Please help me I’ve been stuck for hours

Answers

Answer 1

Answer:

Answer/Step-by-step explanation:

Given that a and b are two corresponding sides of two similar figures, it follows that the ratio of their areas = a²/b².

We would use the above knowledge to solve the questions given as follows:

✔️The first pair similar of shapes:

Missing area = x cm²

Therefore,

x/9 = 8²/4²

x/9 = 64/16

x/9 = 4

Cross multiply

x = 4 × 9

x = 36 cm²

✔️The second pair similar of shapes:

Missing area = x cm²

Therefore,

x/240 = 8²/32²

x/240 = 64/1,024

Cross multiply

x*1,024 = 64*240

x*1,024 = 15,360

Divide both sides by 1,024

x = 15,360/1,024

x = 15 cm²

✔️The third pair similar of shapes:

Missing area = x cm²

Therefore,

x/40 = 3²/2²

x/40 = 9/4

Cross multiply

x*4 = 9*40

x*4 = 360

Divide both sides by 4

x = 360/4

x = 90 cm²

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Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd}
B: {Sum of the numbers showing is 9,11, or 12}
Are events A and B independent? Why?

Answers

Answer:

A and B are not independent.

Step-by-step explanation:

Two events are said to be independent if : $P(A \cap B)=P(A)P(B)$

A: {Sum of the numbers showing is odd}

B: {Sum of the numbers showing is 9,11, or 12}

Given two dice, the sample space is given as:

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

The outcomes of event A:{Sum of the numbers showing is odd} are:

(2,1), (4,1), (6,1), (1,2), (3,2),(5,2), (2,3), (4,3), (6,3)

(1,4), (3,4), (5,4), (2,5), (4,5), (6,5), (1,6), (3,6), (5,6)

P(A)=18/36

The outcomes of event B:{Sum of the numbers showing is 9,11, or 12} are:

(6,3), (5,4),(4,5) (6,5), (3,6), (5,6), (6,6)

P(B)=7/36

The intersection of A and B are:

(6,3), (5,4),(4,5) (6,5), (3,6), (5,6)

$P(A\cap B)=6/36$

We can see from the above that:

$P(A)P(B)=(7)/(36)* (18)/(36)=(7)/(72)\neq P(A\cap B)$

Therefore, events A and B are not independent.

Final answer:

The events A and B are dependent because the outcome of one event affects the probability of the other event happening.

Explanation:

The events A and B are dependent because the outcome of one event affects the probability of the other event happening. To determine if two events are independent, we need to check if the probability of the intersection of A and B is equal to the product of their individual probabilities.

Let's calculate the probabilities:

For event A, we need to find the sum of the numbers showing on the dice. In a fair die, there are 3 odd numbers (1, 3, and 5) out of 6 possible outcomes. So, the probability of event A is 3/6 or 1/2.
For event B, we need to find the sum of the numbers showing on the dice. There are three possible sums that satisfy event B: 9 (3+6, 4+5, 5+4), 11 (5+6, 6+5), and 12 (6+6). Out of the 36 possible outcomes, there are 6 outcomes that satisfy event B. So, the probability of event B is 6/36 or 1/6.
Now, let's check if events A and B are independent by calculating the probability of their intersection. The intersection of A and B is the event that both the sum is odd (event A) and the sum is 9, 11, or 12 (event B). There are no outcomes that satisfy both events A and B. So, the probability of the intersection is 0.
Finally, let's check if the product of the individual probabilities is equal to the probability of the intersection. The product of the individual probabilities is (1/2) * (1/6) = 1/12, which is not equal to 0. Therefore, events A and B are dependent.

In summary, events A and B are dependent because the outcome of one event affects the probability of the other event happening.

Learn more about Probability here:

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When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know whether his IL or FL electric bill is relatively more or less expensive, when compared to the distribution of electric bills for each state. In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20. In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00. Compute the z-scores for Stephan's IL and FL electric bills. Round to three decimal places if necessary.

Answers

Using it's formula, it is found that the z-scores are:

For Illinois, of Z = -0.625.

For Florida, of Z = -0.75.

Due to the lower z-score, the bill is relatively lower in Florida.

Z-score:

In a distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

It measures how many standard deviations the measure is from the mean.

The higher z-score means that the measure X is relatively higher.

In Illinois:

Bill of $83, mean of $85, standard deviation of $3.2, hence $X = 83, \mu = 85, \sigma = 3.2$

Then:

$Z = (X - \mu)/(\sigma)$

$Z = (83 - 85)/(3.2)$

$Z = -0.625$

In Florida:

Bill of $102, mean of $105, standard deviation of $4, hence $X = 102, \mu = 105, \sigma = 4$

Then:

$Z = (X - \mu)/(\sigma)$

$Z = (102 - 105)/(4)$

$Z = -0.75$

Due to the lower z-score, the bill is relatively lower in Florida.

To learn more about z-scores, you can take a look at brainly.com/question/21620274

Answer: The z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

Step-by-step explanation:

Given: Average monthly electric bill in Illinois = $83

Average monthly electric bill in Florida = $102

Formula of z : $z=(X-mean)/(standard\ deviaton)$

In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20.

$z=(83-85)/(3.20)= -0.625$

In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.

$z=(105-102)/(4)=(3)/(4)=0.75$

Hence, the z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

Consider the following functions. f(x) = x − 3, g(x) = x2 Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f − g)(x). Find the domain of (f − g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find f g (x). Find the domain of f g (x). (Enter your answer using interval notation.)

Answers

Answer:

$(f+g)(x)=x-3+x^2$ ; Domain = (-∞, ∞)

$(f-g)(x)=x-3-x^2$ ; Domain = (-∞, ∞)

$(fg)(x)=x^3-3x^2$ ; Domain = (-∞, ∞)

$((f)/(g))(x)=(x-3)/(x^2)$ ; Domain = (-∞,0)∪(0, ∞)

Step-by-step explanation:

The given functions are

$f(x)=x-3$

$g(x)=x^2$

$(f+g)(x)=f(x)+g(x)$

Substitute the values of the given functions.

$(f+g)(x)=(x-3)+x^2$

$(f+g)(x)=x-3+x^2$

The function $(f+g)(x)=x-3+x^2$ is a polynomial which is defined for all real values x.

Domain of (f+g)(x) = (-∞, ∞)

$(f-g)(x)=f(x)-g(x)$

Substitute the values of the given functions.

$(f-g)(x)=(x-3)-x^2$

$(f-g)(x)=x-3-x^2$

The function $(f-g)(x)=x-3-x^2$ is a polynomial which is defined for all real values x.

Domain of (f-g)(x) = (-∞, ∞)

$(fg)(x)=f(x)g(x)$

Substitute the values of the given functions.

$(fg)(x)=(x-3)x^2$

$(fg)(x)=x^3-3x^2$

The function $(fg)(x)=x^3-3x^2$ is a polynomial which is defined for all real values x.

Domain of (fg)(x) = (-∞, ∞)

$((f)/(g))(x)=(f(x))/(g(x))$

Substitute the values of the given functions.

$((f)/(g))(x)=(x-3)/(x^2)$

The function $((f)/(g))(x)=(x-3)/(x^2)$ is a rational function which is defined for all real values x except 0.

Domain of (f/g)(x) = (-∞,0)∪(0, ∞)

$(f + g)(x) = x^2 + x - 3$ , domain: all real numbers.

$(f - g)(x) = -x^2 + x - 3$ , domain: all real numbers.

$(fg)(x) = x^3 - 3x^2$ , domain: all real numbers.

$f(g(x)) = x^2 - 3$ , domain: all real numbers.

To find (f + g)(x), we need to add the functions f(x) and g(x).

The function f(x) = x - 3 and the function $g(x) = x^2.$

So, $(f + g)(x) = f(x) + g(x) = (x - 3) + (x^2).$

Expanding this equation, we get $(f + g)(x) = x^2 + x - 3.$

To find the domain of (f + g)(x), we need to consider the domain of the individual functions f(x) and g(x).

Since both f(x) = x - 3 and $g(x) = x^2$ are defined for all real numbers, the domain of (f + g)(x) is also all real numbers.

To find (f - g)(x), we need to subtract the function g(x) from f(x).

So, $(f - g)(x) = f(x) - g(x) = (x - 3) - (x^2).$

Expanding this equation, we get $(f - g)(x) = -x^2 + x - 3.$

The domain of (f - g)(x) is also all real numbers, since both f(x) and g(x) are defined for all real numbers.

To find (fg)(x), we need to multiply the functions f(x) and g(x).

So, $(fg)(x) = f(x) * g(x) = (x - 3) * (x^2).$

Expanding this equation, we get $(fg)(x) = x^3 - 3x^2.$

The domain of (fg)(x) is all real numbers, since both f(x) and g(x) are defined for all real numbers.

To find f(g(x)), we need to substitute g(x) into the function f(x).

So, $f(g(x)) = f(x^2) = x^2 - 3.$

The domain of f(g(x)) is also all real numbers, as $g(x) = x^2$ is defined for all real numbers, and f(x) = x - 3 is defined for all real numbers.

In summary:

- $(f + g)(x) = x^2 + x - 3$ , domain: all real numbers.

- $(f - g)(x) = -x^2 + x - 3$ , domain: all real numbers.

- $(fg)(x) = x^3 - 3x^2$ , domain: all real numbers.

- $f(g(x)) = x^2 - 3$ , domain: all real numbers.

To Learn more about real numbers here:

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Review the table of values for function f(x).A 2-column table with 7 rows. Column 1 is labeled x with entries negative 2, negative 1, negative one-half, 0, one-half, 1, 2. Column 2 is labeled f (x) with entries 8, 5 and one-half, 4, one-half, negative 1, negative 2, negative 7.

Which number is the value of f–1(–2)?

–8
–7
StartFraction 1 Over 8 EndFraction
1?

Answers

Answer:

D. 1

Step-by-step explanation:

Answer:

Answer is D. 1

Step-by-step explanation:

The answer is D on Edge. (VERIFIED Edge Answer)

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Edge Tip: Answers do not mix or change.

A pair of flip flops is $30. How much will they cost after a 20% discount and 6.5% tax?

Answers

Answer:

25.56

Step-by-step explanation:

30 divided by 4 is 6 so 30- 6=24

6.5% of 24=1.56 sooooo 24+1.56=25.56

Answer:

$6.39

Step-by-step explanation

well, 20% of $30 is $6, so then you just have to add on the tax, which is 39 cents, coming to $6.39

PLEASE HELP I WILL MARK BRAINLIEST

Answers

Answer:

172.12 sq in

Step-by-step explanation:

The figure is comprised of a semicircle, and 2 rectangles

Area of semicircle = 1/2(3.14)4^2 = 25.12

Area of rectangle with length of 9 and width of 7 = 7(9) = 63

Area of rectangle with length of 14 and width of 6 = 6(14) = 84

Total area = 25.12 + 63 + 84 = 172.12 sq in

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You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are shipped have had an egg crack while traveling. You are instructed to accept the shipment if no more than 10 cartons out of the 300 you inspect have cracked eggs. What is the probability that you accept the shipment? (In other words, what is the probability that, at the most, you had 16 cartons with cracked eggs?)a. 1012.b. 3669.c. 5319.d. 4681.e. 5832.f. 6331.