Imagine that you are facing east. Then complete these sentences.
a) You turn 90° to the left to face
b) You turn 45° to the right to face
c) You turn 180° to the left to face
d) You turn 360° to the left to face
e) You turn 90° to the right to face
f) You turn 45° to the left to face
g) You turn 135° to the left to face​

Answer:

13) First blank: 2 Second blank: 5

14) First blank: 7 Second blank: 5

15) First blank: -11 Second blank: -2

16) First blank: 4 Second blank: 3

17) First blank: -3 Second blank: -8

18) First blank: -2 Second blank:6

The general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

-13, -11, -9, -7

Common difference, d = Second term - first term

= -11 - (-13)

= -11 + 13

= 2

Therefore,

Tn = a + (n - 1)d

Where,

Tn = a + (n - 1)d

= -13 + (n - 1)2

= -13 - 2n - 2

Tn = -15 - 2n

So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

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The annual growth rate of the city's population is 13.8%. The population of a city can be modeled using the equation P = 210(1.138)ᵗ, where P is the population in thousands and t is the time in years since July 1, 2006.

To determine the population on specific dates, we can substitute the values of t into the equation. Additionally, we can calculate the annual growth factor and growth rate using the given equation.

The equation P = 210(1.138)ᵗ represents the population of a city as a function of time since July 1, 2006. To find the population on a specific date, we need to substitute the corresponding value of t into the equation. For example, if we want to determine the population on July 1, 2006, we set t = 0 since it is the reference point. Thus, the population on that date is:

P = 210(1.138)⁰

P = 210

Therefore, the population on July 1, 2006, was 210,000 (since P is given in thousands).

To find the population on July 1, 2007, we set t = 1 since it represents one year after the reference point:

P = 210(1.138)¹

P ≈ 239.58

Hence, the population on July 1, 2007, was approximately 239,580.

The annual growth factor in this case is the value inside the parentheses, which is 1.138. It indicates the rate at which the population grows each year.

The annual growth rate can be calculated using the formula: growth rate = (growth factor - 1) * 100%. In this case, the growth rate is approximately (1.138 - 1) * 100% = 13.8%. Therefore, the annual growth rate of the city's population is 13.8%.

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answer in the picture

Answer:

The illustration below shows the graph of yyy as a function of xxx.

Complete the following sentences based on the graph.

Initially, as xxx increases, yyy

Step-by-step explanation:

The probability of a family owning a cat given that the family owns a dog is 0.164

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

Here

probability of a family owning a dog is 0.91,

P(dog) = 0.91

probability of a family owning a cat and a dog is 0.15,

P(dog ∩ cat) = 0.15

according to conditional probability

the probability of occurring of B after event A takes place is

P(A|B)=P(A∩B)/P(A)

so, the probability of a family owning a cat given that the family owns a dog is

        P(dog | cat) =P(dog∩cat)/P(dog)

                            = 0.15/0.91

                            =0.164

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Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

Explanation:

Cam saved $270 per month for three years while working. Considering that money is worth 4.8% compounded monthly, we can calculate the total amount he will have in his savings account when he finishes his studies.

To find the future value, we can use the formula for compound interest:

FV = PV * (1 + r)^n

Where:

FV is the future value

PV is the present value

r is the interest rate per compounding period

n is the number of compounding periods

In this case, Cam saved $270 per month for three years, which gives us a present value (PV) of $9,720. The interest rate (r) is 4.8% divided by 12 to get the monthly interest rate of 0.4%, and the number of compounding periods (n) is 5 years multiplied by 12 months, which equals 60.

Plugging these values into the formula, we get:

FV = $9,720 * (1 + 0.004)^60

≈ $18,034.48

Therefore, Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

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The equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is: D. y = (x+3)² + 2(x+3)-3

What is graph equation?

To move a function 3 units to the left, we need to replace x with (x + 3) in the equation. This is because, if we plug in x + 3 into the equation, we will get the same value as if we had plugged in x but moved 3 units to the left.

So, starting with the original equation y = x² + 2x - 3, we replace x with (x + 3):

y = (x + 3)² + 2(x + 3) - 3

Now, we can simplify this equation to get it into standard form:

y = x² + 8x + 18

Therefore, the equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is:

D. y = (x+3)² + 2(x+3)-3

which simplifies to:

y = x² + 8x + 18.

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Answer:

King Leopold became the monarch of Belgium in 1865

The average cost function is C(x) = 5000x + 20,000/x, where x is the number of machines used in the production. The critical value is C(x) = 20,000 and it happens when x = 2.

If we have a function f(x), the critical point happens when its first derivative is equal to zero.

             f '(x) = 0

In the given problem, the function is:

C(x) = 5000x + 20,000/x

Take the derivative:

C '(x) = 5000 - 20,000/x² = 0

5000 x² = 20,000

x² = 4

x = ±2

Since x is within the interval: 0<x<∞, the solution is x = 2

Substitute x = 2 into the function:

C(2) = 5000 (2) + 20000/2

C(2) = 10000 + 10000 = 20,000

Hence, the critical value is C(x) = 20,000 and it happens when x = 2.

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Answer:

D.

Step-by-step explanation:

We know that to find unit price, we divide the unit in the numerator by the quantity in the denominator.

For the first option, we must put $1.49 as the numerator and 8 as the denominator. It will then look like this:

For our second option, we must put $2.29 as the numerator, and 12 as the denominator. It will look like this:

For our third option, we must put $2.75 as the numerator, and 15 as the denominator. It will look like this:

For our final option, we must put $3.89 as the numerator, and 20 as the denominator. It will look like this:

Therefore, the last option is the best buy because $0.18625 > $0.18333.

Answer:

The expression is not factorable with rational numbers.

Step-by-step explanation:

This problem concerns probability and assumes that the IRS randomly audits a fraction of tax returns each year. The query is about a married couple that filed separate returns, and it wants to know how likely it is that both will be audited, just one will be audited, neither will be audited, and at least one will be audited. The problem assumes that the percentage of audited tax returns is set at 20%.

(a) The probability that both the husband and wife will be audited is equal to the product of the individual probabilities:

P(both audited) = 0.2 * 0.2 = 0.04

(b) The probability that only one of them will be audited is the sum of the probabilities that the husband is audited and the wife is not, and vice versa:

P(only one audited) = 0.2 * 0.8 + 0.8 * 0.2 = 0.32

(c) The probability that neither one of them will be audited is the complement of the probability that at least one of them will be audited:

P(neither audited) = 1 - P(at least one audited) = 1 - (0.2 * 0.8 + 0.8 * 0.2 + 0.2 * 0.2) = 0.36

(d) The probability that at least one of them will be audited is equal to one minus the probability that neither of them will be audited:

P(at least one audited) = 1 - P(neither audited) = 1 - 0.36 = 0.64

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The constant of proportionality is 9.5.

The correct option is (a)

Given,

In the question:

The proportional relationship between the price for a certain number of buckets of golf balls at a driving range.

Buckets 3 5 7

Price (dollars) 28. 50 47. 50 66. 50

To determine the constant of proportionality.

Now, According to the question:

We know that:

Proportional relationship equation:

y = kx, where k-constant of proportionality

In the given table, number of buckets represent input values (x) and the price represents output values (y).

We have for the first column:

x = 3, y = 28.50

Find the value of k by plugging in the values of x and y:

28.50 = 3k

k = 28.50/3

k = 9.5

The options are:

a) 9. 5

b) 10. 5

c) 18. 25

d) 28. 5

Hence, The constant of proportionality is 9.5.

So, The correct option is (a).

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Step-by-step explanation:

5x + 6x + 3x

= 14x.

Now we compare the expressions with the result:

11x + 3x = 14x. (correct)

14x + x = 15x. (incorrect)

2(3x + 4x) = 2(7x) = 14x. (correct)

3x(2 + 1) + 5x = 3x(3) + 5x = 9x + 5x = 14x. (correct)

5x + 3(2x + x) = 5x + 3(3x) = 5x + 9x = 14x. (correct)

Hence our answers are the 1st, 3rd, 4th and 5th.

The calculation can be concluded that the moisture content of the soil is 31%.

Moisture content of the soil is calculated using the formula:

MC = (Wet weight - Dry weight) / Dry weight

Therefore, the first step to calculating moisture content is to determine the wet weight of the soil.

Wet weight of soil and container = 151 g

Weight of empty container = 20 g

Weight of wet soil = 151 g - 20 g = 131 g

Next, the dry weight of the soil needs to be determined.

Dry weight of soil and container = 120 g

Weight of empty container = 20 g

Weight of dry soil = 120 g - 20 g = 100 g

Now that both the wet weight and dry weight have been determined, the moisture content can be calculated:

MC = (Wet weight - Dry weight) / Dry weight

MC = (131 g - 100 g) / 100 g

MC = 31 g / 100 g

The moisture content of the soil is 0.31 or 31%.

This can be written as 31/100 or as a percentage.

The final answer should be rounded off to the nearest hundredth place or two decimal places.

Therefore, the answer is:

Moisture content of the soil = 31 % or 0.31

Therefore, the calculation can be concluded that the moisture content of the soil is 31%.

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The slope-intercept form of the equation of a line is: y = mx + b

Where: y is the dependent variable (usually represented on the vertical axis of a graph). x is the independent variable (usually represented on the horizontal axis of a graph). m is the slope of the line (which represents the rate of change of y with respect to x). b is the y-intercept (which represents the value of y when x is equal to 0). To use this equation, you need to know the slope (m) and the y-intercept (b) of the line. You can find the slope of a line by taking any two points on the line and using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. Once you know the slope, you can substitute it and the y-intercept into the slope-intercept form of the equation of the line to get the equation in its final form.

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hi hope this is what you were looking for, hope this helps.

Answer:

a. 144m

b. After 2 secs

c. Ball hits the ground after 5 secs.

d. 128m

Step-by-step explanation:

A To find max height, find derivative of equation, let it equal zero, and sub in value into original equation: h(t) = -16t² + 64t + 80 h'(t)=-32t+64 -32t+64=0 32t=64 t=2 h(2) = -16(2²) + 64(2) + 80 h(2) = -64+128+80 = 144m B When h=144, t=2. Therefore, the ball reaches its max height after 2 secs. C When the ball hits the ground, h=0: -16t² + 64t + 80=0 t²-4t-5=0 (simplified) (t-5)(t+1)=0 t=5 and t=-1 Discount t=-1 (time cant be neg). Ball hits the ground after 5 secs. D Find h when t=1: h(t) = -16t² + 64t + 80 h(1) = -16(1²) + 64(1) + 80 h(1) = -16+64+80 h(1) = 128m.

Answer:

Either circle will do since they are the same size. If you already know the radius, you can move on. If you don't know the radius, then you can use a ruler to measure the widest part of the circle and then divide it by 2. This will be more accurate than trying to measure half of the diameter. Let's say that the radius of this cylinder is 1 inch (2.5 cm). Write it down.

Step-by-step explanation:

The relationship would be the volume of a cylinder is 3 times the volume of a refraction cup.

A cylindrical shape is a three-dimensional geometrical shape consisting of two parallel circular bases which are connected by some height h.

Part A: To find the volume of a cylinder, we need the dimensions of the cylinder such as the radius of the base of the cylinder and the height of the cylinder.

Part B: We have given the base of the refraction cup as a half-circle, we can calculate the radius of the base.

The diameter is given as 8 cm so, the radius would be half of the diameter.

r = 4cm

Part C:  If you put two refraction cups together, we get the full three-dimensional shape that is a circle.

Part D: The formula for the volume of a cylinder is V=pi r^2 h.

\(V=\pi r^2 h\\V=3.14\times4^2\times 2\\V = 100.48\)

Part E: The volume of a refraction cup = \(4/3\pi r^{3}\)

= 4/3 (3.14)(8)

= 33.49

Part F: The relationship between the value D and the value from Part D is as follows

The volume of a cylinder = 3 times the volume of a refraction cup

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(a) We can use a two-sample t-test to test the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

The null hypothesis is that the mean weight of regular Coke is equal to or less than the mean weight of Diet Coke, while the alternative hypothesis is that the mean weight of regular Coke is greater than the mean weight of Diet Coke. Using a calculator or statistical software, we find that the test statistic is 4.013 and the p-value is 0.0001. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.

(b) Cans of regular Coke probably weigh more than cans of Diet Coke due to the sugar present in regular Coke but not Diet Coke. Sugar has weight and adds to the overall weight of the can. Diet Coke uses artificial sweeteners instead of sugar, which would result in a lower weight for the can.

Note: The answer choices provided are not accurate as they do not address the actual reason for the weight difference.

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Answer:

IV- the amount of students

DV- the amount of dishes

Answer:

15s + 225 is less than or equal to 521

Step-by-step explanation:

The restaurant needs 521 spoons and it only has 225.

There is a very simple answer for this.  

If each set on sale contains 15 spoons (algorithm rule)

So determine s (15 x s) = 15s (calculation principle)

then 15s + 225 is less than or equal to 521

therefore the result is 15s + 225 is less than or equal to 521 spoons

Given:

Required:

We need to solve for L.

Explanation:

Consider the given equation.

Subtract 2W from both sides.

Divide both sides by 2.

Final answer:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

0.75

Step 02:

greater than:

greater than 0.75:

Answer:

20

Step-by-step explanation:

19 + 56(1/56)

= 19 + 56 x 1/56

= 19 + 1

= 20

Answer:

50

Step-by-step explanation:

Step-by-step explanation:

radius of large sphere is R,

then volume is (4/3)*pie*R³

and

the radius of small sphere is r,

then volume is (4/3)*pie*r³

condition is,

volume of larger sphere is twice of the volume of smaller sphere.

then, (4/3)*pie*R³=2*(4/3)*pie*r³;

R³= 2r³

R=(2^⅓)*r

Answer:

the answer is 3/8

Step-by-step explanation:

multiply 7 by 2, and get 14

multiply 1 by 8, and get 8

give both terms new denominators which will be 16

The new fraction will be  \(\frac{14}{16} - \frac{8}{16}\)

Now you can subtract the numerators which will give you 6/16

Now you would simplify the fraction

Divide the fraction by 2 and you get 3/8 which is your answer

Hope this helps:)

Answer: C) X=2

Step-by-step explanation: These angles are equal because they alternate exterior angles. Set them equal to each other,  and just solve for x.