A city planner is laying out four streets that will form the boundary of a park, as shown. She wants to be sure the park formed by the streets is a parallelogram. Which of the following conditions guarantees this?

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 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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The value of x is 10

Similar figures are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

This shows that x-3/21 = x-1/27

21(x-1) = 27(x-3)

divide through by 3

= 7(x-1) = 9 ( x-3)

7x -7 = 9x-27

collect like terms

9x -7x = 27-10

2x = 20

divide both sides by 2

x = 20/2

x = 10

therefore the value of x is 10

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Answer:

Step-by-step explanation:

380.8 grams

Answer:

Step-by-step explanation:

380.8

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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(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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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.

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:

51998

Step-by-step explanation:

To solve the problem, we need to subtract the number of people who watched the first two games from the total number of people who watched all three games:

156330 - (54342 + 49990) = 156330 - 104332 = 51998 people watched the third game.

Therefore, 51998 people watched the third game.

All three expressions are correct based on the properties of arithmetic operations.

Yolanda wrote 16 ÷ 8 = 2, which means she is finding how many times 8 fits into 16. The answer is 2, meaning 16 is divided into 8 equal parts and each part has a value of 2.

Riku wrote 16 ÷ 2 = 8, which means he is finding how many times 2 fits into 16. The answer is 8, meaning 16 is divided into 2 equal parts and each part has a value of 8.

Mariana wrote 8 x 2 = 16, which means she is finding the product of 8 and 2. The answer is 16, meaning 8 multiplied by 2 gives a total of 16.

All three expressions are correct.

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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]

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

The possible values for theta, where 0 degrees is less than theta and 360 degrees is greater than theta, would correspond to an angle measure in the range 0 < theta < 360 degrees.

This range includes all angles greater than 0 degrees and less than 360 degrees, which correspond to a full revolution around a circle.

It's important to note that angle measures are typically represented in either degrees or radians, with 360 degrees corresponding to 2π radians. So, if you need the values of theta in radians, the range would be 0 < theta < 2π.

In general, the possible values for theta are dependent on the context in which they are used and the specific system of measurement being employed. For example, in some cases, the range of possible values for theta may be restricted to between 0 and 180 degrees, or between -180 and 180 degrees, depending on the application.

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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 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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Answer:

x = 20

Step-by-step explanation:

3x + 80 + 2x = 180

5x + 80 = 180

5x = 100

x = 20

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

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?

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 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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"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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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 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:

15=19

Step-by-step explanation:

5×3=6+13

15=19

so 15=19

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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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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Answer:

Step-by-step explanation:

charge it paigon

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:

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 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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