does it pass through

Statement that 95% confidence interval states that 95% of the sample means of specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of population mean is false.

The 95% confidence interval is a range of values that is calculated from sample data and is used to estimate the true population parameter with a certain level of confidence. It provides an interval estimate for the population parameter, such as the population mean.

The value of 1.96 corresponds to the critical value for a 95% confidence interval when the underlying distribution is approximately normal. It is used to determine the margin of error in estimating the population mean. However, it is incorrect to state that 95% of the sample means will fall within plus and minus 1.96 standard deviations of the population mean. The confidence interval provides an estimate of the likely range of the population parameter, not the distribution of sample means.

In reality, the actual proportion of sample means falling within the confidence interval depends on various factors such as the sample size, the population distribution, and the variability of the data.    

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Answer:

the answer is A

Step-by-step explanation:

About 50% of the respondents were at or between 40 and 67.5 years old.

The tree diagram that list all the possible outcomes with their respective probabilities is given below.

It should be noted that to solve this problem, we can use a tree diagram to represent all the possible outcomes at each step of the selection process. The tree diagram below shows the possible outcomes:

            /   B (6/10)            \   Y (4/10)

       B1 /                            \ Y1

         /                              \

    /   B (5/10)    \   Y (4/10)    /   B (6/10)    \   Y (3/10)

B2 /                  \ Y2         B2 /                  \ Y2

  /                    \           /                    \

 |   B (4/10)   \   Y (4/10)  |   B (5/10)   \   Y (3/10)

B3|                  Y3         |                  Y3

 |                     |       |                     |

  \   B (3/10)   /   Y (4/10)  \   B (4/10)   /   Y (3/10)

    \                  \      /                  \

       \                 \   /                     \

            \   B (2/10)   Y4                     B4 \   Y (2/10)

                 |                                      |

                 |                                      |

                  \   B (1/10)                          \   Y (1/10)

                         |                                     |

                         |                                     |

                          \                                    \

                              B5                                    Y5

The branches in the tree diagram represent the possible outcomes at each selection, and the probabilities are shown next to each branch.

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Answer:

3

Step-by-step explanation:

7.2 ÷ 2.4 = 3

Answer:

height:6

if the base is a square that means all the side lengths are equivalent so it would be 8 for side lengths, and the volume is 128. plug it in with the formula to get 6

The height of a pyramid is 8cm

Supposing that:

The length of the sides of the square base the pyramid has = b units

The height of the considered square based pyramid = h units,

Then, its volume is given by: \(V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3\)

Given;

The volume of pyramid= 128cm3

Length of side of square base= 8cm

Now,

128=1/3 x 8x8xh

128= 64/3 xh

h= 128x3/64

h=8

Therefore, the height with the volume 128cm3 will be 8cm

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Answer:

y is 7, x is 14

Step-by-step explanation:

This is a 30-60-90 triangle,

The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,

The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle

So y is

\( \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y\)

Then, that means x is

\(7 \times 2 = 14\)

Answer:

Step-by-step explanation:

Comment

If two secants intersect outside a circle (as these two do) then the angle at which they meet is 1/2 the difference between the intersected arcs. Put much simpler <DCF = 1/2 (arc EG - arc DF)

Givens

Arc EG = 127

Arc DF = 49

Solution

<DCF = 1/2(127 - 49)

<DCF = 1/2(78)

<DCF = 39

The probability that the cube never lands on 3 is 23.25%

Given

Number cube

Toss = 8

First we need to get the probability of landing on 3 in a single toss;

n(3) =

n total = 6

p(3) = \(\frac{1}{6}\)

First we need to get the probability of not  landing on 3 in a single toss;

Opposite probability = 1;

So: P(3) + P(3)' = 1

hence P(3)'=\(\frac{5}{6}\)

for 8 times

\(P(3)' = (\frac{5}{6})^8 \\\) = 0.2352

The probability that the cube never lands on 3 is 23.25%

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Answer:

(y-4) = 2(X+1)

Step-by-step explanation:

The given eqaution is; y = 2x-5.......(i)

Now; the equation is in the form of y= mx+b.

Slope(m1) = 2.

As per the condition of parallel lines, the slope of the 1st equation (m1) = the slope of the 2nd equation (m2).

Therefore, m1= m2= 2

Now, use one point formula for finding the equation of the line which passes through the point.

(y-y1) = m2(x-x1)

~ Put all values.

(y-4) = 2(X+1)

You can simply write up here. But if you want to make it simplified form then, (look below)

~ simplify it.

y = 2x +2+4

The eqaution of the line which is parallel to y = 2x -5 and point (-1,4) is y = 2x + 6.

Answer:

the second table on the bottom

Step-by-step explanation:

To be a function the points have to pass the horizontal line test.

When you plot the graph of a function, then draw a horizontal line across the graph. If the horizontal line touches the graph only once, then the function does have an inverse function.

Answer: your answer is in the pic

Step-by-step explanation:

Answer:

Step-by-step explanation:

Diameter= 22.9

Answer:

(-3,4)

Step-by-step explanation:

the point is on -3 on the x-axis and 4 on the y-axis

Answer:(-3,4)

Step-by-step explanation:took the test and got right

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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If the population standard deviation of a sample decreases without other changes, then the confidence interval will also decrease or become narrower.

If the population standard deviation of a sample decreases without other changes, the standard deviation of the sample mean (known as the standard error of the mean) will also decrease. This will lead to a decrease in the width of the confidence interval, meaning that the interval will become more precise and the confidence level in the estimation of the population mean will increase.

A smaller standard deviation results in a smaller standard error, which in turn leads to a narrower confidence interval and a higher level of confidence in the estimation of the population mean.

This is because the confidence interval is calculated using the standard error and the sample mean, and the standard error is a measure of the variability in the sample mean. So, if the standard deviation decreases, the variability in the sample mean will decrease, resulting in a more precise estimation of the population mean.

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The approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6

To find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches, we will first calculate the surface area (SA) and volume (V) of the ball, and then divide the surface area by the volume.

Step 1: Calculate the surface area (SA) using the formula for the surface area of a sphere:

\(SA = 4 πr^2\)
\(SA = 4 π5^2\)
\(SA = 4 π(25)\)
\(SA=100π\)

Step 2: Calculate the volume (V) using the formula for the volume of a sphere:

\(V = \frac{4}{3} π (r)^{3}\)
\(V = \frac{4}{3} π (5)^{3}\)
\(V = \frac{4}{3} π (125)\)
V = 166.67 π cubic inches

Step 3: Calculate the surface-area-to-volume ratio (SA/V)
\(\frac{SA}{V} = \frac{100}{166.67}\)
\(\frac{SA}{V}=\frac{100}{166.67}\)

\(\frac{SA}{V}= 0.6\)

So the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6. The best answer from the choices provided is A.

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Answer:

P=0.5

Step-by-step explanation:

Attached photo

...

tep-by-step explanation:

Answer:

B

Step-by-step explanation:

This is a neat question

f(x) - g(x) = 2x           Add g(x) to both sides

f(x) = g(x) + 2x

Now you need the right hand side to have 20 added to g(x).

2x must = 20

2x = 20                    Divide by 2

x = 20/2

x = 10

So the answer must be x = 10

The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.

It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.

After that, it's vital to move the compasses to where the upper arc crosses the transverse.

In conclusion, the correct option is C.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

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The interquartile range is the same for the eighth grade and the seventh grade.

From the box plot - I

Minimum= 15

Q1 = 20

Median = 25

Q3 =30

Maximum = 60

So, IQR = 30-20 = 10

From the box plot - II

Minimum= 20

Q1 = 30

Median = 35

Q3 = 40

Maximum = 90

So, IQR = 40-30= 10

Thus, The interquartile range is the same for the eighth grade and the seventh grade.

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The  grade would raise the grade to 58.76%.

To calculate the impact of a 50-point assignment on a 67.0% overall grade, we first need to know the weight of the assignment in the calculation of the overall grade. Let's assume that the assignment is worth 20% of the final grade for the class.

If the overall grade is 67.0%, then the weight of the remaining work in the calculation is 100% - 67.0% = 33.0%. Therefore, the current score for the final piece of work is:

(67.0% x 33.0%) = 22.11%

Adding the score for the 50-point assignment to this gives us the new score for the final piece of work:

22.11% + (50 / 100) x 20% = 32.11%

Since this is the score for the final piece of work, we can now calculate the new overall grade for the class using the updated weightings:

(67.0% x 80%) + (32.11% x 20%) = 58.76%

If the 50-point assignment is worth 20% of the final grade, adding it to a 67.0%.

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Answer:3.5

Step-by-step explanation:

If the eluent were above the 1.5 cm line on the chromatographic paper, it would be considered an unexpected observation.

Normally, during chromatography, the eluent is applied below the baseline or reference line on the paper.

If the eluent exceeds the expected limit and goes above the 1.5 cm line, it can have several implications:

Smearing or spreading: The excess eluent can cause the compounds being separated to spread out more than intended. This can lead to a loss of resolution and poor separation of the individual components.

Incomplete separation: The higher eluent level can disrupt the chromatographic process, resulting in incomplete separation of the compounds. This means that the different components may not be adequately resolved into distinct bands or spots.

Longer analysis time: With the eluent above the expected level, it may take longer for the eluent front to reach the desired distance, as it needs to travel a greater distance on the chromatographic paper. This can increase the overall analysis time and potentially affect the accuracy of the results.

Unreliable measurements: If the eluent exceeds the 1.5 cm line, it can make it challenging to accurately measure the migration distances of the separated compounds. This can introduce uncertainty or errors in the calculations or interpretations of the chromatogram.

In summary, if the eluent is observed above the 1.5 cm line on the chromatographic paper, it is an unexpected observation that can lead to compromised separation, longer analysis times, and potential difficulties in accurate measurements and interpretations of the chromatogram.

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Step-by-step explanation:

 f(x) = 11 - x is the same graph as:..... x + y = 11

The required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

Given that,

The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r².

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
                                  = 1  , 3
Radius of the circle,
\(r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25\)

Equation of the circle with center (1, 3)
\(r^2 = (x - 1)^2 + (y-3)^2\)
\(25 = (x - 1)^2 + (y-3)^2\)

Thus, the required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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Answer:

for question two: 12

for question four: 1/3

for question six: 25.75 (rounded to two decimal places)