consider a trial in which a jury must decide between the hypothesis that the defendant is guilty and the hypothesis that the defendant is innocent. in the framework of hypothesis testing and the u.s. legal system, which of the hypotheses should be the null hypothesis?

Answer:

Below

Step-by-step explanation:

You didn't include the picture......

each cube has a volume of  1/4 * 1/4 * 1/4 = 1/64 cm^3

     count the total number of cubes and multiply by  1/64

                                         to get volume in cm^3

Answer:

2.5a - 1.5 b or

5/2a - 3/2b

Step-by-step explanation:

a + (a - b) + 0.5(a - b) =

a + a - b + 0.5a - 0.5b =

2a - b + 0.5a - 0.5b =

2a - 1.5 b + 0.5a  =

2.5a - 1.5 b

The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Sodium contains in a can of soup is 300mg

Sodium contains in a can of frozen dinners is 450mg

Let the number of cans of soup purchased be x

Then, the number of frozen dinners purchased=x+5

Total sodium purchased=6000mg

So, 300x+450(x+5)=6000mg

Therefore, the system is 300x+450(x+5)=6000mg

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The monthly payment amount a woman has to pay for the car is $462.91.

Here we have to find the monthly payment amount.

The cost of car = $23,800

Down payment = $3,500

Rate(r) = 4.5%

time(t) = 4 years

Periodic interest(i) = 0.045/12

Formula to calculate monthly payment:

A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1

Loan amount = 23800 - 3500

                      = $ 20300

A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1

  = 20300× 0.004488 / 0.196814

  = 462.91

Therefore the monthly payment is $462.91.

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a regression equation for this formula, where x represents the number of years enrolled and y represents the tuition.

y = 34000 - 2300x

Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.

The regression equation for this formula would be:

Y = 34,000 - 2,300x

where Y is the tuition cost and x is the number of years in school.

The equation states that the tuition cost for any year in school (x) is equal to the freshman year tuition cost (34,000) minus 2,300 multiplied by the number of years in school (x).For example, if x = 4 (4 years in school), then the tuition cost for that year would be 34,000 - 2,300(4) = 25,400.

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The volume of foam needed for the 45 cones is

v = 16,956 cm³

We know that the volume of a cone of diameter F and height H is:

V = pi*(D/2)²*H/3

Where pi = 3.14

Here we know that:

D = 12cm

H = 10cm

And we want to find the volume of 45 of these cones, so the total volume of foam needed is:

v = 45*V = 45*(3.14*(12cm/2)²*10cm/3

v = 16,956 cm³

That is the volume of foam needed.

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Answer: 5^2

Step-by-step explanation:

5 x 5 = 25

and (x-7)^2 = 25

The value of n when the function g(n) assumes a value of 3 is of:

n = 10.

In the case of an inverse proportional relationship, as is the case in this problem, the output variable y is obtained as the division of the constant of proportionality k by the input variable x, as follows:

y = k/x.

Considering the variables in this problem, the equation is given as follows:

g(n) = k/n.

g(n)= 10 when n=3, hence the constant is obtained as follows:

10 = k/3

k = 3 x 10

k = 30.

Hence the equation is:

g(n) = 30/n.

When the input variable n when g(n) = 3 is obtained as follows:

3 = 30/n

3n = 30

n = 30/3

n = 10.

(we replaced the output variable g(n) by it's value and solved for the input variable)

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The probability that the sum of the faces is 7 = 15/216

The value of m = 15 and the value of n = 216

In this question, we have been given three regular dice are rolled simultaneously.

We need to find the probability that the sum of the faces is 7.

When three dice are rolled simultaneously, the total number of outcomes

n(S) = 6 * 6 * 6

n(S) = 216

Let event A: sum of the faces is 7

A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}

n(A) = 15

So, the probability that the sum of the faces is 7 = 15/216

Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216

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Part (d) is correct.

i.e. The variance of the random variable associated with this given experiment is 2.4510.

What is Binomial experiment?

It is an experiment with a set number of independent trials, each having the same chance of success and the two outcomes of success or failure. A binominal distribution can be used to describe the likelihood of a certain number of successes.

Given that,

No. of independent trials ( n ) = 10

Probability of success in each trail ( p ) = 0.43

∴ probability of failure in each trial ( q ) = 0.57

we can find the variance of a binomial experiment by using the formula i.e. npq.

∴ Variance = npq

                  = 10 × 0.43 × 0.57

                  = 2.4510.

Hence, part (d) matches with the answer.

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Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.

Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Given that: In ΔCDE

m/∠C = (x-4)°

m/∠D = (9x + 4)°

m/∠E = (2x + 12)°

Now, to find m/∠D

So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.

Putting the sum of all three equal to 180⁰:

∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°

= 180⁰12x +12

= 180⁰x +1 = 15⁰

x = 14⁰

Thus, Putting value of x in m/∠D = (9x + 4)°.

m/∠D = (9 × 14 +4)⁰

m/∠D = 130⁰

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The complete question is as follows:

In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.

when the charged rod is brought closer to the sphere negative charges get induced on the sphere by gathering some electrons from the ground and the negative  remain on the sphere even after disconnecting it.

here the ground acts as a reservoir of electrons.a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere.

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The rounded upper level of the 68% confidence interval estimate is

164.5 ± 3.260.

Given:

a cheese merchant looks a again at the data set about total cheese of sales, in which the sample mean is 164.5 and the sample of standard deviation is 103.

μ = x =164.5

σ = s = 103

n = 987

z score at 68 % :

= 0.9945

Confidence interval CI = x + z * s/[tex]\sqrt{n}[/tex]

= 164.5 + 0.9945 * 103 / √987

= 164.5 ± 3.260

Therefore The rounded upper level of the 68% confidence interval estimate is  164.5 ± 3.260.

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[tex] \Large{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

The distance between two points is given by the following formula:

[tex] \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} [/tex]

Where:

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) [/tex]

[tex] \\ [/tex]

Now, substitute these values into our formula:

[tex] \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

Step-by-step explanation:

11.

The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are (3, 4) and (-1, -4). Then the equation of the line is given as,

(y + 4) = [(4 + 4) / (3 + 1)](x + 1)

y + 4 = 2(x + 1)

y = 2x + 2 - 2

y = 2x - 2

The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

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The margin of error for a sampling distribution is found as 3.34.

Margin of error = z × σ/√n

Thus, put the values;

z-score for 93% confidence level = 1.67

Margin of error = 1.67 ×12/√36

Margin of error = 3.34

Thus, the margin of error for a sampling distribution is found as 3.34.

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A statement which is true about the graphs of f(x) = x and g(x) = f(x + 7) is: C. g(x) is the graph of f(x) translated 7 units to the left.

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Geometry, g(x + 7) or g(x) = f(x + 7) simply means shifting a graph 7 units to the left as illustrated by the graph shown in the image attached below.

In this context, we can reasonably infer and logically deduce that the parent function f(x) = x was shifted by 7 units to the left.

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Complete Question:

Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?

A. g(x) is the graph of f(x) translated 7 units down.

B g(x) and f(x) have the same y-intercept.

C g(x) is the graph of f(x) translated 7 units to the left.

D g(x) is the graph of f(x) translated 7 units to the right.

The converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

A polygon has precisely three sides if it is a triangle. The opposite is also accurate.

Contrarily, a polygon is a triangle if it has precisely three sides. Both of the statements can be joined to create a biconditional because they are both true.

Thus, the converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

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After using the test statistic z, P(3.6<X<53.5) = 0.967.

In the given question, suppose X is a normal random variable with mean 35 and sdev 10.

We have to find P(3.6<X<53.5).

Fro the given question,

Mean x = 35

sdev s = 10

Z = X - mu / sd

P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )

P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )

P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )

P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)

left tail of both

P(3.6<X<53.5) = 0.9678 - 0.0008

P(3.6<X<53.5) = 0.967

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The right answer is:

Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)

Answer:

Step-by-step explanation:

B because that is the letter of my first name!

If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.

What is short-term memory?

Short-term memory is a concept in psychology that defines the capacity for holding a small amount of information in mind for a short interval. The concept of short-term memory is given by Atkinson-Shiffrin. The information of short-term memory can be transformed into long-term memory through rehearsal.

According to several studies, short-term memory has a space limit of 7 ± 2 chunks of information. The fact is written by a cognitive psychologist of Harvard University named George A. Miller and was published in 1956 in psychological reviews.

Hence, If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.

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The slope of the straight line is 4/5

The slope of a line is a measure of the ratio between the rise and run of that line. The slope of a line is an integral quantity used to calculate the equation of a line

In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

The slope of a line basically the change in y-coordinate with respect to change in x-coordinate.

This is easily done with a formula given as

m = y₂ - y₁ / x₂ - x₁

Taking data points from the graph attached;

Substituting the values into the slope equation;

m = -2 - 2 / 0 - 5

m = -4 / - 5

m = 4/5

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After solving, the value of Test statistic z is 1.449.

In the given question,

A sample of 1700 computer chips revealed that 36% of the chips fail in the first 1000 hours of their use.

The company's promotional literature states that 39% of the chips fail in the first 1000 hours of their use.

Then we have to find the value of z statistic.

Hypothesized proportion (p) = 36%=0.36

Sample proportion (p') = 39% = 0.39

Sample size (n) = 1700

Hence,

Test statistic z

z= (0.76-0.78)/√(0.78* 0.22/900)

z= (-0.02)/√(0.78* 0.000244)

z= -0.02/√0.00019032

z= -0.02/0.0138

z = -1.449

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Answer:

1

Step-by-step explanation:

The equation to represent this would be (1 - (1 / 3)) / 2

1 - (1 / 3) = 2 / 3

2 / 3 / 2 = 1 / 3

Unlike fraction 1/7 is converted to equivalent  like fraction 2/14 and the sum of 2/14 + 3/14 = 5/14.

As given in the question,

Given fraction is equal to:

1/7=? + 3/14=?

Here there are two fractions

1/7 and 3/14

LCD( least common denominator) of 7 and 14 is equal to 14.

Now make them like fractions

1/7 is equivalent to

( 1/7) × ( 2/2) = 2/ 14

Now 2/14 and 3/14 are like fractions

Sum of like fractions is:

2/14 + 3/14

= ( 2+ 3) / 14

= 5/ 14

Therefore, the conversion of unlike fraction 1/7 to like fraction is 2/14. And sum of 2/14 + 3/14 = 5/14.

The complete question is:

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum. 1/7=? + 3/14=?

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4.84 HP is the amount of work energy used.

Given info,

A helicopter is lifting an 800-pound unit at a rate of 200 feet per minute.

1 horsepower = 550 foot-pounds per second

⇒ 800 x 200 = 160,000 foot-pounds per minute

                      = 160,000/60 foot pounds per second.

Horsepower = 160,000/60 * 550 = 428/33

                                                       = 4.848 HP

Therefore, the horsepower of work energy used is 4.84 HP

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The wire should be anchored to the ground to minimize the amount of wire needed 20 ft from the left pole.

What is the quadratic equation?

ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x.

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _{l} = 20^{2} + x^{2} = x^{2} + 400[/tex]

Similarly for the 2nd part of the wire

[tex]L^{2} _{t} = 10^{2} + (30 - x^{2})[/tex]

= 100 + 900 - 60x + x²

= x²+ 1000 - 60x

We want to minimize the length of the wires, or [tex]L^{2} _{l} + L^{2} _{r}[/tex]

[tex]\frac{x}{\sqrt{{x}^2 + 400} } + \frac{x - 30}{\sqrt{{x}^2 + 400}} = 0[/tex]

we can take the first derivative of this and set it to 0

x = 20

Hence, the wire should be anchored to the ground to minimize the amount of wire needed  20ft.

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The height of tree in meter is 11.5 meter after the conversion from 37.95 feet to meter.

A conversion factor is measurement value in numbers that is used in converting one unit to another unit by arithmetic operations.  

Given that a tree is 37.95 feet tall and 1 meter is 3.3 feet.

So to find 37.95 feet tree in meter we have to divide 37.95 by 3.3  

= 37.95 / 3.3

= 11.5 meter

1 meter is 3.3 feet, then 11.5 meter is 37.95 feet.

Therefore, the height of tree in meter is 11.5 meter.

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