A student who obtained a percentile rank of 75 on an achievement test is best characterized as having

A) ranked 75th from the top in a group of 100 test takers
B) answered 75% of the test questions correctly
C) scored higher than 75% of the test takers
D) scored 75% higher than the average test taker
E) scored 75% of the highest score

The null and alternative hypotheses to describe the given  situation are;

Null Hypothesis; H₀: μ = 0.3

Alternative Hypothesis; Hₐ: μ < 0.3

Null and alternative hypotheses are basically parameters utilized in statistical hypothesis testing. The null hypothesis of a test is defined as one that is used to predict no effect or no relationship between variables. Meanwhile, the alternative hypothesis of a test is one that states the research prediction of an effect or relationship.

Now, we are told that the known mean weight is 0.3 lbs. However, after looking through an orchard, we see that the farmer believes that the apples might weigh less on average.

Thus, the hypotheses are defined as;

Null Hypothesis; H₀: μ = 0.3

Alternative Hypothesis; Hₐ: μ < 0.3

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To solve the triangle using the Law of Sines, we can use the following formula:

\(\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\)

Given that \(\(\angle A = 38^\circ\), \(\angle C = 73^\circ\), and \(b = 19\),\) we can substitute these values into the formula and solve for the remaining sides \(\(a\) and \(c\).\)

\(\(\frac{a}{\sin(38^\circ)} = \frac{19}{\sin(B)}\) (1)\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\sin(B)}\) (2)\)

From equation (1), we can solve for \(\(\sin(B)\):\)

\(\(\sin(B) = \frac{19}{a} \cdot \sin(38^\circ)\)\)

Substituting this value into equation (2), we can solve for \(\(c\):\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\frac{19}{a} \cdot \sin(38^\circ)}\)\)

Simplifying, we get:

\(\(c = a \cdot \frac{\sin(73^\circ)}{\sin(38^\circ)}\)\)

Now we have expressions for both \(\(a\) and \(c\).\)

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The probability of both events happening together is 2/18 or 1/9. To determine whether events A and B are independent, we need to first calculate their probabilities.

For event A, we can count the number of ways that the sum of the numbers showing is odd. There are 18 possible outcomes when two dice are rolled, and 9 of them result in an odd sum: (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), and (4,1). Therefore, the probability of event A is 9/18 or 1/2.

For event B, we can count the number of ways that the sum of the numbers showing is 9, 11, or 12. There are 18 possible outcomes when two dice are rolled, and 4 of them result in a sum of 9, 2 of them result in a sum of 11, and 1 results in a sum of 12: (3,6), (4,5), (5,4), (6,3), (5,6), (6,5), and (6,6). Therefore, the probability of event B is 7/18.

To determine whether events A and B are independent, we need to see if the probability of both events happening together is equal to the product of their individual probabilities.

If events A and B were independent, then the probability of both events happening together would be the probability of event A multiplied by the probability of event B:

P(A and B) = P(A) * P(B)

Substituting in the values we calculated above:

P(A and B) = (1/2) * (7/18) = 7/36

To calculate the actual probability of both events happening together, we can count the number of outcomes where the sum of the numbers showing is both odd and 9, 11, or 12. There are only 2 such outcomes: (3,6) and (5,6). Therefore, the probability of both events happening together is 2/18 or 1/9.

Since P(A and B) does not equal P(A) * P(B), we can conclude that events A and B are not independent.

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Statistical question is How much does a movie ticket cost at each theater in New York City? and Not statistical questions are How many movie theaters are in New York City? and What movie theater in town has the least expensive popcorn?

The question "How much does a movie ticket cost at each theater in New York City?" is considered statistical because it involves collecting data on the cost of movie tickets at different theaters in New York City.

This question seeks to gather information about the distribution of ticket prices.

The question "How many movie theaters are in New York City?" is not statistical.

It is asking for a specific count or number and does not involve collecting data or analyzing a distribution.

What movie theater in town has the least expensive popcorn? is also not statistical.

It is asking for a specific comparison or ranking based on the cost of popcorn at different movie theaters.

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Answer:

500 sq. ft

Step-by-step explanation:

20 ft x 25 ft = ? ft

500 ft = ? sq. ft

25x0=0

25x2= 50

25x20=500

Answer:

Cindy's backyard has an area of 20 feet x 25 feet = 500 square feet. Therefore, Cindy needs 500 square feet of sod to cover her entire backyard.

Answer:

a. 120/w = l

120/l = w

b. l times w = 120

Step-by-step explanation:

Step-by-step explanation:

120/W=1

120/W= I

I =W is equal to 10

Answer:

24,53cm²

Step-by-step explanation:

rectangle area=length×width=7×3

=21cm²

circle area=1/2Π r²

=1/2×3.14×1.5×1.5

=3.5325cm²

add the two areas

21+3.53=24,53cm²

Answer:

20 yards

Step-by-step explanation:

By the given ratio, the side measurements are 1x, 3x, 4x, 6x, and 9x

We are given the perimeter of this shape is 115. Therefore, 1x+3x+4x+6x+9x=115.

We can solve that for x, so we can find each side measurements' numerical value.

(1+3+4+6+9)x=115

(23)x=115

x=115/23

x=5

So the side measurements are:

1x=1(5)=5

3x=3(5)=15

4x=4(5)=20

6x=6(5)=30

9x=9(5)=45

The third longest sife is 20 yards.

The cost of 15 litres of petrol ​ is rs. 516.7

From the question, we have the following parameters that can be used in our computation:

The cost of 9 litres of petrol is rs.310 .

This means that

Cost of 9 litres of petrol = rs.310

Multiply both sides of the equation by 5/3

So, we have the following representation

5/3 * Cost of 9 litres of petrol = 5/3 *  rs.310

Evaluate the products

Cost of 15 litres of petrol = rs. 516.7

Hence, the cost is rs. 516.7

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Answer:

3 times

Step-by-step explanation:

1.5 times 3 equals 4.5

By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.

For every survey, there are only two possible outcomes.

First- they have bank savings accounts,

second- they do not.

So, by using the binomial probability distribution we can solve this problem.

Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.

Probability = p

Successes repeated = n  times

The  value of the binomial distribution is:

E(Y) = n x p

In this problem, we have that:

p = 0.64

If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,

E(Y) when, n = 50

So,

E(Y)= n x p

= 50 x 0.64

= 32

Hence ,our required answer is 32 adults who would have bank savings accounts

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A linear function is one of the most simplest form of functions. As the name "linear" indicates, a linear function is simply a line, more precisely a straight line.

So it is in the form of f(x) = ax + b.

Lets now check the possible answers : (second answer :) "a curved line", not correct.

(third answer:) "a parabola", this is not a straight line, so not correct.

(fourth answer:) "a wavy line", not a straight line, so not correct.

The only correct answer is the first one : a line passing through the x axis at negative 2 and the y axis at negative 6.

Answer:

r≤11

Step-by-step explanation:

well there is four riders already on there and the maximum is 15 so you would subtract 4-15 That's 11 and there can be less than 11 or equal to 11 so it would be less than or equal to 11

Answer:

\(y=- \sqrt{\dfrac{1}{2}x}\)

Step-by-step explanation:

Parent functions are the simplest form of a given family of functions.

Transformations of graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

\(\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a \\ & \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a \\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a \end{aligned}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

Given parent function:

\(y=\sqrt{x}\)

Horizontal stretch:

As this is a horizontal stretch, the x variable should be multiplied by a value between zero and 1:

\(\implies y= \sqrt{\dfrac{1}{2}x}\)

Reflected in the x-axis:

To reflect a function in the x-axis, simply make the function negative:

\(\implies y=- \sqrt{\dfrac{1}{2}x}\)

Answer:

75 words in 10 mins

Step-by-step explanation:

450 words in 60 mins, 450/6 is 75 meaning he can type 75 in 10 mins.

Answer:

30 minutes ................ 450 words

1 minute ..................

30

450

=15 words

6 minutes .............. 15×6=90 words

Answer:

38 cups

Step-by-step explanation:

8c + 30 = 334

8c = 334 - 30

8c = 304

c = 304 ÷ 8

c = 38 cups

The total number of cups ordered by Eddie is 8

Design fee = $30

Cost per cup = $8

Total cost of order = $334

Let the number of cups ordered = p

The total cost of order can be represented by the equation :

Design cost + (cost per order × Number of orders)

$30 + (8p) = $334

8p = 334 - 30

8p = 304

p = 303 / 8

p = 38

Hence, the number of cups ordered is 8

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\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{\dfrac{1}{2}a = 7}}\\\\\large\text{MULTIPLY 2 to BOTH SIDES}\\\\\large\boxed{\mathsf{2\times\dfrac{1}{2}a= 2\times7}}\\\\\large\text{CANCEL out: }\rm{2\times\dfrac{1}{2}}\large\text{ because it gives you 1.}\\\large\text{KEEP: }\rm{2\times7}\large\text{ because it helps you get your a-value}\\\\\large\boxed{\mathsf{a = 2\times7}}\\\\\\\large\text{SIMPLIFY IT!}\\\\\large\boxed{\mathsf{a = 14}}\\\\\\\huge\boxed{\text{Therefore, your answer is: \boxed{\mathsf{a = 14}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

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The expression that is equivalent to the given expression, (8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y), is 8x²y² - 15x²y + xy² + 5y

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is

(8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y)

To determine the expression that is equivalent to the given expression, we will simplify the given expression.

Simplifying the expression

(8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y)

Clear the parentheses by applying the distributive property

8x²y² - 9x²y + 9y - 6x²y + xy² - 4y

Collect like terms

8x²y² - 9x²y - 6x²y + xy² - 4y + 9y

Simplify

8x²y² - 15x²y + xy² + 5y

Hence, the equivalent expression is 8x²y² - 15x²y + xy² + 5y

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Answer:

In 5 weeks, Ayana and Michelle have the same amount of money saved

(Namely $75)

Step-by-step explanation:

Ayana has $200 and spends $25 per week.

Michelle has $0 and saves $15 per week.

So, after one week,

Ayana has $200 - $25 = $175

Michelle has $0 + $ 15 = $15

After 2 weeks,

Ayana has $175 - $25 = $150

Michelle has $15 + $15 = $30

After 4 weeks,

Ayana has $150 - $50 = $100

Michelle has $30 + $30 = $60

After 5 weeks,

Ayana has $100 - $25 = $75

Michelle has $60 + $15 = $75

So, in 5 weeks, Ayana and Michelle have the same amount of money saved

Ayana and Michelle will have the same amount of money saved in 5 weeks.

To calculate the number of weeks Ayana and Michelle will take to have the same ammount of money, we have to make use of assumption. The reason for this is, as the number of weeks are yet to be found, so the value can only be found by substituting that particular entity into a variable.

Let's assume that number of weeks Ayana and Michelle will take to have the same ammount of money is "x".

So, Amount saved by Ayana after x weeks will be $200 - $25*x,

Amount saved by Michelle in x weeks will be $15 * x.

In the question, we have been told that Ayana and Michelle have the same amount of money saved, So we need to equate to above two equations to find the value of "x".

$200 - $25*x = $15 * x

$200 = $15 * x + $25*x

$200 = $40*x

$200 / $40 = x

x = 5

Therefore, Ayana and Michelle will take 5 weeks to have the same amound of money saved.

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The probability that all coins show heads up is 1/16.

The probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.

Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.

Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.

And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.

You can simplify this by calculating (1/2)^4.

= 1/16

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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?

Answer:

With the discounts, you saved a total of $4.90. You still owe $29.10.

Step-by-step explanation:

Shoes:

10% of 24 is 2.4

The shoes cost 21.60  with the 10% discount and before tax.

Belt:

25% of 10 is 2.5

The belt cost $7.50 with the 25% discount and before tax.

Total:

You still owe 29.10 for the belt and shoes before tax.

You saved $2.4 on the shoes and $2.5 on the belt (total of $4.90)

Answer:

C.

Step-by-step explanation:

You can assign each variable a ride, let's say the teacup is t, the roller coaster is r, and the spinning vortex is s. Now we can create algebraic expressions to find the values of each ride :

Kristen: 2t+2r+s=20

Jorge: t+r+3s=25

Lakesha: 5t+2r+s=29

Now we can use elimination to find each variable:

2t+2r+s=20

-2t-2r-6s=-50

The t and r cancel out, so find s

-5s=-30

s=6, so the spinning vortex is $6.

Now, substitution

2t+2r+s=20     -5t-2r-s=-29

2t+2r+6=20    -5t-2r-6=-29

2t+2r=14          -5t-2r=-23

2t=-2r+14

t=-r+7

Now plug in for t

-5(-r+7)-2r=-23

5r-35-2r=-23

3r=12

3r/3=12/3

r=4, which means the roller coaster is $4

Now we can just plug in both of those and solve for t with any equation

t+r+3s=25

t+4+3(6)=25

t+4+18

t+22=25

t=3

Now we know that the teacups have to be $3, the rollercoaster has to be $4, and the spinning vortex has to be $6. Marc's equation is:

3t+2r+2s = Money marc spent

Plug in the values

3(3) + 2(4) + 2(6) = Money marc spent

9+8+12 = Money marc spent

29 = Money marc spent

Marc spent $29, your answer is C

Answer:

20.1

Step-by-step explanation:

take the base. a right triangle is formed with 12 and 8 sides

the hypotenuse = 14.42 which will be the base to right triangle former by ht 14 cm

now the hypotenuse is the diagonal

14.42^2+14^2 = 403.9

diagonal=20.1

Lily would predict the population of mussels to be 58 after one year if the population grows at the same percentage rate each month

The population of mussels increased by 22 - 10 = <<22-10=12>>12 mussels in 3 months. The rate of increase per month is 12 mussels / 3 months = 4 mussels/month.

Therefore, the equation for the population of mussels after one year is y = 4 mussels/month * 12 months + 10 mussels, or y = 48 mussels + 10 mussels.

The final equation is y = 58 mussels.

This means that Lily would predict the population of mussels to be 58 after one year if the population grows at the same percentage rate each month.

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Answer:

g(x)=\(-2x^{2}\)+1

Step-by-step explanation:

Answer:

g(x) = (x +2)² + 1

Step-by-step explanation:

original function is moved 2 units to the left and 1 unit up so

g(x) = (x-(-2))²+1

g(x) = (x +2)² + 1

Answer:

Step-by-step explanation:

Given the price of 5 units for $5.75

The unit rate is:

Correct choice is C