Label the horizontal and vertical sides of the triangle with expressions representing their length.

Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.

In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the   system of experimentation.

Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.

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The probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7 is 28.43%. Correct option is D.

To calculate the probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7, we need to use the standard normal distribution and the z-score.

First, we can find the z-score for 82 using the formula:

z = (x - mu) / sigma

where x is the value of interest (in this case, 82), mu is the mean (78), and sigma is the standard deviation (7).

z = (82 - 78) / 7

z = 0.57

Next, we can use a z-table or a calculator to find the area under the standard normal curve corresponding to a z-score of 0.57. The area represents the probability that a score will be greater than 82.

Using a standard normal table, we find that the area to the right of z = 0.57 is 0.2843 or approximately 28.43%. Therefore , correct option is D.

In conclusion, by calculating the z-score and using a standard normal distribution table, we can find the probability that a score will be greater than a certain value in a normal distribution with a known mean and standard deviation.

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Complete question is:

A normal distribution with a mean of 78 and a standard deviation of 7, what is the probability that a score will be greater than 82?

group of answer choices

A. 23.89%

B. 26.11%

C. 76.11%

D. 28.43%

E. 52.22%

Answer:

combine like terms

Step-by-step explanation:

f(x) is continuous for all values of x, as it can be evaluated for any real number, including both rational and irrational numbers.

f(x) is continuous for all values of x. This means that the function can be evaluated for any real number, including both rational and irrational numbers.

For rational numbers, f(x) = 0. This is because rational numbers can be expressed as a fraction, and when a fraction is divided by itself, the result is always 1. We can express this mathematically as f(x) = x/x = 1 * 0 = 0.

For irrational numbers, f(x) = 7. This is because an irrational number cannot be expressed as a fraction, and so when an irrational number is divided by itself, the result is undefined. In this case, we can define f(x) as 7, since it is a constant value that is independent of the value of x. We can express this mathematically as f(x) = x/x = undefined * 7 = 7.

Therefore, f(x) is continuous for all values of x, as it can be evaluated for any real number, including both rational and irrational numbers.

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Based on the given information, it is not possible to determine the p-value, decision to reject (rh0) or failure to reject (frh0) without additional data or context.

To assess whether the relaxation exercise slowed brain waves, a statistical analysis should be conducted on a sample from the population.

The analysis would involve measuring brain waves before and after the exercise and comparing the results using appropriate statistical tests such as a t-test or ANOVA. The p-value would indicate the probability of observing the data if there was no effect, and the decision to reject or fail to reject the null hypothesis would depend on the predetermined significance level.

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Answer:

T8 = -1280

Step-by-step explanation:

Tn = ar^n - 1

T8 = ar^7

T8 = -10*2⁷

T8 = -1280

The set of data 6, 2, 2, 2  will have the least dispersion from its mean.

From four sets of data, we take the mean of 6,2,2,2

\(\rm mean =\dfrac{ Sum \ of\ data}{Number \ of\ data}\)

So the mean will be

\(\rm mean =\dfrac{ 6+2+2+2}{4}=\dfrac{12}{4} =3\)

So the mean of the data (6,2,2,2) is 3 which has the least dispersion from its every data as compared to the other data

Thus the set of data 6, 2, 2, 2  will have the least dispersion from their mean.

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Answer:

c: 6,2,2,2

Step-by-step explanation:

The equation of the  given model is y = 13.16x + 251.05

First choose two point

The first point = (44, 830)

The second point = (63, 1080)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The  slope of the line = (1080-830) / (63 - 44)

= 250 / 19

Consider the point (44, 830)

The point slope form is

\(y-y_1=m(x-x_1)\)

Where m is the slope of the line

y - 830 = 250/19(x - 44)

y - 830 = (250/19)x - 11000/19

y = (250/19)x - 11000/19 + 830

y = 250/19 x + 4770/19

y = 13.16x + 251.05

Hence, the equation of the  given model is y = 13.16x + 251.05

The complete question is

The table shows the fat content and calories for the burgers at a fast food chain.

Fat (g) 25 44 63 32 37 20 11 52

Calories 590 830 1080 680 750 420 310 820

Write the best fit line that models the impact of fat content on calories. Explain how you got your answer.

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Therefore, a maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

Let the length of the field =  feet

 And the width of the field =  feet

Therefore, area of the rectangular field = Length × Width

                                                             A =  x*y  square feet

Since, length of the fence = 100 feet

And the farmer has to enclose three sides of the rectangle as shown in the figure attached.

Therefore, length of the fence = length + 2(width)

                                               = (x+2y) feet

Hence,  (x+2y)=100

x=100-2y

By substituting the value of 'x' in the expression for the area of the rectangular field.

A=(100-2y)y

A=-2y^2+144y

Find the derivative of the expression with respect to y ,

A'= -4y+100

A'=0

4y=100

y=25

A=-2*625+2500

A=2500-1250

A=1250 square feet

Therefore, maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

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Answer: For the first 5 months she pays a monthly$15 membership fee. Use the explicit rule f(n) = 15n + 10

Step-by-step explanation:

The table of the ordered pairs and the graph is plotted.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Emma who pays $10 to join a gym. For the first 5 months she pays a monthly $15 membership fee. The explicit rule that represents the situation above is f(n) = 15n+10.

We have the function as -

f(n) = 15n+10.

We can create a table as follows -

[n]         f[n]

1            25

2           40

3           55

4           70

5           85

Refer to the graph of the function f(n) = 15n+10 attached.

Therefore, the table of the ordered pairs and the graph is plotted.

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Answer:

Step-by-step explanation:

If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.

34= 18+x

I hope this helps!

Step-by-step explanation:

2:10:16=2/10=1/5÷16

\(1 \div 5 \div 16\)

1/5×1/16

=1/80

Answer:

3

Step-by-step explanation:

Variables are the letters.

I hope this could help!!!

Answer:

3

Step-by-step explanation:

Answer: 26, 28, 30

Explanation:

Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.

We can write the given information as an equation:

3 * (x + 4) = 2 * x + 38

We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:

3 * (x + 4) - 2 * x = 38

Then we can distribute the 3 and the -2 to get:

3 * x + 12 - 2 * x = 38

And then we can combine like terms on each side of the equation:

x + 12 = 38

Finally, we can subtract 12 from both sides to solve for x:

x = 26

Therefore, the three consecutive even integers are 26, 28, and 30.

We can check our solution by substituting these values back into the original equation and verifying that it holds true:

3 * (26 + 4) = 2 * 26 + 38

3 * 30 = 52 + 38

90 = 90

The equation holds true, so our solution is correct.

The area of the sector is 472.6 ft²

For finding the area of the sector, you need apply the formula:

\(A=\pi r^2* \frac{\alpha }{360}\), where:

r= radius

α= central angle

The question gives:

r= radius= 19 ft

α= central angle = 150°

Thus, the area of the sector will be:

\(A=\pi r^2* \frac{\alpha }{360}=\pi *19^2*\frac{150}{360} =472.6\)

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Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

\(f(x)=a(x-2)(x-6)\)

Substituting in the coordinates of the vertex,

\(-4=a(4-2)(4-6)\\\\-4=a(2)(-2)\\\\-4=-4a\\\\a=1\)

So, the equation is \(f(x)=(x-2)(x-6)\).

On expanding, we get \(f(x)=x^2 - 8x+12\)

Answer:

Step-by-step explanation:

yes just a different spelling

Answer:

Option 3 11/9

9

1

Step-by-step explanation:

Given : In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon.

To find : How much cinnamon does the spice mix contain per pound?

Solution :

In \frac{3}{4}

4

3

pounds of a spice mix have \frac{5}{6}

6

5

cup of cinnamon.

So, In In 1 pounds of a spice mix have \frac{\frac{5}{6}}{\frac{3}{4}}

4

3

6

5

cup of cinnamon.

Now, we solve the fraction

=\frac{\frac{5}{6}}{\frac{3}{4}}=

4

3

6

5

=\frac{5\times 4}{6\times 3}=

6×3

5×4

=\frac{10}{9}=

9

10

=1\frac{1}{9}=1

9

1

Therefore, Option 3 is correct.

Cinnamon does the spice mix contain per pound is =1\frac{1}{9}=1

9

1

cup.

Answer:

it would be the second one

Step-by-step explanation:

The \($n^{th}$\) term of the given sequence is \($$a_n = (-1)^{n+1} \frac{n}{n+4}$$\)

The given sequence is  

\($$-\frac{1}{5}, \frac{2}{6}, -\frac{3}{7}, \frac{4}{8}, \dots$$\)

The problem is to find the first 5 terms and the \($n^{th}$\) term of the given sequence.

Step-by-step explanation: The given sequence is

\($$-\frac{1}{5}, \frac{2}{6}, -\frac{3}{7}, \frac{4}{8}, \dots$$\)

To find the first 5 terms of the given sequence, we will plug in the values of n one by one.

We have the sequence formula,

\($$a_n = (-1)^{n+1} \frac{n}{n+4}$$\)

When n = 1,

\($$a_1 = (-1)^{1+1} \frac{1}{1+4} = -\frac{1}{5}$$\)

When n = 2,

\($$a_2 = (-1)^{2+1} \frac{2}{2+4} = \frac{2}{6} = \frac{1}{3}$$\)

When n = 3,

\($$a_3 = (-1)^{3+1} \frac{3}{3+4} = -\frac{3}{7}$$\)

When n = 4,

\($$a_4 = (-1)^{4+1} \frac{4}{4+4} = \frac{4}{8} = \frac{1}{2}$$\)

When n = 5,

\($$a_5 = (-1)^{5+1} \frac{5}{5+4} = -\frac{5}{9}$$\)

Thus, the first 5 terms of the given sequence are \($$-\frac{1}{5}, \frac{1}{3}, -\frac{3}{7}, \frac{1}{2}, -\frac{5}{9}$$\)

Now, to find the \($n^{th}$\) term of the given sequence, we will use the sequence formula.

\($$a_n = (-1)^{n+1} \frac{n}{n+4}$$\)

Thus, the \($n^{th}$\) term of the given sequence is \($$a_n = (-1)^{n+1} \frac{n}{n+4}$$\)

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With a greater mean value , we can conclude that the sixth period class test was better than the second period .

Second period class:

Mean = (55+70+6*75+6*80+2*85+3*90+95)/20

Mean = 1590/20 = 79.5

Sixth period class:

Mean = (65+3*75+5*80+6*85+3*90+2*95)/20

Mean = 1660/20 = 83

Therefore, From the mean values , we can infer that students performed better in test for the sixth period class than the second .

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To find the perimeter of a shape, you need to add up the measurements of all the sides to find it. I hope this helps. Let me know if you need some help with some perimeter problems :)

Answer:

262 pennies

Step-by-step explanation:

If Layla already has 388 pennies and she needs 600 pennies total, all she needs to do is is take the amount she already has away from 600:

Answer:

39.   An adult male Western Banded Gecko is 5 1/2 (or 5.5) inches long.

41.    13,000 feet long, because 1 4/9 of 9,000 is 13,000.

43.  to answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:

35/50 >= 3/4

that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:

35/50 >= 3/4

7/10 >= 3/4

now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:

7/10 >= 3/4

(2/2)(7/10) >= (5/5)(3/4)

2*7/2*10 >= 5*3/5*4

14/20 >= 15/20

we can see that the inequality does not hold, so,

35/50 >= 3/4

does not hold either, therefore the Constitution cannot be ammended

40.  10 students play chess and sudoku,

30*2/5 is 12, out of 12; the number of students that play chess,5/6 play sudoku.

So..12*5/6 is 10 and that is the number of students that play both sudoku and chess.

42. Four fifths of 7/8 will be less than 7/8 (because you've multiplied by a number less than 1).

Similarly, 7/8 of 4/5 will be less than 4/5.

This means that the product will be less than each of the original factors.  

answer: no

44.  The answer is 7/12 because 3/4 - 1/6= 7/12

3/4 converts to 9/12 and 1/6 converts to 2/12. The domanaters stay the same, but 9-2=7. that is how you get 7/12

Answer:

Value of a in term of x = 8/x

Step-by-step explanation:

Given:

14 = ax + 6

Find:

Value of a in term of x

Computation:

⇒ 14 = ax + 6

Step 1; Subtract 6 from both side

⇒ 14 - 6 = ax + 6 - 6

We get step 2

⇒ 8 = ax

Divide x from both side and we get step 3

⇒ 8 / x = ax / x

Step 4

⇒ 8/x = a

Step 5

⇒ a = 8/x

Value of a in term of x = 8/x

Coverage represents the percentage of the 10 intervals that cover the exact true population mean. This is because the Confidence Interval for a Mean is used to estimate the true population mean with a certain particular level of confidence.

The "cover" percentage in the app refers to the proportion of intervals that include the true population mean, while the "do not cover" percentage refers to the proportion of the intervals that do not include the true population mean.

Therefore, Coverage is a measure of how well the Confidence Interval for a Mean is able to capture the true population mean.

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If mXWZ = 25, the value of x is 5. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 15 from both sides:  mXWZ - 15 = 2x

Now, we can divide both sides by 2:

(mXWZ - 15) / 2 = x

However, we don't know the value of mXWZ, so we can't solve for x exactly. We can only simplify the expression by dividing both sides by 2:

x = (mXWZ - 15) / 2

If we are given a value for mXWZ, we can substitute it into the equation and solve for x. For example, if mXWZ = 25:

x = (25 - 15) / 2 = 5

Therefore, if mXWZ = 25, the value of x is 5. However, without knowing the value of mXWZ, we cannot determine the exact value of x. We can only express our answer in terms of mXWZ and simplify the expression.

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