you have invented a drug that you think will relieve anxiety and help students score better on exams. you want to test the drug on a group of statistics students who are about to take their final exam. you will give some students your new drug and others a dummy pill. why?

Answer:

[tex]4\sqrt{3} - 4i = \boxed{\left(8, \dfrac{\pi}{6}\right)}[/tex]

Step-by-step explanation:

Given complex number is:
To plot this on polar coordinates use the fact that a complex number of the form [tex]z=x+yi[/tex] can be converted to polar form [tex](r, \theta)[/tex] using the relationship

[tex]r = \sqrt{x^2 +y^2) }\\\mathrm{and}\\\theta = cos^{-1}\left(\dfrac{x}{r}}\right)[/tex]

Comparing [tex]4\sqrt{3} - 4i[/tex] and [tex]z=x+yi[/tex]

we see that

[tex]r = \sqrt{(4\sqrt{3})^2 + (-4)^2}\\\\r = \sqrt{48 + 16}\\\\\\r = \sqrt{64} = 8\\\\\theta = cos^{-1} \left(\dfrac{4\sqrt{3}}{8}\right)[/tex]
[tex]\theta = \cos^{-1} \left(\dfrac{\sqrt{3}}{2}\right) = 30^\circ = \dfrac{\pi}{6} \;radians[/tex]

So in polar coordinates,

[tex]4\sqrt{3} - 4i = \left(8, \dfrac{\pi}{6}\right)[/tex]

The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.

The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).

So we can write an equation to represent the total cost:

0.62x + 0.52 (5000 - x) = 2798

Expanding the second term:

0.62x + 2600 - 0.52x = 2798

Combining like terms:

0.10x = 198

Finally, solving for x:

x = 1980

So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

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The simplification of the given fraction above would be = 9⅘

A fraction is defined as the part of a whole value which is represented in the form of a numerator and a denominator.

The given fraction that requires simplification is as follows:

= 4/5 × 12

= 48/5

= 9⅘

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The length of side AC rounded to 1 decimal place is 17.3 cm.

The figure on the image is a right triangle.

From the image;

using the trigonometric ratio, we determine the length of side AC.

Tangent = Opposite / Adjacent

tan( 68 ) = AC / 7

AC = tan( 68 ) × 7

AC = 17.3 cm

Therefore, side AC has a length of 17.3 cm.

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P(30)=3, If Ms. Crowley has 30 students in her class, she must buy 3 packs of red paper mate flair pens.

P(0)=0, and if she has 0 students, she does not need to buy any pens.

To find the number of packs of pens Ms. Crowley must buy, we need to divide the number of students by the number of pens in each pack and then round up to the nearest whole number.

This is because if Ms. Crowley has 30 students, for example, and each pack contains 12 pens, then 30 ÷ 12 = 2.5, which means she needs 3 packs of pens to ensure that every student has a pen.

Using this calculation, we can find the number of packs of pens Ms. Crowley must buy for each number of students:

P(30) = ceil(30 ÷ 12) = ceil(2.5) = 3

P(0) = ceil(0 ÷ 12) = ceil(0) = 0

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The number of bacteria that is left is 38

The half-life is the time it takes for half of the bacteria to reduce

The time is given as 1.5 hours

After 1.5 hours:

The number will have gone through 6 / 1.5 = 4 half-lives.

So, the number of bacteria cells after 6 hours will be 600 * (1/2)^4

Evaluate

600 * (1/2)^4 = 600 / 16 = 37.5

Approximate

600 * (1/2)^4 = 600 / 16 = 378

Since the number of bacteria cells is 37.

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If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.

In 2005 the population was 2 million and it had increased to 3 million by 2017.

If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.

The amount of taxes of the city is proportion to the population of that city.

Tax(T) = kP(Population)

where k is a constant.

In 2005 Population = 2 millions and T = 20 billion. So

20 = 2k

Divide by 2 on both side, we get

k = 10

In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:

t = 10 × 3

t = 30 billion

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The complete question is:

The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?

Answer:

Step-by-step explanation:

380.8 grams

Answer:

Step-by-step explanation:

380.8

Answer:

Step-by-step explanation:

If 2 angles are complementary, they are equal to 90 degrees. So, lets say that the measure of the first angle is x, and the measure of the second angle is y.

Since x measures 4.2 degrees more than its complementary angle (y), we can say that x - 4.2 = y

And, since they are complementary angles, x+y = 90.

We can now use a system of equations to solve. Since we know y = x-4.2, we can substitute y with x-4.2, making the equation x + x - 4.2 =90.

Simplify:

x+x-4.2=90

2x -4.2 =90

2x = 94.2

x= 47.1

Since y=x-4.2, we can now find y.

y = x-4.2

y= (47.1)-4.2

y=42.9

So, the measure of the angles is 47.1° and 42.9°.

Hope this helps!

The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).

In hypothesis testing, the level of significance is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true. It is also known as the p-value and is usually denoted by the symbol α (alpha). The formula for calculating the level of significance is:

α = P (Statistic ≥ Observed Statistic | H0 is true)

For example, suppose we are testing a hypothesis that the mean height of all people in a population is 160cm. We select a sample of 50 people and measure the mean height to be 162cm. Assuming the null hypothesis is true, the level of significance is calculated as follows:

α = P (Statistic ≥ 162 | H0 is true)

This p-value measures the probability of obtaining a result that is at least as extreme as the observed result (162cm), if the null hypothesis is true. If this p-value is less than the predetermined significance level (usually 0.05 or 0.01), then the null hypothesis is rejected and we accept the alternative hypothesis.

The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).

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The equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.

70 = 14t

To find the number of teams in the contest, we can use the equation 70 = 14t. This equation states that the total number of water balloons, 70, is equal to the number of teams, t, multiplied by the number of balloons each team gets, 14.

To solve this equation, we can divide both sides of the equation by 14. This will give us the equation t = 70/14. We can then simplify this equation by dividing 70 by 14. This gives us t = 5. This means that there are 5 teams in the contest.

Therefore, the equation 70 = 14t can be used to find the number of teams in the contest. By solving this equation, we found that there were 5 teams in the contest.

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Answer:

it is 2 minus six

2-6

Step-by-step explanation:

hdgeheksdiddh

Answer:

-27/64

Step-by-step explanation:

Exact form

-27/64

Decimal Form

-0.421875

There are 95,040 different ways for the first five cars to go through the toll booth.

The first car can be chosen in 12 ways. After the first car has been chosen, the second car can be chosen in 11 ways. This process continues, so the third car can be chosen in 10 ways, the fourth car can be chosen in 9 ways, and the fifth car can be chosen in 8 ways.

So the total number of ways to choose the first five cars is as follows:

12 x 11 x 10 x 9 x 8 = 95,040

Therefore, there are 95,040 different ways for the first five cars to go through the toll booth.

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Answer:

[tex]5.06*10^{13}[/tex]

Step-by-step explanation:

[tex](4.6*10^6)(1.1*10^7)=(4.6*1.1)(10^6*10^7)=5.06*10^{13}[/tex]

Answer:

Step-by-step explanation:

charge it paigon

(C) The difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.

The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.

A residual is a discrepancy between an observed and expected value for the response variable y.

In the event that it is positive, the observed value exceeds the expected value.

The information that was ignored throughout the (first) cycle of the modeling is contained in the residuals, which serve as a significant source of information.

They must thus divulge something to us.

It is possible to describe the residual plot to the students as a kind of magnifier for the modeling procedure.

Therefore, (C) the difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.

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The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

x indicates the number of cards removed

that means

x = 1, 2, ..., 52

The probability of picking an ace is

P(ace) = 4/52

that means:

P(Ace') = 48/51 ----- Cards are selected without replacement

If x Ace is chosen, remaining cards are 52 - x

Using the above as a guide, it looks like this:

For x = 1, 2, ..., 52, PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x). 

Probability is the magnitude of the chance (likelihood) of something events will occur. Based on the definition of probability, there are the important things are the magnitude of the opportunity and the event will occur.

The probability that an event will occur is between 0 and with 1. If an event has a chance of happening 0, then this event is definitely not going to happen. If an event has chance will occur 1, then the event will definitely occur. With thus it can be concluded that the smaller the probability of an event (the closer the probability is to 0), the smaller the chance of the event

it will happen.

Conversely, the greater the probability of an event (the closer the probability is to 1), the greater the chance of the event it will happen.

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The effective annual yield (EAY) is 2.83%

The effective annual yield (EAY) is the true annual interest rate that an investor earns after taking into account the effect of compounding. To calculate the EAY, you need to find the interest rate that will make the formula (1 + r/n)^n = final balance/initial balance hold true, where r is the interest rate and n is the number of times compounding occurs in a year.

Given the initial balance of $2,000 and a final balance of $2,056.72 after one year, we can use the following formula to calculate the EAY:

(1 + r/n)^n = $2,056.72/$2,000

Since the interest rate is given as 2.80%, and the number of times compounding occurs in a year is not given, we'll have to assume n. A common assumption for n is 12, which represents monthly compounding. Plugging in the numbers, we have:

(1 + 0.028/12)^12 = $2,056.72/$2,000

Solving for r, we get:

r = 12 * (($2,056.72/$2,000)^(1/12) - 1)

r = 2.83%

So the effective annual yield (EAY) is 2.83%.

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Any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.

I linear function is a mathematical expression involving variable that when craft create is straight line linear function are used to model relationship between two variable such is cost and revenue price in demand in distance and time linear function can also be used to solve equation and the specialily useful for predicting future outcomes.

The domain of the linear function is {x | −4 < x < 6}, which means that the x-values of the function are all real numbers greater than -4 and less than 6. This means that any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.

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The missing rectangle has a relative frequency of 0.15, and this is the same as the height.

Let us define what a frequency and relative frequency are

The frequency of a datum is the number of times a given item (datum) appears in the data set.

While the relative frequency is the fraction or proportion of times taken from the whole in which an item/datum occurs.

So, from the image I uploaded, the relative frequency column represents the height of the histogram. Let the height of the missing rectangle be x.

Therefore the heights of the rectangles written from left to right are 0.05, 0.1, 0.15, x, 0.25, 0.2, and 0.1.

From the definition of relative frequency, the total sum of relative frequency is 1, if represented as decimals or fractions it can either be expressed in percentage, or decimal (fractions). In this question, it is represented in decimal, and the sum of all the relative frequency is 1.

0.05 + 0.1 + 0.15 + x + 0.25 + 0.2 + 0.1 = 1 ;

0.85+ x =1

Therefore, x = 1 - 0.85= 0.15

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To find the simple interest rate, you can use the following formula:

Simple interest rate = (ending balance - starting balance) / (starting balance * number of years)

In this case, the starting balance is $7,590, the ending balance is $11,916.30, and the number of years is 10. Plugging in these values, we have:

Simple interest rate = ($11,916.30 - $7,590) / ($7,590 * 10)

= ($4,326.30) / ($7,590 * 10)

= $4,326.30 / $75,900

= 0.057 or 5.7%.

Therefore, the simple interest rate is 5.7%.

Answer:

Suppose an investor invested $7,590 in a savings account with basic yearly interest 10 years ago. The account currently has a balance of $11,916.30. 5.7% is the basic interest rate.

Why do we call something "interesting"?

You must pay interest on money you borrow, and you must add interest to money you lend. The most typical approach to display interest is as a percentage of the annualized principal amount of a loan. This ratio represents the interest rate on the loan.

What is meant by an interest example?

By examining the rate, a person can figure out exactly how much interest they will accrue or pay on a loan. For example, if a $100 loan had a nominal interest rate, there would be a $6 interest fee.of 6% ($100 X 0.06). Despite an increase in loan size, the rate doesn't change. Even if the loan amount were increased to$1,000, the borrower would still be expected to pay 6% of the total.

Step-by-step explanation:

Answer:

63°

Step-by-step explanation:

The sum of the interior angles of a triangle add up to 180.

90 + (12x + 3) + (5x + 2) = 180     now solve for x

17x + 95 = 180

17x = 180 - 95 = 85

x = 85/17 = 5

m∠A = 12(5) + 3 = 63

Answer:

YB = 11.2

Step-by-step explanation:

Δ AYZ and Δ ABCare similar by the AA postulate

then the ratios of corresponding sides are in proportion , that is

[tex]\frac{AY}{AB}[/tex] = [tex]\frac{AZ}{AC}[/tex] ( substitute values )

[tex]\frac{7}{7+YB}[/tex] = [tex]\frac{15}{15+24}[/tex] = [tex]\frac{15}{39}[/tex] ( cross- multiply )

15(7 + YB) = 7 × 39 = 273 ( divide both sides by 15 )

7 + YB = 18.2 ( subtract 7 from both sides )

YB = 11.2

The length of YB would be; 11.2

We know that proportion is a fraction of a total amount, and the measures are related using a rule of three.

Since Δ AYZ and Δ ABC are similar by the AA postulate

Then the ratios of corresponding sides are in proportion , that is

AY/AB = AZ/AC

cross- multiply ;

15(7 + YB) = 7 × 39 = 273

7 + YB = 18.2

Hence, YB = 11.2

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Answer: 30 miles

Step-by-step explanation:

We are given a constant rate of 210 miles in 7 hours. Since we are trying to find how far Carter travelled in 1 hour, we can set up a proportion.

[tex]\frac{210}{7} =\frac{x }{1}[/tex]                        [cross multiply]

[tex]210=7x[/tex]                      [divide both sides by 7]

[tex]x=30[/tex]

Therefore, Carter travelled 30 miles in one hour.

The sum of the diagonals is 60, rounded to the nearest tenth.

Let's call the width of the rectangle "w". Then the length is 3 times the width or 3w. The area of the rectangle is 1800 square meters, so:

w * 3w = 1800

w^2 * 3 = 1800

w^2 = 600

w = √600 = √(600^(1/2)) = √(600^(1/2)) = 6 √(10^(1/2))

So the width is 6 √(10^(1/2)) and the length is 3 * 6 √(10^(1/2)) = 18 √(10^(1/2)).

The sum of the diagonals is the square root of the sum of the squares of the lengths of the two sides, so:

d = √(w^2 + (3w)^2)

d = √(w^2 + 9w^2)

d = √(10w^2)

d = √(10 * w^2)

d = √(10 * (6 √(10^(1/2)))^2)

d = √(10 * (6^2 * (10^(1/2)))^2)

d = √(10 * (36 * 10))

d = √(10 * 360)

d = √3600

d = 60

So the sum of the diagonals is 60, rounded to the nearest tenth.

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"Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.

Differentiated stratified sampling. By employing a characteristic to divide the population, we can then obtain a proportional randomized sample of each group.

Thus, "Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.

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Answer:

Step-by-step explanation:

when there is a plus before a negative, ignore it, the negative makes it irrelavant.

-4-3=-7

-4y-7

The mass of a banana is about C. 150 g.

A can of cola would be around A. 300 ml.

From the options, the best estimate for the mass of a banana is 150 g. This is because 1. 5 kg is much too heavy for a single banana which makes 15 kg ridiculously heavy. 15 g would be too light however as this is the mass of about 6 pennies.

There are several quantities for a can of cola, and they are all in 100s of milliliteters. The most likely quantity of a can of cola from the options is therefore 300 ml.

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The slope of the dashed line on the graph is 1 (rise/run). This can be determined by dividing the difference in the cost of tickets (20) by the difference in the number of tickets (1).

The slope of the dashed line on the graph is 1. To determine the slope, you need to divide the rise (difference in the cost of tickets) by the run (difference in the number of tickets). In this case, the difference in the cost of tickets is 20 (from $20 for 1 ticket to $40 for 2 tickets). The difference in the number of tickets is 1 (from 1 ticket to 2 tickets). Therefore, the slope of the dashed line on the graph is 1 (20/1). This means that the cost of tickets increases by $20 for every additional ticket purchased. For example, if you purchase 3 tickets, the total cost will be $60 (3 tickets x $20 = $60). If you purchase 4 tickets, the total cost will be $80 (4 tickets x $20 = $80).

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Together, Lindsay and Lorraine needs to jump 21 more jumps in a row.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Number of jumps got by Lindsay = 14

Number of jumps got by Lorraine = 13

Total number of jumps gotten by both = 27

Let j be the number of jumps they need to jump more.

j = 48 - 27

j = 21

Hence 21 more jumps would be needed.

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