How to find area of the base for a cube

B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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Answer:

m = 5/2

Step-by-step explanation:

The slope is rise/run or (y2 - y1) / (x2 - x1)

The y decrease by 5, and the x decrease by 2, so the slope is

-5/-2 = 5/2

So, m = 5/2

Hello!

We are going to find the slope of the line that passes through our given points: (8, 9) and (6, 4).

To find the slope, we will use the slope formula, which states:

m = (y2-y1)/(x2-x1)

Our variables in the formula are given by the coordinates that we know.

(x1, y1)

(8, 9)

And

(x2, y2)

(6, 4)

Solve:

Plug in the coordinates into the correct variable and solve:

m = (y2-y1)/(x2-x1)

m = (4 - 9)/(6 - 8)

m = -5/(6 - 8)

m = -5/-2

Simplify:

m = 5/2

Therefore, the slope of the line is 5/2.

Answer:

5/2

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Using the test statistic, at the 0.05 level of significance, we do not find sufficient evidence to support the political scientist's claim and hence reject the null hypothesis.

To determine whether there is enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65%, we can perform a hypothesis test using the given data.

Let's set up the null and alternative hypotheses:

H₀: p ≤ 0.65 (Null hypothesis: The proportion of college students interested in election results is 65% or less)

Ha: p > 0.65 (Alternative hypothesis: The proportion of college students interested in election results is more than 65%)

We are given that the sample size is 265 college students, and out of this sample, 180 students say they're interested in their district's election results.

To perform the hypothesis test, we'll calculate the test statistic, which is the z-statistic in this case, using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

Where p is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

Let's calculate the sample proportion:

p = 180 / 265 ≈ 0.679

Now, we can calculate the test statistic:

z = (0.679 - 0.65) / √(0.65(1-0.65)/265) ≈ 1.295

Next, we'll compare the test statistic with the critical z-value at a 0.05 level of significance (α = 0.05) for a one-tailed test.

Using a standard normal distribution table or a statistical calculator, the critical z-value at α = 0.05 is approximately 1.645.

Since the test statistic (1.295) does not exceed the critical z-value (1.645), we fail to reject the null hypothesis. In other words, we do not have enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65% based on this sample.

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The piecewise function graphed below is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:

\(f(x) = 3, -4 \leq x \leq -2\)

For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:

\(f(x) = x + 2, -2 < x \leq 3\)

For x greater than 3 until 5, the function is constant at -1, hence the definition is:

\(f(x) = -1, 3 < x \leq 5\)

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Answer:

1] x=4.21

2] 52.5

3] 3.82

4] 38.73

5] 32.005

6] 31.21

Step-by-step explanation:

Answer:

You would move 10 units to the right from zero on the x-axis

Answer:

10 spaces to the right to get to 10 and up 8 to get to 8

Answer:

:)

Step-by-step exp

16/.8 = 20

Answer:

20

Step-by-step explanation:

The correct equation is,

⇒ 8(x + 6) = 144

Now, We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Thus, The correct equation is,

8(x + 6) = 144

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The fraction for the given situation is 7/3. Therefore, option D is the correct answer.

Given that, there are 7 apple pies.

3 people will share the pies equally.

Equal share of pie = Number of apple pies/Number of people

Equal share of pie = 7/3

So, the fraction is 7/3 of a whole

Therefore, option D is the correct answer.

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Answer:

4 can go into 9 twice with 1 left over

Twice=2

2 wholes

1 leftover out of 4

2 1/4

It’s B

Step-by-step explanation:

hope this helps

The total number of rankings is the product of the number of students at each step. Total number of different rankings possible = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 10! ≈ 3.6 × 10^6.

Given that an introductory statistics class has 4 freshmen and 6 sophomores. The students are ranked based on their performance. Therefore, it is required to find the number of different rankings possible. Step 1: Find the total number of students in the class. Total number of students in the class = number of freshmen + number of sophomores = 4 + 6 = 10Step 2: Find the number of ways to select the first-ranked student. There are 10 students to choose from for the first position. Therefore, the number of ways to select the first-ranked student is 10.Step 3: Find the number of ways to select the second-ranked student. There are 9 students remaining after selecting the first-ranked student. Therefore, the number of ways to select the second-ranked student is 9.Step 4: Find the number of ways to select the third-ranked student.There are 8 students remaining after selecting the first two-ranked students.

Therefore, the number of ways to select the third-ranked student is 8.Step 5: Continue the process until all students are ranked. The total number of rankings is the product of the number of students at each step.Total number of different rankings possible = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 10! ≈ 3.6 × 10^6.

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Answer:

1 = B

2 = 3/7

3 = B

4 = J

5 = 1/25

6 = H

7 = D

8 = G

9 = A

10 = 1/3

11 = D

Step-by-step explanation:

Answer:

<1 =73

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

72+ 35 + <1 = 180

Add like terms

107 + <1 = 180

Subtract 107 from each side

<1 = 180-107

<1 =73

⇒ common ratio =r=3 and the given sequence is geometric sequence. Where an is the nth term, a is the first term and n is the number of terms. ⇒ 12th term is 708588 .

(May be wrong for some other users, although it's correct for me.)

its letter b. 120 degrees

Answer:

1.96

Step-by-step explanation:

The value of the z-score for the value of sample 48 will be negative 0.4.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The mean is 50 and the standard deviation is 5.

Then the value of the z-score for the value of sample 48 will be

z = (x - mean) / (standard deviation)

Then we have

z = (48 - 50) / (5)

z = -2 / 5

z = -0.4

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Answer:

5

Step-by-step explanation:

p has an odd degree and an odd leading coefficient.

So,

Answer:  see below

Step-by-step explanation:

8)   3x ≥ 24

   ÷3    ÷3  

     x  ≥  8

Graph:        ·--------→

                 8

Interval Notation: [8, ∞)

The equation of the tangent line to the curve r=2sin5θ at θ=π/3 is \(y=\frac{1}{6}(-2 \sqrt{3} x-3(1+\sqrt{3}))\).

To find the equation of the tangent line to the curve r=2sin5θ at θ=π/3, we first need to find the value of r and the slope of the tangent line at θ=π/3.

We know that r=2sin5θ, so at θ=π/3,

we have

r = 2 sin 5(π/3)

= 2 sin (5π/3)

=2 sin(-π/3)

= \(2(-\sqrt{3}/2)\)

= \(-\sqrt{3}\).

To find the slope of the tangent line, we need to take the derivative of r with respect to θ and evaluate it at θ=π/3.
r = 2sin5θ
dr/dθ = 10cos5θ

So at θ=π/3, we have

dr/dθ = 10 cos 5(π/3) = 10cos(5π/3) = 5

The slope of the tangent line is equal to the derivative of r with respect to θ, divided by the derivative of y with respect to x.

Since \(r = \sqrt{(x^2 + y^2)}\) and y = r sin θ and x = r cos θ, we have:

dy/dx = (dy/dθ) / (dx/dθ)

= (cos θ) / (-sin θ)

= -cot θ

So at θ=π/3, we have

dy/dx = -cot(π/3) = -1/√3.

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line.

The point-slope form is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the point of tangency, and m is the slope of the tangent line.

At θ=π/3, we have  \(r= -\sqrt{3}\) and θ = π/3, so the point of tangency is \((x_{1}, y_{1}) = (-\sqrt{3}/2, -\sqrt{3}/2)\).

Substituting in m = -1/√3 and \((x_{1}, y_{1}) = (-\sqrt{3}/2, -\sqrt{3}/2)\), we get:
\(y + \sqrt{3}/2 = \frac{-1}{\sqrt{3}}(x + \sqrt{3}/2)\)

Simplifying, we get:
\(y=\frac{1}{6}(-2 \sqrt{3} x-3(1+\sqrt{3}))\)

So, the equation of the tangent line to the curve r=2sin5θ at θ=π/3 is \(y=\frac{1}{6}(-2 \sqrt{3} x-3(1+\sqrt{3}))\).

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The probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I can be denoted as P(S|C'). The correct option is (a) P(S'|C').

To represent the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I, we need to consider the complement of the events.

The complement of event C (grade of B or better in Calculus I) is C' (grade less than B in Calculus I). Similarly, the complement of event S (grade of A in Statistics I) is S' (grade other than A in Statistics I).

Therefore, the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I is denoted as P(S|C'). This notation indicates the conditional probability of event S occurring given that event C' has occurred.

Among the given options, (a) P(S'|C') correctly represents the desired probability. Option (b) P(CIS) represents the joint probability of events C, I, and S, which is not relevant to the given question.

Option (c) P(SIC) represents the joint probability of events S, I, and C, which is also not relevant. Option (d) P(SIC) is a duplicate of option (c) and does not represent the desired probability.

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To find the fraction of the states that Jorge's family has visited, we can use the formula:

visited states / total states

In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:

38 / 50

You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is

19/25

So, Jorge's family has visited 19/25 of the states in America.

Jorge's family has visited 19/25 of the states in America.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:

38 / 50

You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is

19/25

19 out of the 25 American states have been visited by the Jorge family.

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Height of the goalpost is 3.21 m.

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Now, We know that;

As per the rule of reflection in physics,

Angle of incidence = Angle of reflection

Hence, As we can see in the picture attached, both the angles (θ) are equal.

m ∠ACB = m ∠ECD = 90° - θ

m ∠ABC = m ∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

AB / ED = CB / CD

1.65 / ED = 4.95 / 9.65

15.92 = 4.95 ED

ED = 3.21 m

Thus, Height of the goalpost is 3.21 m.

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Answer:

25

Step-by-step explanation:

As the triangles within the bigger triangle are similar, the sides are in proportion.

⇒ \(\frac{18}{30} = \frac{15}{w}\)

⇒ \(\frac{3}{5} = \frac{15}{w}\)

⇒ 3w = 75

⇒ w = 25

The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.

P is the total number of permutations, which is equal to 12.

The correct answer is OB, which lists all 12 permutations.

P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.

There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.

Therefore, P2 is equal to 16.

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A) 80

B)-60

C) 2

D) -54

Step-by-step explanation:

Of the following options, the one that is not affected by an extreme value in the data set is the mode. The correct answer is B.

The mode is simply the value that occurs most frequently in the data set. Since it only depends on the frequency of each value, the mode is not affected by extreme values.

On the other hand, the mean, range, and standard deviation are all sensitive to extreme values.

The mean can be heavily influenced by extreme values, as it is calculated by summing up all the values in the data set and dividing by the total number of values.

The range is the difference between the highest and lowest values in the data set, and a single extreme value can greatly affect this difference.

The standard deviation measures how spread out the data is, and an extreme value can increase the standard deviation by making the data more spread out.

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