A math exam has 45 multiple choice questions, each with choices a to e. One student did not study and must guess on each question 20. What are the mean and variance of this binomial distribution? 22. Estimate the probability that the student fails the exam i.e. gets 22 or fewer questions 23. gets five or more questions correct 24. gets between 9 and 18 questions (both inclusively) correct

According to the given statement the values are:

The range = 19

Interquartile Range will be = 8.25

Sample Variance =33.93

Sample Standard deviation = 5.82

The dispersion of your data's middle quartile is measured by the interquartile range (IQR). It is the range for your sample's middle 50%. Assess geographical variability where the majority of your numbers are by using the IQR. Larger numbers suggest a wider dispersion of your data's center region.

According to the given data:

finding the range =  Maximum value + Minimum value

                            = 34 - 15

                            = 19

The range = 19When ordering the observations, we obtain:

15,20,24,26,26,27,30,34

Where ,

n = 8

Q1=(n+14)the observation's term value

=(94)the observation's term value

=(2.25)the observation's term value

=2nd observation +0.25[3rd-2nd]

=20+0.25[24-20]

=20+0.25(4)

=20+1

=21

Q3=(3(n+1)4)the observation's term value

=(3⋅94)the observation's term value

=(6.75)the observation's term value

=6th observation +0.75[7th-6th]

=27+0.75[30-27]

=27+0.75(3)

=27+2.25

=29.25

Now finding the Interquartile Range

= Q3 -Q1

= 29.25 - 21

=8.25

The  Interquartile Range will be = 8.25

Sample Variance S2=∑x2-(∑x)2nn-1

=5338-(202)28/7

=5338-5100.5/7

=237.57

=33.9286

Sample Variance =33.93

S=√∑x2-(∑x)2nn-1

=√5338-(202)28/7

=√5338-5100.5/7

=√237.5/7

=√33.9286

=5.8248

Sample Standard deviation = 5.82

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Yes, there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be a = 5,184p.

It should be noted that the information is to simply know if there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be:

= Number of pixels / Screen size

= 31.104 / 6

= 5.184

Therefore, the equation representing the relationship will be a = 5,184p.

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Answer:

1. 9/10

2. 15/16

4. 3/5

5. 3/5

Step-by-step explanation:

1. 7/10 + 2/10 = 9/10

2. 13/16 + 2/16 = 15/16

4. 7/15 + 2/15 = 9/15 = 3/5

5. 9/20 + 3/20 = 12/20 = 3/5

Answer: 1 r1 for second

Step-by-step explanation: 13/16+2/16=15/16 divide 15/16 gets 1 r1

angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer: y = 4

Step-by-step explanation:

y - 4 = -2(x + 3)

(-3, ? )

y - 4 = -2(- 3 + 3)

y - 4 = -2 · 0

y - 4 = 0

y - 4 + 4 = 0 + 4

y = 4

(-3, 4)

Answer:

what subject is this?

Step-by-step explanation:

sorry im still grade 3

The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.

The equation that shows the relationship between the angles in the triangle is determined as follows;

The sum of angles in a triangle is equal to 180 degrees.

So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;

angle 1 + angle 2 + angle 3 = 180

We can re-write the equation as follows;

m∠1 + m∠2 + m∠3 = 180

Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.

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The radius of the cylindrical shaped soup can is r = 3.3 cm

Given data ,

A company is designing a soup can that is in the shape of a right circular cylinder. The height of the can will be 3 times the radius of the can. The volume of the can will be 350 cubic centimeters

Now , Volume of Cylinder = πr²h

where h = 3r

On simplifying , we get

350 = πr²3r

350 = 3πr³

Divide by 3π on both sides , we get

r³ = 37.13615

Taking cube root on both sides , we get

r = 3.3 cm

Hence , the radius of soup can is r = 3.3 cm

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The ultimate purpose of constructing a standard curve is to use it to calculate the concentration of a substance in solution.

What is a standard curve?

A standard curve is a graphical representation of a mathematical function that relates the concentration of a solution to the amount of light that passes through it. The majority of standard curves have a linear relationship between the dependent and independent variables. These curves are particularly useful for chemical tests that require the use of an instrument, such as a spectrophotometer.

A standard curve is created by generating a series of known concentrations of a specific compound in a solution. The absorption values are measured, and the data are then plotted on a graph. The resulting data points can then be utilized to create a standard curve, which can be used to identify the concentration of unknown samples.

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Answer:

21 pencils for Nick and 63 pencils for Lance

Step-by-step explanation:

Now let's make an equation out of the information above:

3x + x = 84

Now solve for x.

3x + x = 84

4x = 84

x = 84/4

x = 21

So Nick has 21 pencils

Now for Lance:

3x

3 * (21) = 63

So Lance has 63 pencils

63 + 21 = 84 pencils

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

B) -17

Step-by-step explanation:

46+(-85)+22

68+(-85)

68-85

-17

Answer:

20°

Step-by-step explanation:

4x + 5x = 180° ( being co-interior angles)

9x = 180°

x = 180°/ 9

x = 20°

Hope it will help :)

A parameter can change for a set population when there is a change in the population distribution or when the population is no longer considered "set". A parameter is a fixed numerical characteristic of a population that is measured by a statistic.

When there is a change in the distribution of a population, the parameter that describes the population will change. For example, the mean of a population will change if there is a shift in the distribution of scores. Similarly, the standard deviation will change if there is a change in the variability of scores.

A parameter can also change if the population is no longer considered "set". For example, if a population is defined as all the residents of a particular city, the parameter will change if people move in or out of the city. In this case, the parameter can be thought of as a snapshot of the population at a particular point in time.

In conclusion, a parameter can change for a set population when there is a change in the population distribution or when the population is no longer considered "set".

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Answer:

A = 5808

P = 308

Step-by-step explanation:

Hope This Helps! :)

a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:

Distance between point A and C:

d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]

    = sqrt[(14 - 2)^2 + (9 - 4)^2]

    = sqrt[144 + 25]

    = sqrt(169)

    = 13

Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.

Distance between point B and C:

d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]

    = sqrt[(7 - 2)^2 + (16 - 4)^2]

    = sqrt[25 + 144]

    = sqrt(169)

    = 13

Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.

Therefore, points A and B are on the circle with center C(2, 4) and radius 13.

b) The midpoint of line segment AB can be found using the midpoint formula:

M = [(x_A + x_B)/2, (y_A + y_B)/2]

 = [(14 + 7)/2, (9 + 16)/2]

 = [10.5, 12.5]

The slope of line segment AB can be found using the slope formula:

m_AB = (y_B - y_A)/(x_B - x_A)

    = (16 - 9)/(7 - 14)

    = -7/-7

    = 1

The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:

m_CM = -1/m_AB

    = -1/1

    = -1

The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:

y - y_C = m_CM(x - x_C)

y - 4 = -1(x - 2)

y = -x + 6

The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.

Hence, we have shown that line segment CM is perpendicular to line segment AB.

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Answer:

I think it's 50

Step-by-step explanation:

48

49

50

51

52

50 8s inbetween the two

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer:

The median/middle is 5 and the minimum is 0 and the maximum is 11. The first quartile is 7/5= 1.4 and the second is 4/2 = 2

Step-by-step explanation:

The five number summary for the data set 0,2,2,4,5,5,5,5,7,11 is as minimum value is 0, maximum value is 11, median is 5, first quartile is 2 and second quartile is 5.

The five number summary for the data set provides the basic information of a data set. This consist of minimum value, maximum value, median, first quartile, and second quartile.

The provided data set is,

0,2,2,4,5,5,5,5,7,11

The data is arranged in the increasing order. The minimum value in this number is 0 while the maximum number is 11.

As the middle value of the data is 5. Thus, the median of this number is,

\(m=5\)

The first quartile is the median in the lower half of the data. In this data lower half consist 0,2,2,4,5 which has the median or first quartile as,

\(Q_1=2\)

Similarly, the second quartile is,

\(Q_1=5\)

Thus, the five number summary for the data set 0,2,2,4,5,5,5,5,7,11 is as minimum value is 0, maximum value is 11, median is 5, first quartile is 2 and second quartile is 5.

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Answer:

For y=x-3. (0,2) the equation is y=x+2

For y=3-x. (0,2) the equation is y=2-x

For y=3x+1. (0,3) the equation is y=3x+3

For y=-1/2x+4. (0,1) the equation is y=-1/2x+1

Step-by-step explanation:

How I got my answers:

For y=x-3: the gradient is 1 because we do not have anything before x.

For the points given for example (0,2) x is zero  and y-intercept is 2. same for the rest of the points.

Now you can write your equation in the form y=mx+b

where m is your gradient, and b is the y point. So you say y=1x+2 for the first one. Do the same for the rest. Remember 1x is the same as x so you can leave out 1.

You can comment if you did not understand my explanation because this explained how you can do it.

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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Answer:

6.7+1.2=7.9

Step-by-step explanation:

6+1=7

0.7+0.2=0.9

so 7+0.9=7.9

so u have to break the numbers as tens and units

Answer: the rate unit is 1/3

Step-by-step explanation:

What I used was a up right techniqu so you go up 1 and to the right 3 times

The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

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

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

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

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

\(M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\\)

Therefore, Haley should sample 12,724 soldiers.

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