please help for a better grade in math

Using a confidence level of 95%, the margin of error for the mean GRE score of graduate students is approximately 14.15. The upper bound of the confidence interval is 314.15, and the lower bound is 285.85. This means we are 95% confident that the true population mean GRE score falls between these two values.

To calculate the margin of error, we use the formula:

Margin of Error = Z * (Standard Deviation / √n)

In this case, the standard deviation is 47 and the sample size (n) is 50. The Z-value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:

Margin of Error = 1.96 * (47 / √50) ≈ 14.15

This means that the sample mean of 300 is expected to be within 14.15 points of the true population mean GRE score.

The confidence interval is then constructed by adding and subtracting the margin of error from the sample mean:

Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

= (300 - 14.15, 300 + 14.15) = (285.85, 314.15)

Interpreting the confidence interval, we can say that we are 95% confident that the true population mean GRE score for graduate students falls within the range of 285.85 to 314.15. This means that if we were to repeat the sampling process and calculate the sample mean GRE scores multiple times, approximately 95% of the confidence intervals obtained would contain the true population mean.

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Answer: 0.1714 miles / hour

Step-by-step explanation:

Given the following :

Distance to the store = 3 miles

Time taken to get to store = 12 hours

Time taken to return = 23 hours

The average rate of speed for the trip =?

Average Speed = total distance traveled / total time taken

Total distance traveled = 2 × 3 miles = 6 miles

Total time taken = 12 + 23 = 35 hours

Average speed = 6 miles / 35 hours

Average speed = 0.1714 miles / hour

Answer:

0.1714 mph

5.14 mph

Step-by-step explanation:

The true statements are '

A.) The y-intercept is (0,-3)

C.) The range is [-1,∞)

D.)The vertex is (-2,-1)

E.)The domain is (-∞,∞)

The y-intercept is a term used in coordinate geometry to describe the point at which a line crosses or intersects the y-axis. In other words, it is the point at which the line crosses the vertical axis on a Cartesian coordinate plane.

In geometry, a vertex is a peak point of the curve.

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Answer:

Step-by-step explanation:

Start at -8. Make a point there.

Then, go up 5 and to the right 1 and make a dot there.

From that same -8 point go down 5 and to the left 1.

You can do a couple if you like. Lastly, draw a line connecting the dots and there is your graphed line.

Edna has visited 44 countries.

For given question,

Edna has spent her whole life traveling. she has been to 4 different continents and to 11 countries on each continent.

Here each continent  has 11 countries.

She visited 4 different continents.

So, the total number of countries she has visited would be given by an expression,

11 × 4

We solve above expression to  determine how many countries Edna has visited.

11 × 4 = 44

Therefore, approximately 44 countries Edna has visited.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

9:6 27:18 and 81: 54

Step-by-step explanation:

Answer: 39.66

Step-by-step explanation: hope this helps!!!!

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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The expressions 3(5 − 2x) and 3(2x) − 3(5) are not equivalent

Given,

3(5 − 2x) and 3(2x) − 3(5)

We need to find out whether they are equivalent or not.

Expressions is a statement that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Find 3(5 - 2x).

Using the property of multiplication over subtraction.

3x5 - 3x(2x)

15 - 6x

Find 3(2x) - 3(5)

Removing the bracket.

6x - 15

We see that,

15 - 6x ≠ 6x - 15

The expressions are not equal.

Thus the given expressions 3(5 − 2x) and 3(2x) − 3(5) are not equivalent.

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Answer:

7. To perform a t-test when the sample size is small, the sample must show no evidence of strong skewness and must contain no outliers.

Step-by-step explanation:

These are the two conditions required for performing a t test

- Sample Size: A small sample size can reduce the statistical power of a t-test, making it more challenging to detect significant differences between groups. Generally, a larger sample size is desirable to obtain more reliable and representative results.

- Skewness: Skewness refers to the asymmetry of the distribution of data. In a t-test, assuming normality of the data is important for accurate results. If the data exhibits strong skewness, the assumption of normality may be violated. In such cases, alternative non-parametric tests or transformations of the data may be more appropriate.

- Outliers: Outliers are extreme values that significantly differ from the rest of the data. They can have a disproportionate impact on the results of a t-test, particularly when the sample size is small. Outliers can distort the mean and affect the assumptions of normality and homogeneity of variance.

While the presence of skewness or outliers does not prohibit the use of a t-test with a small sample size, it is important to interpret the results with caution and consider alternative approaches if necessary. Robust statistical methods, such as non-parametric tests or bootstrapping, can be useful when dealing with non-normal or outlier-prone data, especially with small sample sizes. Additionally, visual inspection of the data distribution, such as through histograms or box plots, can help identify potential skewness or outliers.

The curve is passing through (0, 2) and (0, -3).

The zeroes of the polynomial function are 2 and -3.

The number of zeroes is 2. Then the degree of the polynomial will be 2. So, the function is a quadratic function.

The zeroes of the function represent the x-intercepts. Then the curve is passing through (0, 2) and (0, -3).

Thus, the correct option is B.

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It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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Answer:

sqrt(241) or about 15.52 rounded

Step-by-step explanation:

a^2+b^2=c^2

4^2+15^2=c^2

16+225=c^2

241=c^2

sqrt(241)=c

Answer:

-1/2

Step-by-step explanation:

The line passes through (0,2) and (2,1)

Slope = (1-2) / (2-0)

= -1/2

This declaration is True.

The anticipated variability or widespread deviation of the means from MANY unique random samples is known Sampling distribution.

The standard deviation of this distribution, i.e. the standard deviation of sample means, is called the standard error. The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean.

What is the suggest variance and fashionable deviation of the sampling distribution of the pattern mean?

Since the suggest is 1/N times the sum, the variance of the sampling distribution of the suggest would be 1/N2 instances the variance of the sum, which equals σ2/N. The widespread error of the suggest is the standard deviation of the sampling distribution of the mean.

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The given question is incomplete, complete question is:

The expected variability or standard deviation of the means from MANY different random samples is known as what quantity: a. Sampling variability b. Standard error (panel 51 from slides), itâs also said in the video c. Sampling distribution d. Parameter

The statement you provided is unclear and does not convey a specific question or prompt. It seems to be an incomplete statement or a partial description of a concept. Please provide more context or clarify your question so that I can assist you better.

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Answer:

B

Step-by-step explanation:

x² - 24x + 144

consider the factors of the constant term (+ 144) which sum to give the coefficient of the x- term (- 24)

the factors are - 12 and - 12 , since

- 12 × - 12 = + 144 and - 12 - 12 = - 24 , then

x² - 24x + 144 = (x - 12)(x - 12) = (x - 12)²

Answer:

B

Step-by-step explanation:

Given :

x² - 24x + 144

Splitting the middle term :

x² - 12x - 12x + 144

x (x - 12) - 12 (x - 12)

(x - 12) (x - 12)

(x - 12)²

\(f(x) = 2 {x}^{2} + 2x - 24 \)

\(f(x) = 2( {x}^{2} + x - 12) \)

\(0 = 2( {x}^{2} + x - 12)\)

Divided sides by 2

\( {x}^{2} + x - 12 = 0 \)

\((x + 4)(x - 3) = 0\)

_________________________________

\(x + 4 = 0\)

\(x = - 4\)

_________________________________

\(x - 3 = 0\)

\(x = 3\)

Thus the actual roots are -4 and 3.....

And we're done.

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Answer:

x= 3, -4

Step-by-step explanation:

Set  2 x ² +  2 x  −  24  equal to  0 .

   2 x   ² +  2 x  −  24  =  0

Solve for  x .

Factor the left side of the equation.

2 ( x²   +  x  −  12 )  =  0

Factor  

x  ² +  x  − 12  using the AC method.

2 ( x  −  3 ) ( x  +  4 )  =  0

If any individual factor on the left side of the equation is equal to  0 , the entire expression will be equal to  0 .

x − 3 = 0

x + 4 = 0

Add  3  and subtract 4 to both sides of the equation.

x = 3

x = -4

The correct answer is option A: 0.415.The probability that a randomly selected three-year-old is in daycare is 0.415. This is because the given information tells us that 41.5% of three-year-olds are enrolled in daycare.

Option A: 0.415 is the right answer.The likelihood of a randomly picked three-year-old being in creche is 0.415. This is due to the fact that 41.5% of three-year-olds are enrolled in nursery, according to the data.

Because a randomly chosen three-year-old can be in creche or not, the likelihood that a randomly chosen three-year-old is in creche is the same as the proportion of three-year-olds enrolled in creche, which is 0.415, or 41.5%.

To elaborate, probability is a measure of the possibility that an event will occur. It is usually a number between 0 and 1, with 0 indicating that the occurrence is impossible and 1 indicating that the event is unavoidable.

In this scenario, the event is picking a three-year-old who is enrolled in creche, with a chance of 0.415, or 41.5%, of this event occuring.

Therefore, the correct answer is option A: 0.415.

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Answer:

one million one hundred thousand three hundred

The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

Given that,

The set are U={22,23,24,25,26,27,28,29,30}

O={prime number}={23,29}

R={even numbers}={22,24,26,28,30}

We have to find (O∪R)',(O∩R)' and O∩R

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent elements can be anything, including people, alphabetic letters, numbers, shapes, variables, etc.

First,

O∪R= {23,29}∪{22,24,26,28,30}

O∪R= {22,23,24,26,28,29,30}

Now,

1. (O∪R)'=U-(O∪R)

(O∪R)'= {22,23,24,25,26,27,28,29,30} - {22,23,24,26,28,29,30}

(O∪R)'= {25,27}

2. O∩R={23,29}∩{22,24,26,28,30}

O∩R={Φ}

3. (O∩R)'=U-(O∩R)

(O∩R)'= {22,23,24,25,26,27,28,29,30} -{Φ}

(O∩R)'= {22,23,24,25,26,27,28,29,30}

Therefore, The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

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Answer:

What do you mean by infinite amount of answers?

Step-by-step explanation:

Answer:

10 cups

Step-by-step explanation:

He buys 1 pint of juice and 1/2 gallon of juice.

We have to convert pint and gallon to cups and then add them.

1 pint = 2 cups

1 gallon = 16 cups

1/2 gallon = 1/2 * 16 = 8 cups

Therefore,

2 + 8 = 10 cups

Fernando buys 10 cups of juice.

The constant of proportionality is 10.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality is the fixed or constant pace at which ratios rise and decrease. Two ratios are said to be directly proportional if they share the same constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality. The constant of proportionality is the name given to this consistent pace of growth or decline.

a)

since , 1 cm = 10mm

9cm = 90mm

12.5cm = 125mm

50cm = 500mm

88.49cm = 884.9mm

b)

The constant of proportionality is 10.

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Answer:

Step-by-step explanation:

-16 + 12s - 22t + 6u

The composite function (g.h)(9) when evaluated is -84

The function definitions are given as

g(t) = -2t+4

h(t) = t - 3

(g.h)(t) represents the composite function of g and h, multiplied togeter

That is:

(g.h)(t) = g(t) * h(t))

By substituting the function values, we have

(g.h)(t) = (-2t + 4) * (t - 3)

To find (g.h)(9), we simply substitute t = 9:

(g.h)(9) = (-2 * 9 + 4) * (9 - 3)

Evaluate

(g.h)(9) = -84

Therefore, (g.h)(9) = -84

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Answer:

Out put would be - 2

Step-by-step explanation:

\(y = 3x \div 9 \\ y = \frac{3x}{9} \\ y = \frac{x}{3} \\ plug \: x = - 6 \\ y = \frac{ - 6}{3} \\ \huge \purple{ \boxed{ y = - 2}}\)

The domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

All functions are relations in which there is no value of the domain related to more than one value of the range, functions in explicit form related the variable of the range in terms of the variable of the domain.

Based on the information shown in the graph, the domain is represented by the set of values of the time, that is, the horizontal axis, and the range is represented by the set of values of the height, that is, the vertical axis.

Hence, the domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

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