HELP!!! use the law of sines! ​

(a) The Null And Alternate hypothesis are stated below,

(b) The value of test-statistic is 3,

(c) The "p-value" is 0.0013,

(d) The hypothesis is rejected because p-value is less than 0.025.

Part (a) : The appropriate null and alternative hypotheses are:

Null hypothesis (H₀): The average LSAT score at the University of Pennsylvania is equal to or less than the national average of 1,300.

Alternative hypothesis (Hₐ): The average LSAT score at the University of Pennsylvania is significantly higher than the national average of 1,300.

Part (b) : To calculate the test-statistic, we use formula : t = (x' - μ)/(s / √n),

where x' = sample mean, μ = hypothesized population mean, s = sample standard deviation, and n = sample size.

Substituting the given values,

We get,

t = (1375 - 1300)/(125 / √25) = 3;

So, the value of the test statistic is 3.

Part (c) : To calculate "p-value", we need to find the probability of getting a t-value as extreme or more extreme than 3, assuming that the null hypothesis is true.

We know that for a two-tailed test at a significance level of 0.03, the p-value is approximately 0.0013.

Part (d) : To test the hypotheses using the p-value, we compare it to the significance-level.

Since the p-value is less than 0.025 (half of the significance level for a two-tailed test), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

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The given question is incomplete, the complete question is

The admissions officer for the graduate programs at the university of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300. an accepted standard deviation for LSAT scores is 125. random sample of 25 scores had an average of 1,375.

(a) State the appropriate null and alternative hypotheses.

(b) Calculate the value of the test statistic

(c) Calculate the p-value.

(d) Use the p-value to test the hypotheses and conduct the test at the 0.025 level.

All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

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The labeled part that best matches each term or phrase as:

Radii of concentric circles: Segment AC, Segment BD, Segment EF

Congruent circles: Circle A and Circle B

Internally tangent circles: Circle A and Circle C

Externally tangent circles: Circle B and Circle C

In geometry, a circle is a closed two-dimensional figure that consists of all the points that are equidistant from a fixed point called the center. The distance between the center and any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. Circles are used in many fields of study, including mathematics, physics, engineering, and art. They are important in geometry, trigonometry, calculus, and other areas of mathematics, and are used to model a wide range of real-world phenomena, such as the orbits of planets, the shape of wheels, and the curvature of lenses.

Here,

Radii of concentric circles: C and D (any radii of the circles can be considered as radii of concentric circles)

Congruent circles: A and B (circles that have the same radius are congruent)

Internally tangent circles: A and C (circles that touch or intersect at a point within both circles are internally tangent)

Externally tangent circles: B and D (circles that touch or intersect at a point outside both circles are externally tangent)

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The parameterized plane that contains the three points is r(s,t) = (1,−2,−5) + s(−11,−4,−7) + t(14,22,15).

To parameterize the plane that contains the three points (1,−2,−5), (−10,−6,−12), and (15,20,10), we can use a vector equation.

We can choose any of the given points as r. Let's choose (1,−2,−5) as our r

r = (1,−2,−5).

To find v, we need to subtract r from any two points on the plane. Let's choose (−10,−6,−12) and (15,20,10) as our points.

⃗v = (−10,−6,−12) - (1,−2,−5) = (−11,−4,−7).

Similarly, we can subtract r from another pair of points. Let's choose (−10,−6,−12) and (15,20,10) again.

⃗w = (15,20,10) - (1,−2,−5) = (14,22,15).

Now we have all the necessary components to parameterize the plane.

r(s,t) = (1,−2,−5) + s(−11,−4,−7) + t(14,22,15).

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Answer:

The decimal of 17/6=2.8333333333

Answer:

17/6 = 2.83333333 or 2.80 rounded down

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

$4.80 divided by 12 = 0.4

Answer:

2.50 per ounce

Step-by-step explanation:

divide 12 by 4.80

Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

If you mean x = 0.666…, then

10x = 6.666…

10x - x = 6.666… - 0.666…

9x = 6

x = 6/9 = 2/3

If you mean x = 0.060606…, then

100x = 6.060606…

100x - x = 6.060606… - 0.060606…

99x = 6

x = 6/99 = 2/33

Step-by-step explanation:

Pam and Erin want the gardens to be proportional.

proprtional- equal

Pams garden has a length of 16 and width of 12. To find the area of Pam's garden multiply the length by the width.

16×12= 192

Now that we know the area of Pam's garden, we can set up and equation for Erin's garden. Since they have to be equal we know that Erin's garden should equal 192. Thus we solve for the length by dividing the width from the total.

192÷21=9.14

ANSWER:

The option C

STEP-BY-STEP EXPLANATION:

We can calculate the equation that represents the situation as follows:

let r, right shoe

let l, left shoes

The statment is 3l = 15, the option C

The present ages of the father and son are 36 and 9, respectively.

The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. To find the present ages of the father and son, we can set up a system of equations.

Let's denote the present ages of the father as "F" and the present age of the son as "S".

From the information given, we have two equations:

Equation 1: F + S = 45 (The sum of their ages is 45)
Equation 2: (F - 5)(S - 5) = 4(F - 5) (Five years ago, the product of their ages was four times the father's age at that time)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:

From Equation 1, we can express F in terms of S: F = 45 - S

Now, substitute F in Equation 2 with 45 - S:

(45 - S - 5)(S - 5) = 4(45 - S - 5)

Simplify the equation:

(40 - S)(S - 5) = 4(40 - S)

Expand and simplify:

40S - 5S - 200 + 25 = 160 - 4S

Combine like terms:

35S - 175 = 160 - 4S

Add 4S to both sides:

35S + 4S - 175 = 160

Combine like terms:

39S - 175 = 160

Add 175 to both sides:

39S = 335

Divide both sides by 39:

S = 335/39

Simplify:

S ≈ 8.59

Since age cannot be in decimal places, we can approximate the son's age to the nearest whole number:

S ≈ 9

Now, substitute S = 9 into Equation 1 to find the father's age:

F + 9 = 45

Subtract 9 from both sides:

F = 45 - 9

F = 36

Therefore, the present ages of the father and son are 36 and 9, respectively.

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Angie would take 75 minutes to mow the lawn by herself.

To find out how long will Angie take to mow the lawn:

Let's take Angie's time as x.

Now, multiply by 50x to obtain:

Therefore, Angie would take 75 minutes to mow the lawn by herself.

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For every product sold, the employee's earnings increase by $225.

Option C is the correct answer.

We have,

The expression for the amount of money an employee earns monthly after selling n products is given as:

$1,500 + $225n.

Here,

$1,500 is the fixed monthly earning, and $225n represents the earning from selling n products.

Thus,

For every product sold, the earning increases by $225.

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Answer:

The answer is 1788 as it is imputed in the photo

Taylor will end up paying $2496 in interest over the 12-year period when compounded monthly.

To calculate the total amount Taylor will end up paying in interest, we need to find the difference between the total amount paid and the original loan amount.

The formula to calculate the total amount paid for a loan is given by:

Total Amount Paid = Monthly Payment × Total Number of Payments

In this case, the monthly payment is $59 and the total number of payments is 12 years * 12 months/year = 144 payments.

Total Amount Paid = $59 × 144 = $8496

Now, to find the amount paid in interest, subtract the original loan amount from the total amount paid:

Interest Paid = Total Amount Paid - Original Loan Amount

Interest Paid = $8496 - $6000 = $2496

Therefore, Taylor will end up paying $2496 in interest over the 12-year period.

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The equation which must be true about the diagram which represents the construction of a line parallel to AB, passing through point P is IJ = PQ.

The correct answer choice is option C.

IJ = PQ

corresponding angles are equal

Corresponding angles are angles which occupy the same position at each intersection where a straight line crosses two other straight lines.

Corresponding angles are equal when two lines are parallel.

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The joint probability mass function (PMF) for the random variables x and y can be represented in a table with rows and columns corresponding to the possible values of x and y, respectively.

In this case, x represents the number of heads on the first toss, and y represents the total number of heads over all three tosses. There are two possible outcomes for each coin toss: heads (H) or tails (T). Thus, there are 2^3 = 8 possible outcomes for three coin tosses, which can be listed as follows: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. For the first toss, there are two possible outcomes: H or T. Thus, x can take on the values x = 0 or x = 1, with probabilities P(x = 0) = 1/2 and P(x = 1) = 1/2.

For the total number of heads over all three tosses, there are four possible outcomes: 0, 1, 2, or 3 heads. The joint probabilities can be calculated by considering the possible outcomes for each value of x. For example, if x = 0 (i.e., the first toss is a tail), then y can only be 0 or 1, depending on the outcomes of the second and third tosses. The probabilities of these outcomes are P(x = 0, y = 0) = 1/8 and P(x = 0, y = 1) = 3/8. The joint probability mass function for x and y can be summarized in a table as follows:

y=0 y=1 y=2 y=3

x=0 1/8 3/8 3/8 1/8

x=1 1/8 3/8 3/8 1/8

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Answer:

  j(0, 2)

Step-by-step explanation:

You want to know the coordinates of point J in parallelogram GBJF, given G(-4, 1), B(-2, 3), F(-2, 0).

In a parallelogram, the diagonals bisect each other. This means their midpoints are the same.

  (G +J)/2 = (B +F)/2 = M

  G +J = B +F . . . . . . . . multiply by 2

  J = B +F -G

  J = (-2, 3) +(-2, 0) -(-4, 1)

  J = (-2-2+4, 3+0-1) = (0, 2)

The coordinates of point J are (0, 2).

<95141404393>

Answer:

the answer shoudl be OB 4

\((20341)_5\\\\=(2 \times 5^4 + 0 \times 5^3 + 3 \times 5^2 +4 \times 5^1 +1\times 5^0)_{10}\\\\=(2 \times 625+0+3 \times 25 +20 +1)_{10}\\\\=(1250+75+21)_{10}\\\\=(1346)_{10}\)

Answer: it’s C

Step-by-step explanation: ^

Answer:

the domain of f(x) is x > 0

Step-by-step explanation:

mark brainliest

Answer:

they are both parralel

Step-by-step explanation:

The rate of change of the x-component is given by dr/dt = 2t, where t represents the time in seconds.

The equation for the rate of change of the volume of the right circular cylinder with respect to time is given by dV/dt = π(2\(t^3\))(2\(t^2\) + 2t).

At a specific moment, the rate of change of the x-component can be determined by differentiating the equation for the radius with respect to time and evaluating it at that moment.

The volume V of a right circular cylinder is given by V = π\(r^2\)h, where r is the radius and h is the height.

In this case, the radius r is given by r = \(t^2\) and the height h is given by h = \(t^{(2/1)}\) = \(t^2\).

To find the rate of change of the volume with respect to time, we differentiate the volume equation with respect to time:

dV/dt = d(π\(r^2\)h)/dt

= π(2r)(dr/dt)h + π\(r^2\)(dh/dt)

= π(2\(t^2\))(2t)(\(t^2\)) + π(\(t^4\))(2t)

= π(4\(t^4\))(2\(t^2\) + 2t)

= 8π\(t^6\) + 8π\(t^5\).

Therefore, the equation for the rate of change of the volume with respect to time is dV/dt = 8π\(t^6\) + 8π\(t^5\).

To determine the rate at which the x-component is changing at a specific moment, we need to differentiate the equation for the radius r with respect to time and evaluate it at that moment.

The equation for the radius is r = \(t^2\).

Differentiating this equation with respect to time, we have:

dr/dt = 2t.

So, at the specific moment, the rate of change of the x-component is given by dr/dt = 2t, where t represents the time in seconds.

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The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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Answer:

1. 6

2. 9

3. 9

4. 6

5. 9

6. 6

Step-by-step explanation:

The answers are in the order listed on your assignment page.

Hope this helps :)

Answer:

{(3, 10), ( -2, 10), (5, 10), (10, 10)}

Step-by-step explanation:

From what I know about functions is that for each number there can only be one input meaning that a number can't be used for another number for example if there is a 3 and it has a number which is 7 it can't have another output in this case 3 has another output which is 22 and that can't happen, meaning that this isn't a function. The other 2 are the same there is a number that has more than one output. The only one that has one input for every output is the last answer choice. {(3, 10), ( -2, 10), (5, 10), (10, 10)} is the only one that shows a function. Because for every input/number there is exactly one output.

1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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