what is the equivalent expression plzz help

The diameter of the sphere is 14 cm.

Sphere is a three dimensional object , it has no edges or vertices and is round in shape.

The surface area of the sphere is given by 4πr²

As radius = diameter /2

Surface area =  4π r²

196 π = 4π *(d/2)²

196/4 = d²/4

49 *4 = d²

d = 14 cm

Therefore the diameter of the sphere is 14 cm.

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The frequency table shows that:

To construct frequency table with a range of 6 classes, we will determine range of the data which is difference between the largest and smallest value in the data set.

Data are: 42, 43, 46, 46, 47, 47, 48, 49, 49, 50, 51, 51, 51, 51, 51, 52, 52, 54, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 57, 57, 57, 57, 58, 60, 61, 61, 61, 62, 64, 64, 65, 68, 69

Age Interval     Frequency

40 - 45                    2  

46 - 51                    13

52 - 57                   31

58 - 63                    6

64 - 69                    5

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Answer:

The answer is 13.72 because 1.4^3=2.744 and 2.744*5=13.72

Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

Answer:32/5

Step-by-step explanation:

32/5

Answer:

Solution: 6.4% as a fraction is 32/5.

Step-by-step explanation:

Answer:

41 x 18 = 738 + 14 = 752

Step-by-step explanation:

Its says that there 42 rows .First row has 14 seats and the rest of 41 rows has with + 4 more so every row has 18 seats ,and asks how many seats are in total in the theater . To show that you understood the question you have to multiply 41x18 which gives 738 and then add + 14 from the first row so you can find out how many seats are in total .Hope that helps .

Answer:

8

Step-by-step explanation:

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

Describe a formula. To create the expression known as an equation, two sides are connected by the equals symbol (=). The variables in the equation 2x+1 = 9 are 2x+1 on the left and 9 on the right (RHS).

To simplify the equation 2/3x + 5 = 1/5 - 2x, we can start by getting rid of the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators of the fractions, which is 15.

So, we have:

15 * (2/3x + 5) = 15 * (1/5 - 2x)

Expanding the left-hand side, we get:

10x + 75 = 3 - 30x

Bringing all the x terms to one side and all the constant terms to the other, we get:

10x + 30x = 3 - 75

Combining like terms, we get:

40x = -72

Dividing both sides by 40, we get:

x = -72/40 = -9/5

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

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Given a Math exam with 7 short answer questions and Peter intending to answer three of them, there are a total of 35 different combinations of short answer questions he can choose.

To determine the number of combinations, we can use the concept of combinations in combinatorics. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations of choosing r items from a set of n items.

n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, Peter wants to answer three out of the seven questions, so we can calculate it as:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!)

Simplifying further:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

4! = 4 * 3 * 2 * 1

C(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (4 * 3 * 2 * 1)]

After canceling out common terms, we get:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different combinations of short answer questions Peter can choose to answer.

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Using binomial distribution;

a. The probability that x < 29 is 0.0516

b. The probability that 28 ≤ x ≤ 31 is 0.1257

c. The probability that x = 31 is 0.0895

d. The expected value of x is 30.08

e. The variance of x is 8.0568.

This problem can be solved using the binomial distribution since we have a random sample of new freshmen and we're interested in the number of them who graduate within 6 years. Let's calculate the probabilities and expected value.

a) To find the probability that X < 29, we need to calculate the cumulative probability for X = 0, 1, 2, ..., 28. Using the binomial probability formula, the probability of X = x is given by:

\(P(X = x) = C(n, x) * p^x * (1 - p)^(^n ^- ^x^)\)

Where n is the sample size, x is the number of successes, p is the probability of success (proportion of freshmen who graduate within 6 years), and C(n, x) represents the binomial coefficient.

In this case, n = 64, p = 0.47, and we want to calculate:

P(X < 29) = P(X = 0) + P(X = 1) + ... + P(X = 28)

Calculating this probability involves summing up 29 terms using the formula mentioned above. This can be done manually, or you can use a calculator or software with binomial distribution functionality to find the result. The probability is approximately 0.0516.

b) To find the probability that 28 ≤ x ≤ 31, we need to calculate the probabilities for X = 28, 29, 30, and 31, and then sum them up:

P(28 ≤ X ≤ 31) = P(X = 28) + P(X = 29) + P(X = 30) + P(X = 31)

Using the binomial probability formula mentioned earlier, calculate each probability and sum them up. The probability is approximately 0.1257.

c) To find the probability that X = 31, we use the binomial probability formula:

\(P(X = 31) = C(64, 31) * 0.47^31 * (1 - 0.47)^(^6^4 ^- ^3^1^)\)

Calculate this probability using the binomial coefficient and the values provided. The probability is approximately 0.0895.

d) The expected value (mean) of X can be calculated using the formula:

E(X) = n * p

In this case, n = 64 and p = 0.47. Substituting these values, we have:

E(X) = 64 * 0.47 = 30.08

Therefore, the expected value of X is approximately 30.08.

e) The variance of X can be calculated using the formula:

Var(X) = n * p * (1 - p)

Again, substituting the given values, we have:

Var(X) = 64 * 0.47 * (1 - 0.47) = 8.0568

Therefore, the variance of X is approximately 8.0568.

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The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:

n = 9604.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The margin of error is modeled as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

We have no estimate of the proportion, hence it is used as follows:

\(\pi = 0.5\)

The margin of error is of M = 0.01, hence the sample size is obtained as follows:

\(0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.01\sqrt{n} = 1.96 \times 0.5\)

\(\sqrt{n} = 98\)

n = 98²

n = 9604.

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Answer:

x = -5

Step-by-step explanation:

Multiply each x and 3 by -4, obtaining

-4x - 12 = 8

Now solve for x by combining the constants:

-4x = 20, or

x = -5

Answer: x=-5

Step-by-step explanation: distribute the -4 first to both x and 3

-4x-12 = 8 then add 12 to both sides to isolate x

-4x= 20

divide by -4 and you get  x= -5

check it

-4(-5+3)

-4(-5)= 20 (a negative times a negative makes a positive)

then -4(3)= -12

20-12= 8

it checks out, hope this helps ^_^

The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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Answer: $68.99

Step-by-step explanation:

12% of 61.60 is 7.39200, if you simplify the total, you would get 7.39. Then, you add the total with the sale price to get the original price. Which in this case is $68.99.

Scale factor of greater than 1 indicates the size of the shape will increases

The scale factor is defined as the ratio between the original size of the figure and the new size of the figure.

The scale factor of the figure maybe greater than 1 or the between 0 and 1

If the scale factor of the figure is between 0 and 1, then the size of the figure will decreases, the new size of the figure will be less than original figure

Similarly, if the scale factor is greater than 1, the size of the figure will increase, new figure will be larger than original figure

Therefore, if the scale factor is greater than 1  the figure will enlarge

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Answer:2/3

Step-by-step explanation:

Answer:

X=50000/3 for x>0

Step-by-step explanation:

First get rid of log (3), toss it over exuation sign.

Then calculate the formula for double angle (sin 2x = sin²X + sin(X) x cos (X) + cos²X)

After you do that you should be able to divide everything with cos²X and get polynomial exuation which is solved by substitution method (you'll get tan and then switch it for lets say letter: t

Yes, the lines AB and PQ are parallel lines and have same direction.

Coordinates of the line AB and PQ :

A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)

Slope =  (y₂ - y₁)/ (x₂ -x₁)

Substitute the value in the formula:

Slope of the line AB = ( 4 - 1 )/ ( 3 - 1 )

⇒ Slope of the line AB = 3 /2

Slope of the line PQ = ( 10 - 1 )/ ( 7 - 1 )

⇒ Slope of the line PQ = 9 /6

⇒ Slope of the line PQ = 3 /2

Slope of line AB and PQ are equal it implies they are parallel lines.

Therefore, both the lines AB and PQ are parallel lines to each other and are in the same direction.

The above question is incomplete , the complete question is:

Are lines AB and PQ parallel? And if so, do they point in the same direction? A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)

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Answer:

your mixed fraction would be 12 37/100

Step-by-step explanation:

The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.

You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

3 * 10 ^3

Step-by-step explanation:

Divide the numbers

3.9 / 1.3

3

Subtract the powers of 10

10^5 / 10^2 = 10 ^ (5-2) = 10^3

The result is 3 * 10 ^3

\( \frac{3.9 \times {10}^{5} }{1.3 \times {10}^{2} } \\ = \frac{3.9}{1.3} \times {10}^{5 - 2} \\ = 3.0 \times {10}^{3} \)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

2

Step-by-step explanation:

copy the proportion;

1 x

- = ----

8 16

16/8 = 2

1 x 2 = 2

Answer:

πr²= 12.56

r²=12.56/3.14 = 4

r= 2

therefore , diameter = 2r = 2×2= 4 mm

The number of data packet arrivals in t seconds at a multiplexer is a Poisson random variable with λ = λt, where λ = 1 packets/second. This means that the expected number of arrivals in t seconds is λt, or t in this case. The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. In this case, the events are the data packet arrivals at the multiplexer.

To find the probability of n data packet arrivals in t seconds, we can use the formula for the Poisson distribution:

P(X = n) = (λt)^n * e^(-λt) / n!

Plugging in the values for λ and t, we get:

P(X = n) = (1*t)^n * e^(-1*t) / n!

Simplifying, we get:

P(X = n) = t^n * e^(-t) / n!

This is the probability of n data packet arrivals in t seconds at a multiplexer with a Poisson random variable with λ = λt, where λ = 1 packets/second.

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Answer:

1. 200

2. 78

3. 50%

4. 20%

5. 14.52

6. 72

7. 30

8. 27

9. 50%

10. 20%

I hope this helps:D