Choose the best answer.
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a

The length of other leg is 12.96 cm.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Given:

H= 13 cm

P = 1 cm

Using Pythagorean theorem

H² = P² + B²

13² = 1² + B²

169 = 1 + B²

168 = B²

B= √168

B = 12.96 cm

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The function is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|. The correct option is B.

The absolute value or modulus of a real number x, denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically,|x|=x.

In the given image the function is represented by the equation y = | x - 2 |. Now the similar function which is increasing and decreasing over the same intervals as the function in the graph is y = | x+ 2|.

Therefore, the correct option for the function is B.

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Answer:

31) -$1.25

32) $0.50

Step-by-step explanation:

Problem 31

[tex]E(X)=\frac{1}{4}(-5)+\frac{1}{4}(-20)+\frac{1}{2}(10)=-\frac{5}{4}-5+5=-\frac{5}{4}=-1.25[/tex]

Hence, this person would expect to gain -$1.25 (or lose $1.25) if they play this game.

Problem 32

[tex]E(X)=\frac{1}{4}(2)+\frac{1}{4}(20)+\frac{1}{2}(-10)=\frac{1}{2}+5-5=\frac{1}{2}=0.50[/tex]

Hence, this person would expect to gain $0.50 if they play this game.

Answer:

31. -$1.25

32. $0.50

Step-by-step explanation:

The expected value is the sum of the product of each probability and its corresponding winnings or loss.

31.

p(win $10) = 1/2

amount of winnings = $10

p(loose $5) = 1/4

amount of loss = $5

p(loose $20) = 1/4

amount of loss = $20

expected value = (1/2)($10) + (1/4)(-$5) + (1/4)(-$20)

expected value = -$1.25

32.

p(win $2) = 1/4

amount of winnings = $2

p(win $20) = 1/4

amount of winnings = $20

p(loose $10) = 1/2

amount of loss = $10

expected value = (1/4)($2) + (1/4)($20) + (1/2)(-$10)

expected value = $0.50

0600 Mountain Daylight Time is equivalent to 1200 Zulu/UTC/GMT.  

Mountain Daylight Time (MDT) is a time zone that is observed in several regions of North America during the summer months when Daylight Saving Time is in effect. It is 6 hours behind Coordinated Universal Time (UTC-6) during Daylight Saving Time.

Coordinated Universal Time (UTC) is the primary time standard by which the world regulates clocks and time. It is used in many scientific, technical, and military fields, as well as in international air traffic control.

Zulu time is a term used in aviation and military operations to refer to Coordinated Universal Time (UTC). The term "Zulu" is used because it is the letter "Z" in the NATO phonetic alphabet, and it is used to avoid confusion with other time zones during radio communication.

To convert 0600 Mountain Daylight Time to Zulu/UTC/GMT, you need to account for the time difference between Mountain Daylight Time (MDT) and Zulu/UTC/GMT.

During daylight saving time, Mountain Daylight Time is 6 hours behind Coordinated Universal Time (UTC-6). So, to convert 0600 MDT to UTC/GMT, you would need to add 6 hours.

Therefore, 0600 Mountain Daylight Time is equivalent to 1200 Zulu/UTC/GMT.

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The statement that is true is: The slope of function A is greater than the slope of function B.

The slope of a function is a measure of how steeply the function increases or decreases as the input value (x) changes. It is defined as the rate of change of the output value (y) with respect to the input value (x).

Using two points form the table of Function A, (-2, -11) and (4, 19):

Slope (m) = change in y / change in x = (-11 - 19) / (-2 - 4)

= -5

Given Function B as y = x + 1, the slope is m = 1.

Therefore, we can state that, function A has a greater slope than B.

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Answer: F = 4

Step-by-step explanation:

Juts plug in the numbers that you know so you should have   (5*20)/(5^2)

That is equal to 100/25 which is the same as 4. Therefore, F = 4

The statement "If Events A and B are mutually exclusive, then both events cannot occur simultaneously." is true.

Therefore the answer is B.

This statement is true, but it is not a general property of probability. In probability, events are considered mutually exclusive if they cannot occur at the same time, but there is no requirement that one of the events must occur. For example, if Events A and B are the rolling of a dice resulting in an even number and rolling a dice resulting in a number greater than 4, respectively, they are mutually exclusive events but both events may not occur (if a 3 is rolled, for example).

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Answer:

ac and bd

Step-by-step explanation:

iii I will get it on Monday or tomorrow if possible so we will have it done and done so that you will get the information you needed and you are going for it on a day 5o and you have to be my mom when I come back home and you are going out to the

The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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The binary representation of 11 is 1011. To convert decimal to binary, divide the decimal number by 2, taking the remainder at each step and concatenating the remainders in reverse order.

To convert decimal (base 10) to binary (base 2), you can divide the decimal number by 2, repeatedly taking the remainder at each step. The binary representation is obtained by concatenating the remainders in reverse order.

Here's how the conversion works for 11:

11 divided by 2 gives a quotient of 5 and a remainder of 1.

5 divided by 2 gives a quotient of 2 and a remainder of 1.

2 divided by 2 gives a quotient of 1 and a remainder of 0.

1 divided by 2 gives a quotient of 0 and a remainder of 1.

Reading the remainders in reverse order (from the last division to the first), we get 1011, which is the binary representation of 11.

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Answer:

The sum of two numbers = 12

x+y=12

product of two numbers = 35

xy=35

The sum of reciprocals =  x

1

​

+

y

1

​

=

xy

x+y

​

=

35

12

​

Step-by-step explanation:

Answer: 10 and 14.

Step-by-step explanation:

Let the numbers be x and y.

Make and solve a system of equations:

[tex]\displaystyle\\\left \{ {{\frac{x+y}{2}=12\ \ \ \ (1) } \atop {\frac{1}{4}xy=35\ \ \ \ (2) }} \right. \\\\\\[/tex]

Multiply equation (1) by 2 and equation (2) by 4:

[tex]\displaystyle\\\left \{ {{x+y=24} \atop {xy=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {(24-y)*y=140\right.\\\\\\\left \{ {{x=24-y} \atop {24y-y^2=140}} \right. \\\\\\\left \{ {{x=24-y} \atop {-y^2+24y-140=0\ \ \ \ (3)}} \right.[/tex]

Multiply equation (1) by (-1):

[tex]y^2-24x+140=0\\\\y^2-10x-14x+140=0\\\\y(y-10)-14(y-10)=0\\\\(y-10)(y-14)=0\\\\y-10=0\\\\y=10.\ \ \ \ \Rightarrow\\\\x=24-10\\\\x=14\\\\y-14=0\\\\y=14.\ \ \ \ \Rightarrow\\\\x=24-14\\\\x=10.[/tex]

According to the empirical rule, the observations in a data set that can be reasonably approximated by a normal curve lie within two standard deviations of the mean is 95% .

The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that describes the approximate distribution of data that can be reasonably approximated by a normal curve. The rule states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

In other words, if a set of data is normally distributed (meaning it follows a bell-shaped curve), we can use the empirical rule to estimate the proportion of the data that falls within a certain range of values.

For example, let's say we have a data set that has a mean of 50 and a standard deviation of 10. Using the empirical rule, we can estimate that approximately:

68% of the data falls between 40 and 60 (one standard deviation from the mean)

95% of the data falls between 30 and 70 (two standard deviations from the mean)

99.7% of the data falls between 20 and 80 (three standard deviations from the mean)

It's important to note that the empirical rule is only an approximation, and it only applies to data that is approximately normally distributed. In some cases, the actual distribution

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The statement "If f is differentiable at a, then f is continuous at a" is true, but "If f is continuous at a, then f is differentiable at a" is false.

Differentiability and continuity are two important concepts in calculus. A function is said to be continuous at a point if the values of the function approach a finite limit as the independent variable approaches the same value. In other words, there are no sudden jumps or breaks in the function at that point.

On the other hand, a function is said to be differentiable at a point if the limit of the rate of change of the function exists as the independent variable approaches the same value. This rate of change is called the derivative of the function and it is used to determine the slope of the function at that point.

So, it is true that if a function is differentiable at a point, then it is also continuous at that point. In other words, a continuous function must be differentiable. However, the reverse is not necessarily true. A function can reach a point where it is continuous but not differentiable. For example, the absolute value function is continuous everywhere but it is not differentiable at x = 0.

Therefore, we can say that if f is differentiable at a, then f is continuous at a. But if f is continuous at a, it does not imply that f is differentiable at a.

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Answer:

This is false.

Step-by-step explanation:

The correct answer would be 652.5

The width of the rectangular box is W = 8 inches

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangular box be V = 264 inches³

Let the height of the rectangular box be H = 3 inches

Let the length of the rectangular box be L

Let the width of the rectangular box be W

Now , L = 3 + W

And , Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

264 = 3 x ( W ) x ( 3 + W )

On simplifying the equation , we get

Divide by 3 on both sides of the equation , we get

3W + W² = 88

Subtracting 88 on both sides of the equation , we get

W² + 3W - 88 = 0   be equation (1)

On factorizing the equation , we get

W² + 11W - 8W - 88 = 0

Taking the common factors of the equation , we get

W ( W + 11 ) - 8 ( W + 11 ) = 0

On further simplification , we get

( W - 8 ) ( W + 11 ) = 0

The width cannot be negative , so

( W - 8 ) = 0

Adding 8 on both sides , we get

W = 8 inches

Hence , the width of the rectangular box is 8 inches

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Answer:

y=13 x=16 i think

Step-by-step explanation:

The total amount of the bill is $102.59625.

Percentage is defined as the parts of a number per fraction of 100 or a part per 100.

Percentage is usually denoted by the symbol '%'.

We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Given that,

Amount of bill for a restaurant = $81.75

Percentage of sales tax = 7.5%

Amount of sales tax = 7.5% of $81.75

                                 = 7.5% × 81.75

                                 = 0.075 × 81.75

                                 = $6.13125

Percentage of gratuity = 18%

Amount of gratuity = 18% of $81.75

                               = 18% × 81.75

                               = 0.18 × 81.75

                               = $14.715

Total amount in the bill = $81.75 + $6.13125 + $14.715

                                       = $102.59625

Hence the total bill from the restaurant is $102.59625.

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Answer: The function has three x-intercepts.

Step-by-step explanation:

To find the x-intercepts of a function, we need to find the values of x for which the function equals zero.

So, to find the x-intercepts of the function:

F(x) = (x+5)^3(x-9)(x-1)

We need to solve the equation:

F(x) = 0

We can see that the function will be equal to zero when any of the factors on the right-hand side is equal to zero. Therefore, we need to solve the following four equations:

(x+5) = 0, which gives x = -5

(x-9) = 0, which gives x = 9

(x-1) = 0, which gives x = 1

(x+5)^3 = 0, which gives x = -5

The last equation, (x+5)^3 = 0, has a triple root at x = -5, since the factor (x+5) appears three times. Therefore, there are a total of three x-intercepts for the function:

x = -5 (with multiplicity 3), x = 1, and x = 9.

Using the conversion formula of converting pounds to kilograms, we get that 148 lb is 67.131478 kilograms

To convert 148 pounds (lb) to kilograms (kg), we need to use the conversion factor 1 lb = 0.45359237 kg.

So, we can multiply 148 lb by 0.45359237 kg/lb to get the equivalent weight in kilograms:

148 lb x 0.45359237 kg/lb = 67.131478 kg

Therefore, 148 lb is equal to 67.131478 kg.

To understand the conversion factor, we need to know that pounds and kilograms are both units of mass, but they are used in different parts of the world. In the United States and some other countries, pounds are the common unit of mass, while in most other countries, kilograms are used. The conversion factor relates the number of pounds to the number of kilograms, so that we can easily convert from one unit to the other. It is important to use the correct conversion factor to ensure accurate conversions.

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The time it will take to do all the activities at the same time is given as follows:

60 minutes = one hour.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods of each event are given as follows:

The least common factor is obtaining factoring these numbers according to their prime factors, as follows:

15 - 12 - 10|2

15 - 6 - 5|2

15 - 3 - 5|3

5 - 1 - 5|5

1 - 1 - 1

Hence:

lcm(15,12,10) = 2² x 3 x 5 = 60 minutes.

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Answer:Step 2

Step-by-step explanation: Bc Im right

The value of x and y in the given congruent triangles, are 7 and 13

The triangles which share congruent corresponding angles and sides are called congruent triangles.

Given that, Δ LMN ≅ Δ RST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9, we need to find the x and d,

Since, we know that, the congruent triangles have congruent corresponding angles.

Here, the congruent triangles are :

∠ L = ∠ R

∠ M = ∠ S

∠ N = ∠ T

We know that, the sum of angles of a triangle is 180°,

∠ R + ∠ S + ∠ T = 180°

∠ R + 70º + 4y + 9 = 180°

49º + 70º + 4y + 9 = 180°

128º + 4y = 180º

4y = 52º

y = 13º

∵

∠ M = ∠ S

10x = 70º

x = 7

Hence, the value of x and y in the given congruent triangles, are 7 and 13

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The required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.

Rate of change is defined as the change in value with rest to another value is called rate of change.

Here,
Given that,
f(x) = x² + 4x -15

Now, put x = -3
f(-3) = 9 - 12 - 15
f(-3) = -18

Now put x = 6
f(6)= 36 + 24 - 15
f(6) = 45

Since we know that, the rate of change of function is given as,
f'(x) = f'(a) - f'(b) / a -b

f'(x) =f'(6) - f'(-3) / a - b

f'(x) = 45 - (-18) / 6 -(-3)
f'(x) = 63 / 9
f'(x) = 7

Thus, the required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.

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The total number of ways is 45.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Ms. Kelley needs to hire one biology teacher and one chemistry teacher for the science department.

The number of ways to choose one biology teacher from a pool of 9

is 9.

The number of ways to choose one chemistry teacher from a pool of 5

is 5.

Now,

According to the multiplication principle of counting.

The total number of ways to hire one teacher from each subject.

= The number of ways to choose one biology teacher x The number of ways to choose one chemistry teacher.

= 9 x 5

= 45

Therefore,

The total number of ways Ms. Kelley can hire a staff that includes one teacher in each subject is 45.

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The system of equations has its solution to be (3, 4)

From the question, we have the following parameters that can be used in our computation:

2x + y = 10

3x - y = 5

Add the equations

So, we have

5x = 15

Divide by 5

x = 3

Recall that

2x + y = 10

So, we have

6 + y = 10

Evaluate

y = 4

Hence, the solution is (3, 4)

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Answer:

26.6°

Step-by-step explanation:

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).

If we know that the angle shown is a right angle, we also know that a right angle is equal to 90°. To solve for the value of c, we can use this equation:

Therefore, the value of c is 26.6°.

Answer:

B

Step-by-step explanation:

The rate at which she travels is called the rate of speed.

rate of speed = distance / time

r = d/t

She wants to know the time, so we solve the above equation for time.

r = d/t

rt = d

t = d/r

t = 300/r

300/r = t

Answer: B

Answer:

B. t = 300/r

Step-by-step explanation:

translate the question into math

usually

speed is shown as

kilometers per hour

RATE MEANS SPEED

translate kilometers per hour

kilometers = 300 km

per= /

hour = t

speed = 300 km/t

SPEED MEANS RATE

rate = r

r = 300 km/t or 300/t

r = 300/t

t = 300/r

note: rate or speed can be gotten by

SLOPE of line in a graph  

HYPOTENUSE of a triangle from a slope of a line in a graph

DERIVATIVE which is a slope of curve in a graph

Answer:

200

Step-by-step explanation:

9% of 200 =

200 x 0.9 =

18

Let the smaller polygon have side lengths a and the larger polygon have side lengths b. Since the polygons are similar, the ratio of corresponding side lengths is the same as the ratio of their areas. That is:

b^2 / a^2 = 128 / 98

Simplifying this expression, we get:

b / a = √(128 / 98) = √(64 / 49) = (8 / 7)

Now we can use the fact that the perimeter of the smaller polygon is 42 inches:

4a = 42

a = 10.5

Substituting this into the ratio we found above, we get:

b = (8 / 7) * a = (8 / 7) * 10.5 = 12

Therefore, the larger polygon has a perimeter of:

4b = 4 * 12 = 48 inches.

The decimal equivalent of 17/22 rounded to the nearest hundredth is 0.77. The result of dividing the quantifier by the denominator is 0.7727272727272727.

The decimal equivalent of the fraction 17/22 can be found by dividing the numerator by the denominator. To round the decimal to the nearest hundredth, we look at the third decimal place and round up or down accordingly. Step-by-step explanation:

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