what are two diffrent if-then statements implied by Theorem 2-13?

Using conditional probability, it is found that there is a 0.00002 = 0.002% probability that an event that occurs in this region is that of an authorized user .

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

Probability of an event in this region:

Hence:

\(P(A) = 0.01\frac{1}{1000} + 0.5\frac{999}{1000} = \frac{0.01 + 0.5(999)}{1000} = \frac{499.51}{1000}\)

The probability of an event and an authorized user is:

\(P(A \cap B) = 0.01\frac{1}{1000} = \frac{0.01}{1000}\)

Hence, the conditional probability is:

\(P(B|A) = \frac{\frac{0.01}{1000}}{\frac{499.51}{1000}} = \frac{0.01}{499.51} = 0.00002\)

0.00002 = 0.002% probability that an event that occurs in this region is that of an authorized user .

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The results show that the most common response was access, with 27% of the respondents choosing it as the most urgent health problem.

Cost came in second place, with 20% of the respondents choosing it. Obesity and cancer followed closely behind, with 14% and 13% of the respondents choosing them, respectively. Government interference and the flu were the least common responses, with only 3% and less than 0.5% of the respondents choosing them, respectively.

The margin of sampling error for the poll is ±4 percentage points, which means that if the poll was conducted multiple times, 95% of the time, the results would be within 4 percentage points of the actual population values.

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Answer:

I got it!

Step-by-step explanation:

For question a: x = 4

For question b: y = 4

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

  y-intercept: 100

  100 is Jason's base pay amount

Step-by-step explanation:

In the given equation, the term 100 does not depend on x, the value of computers sold. The pay is said to consist of base pay plus commission that depends on sales. The term that has a dependence on sales is 0.03x, so the other term in Jason's pay equation must be his base pay.

  The y-intercept is $100, Jason's daily base pay.

\(c\leq 50\\\\(c=child)\\\\Sorry \ if \ this \ didn't \ help \ you.\)

With given percentages of taxes on income, Alex and Tory owe $18,882 in federal taxes.

what exactly is a percentage?

A percentage is a way of representing a number as a fraction of 100. It is often denoted by "%". For example, 50% means 50 out of 100, or 0.5 as a decimal. Percentages are commonly used to express rates, ratios, and proportions in many areas such as finance, statistics, and everyday life.

Now,

Since the couple is married and filing jointly, their standard deduction is $25,900. Thus, their taxable income is $150,000 - $25,900 = $124,100.

From the tax table, the tax on the first $19,750 is 10% and the tax on the next $60,500 ($80,250 - $19,750) is 12%. The remaining taxable income is $124,100 - $80,250 = $43,850, which falls into the 22% tax bracket.

Therefore, the tax owed on the first $19,750 is $1,975 (10% of $19,750), the tax owed on the next $60,500 is $7,260 ($1,975 plus 12% of $60,500 - $19,750), and the tax owed on the remaining $43,850 is $9,647 (22% of $43,850).

The total tax owed is the sum of these amounts: $1,975 + $7,260 + $9,647 = $18,882. Therefore, Alex and Tory owe $18,882 in federal taxes.

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.

Least Common Multiple is the meaning of the abbreviation LCM.

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

It can also be computed using two or more numbers.

Finding the LCM of a given collection of numbers can be done in a variety of ways.

Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.

The smallest number among all numbers is called the least common multiple of two or more numbers.

According to our question-

The number LCM is equal to 40.

4 × 5 × x = 40

20 × x = 40

20x=40

x=2

The larger number is equal to 4 x=4(2)=8.

The smaller value is =5x=5(2)=10.

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Complete question-

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?

Answer:

true

Step-by-step explanation:

because any other even number you can multiply something by 2 to get that number.

hope this helps

Answer: True

Step-by-step explanation: 2 is the only even prime number.

2 is an even number that has only itself and 1 as factors so it is the only even number that is a prime.

Answer:

Step-by-step explanation:

You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.

If you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...

  C = πd

so the total circumference is ...

  C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units

The perimeter of the figure is about 47.12 units.

The area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...

  A = (π/4)d²

The total area of the circles of diameters 4 and 11 is ...

  A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)

The area of the central rectangle is added to the areas of the semicircles. Its area is ...

  A = LW

  A = (11)(4)

The area of the entire figure is the sum of the circle areas and the rectangle area:

  total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units

The area of the figure is about 151.60 square units.

__

Additional comment

You usually see the formula for the area of a circle as ...

  A = πr²

Since r = d/2, we can express this using d as ...

  A = π(d/2)² = π(d²)/(2²) = (π/4)d²

You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.

The value of angle C to the nearest tenth is 21.6°

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

c² = a² + b² - 2ab cosC

8² = 14² + 19² - 2 × 14 × 19 cos C

64 = 196+ 361 - 532cosC

64 = 557 - 532 cosC

532cos C = 557 -64

532cos C =

cosC = 493/532

cos C = 0.93

C = 21.6°( nearest tenth)

Therefore the value of angle C is 21.6°

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Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.

The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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The point only can be on the unit circle and on the second quadrant if:

x = -√55/8

We know that we have a point of the form:

P = (x, y)

And the value of y is:

y = 3/8

Then our point is:

P = (x, 3/8)

And it is on the unit circle, then the values of x and y are solutions of:

x^2 + y^2 = 1

x^2 + (3/8)^2 = 1

x^2 = 1 - (3/8)^2 = 1 - 9/64 =

x^2 =  64/64 - 9/64

x^2 = 55/64

x = ±√(55/64) = ±√55/8

And P is on the second quadrant, then we take the negative option:

x = -√55/8

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Answer:

Slope: 1

Y-intercept: (0,3)

Step-by-step explanation:

The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.

Y intercept: (0, 3)

For slope, you can use the formula rise over run. \(\frac{Rise}{Run}\)

From the picture, I have drawn the rise over run, which is \(\frac{3}{3}\), which is also 1.

Slope: 1

Hope this helped.

Answer: 1

Step-by-step explanation: got it right on edge

9514 1404 393

Answer:

  a = 94.8, B = 29.3°, C = 31.7°

Step-by-step explanation:

Side 'a' can be found using the Law of Cosines:

  a² = b² +c² -2bc·cos(A)

  a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8

Then one of the other angles can be found from the Law of Sines.

  sin(C)/c = sin(A)/a

  C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°

Then the remaining angle can be found to be ...

  B = 180° -A -C = 180° -119° -31.7° = 29.3°

__

The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

The gas usage was 57 and the rate for gas is 25 therms At or below baseline usage: $1.15 per therm Above baseline usage: $1.41 per therm, so in this case we use the above baseline usage $1.41 per therm

57 * $1. 41 = $80.37

The Electricity usage was 1,049 kwh and the rate Baseline usage: 450 Kwh

At or below baseline usage: $0.40 per kwh Above baseline usage: 90.56 per Kwh. In this case 1,049 kwh is above for the baseline 450 kwh, so we use 90.56 per Kwh

1,049 kwh *$ 90.56 = $94997.44

Then we sum the gas, electricity and taxes to know the total energy bill

$80.37 + $94997.44 + $14.36 = $95092.17

Answer:

38 pills

Step-by-step explanation:

To find the number of pills, you need to divide the weight of each pill by the total weight needed.

0.76 grams / 0.02 grams = 38 pills

Answer:

Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!

The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.  

The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.

This quiz was completed on k12, lesson 3.03.

The question is an illustration of equation of circles.

From the question, we understand that:

\(\mathbf{h = 5\ ft\ 8\ in }\) ---- the height at which the dartboard was hung

\(\mathbf{d = 18\i n }\) ---- the diameter of the dartboard

\(\mathbf{B = 10ft}\)  --- the bull's eye

\(\mathbf{D = (10.25ft, 5ft)}\) --- Sasha's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

\(\mathbf{h = 5\ ft\ 8\ in }\)

\(\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }\)

\(\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }\)

Take LCM

\(\mathbf{h = \frac{15 + 2}{3}\ ft }\)

\(\mathbf{h = \frac{17}{3}\ ft }\)

\(\mathbf{d = 18\i n }\)

\(\mathbf{d = \frac{18}{12}ft}\)

\(\mathbf{d = \frac{3}{2}ft}\)

Divide by 2 to calculate radius

\(\mathbf{r = \frac{3}{2*2}ft}\)

\(\mathbf{r = \frac{3}{4}ft}\)

The equation of the circle is represented as:

\(\mathbf{(x - a)^2 + (y - b)^2 = r^2}\)

In this case:

\(\mathbf{a = B = 10ft}\) -- the distance between the bull's eye and the wall

\(\mathbf{b = h = \frac{17}{3}\ ft }\) ---- the height at which the dartboard was hung

So, we have:

\(\mathbf{(x - a)^2 + (y - b)^2 = r^2}\)

\(\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}\)

Evaluate the exponents

\(\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}\)

Hence, the equation of the circle is: \(\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}\)

Does Sasha’s dart land on the dartboard?

Yes her dart lands on the dartboard because

\(\mathbf{D = (10.25ft, 5ft)}\) is within the circumference of the dartboard

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Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer:

74 and 18

Step-by-step explanation:

Answer:

Triangle A has one right angle

Step-by-step explanation:

a triangle can only have one right angle in it

this angle can be symbolized by the little square thing you see in the corner of the first picture

The mode of the data represented in this line plot will be 8.

Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.

The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.

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Answer:

-25

Step-by-step explanation:

= 2*(2) - 28 - 1

= 4 - 29

= -25

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

d

d

b

a

c

a

b

Step-by-step explanation: