, 5).

Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:

x^2 - 2 < y^2 - 2

Simplifying, we get:

x^2 < y^2

Taking the square root of both sides, we get:

|x| < |y|

So the solution set is:

Df = [3, infinity)

|x| < |y| means that either x < y or -x < y. Therefore, the solution set can be divided into two parts:

Part 1: x^2 - 2 < 0, i.e., x is in the interval (-sqrt(2), sqrt(2)). For this part, we have:

Df intersect (-sqrt(2), sqrt(2)) = empty set

Part 2: x^2 - 2 >= 0, i.e., x is outside the interval (-sqrt(2), sqrt(2)). For this part, we have:

Df intersect (-infinity, -sqrt(2)] union [sqrt(2), infinity) = [3, infinity)

Therefore, the inequality is true for all x in the interval [3, infinity) except for the interval (-sqrt(2), sqrt(2)).

Step-by-step explanation:

The figures that complete the two-way frequency table are attached accordingly.

Let represent the table like this:


                      Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     A                    90
Iced Tea           B                  C                        D                    E
Total                 75                 F                       G                    160

NOte that:

A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2

D=11

Thus C = 22
F = 45 + C
F = 45 + 22
F = 22


G = A + D = 18

?thus, the completed two-way frequency table is:


                    Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     7                    90
Iced Tea           B                  22                     11                    70
Total                 75                 67                    18                    160

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The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

Quadratic equation is of the form

[tex]f(x) = ax^2 + bx + c[/tex]

the transformations

Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.

[tex]g(x) = -ax^2 - bx - c[/tex]

Shift it horizontally to the right by 2 units: Our function becomes:

[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]

Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.

[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]

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The value of the radius of the cone is, 5 inches

We have to given that;

The volume of a cone is 35π cubic inches.

And, the height is 4.2 inches.

Now, We know that;

Volume of cone is,

V = πr²h/3

Hence, We get;

35π = π × r² × 4.2 / 3

105 = 4.2r²

r² = 105/4.2

r² = 25

r = 5 inches

Thus, The value of the radius of the cone is, 5 inches

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Answer:

x= -18

Step-by-step explanation:

-2/3x + -21/4 = 27/4

-8x-63=81

-8x-63+63=81+63

-8x=144

-8x/-8 = 144/-8

x=-18

The probability that they are the 2 oldest people in the group is 0.011

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

The probability of an event A is denoted by P(A)

From the question above, let us calculate the probability.

The probability that the first person selected is the oldest is 1/10.

Then, the probability that the second person selected is the second oldest is 1/9, since there are only 9 people left to choose from.

Therefore, the probability of selecting the two oldest people in the group is:

1/10 * 1/9 = 1/90

So, the probability of selecting the two oldest people in the group is 1/90 or approximately 0.011 or 1.1%.

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Answer: The jar that would experience the greatest pressure is Jar D.

This is because the pressure of a gas is directly proportional to its temperature (according to the ideal gas law). Since all four jars have the same number of gas molecules, the jar with the highest temperature (Jar D) would have the greatest pressure.

Step-by-step explanation:

The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.

It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.

By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).

So,

5/6 × 6/5

= 30/30

= 1

Hence, 6/5 is the multiplicative inverse of 5/6

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The diameter of the circle is 396 units.

The length of the arc is 0.83π units.  

The length of an arc of a circle is given by the formula:

L = θ/360 * πd

where θ is the measure of the angle and is the diameter of the circle

Given: θ = 80° and L = 88π

L = θ/360 * πd

88π = 80/360 * π * d

88 = 80/360 * d

80 * d = 88 * 360

80d = 31680

80d = 31680/80

d = 396 units

PART 2

If  θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12

L = θ/360 * πd

L = 25/360 * π * 12

L = 0.83π units

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- To answer a question about a sale transaction on rental property that closes on December 16, you need to calculate how much rent the landlord owes to the buyer for the remaining days of December.

- You can use a formula called prorated rent to calculate the amount of rent that is proportional to the number of days that the buyer owns the property. Prorated rent splits the amount between the previous and new owners of a rental property.

- The formula for prorated rent is: Prorated Rent = (Monthly Rent / Number of Days in Month) x Number of Days Rent Owed

- In your case, the monthly rent is $713, the number of days in December is 31, and the number of days rent owed is 16 (from December 16 to December 31). The closing day is the buyer's, so the landlord owes rent for that day as well.

- Plugging these values into the formula, you get: Prorated Rent = (713 / 31) x 16 = 368.26

- This means that the landlord owes $368.26 to the buyer for the remaining days of December.

I hope this helps you answer your question.

The time required for the amount to double and triple are 19.53 and 30.95 respectively.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]f(t) = P_{0}e^{rt}[/tex]

Where:

Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;

[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]

Taking the natural log (ln) of both sides of the equation, we have:

0.0355t = ln(2)

Time, t = 19.53

Similarly, a function for the time required for the amount to triple is given by;

[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]

Time, t = 30.95

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a) The number of ways that four people can be selected from this group of fifteen is: 1365 ways

b) The number of ways that four Republicans can be selected from the eight Republicans is: 70 ways

c) The probability that the selected group will consist of all republicans is: 5.13%

The selection of people from a given list can be done in the following way: if we want to select r people from a list of n people, then we can do so in:

nCr = n!/(r!(n - r)!)

In the first part of the question, we don't need to decide on specific people from each group, but in the subsequent parts, it becomes an added restriction.

A. This can be done in:

15C4 = 15!/(4!(15 -4!)

= 1365 ways

B. This can be done in:

8C4 = 8!/(4!(8 - 4)!)

= 70 ways

C. The chances that all are republicans is a measure of the ratio of the answer in the first question to the second:

70/1365 = 0.0513 = 5.13%

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The expected profit for the first mall is $1,750,000

Given data ,

Let the probability be represented as A and B

Now , For Event A:

Probability of success at the first mall (P(A)) = 2 (given)

Profit if successful (P(A) * Profit | Success) = 2 * $1,050,000 = $2,100,000

Loss if unsuccessful (Loss | Failure) = -$350,000

For Event B:

Probability of success at the second mall (P(B)) = unknown (to be calculated)

Profit if successful (P(B) * Profit | Success) = P(B) * $700,000

Loss if unsuccessful (Loss | Failure) = -$210,000

Expected Profit for Event A = P(A) * Profit | Success + (1 - P(A)) * Loss | Failure

Expected Profit for Event A = 2 * $1,050,000 + (1 - 2) * -$350,000

Expected Profit for Event A = $2,100,000 - $350,000

Expected Profit for Event A = $ 1,750,000

Hence , the profit is $ 1,750,000

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The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is K -  273.15. Therefore, the correct option is option C.

Temperature is a unit of warmth or coldness that can be defined in the context of any number of arbitrary scales. It indicates the direction through which the energy from heat will naturally flow, i.e., through a hotter (body) to a colder (body) body. Temperature cannot be the same as a thermodynamic system's energy; for instance, a blazing match is significantly hotter than an iceberg.

K = C + 273.15

K - 273.15 = C + 273.15 - 273.15

K -  273.15 = C

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.

When solved for C, the equation is

C = K – 273.15

C = 273.15 – K

C = K + 273.15

C = 273.15K

Answer:

-21

Step-by-step explanation:

4×(-4)+35÷(-7)

Plus and minus together makes minus

Multiplication and division goes first

-16-5= - 21

The area of the entire space is 38.57 units².

We have,

From the figure,

Total area.

= Semicircle + Rectangle + Trapezium + Rectangle

Now,

Semicircle:

Radius = 2 units

Rectangle:

Length = 4 units

Width = 3 units

Trapezium:

Parallel sides = 5 units and 3 units

Height = 1 unit

Rectangle:

Length = 2 units

Width = 5 units

Now,

Area of the entire space.

= πr² + 4 x 3 + 1/2 x 1 x (5 + 3) + 2 x 5

= 22/7 x 2 x 2 + 12 + 1/2 x 1 x 8 + 10
= 88/7 + 12 + 4 + 10

= 12.57 + 12 + 4 + 10

= 12.57 + 26

= 38.57 units²

Now,

1 unit = 7 feet

So,

= 38.57 X 7² feet²

= 1889.93 feet²

Thus,

The area of the entire space is 38.57 units².

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The solution is, Option 4 is correct., the graph represents the following system of inequalities.

Explanation:

We are given two inequality y<-x-4 and y>2x-3.

We need to choose correct graph from given choices.

First we draw the graph of each equation

Equation 1: y<-x-4

We draw the graph using slope intercept form.

Slope=-1 and y-intercept (0,-4)

Test point (0,0). Put (0,0) into equation 1 y<-x-4

We get . This is false statement. Graph will shade away from point (0,0).

Equation 2: y<2x-3

We draw the graph using slope intercept form.

Slope=2 and y-intercept (0,-3)

Take test point (0,0). Put (0,0) into equation 2, y>2x-3

We get . This is true statement. Graph will shade towards the point (0,0).

Please take a look attachment for the graph.

Option 4 is correct.

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complete question:

Which graph represents the following system of inequalities?

y < -x - 4

y > 2x - 3

Answer:

If the probability of an event is 0.20, the odds in favor of the event can be calculated as follows:

- Divide the probability of the event occurring by the probability of the event not occurring:

0.20 / (1 - 0.20) = 0.20 / 0.80

- Simplify the fraction:

0.20 / 0.80 = 1 / 4

Therefore, the odds in favor of the event are 1 to 4.

Step-by-step explanation:

The odds in favor of an event with a probability of 0.20 is a ratio of 1 to 4.

The question is about calculating the odds in favor of an event with a probability of 0.20. The odds in favor of an event is defined as the ratio of the probability that the event will happen to the probability that it will not happen.

In this case, the probability of the event is 0.20, therefore the probability that it will not happen is 1 - 0.20 = 0.80. So, the odds in favor of the event are 0.20 to 0.80 or it can be simplified to 1 to 4.

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The standard deviation of the sample mean differences is, 16.98.

Since, We know that;

Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.

Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.

In order to see how they differ, we need to first subtract them from each other,

So, we get:

21.2 - 17.6 = 3.6

We then divide this number with the first standard deviation as follows:

⇒ 3.6/21.2 x 100

⇒ 16.98

Therefore, the standard deviation of the sample mean is, 16.98.

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The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

We have,

To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:

= (Monthly payment x Number of months) + Down payment

= ($473 x 60) + $2,420

= $28,780

To determine the cost of buying the car, we first need to calculate the total loan amount:

= Cost of car - Down payment + Residual value

= $34,000 - $5,000 + $16,400

= $45,400

Now,

Total loan cost = (Monthly payment x Number of months) + Down payment

Total loan cost = ($623 x 60) + $5,000

Total loan cost = $42,380

So,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:

Cost of buying - Cost of leasing = $42,380 - $28,780

Cost of buying - Cost of leasing = $13,600

So,

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

Thus,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

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1) The scale factor of dilation is 1/3

2) The orientation is preserved in dilation of A to A'

3) The congruence is not preserved in dilation of A to A'

We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.

Here from the attached graph we can observe that the square A is transformed to A'

The side length of square A is 18 units and the side length of square A' is 6

So, the scale factor would be,

r = A' / A

r = 6/18

r = 1/3

We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.

So, the dilations do not preserve congruence, as it changes the size of a figure.

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The  vector-valued function is continuous at t=2,

are

A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

We are required  to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the  vector-valued function is continuous at t=2.

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Jay's score for the last quiz is 14.

Let's use the formula for finding the mean:

Mean = (Sum of all scores) / (Number of scores)

We can rearrange this formula to solve for the unknown score:

Unknown score = (Mean x Number of scores) - (Sum of all other scores)

Given that Jay's mean score for four quizzes is 9, we have:

Mean = 9

Number of scores = 4

Jay's scores for the first three quizzes are 8, 5, and 9. The sum of these scores is:

Sum of first three scores = 8 + 5 + 9 = 22

Using the formula above, we can find Jay's score on the fourth quiz:

Unknown score = (Mean x Number of scores) - (Sum of all other scores)

Unknown score = (9 x 4) - 22

Unknown score = 36 - 22

Unknown score = 14

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