use theorem 1.4 to prove the following facts: (a) p[a ∪b] ≥p[a] (b) p[a ∪b] ≥p[b]

Answer:

5.428571428571429

Step-by-step explanation: just do 38 divided by 7 on a calculator

Answer:

How though?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangles are all similar, so corresponding sides are proportional.

__

  long side/short side = x/6 = 12/x

  x² = 72 . . . . . . . multiply by 6x

  x = 6√2 . . . . . . take the square root

__

  hypotenuse/long side = y/12 = (12+6)/y

  y² = 216 . . . . . multiply by 12y

  y = 6√6 . . . . . take the square root

Hannah = 50 mps

Thomas:

12 miles in 15 mins

24 miles in 30 mins'

48 miles in 60 mins

48 mph

Faster speed: Hannah

Hannah drove at 50 mps which was 2 mps faster than Thomas.

Answer: Thomas speed = 12/15 = 0.8

Thomas can go 0.8 miles in a min.

Hannah can go 50/60 mph which is 0.833 (repeats 3 forever) miles per min.

Thus, Hannah is faster than Thomas.

Brainly would be nice <3

Answer: microscope

Step-by-step explanation:

a camera is equipment for a photographer

a microscope is equipment to a biologist

The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.

Probability of an event is a number that shows what is the possibility of an event occur.

we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.

\(= \frac{(17 - 18.6 years)}{1.308333 years}\)

\(= \frac{(-1.6) }{1.308333}\)

\(= -1.22293\)

\(= approx. 1.22.\)

The area from the mean to +ve or -ve 1.22 is .3888

We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.

So, the growth plates will fuse before age 17 \(= .5000-.3888 = 0.1112\)

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Answer:

d i think

Step-by-step explanation:

Answer: C

Step-by-step explanation:

our points are

(0, 64) and (17, 30)

slope = 30-64/17-0 = -34/17 = -2

y=-2x+64 aka C

Answer:

\(a=4\)

\(b=e^2\)

Step-by-step explanation:

We are given that

\(f(x)=aln(bx)\)

f(e)=12

f'(2)=2

We have to find the constants a and b

Substitute x=e

\(f(e)=aln(be)\)

\(12=aln(be)\)

\(ln(be)=\frac{12}{a}\)

\(f'(x)=\frac{a}{x}\)

Using the formula

d(lnx)/dx=1/x

\(f'(2)=\frac{a}{2}\)

\(2=\frac{a}{2}\)

\(a=4\)

Substitute a=4

\(ln(be)=12/4=3\)

\(be=e^{3}\)

\(b=e^{3}/e\)

\(b=e^2\)

7) 13 + -2 = 13 + (-2) = 13 - 2 = 11

8) -12 - 8 = - (12 + 8) = - (20) = -20

The approximate probability that the project will take more than 130 days to complete is 0.6056, or approximately 60.56%.

To calculate the probability, we need to use the concept of the normal distribution. The mean completion time is given as 120 days, and the variance is 64. The standard deviation can be calculated as the square root of the variance, which in this case is √64 = 8 days.

Next, we need to find the z-score, which measures the number of standard deviations a given value is from the mean. The formula for calculating the z-score is (x - μ) / σ, where x is the value we are interested in (130 days), μ is the mean (120 days), and σ is the standard deviation (8 days).

Substituting the values into the formula, we get (130 - 120) / 8 = 10 / 8 = 1.25. This means that the value of 130 days is 1.25 standard deviations above the mean.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 1.25, which is approximately 0.3944. However, since we want to calculate the probability of the project taking more than 130 days, we need to subtract this probability from 1 (since the area under the curve is equal to 1).

Therefore, the approximate probability that the project will take more than 130 days to complete is 1 - 0.3944 = 0.6056, or approximately 60.56%.

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Answer:

2000

Step-by-step explanation:

Multiply. Scientific Notation:

2 ⋅ 10-3

Answer:

a=13 3/4 (13.75)

Step-by-step explanation:

1 2/5a=19 1/4

a=19 1/4÷1 2/5

a=19 1/4÷7/5

a=19 1/4x5/7

a=77/4x5/7

a=385/28

a=13 21/28

a=13 3/4

Answer:

$125

Step-by-step explanation:

a rent collector is entitled to 2½% of all rents collected if he collected rents totaling $5,000.00 calculate his commission:

2 1/2% = 0.025

$5,000 * 0.025  = $125

Answer:

D) 1.0 mph

Step-by-step explanation:

Own speed the boat = x

rate(speed) of the current = a

Speed of the boat downstream = (x + a)

Speed of the boat upstream = (x - a)

Speed of the boat downstream = 40 mi/4 h = 10 mi/h

Speed of the boat upstream = distance/time = 40 mi/ 5 h = 8 mi/h

x + a = 10

x - a = 8

2x      = 18

x = 9

x + a = 10

9 + a = 10

a = 1 mi/h

The equation ln(3x) = 2x - 5 is a logarithmic equation. To solve it, we will first isolate the logarithmic term and then use appropriate logarithmic properties to solve for x.

Start with the given equation: ln(3x) = 2x - 5.

Exponentiate both sides of the equation using the property that e^(ln(y)) = y. Applying this property to the left side, we get e^(ln(3x)) = 3x.

The equation becomes: 3x = e^(2x - 5).

We now have an exponential equation. To solve for x, we need to eliminate the exponential term. Taking the natural logarithm of both sides will help us do that.

ln(3x) = ln(e^(2x - 5)).

Applying the logarithmic property ln(e^y) = y, the equation simplifies to: ln(3x) = 2x - 5.

We are back to a logarithmic equation, but in a simpler form. Now, we can solve for x.

ln(3x) = 2x - 5.

Rearrange the equation to isolate the logarithmic term:

ln(3x) - 2x = -5.

At this point, we can use numerical methods or graphing techniques to approximate the solution. The solution to this equation, rounded to the nearest hundredth, is x ≈ 0.79.

Therefore, the solution to the equation ln(3x) = 2x - 5, rounded to the nearest hundredth, is x ≈ 0.79.

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A sample size of approximately 4,148 newborns is required to obtain a 99% confidence interval for the proportion of all newborns who are breast-fed exclusively in the first two months of life to within 2 percentage points.

To calculate the required sample size for a 99% confidence interval with a margin of error (precision) of 2 percentage points for the proportion of newborns breast-fed exclusively in the first two months of life,

we will use the following formula:
\(n = (Z^2 * p * (1-p)) / E^2)\)
where:
n = required sample size
Z = Z-score for the desired confidence level (in this case, 99%)
p = estimated proportion (since we don't have this value, we will use 0.5 for the most conservative estimate)
E = margin of error (2 percentage points, or 0.02 in decimal form)
For a 99% confidence interval, the Z-score is 2.576.

Now, let's plug these values into the formula:
\(n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2\)
n = (6.635776 * 0.5 * 0.5) / 0.0004
n = 1.658944 / 0.0004
n ≈ 4147.36
Since we cannot have a fraction of a person, we will round up to the nearest whole number.

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Answer:

Is it free points

Step-by-step explanation:

Please give me BRAINLIEST too

Answer:

holy cow thank you so much you are sooo nice!!!! have a great day lol

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

f(x)=x-14     g(x)=x^2+14

fog=f(g(x)

=f(x^2-+14)

=f(x^2+14)-14

fog(x)=x^2

Using geometric sequence, a) The fine on day n is $2^n (2 to the power of n). b) It would take log_2(D/2) + 1 days for the fine to reach D dollars.

In this court case, the fine on each subsequent day is equal to the square of the previous day's fine. This means that the fine follows a geometric sequence, where the common ratio is the square of the previous term.

a) To find the fine on day n, we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1)

Where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

In this case, a_1 = 2 (the fine on the first day), r = 2 (the common ratio), and n is the day number. Plugging these values into the formula, we get:

a_n = 2 * 2^(n-1)

So the fine on day n would be 2 * 2^(n-1) dollars.

b) To find how many days it would take the fine to reach D dollars, we can use the formula for the nth term of a geometric sequence and solve for n:

D = 2 * 2^(n-1)

Dividing both sides by 2, we get:

D/2 = 2^(n-1)

Taking the logarithm of both sides with base 2, we get:

log_2(D/2) = n - 1

Adding 1 to both sides, we get:

n = log_2(D/2) + 1

So it would take log_2(D/2) + 1 days for the fine to reach D dollars.

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Answer:

y = 5x + 3

if:

x = 1, then y = 8

x = 2, then y = 13

x = 3, then y = 18

x = n, then y = 5n + 3

Step-by-step explanation:

if:

x = 1, then y = 8

x = 2, then y = 13

x = 3, then y = 18

x = n, then y = 5n + 3

Answer:

Inequality form: x < 1

Step-by-step explanation:

Answer:

5^5+4/5^6

5^9/5^6

5^9-6

5^3

125

Step-by-step explanation:

Firstly the powers of 4 adds up

Then net power is formed by (9-6) ie 3

Lastly 5^3 is result which is 125

Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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Answer:

-2, -1

Step-by-step explanation:

B is the answer for you. Have a good day!

To approximate the class width for a frequency distribution of quantitative data, we calculate the difference between the upper and lower class limits.

This difference is then divided by the desired number of classes. This calculation provides an estimate of the width of each class, which should be rounded up to a convenient number. Thus, the formula to approximate class width for a frequency distribution of quantitative data is:

Class Width = (Maximum Value - Minimum Value) / Number of Classes

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We need a sample size of 1068 voters to achieve a 95% confidence interval with a margin of error of 2.33 percentage points. To calculate the sample size needed for a 95% confidence interval, we need to use the formula:

n = (z* σ / E)^2
where n is the sample size, z* is the critical value for a 95% confidence level (which is 1.96), σ is the standard deviation (which is unknown), and E is the margin of error (which is 2.33 percentage points or 0.023).
Since we don't know the standard deviation, we can use the worst-case scenario and assume that p = 0.5 (which maximizes the sample size). Thus, we can estimate the standard deviation as:
σ = sqrt(p(1-p)/n) = sqrt(0.5(1-0.5)/n) = 0.5/sqrt(n)
Substituting this into the sample size formula, we get:
n = (z* σ / E)^2 = (1.96 * 0.5/sqrt(n) / 0.023)^2
Solving for n, we get:
n = (1.96 * 0.5 / 0.023)^2 = 1067.89
Rounding up to the nearest whole number, we need a sample size of 1068 voters to achieve a 95% confidence interval with a margin of error of 2.33 percentage points.

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The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".

Given:

Length of the garden = 24 feet

Diagonal of the garden = 30 feet

Using the Pythagorean theorem, we can set up the following equation:

\(24^2\) + \(w^2\) = \(30^2\)

Simplifying:

576 + \(w^2\) = 900

Subtracting 576 from both sides:

\(w^2\) = 900 - 576

\(w^2\) = 324

Taking the square root of both sides:

w = √324

w = 18

So, the width of the garden is 18 feet.

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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.

Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.

The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).

The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.

In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

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Normal CurveThe normal curve is a bell-shaped curve that is symmetrical, and the curve's mean, median, and mode all are equal and located at the center. It is also called the Gaussian curve after the mathematician Carl Friedrich Gauss. Normal distribution is a common statistical analysis technique used to model various phenomena in probability theory, physics, finance, and social science. It can be characterized by its mean and standard deviation.MeanMean is the arithmetic average of the numbers in a dataset. To find the mean, sum all the numbers in the dataset and then divide by the total number of values in the dataset. For the given problem, the mean is 500.Standard DeviationThe standard deviation is a measure of the spread of data from its mean. It measures how far the data values are from their mean. For the given problem, the standard deviation is 100.(b)Convert SAT-Math score of a student with 590 to z-score.z-score = (score - mean) / standard deviationz-score = (590 - 500) / 100 = 0.9(C)What percentage of students would have a SAT-Math score greater than 590?The formula for calculating the percentage of students with a SAT-Math score greater than 590 is:P(Z > 0.9) = 1 - P(Z ≤ 0.9)From the normal distribution table, the area to the left of 0.9 is 0.8159, and the area to the right of 0.9 is 1 - 0.8159 = 0.1841. Therefore, the percentage of students with a SAT-Math score greater than 590 is 18.41%.(d)What percent of students would be expected to have a SAT-Math score between 450 and 550?We can calculate the z-scores for each of the scores using the formula,z-score = (score - mean) / standard deviationz-score for 450 = (450 - 500) / 100 = -0.5z-score for 550 = (550 - 500) / 100 = 0.5From the normal distribution table, the area to the left of -0.5 is 0.3085, and the area to the left of 0.5 is 0.6915. The area between these two values is 0.6915 - 0.3085 = 0.3830, which is 38.3%.(e)What is the probability of having a SAT-Math score less than 540?The formula for calculating the probability of having a SAT-Math score less than 540 is:P(Z < (540 - 500) / 100)From the normal distribution table, the area to the left of 0.4 is 0.6554. Therefore, the probability of having a SAT-Math score less than 540 is 0.6554 or 65.54%.

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1. Characteristics of normal curve: The normal curve is a type of probability distribution.

Some of the characteristics of the normal curve are:

It is a bell-shaped curve, symmetrical and unimodal with a single peak in the center of the curve.It is characterized by a mean, median, and mode that are all equal.It is asymptotic, meaning that the tails of the curve extend to infinity without ever touching the x-axis.

2. Conversion of SAT score to z-score:

Formula to find z-score is: z = (x - μ) / σ

where z = z-score, x = raw score, μ = mean and σ = standard deviation

So, for a student with a math SAT-Math score of 590, the z-score would be:

z = (590 - 500) / 100z = 0.9

Therefore, the z-score for a student with a math SAT-Math score of 590 is 0.9.3.

Percentage of students with SAT-Math score greater than 590:

To find the percentage of students who would have a SAT-Math score greater than 590, we need to find the area under the normal curve to the right of the z-score corresponding to 590.

Using a standard normal table, we find that the area to the right of a z-score of 0.9 is 0.1841 or 18.41%.

Therefore, approximately 18.41% of students would have a SAT-Math score greater than 590.

4. Percentage of students with SAT-Math score between 450 and 550:

To find the percentage of students who would be expected to have a SAT-Math score between 450 and 550, we need to find the area under the normal curve between the z-scores corresponding to 450 and 550.

Using a standard normal table, we find that the area to the left of a z-score of -0.5 is 0.3085, and the area to the left of a z-score of 0.5 is 0.6915.

Therefore, the area between -0.5 and 0.5 is:

0.6915 - 0.3085 = 0.3830 or 38.30%

Therefore, approximately 38.30% of students would be expected to have a SAT-Math score between 450 and 550.5.

Probability of having a SAT-Math score less than 540:

To find the probability of having a SAT-Math score less than 540, we need to find the area under the normal curve to the left of the z-score corresponding to 540.

Using a standard normal table, we find that the area to the left of a z-score of 0.4 is 0.6554.Therefore, the probability of having a SAT-Math score less than 540 is approximately 65.54%.

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The following descriptions of the function passing through (0,7) and (4,4) are true:

The slope of the function is -3/4 and the y-intercept is 7.

The function is linear and continuous.

y=-3/4x + 7 represents this function.

y = -4/3x + 9 represents this function.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. A function is often represented by a mathematical expression, formula or graph. Functions can be described using different notations, such as f(x), y = f(x), or y = g(u,v), and they can take various forms, such as linear, quadratic, polynomial, exponential, logarithmic, trigonometric, and many others.

Here,

To determine which descriptions of the function are true, we need to use the information given about the two points (0,7) and (4,4) to find the slope and y-intercept of the linear function that passes through them. Using the formula for the slope of a line:

slope = (4 - 7) / (4 - 0) = -3/4

So the slope of the function is -3/4.

To find the y-intercept, we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. We can use either of the two points given:

y - 7 = (-3/4)(x - 0)

y - 7 = (-3/4)x

y = (-3/4)x + 7

So the y-intercept of the function is 7.

Using this information, we can now evaluate the given descriptions of the function:

y = 7x - 3/4: This represents the function, but the slope is incorrect (should be -3/4).

The function is decreasing: This is not true, since the slope is negative but less than -1.

y=-3/4x + 7: This represents the function, and the slope and y-intercept are both correct.

The slope of the function is -4/3 and the y-intercept is 9: This is not true, since the slope is -3/4 and the y-intercept is 7.

The function is increasing: This is not true, since the slope is negative.

The slope of the function is -3/4 and the y-intercept is 7: This is true, as shown by the calculations above.

y = -4/3x + 9: This represents a different function with a different slope and y-intercept.

The function is linear and continuous: This is true, since the function is a linear equation and is continuous over its domain.

The function is linear and discrete: This is not true, since the function is continuous over its domain.

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