Which statement best describes the relationship between x and y in the equation y = 3x? A. The value of y is three less than the value of x. B. The value of y is three times the value of x. C. The value of x is three more than the value of y. D. The value of y is three more than the value of x.

The probability that a student in the class has a dog is 1/1501501, the probability that a student has a cat is 6/1001001, the probability that a student has both a dog and a cat is 1/2002002.

To answer the given questions, we can use the information provided in the survey. Let's break it down step by step:
p(d) = 1/1501501
p(c) = 6/1001001
p(d and c) = 1/2002002
p(d or c) = (1/1501501) + (6/1001001) - (1/2002002)

The probability that a student in the class has a dog, p(d), can be calculated by dividing the number of students who have a dog (200) by the total number of students surveyed (300300300). Therefore,

p(d) = 200/300300300

= 2/3003003

= 1/1501501.

Similarly, the probability that a student in the class has a cat, p(c), can be calculated by dividing the number of students who have a cat (180) by the total number of students surveyed (300300300). Therefore,

p(c) = 180/300300300

= 6/1001001.

The probability that a student in the class has both a dog and a cat, p(d and c), can be calculated by dividing the number of students who have both a cat and a dog (150) by the total number of students surveyed (300300300). Therefore,

p(d and c) = 150/300300300

= 1/2002002.

To calculate the probability that a student in the class has either a dog or a cat, p(d or c), we can use the formula

p(d or c) = p(d) + p(c) - p(d and c).

Plugging in the values, we get

p(d or c) = (1/1501501) + (6/1001001) - (1/2002002).

In conclusion, the probability that a student in the class has a dog is 1/1501501, the probability that a student has a cat is 6/1001001, the probability that a student has both a dog and a cat is 1/2002002, and the probability that a student has either a dog or a cat is (1/1501501) + (6/1001001) - (1/2002002).

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Answer:

2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period. Subtract one and multiply the resulting number by 100 to give it a percentage representation.

Step-by-step explanation:

Therefore, 65% of all nurses have a starting salary, z = invNorm(0.35) ≈ -0.3853 and z = (41861.5 - 67694) / 10333 ≈ -2.49.

b) We need to find P(X ≥ 78371.8). To do this, we can standardize the value using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. Then we can look up the probability in a standard normal distribution table or use a calculator.

\(z = (78371.8 - 67694) / 10333 \approx 1.04\)

Using a standard normal distribution table or calculator, we find that P(Z ≥ 1.04) ≈ 0.1492. Therefore, the probability that a randomly selected nurse has a starting salary of 78371.8 dollars or more is about 0.1492.

c) We need to find P(X ≤ 91407.1). Again, we can standardize the value and look up the probability in a standard normal distribution table or use a calculator.

\(z = (91407.1 - 67694) / 10333 \approx 2.30\)

Using a standard normal distribution table or calculator, we find that P(Z ≤ 2.30) ≈ 0.9893. Therefore, the probability that a randomly selected nurse has a starting salary of 91407.1 dollars or less is about 0.9893.

d) We need to find P(78371.8 ≤ X ≤ 91407.1). We can standardize the values and use a standard normal distribution table or calculator to find the probability.

z1 = (78371.8 - 67694) / 10333 ≈ 1.04

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Using a standard normal distribution table or calculator, we find that P(1.04 ≤ Z ≤ 2.30) ≈ 0.4657. Therefore, the probability that a randomly selected nurse has a starting salary between 78371.8 and 91407.1 dollars is about 0.4657.

e) We need to find P(X ≤ 41861.5). Again, we can standardize the value and use a standard normal distribution table or calculator.

z = (41861.5 - 67694) / 10333 ≈ -2.49

Using a standard normal distribution table or calculator, we find that P(Z ≤ -2.49) ≈ 0.0062. Therefore, the probability that a randomly selected nurse has a starting salary that is at most 41861.5 dollars is about 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse. This is because the probability of getting a starting salary at or below this value is very small, as we calculated in part (e).

g) We want to find the value x such that 65% of all nurses have a starting salary greater than x. This means we need to find the 35th percentile of the distribution, which we can do using a standard normal distribution table or calculator.

z = invNorm(0.35) ≈ -0.3853

Using the formula z = (x - μ) / σ, we can solve for x:

-0.3853 = (x - 67694) / 10333

x - 67694 = -0.3853 * 10333

x ≈ 63757.72

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Answer:

2=4,6,8,10,12

3=6,9,12,15,18

4=8,12,16,24,32

5=10,15,20,25,30

11=22,33,44,55,66

Question :

Cone is formed from 3200 ft³ of gravel, if the height of the cone is 24 ft what is the radius in feet of the base of the cone

Answer:

11.3 feet

Step-by-step explanation:

The volume of a cone = πr²h/3

We are asked to find the radius

The formula is given as:

r = √3V/πh

V = 3200 ft³

h = 24 ft

r = √3 × 2400/π × 24

r = 11.28379 ft

Approximately = 11.3 ft

The radius in feet = 11.3 ft

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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To answer this question, you need trigonometry.

Are you familiar with the chant soh cah toa?

In here, you can see that the side you have is adjacent to the angle you have, and you're trying to find the opposite side. This means you need tangent = opposite ÷ adjacent

If the angle was 30° 45° or 60° Then there is a table you can use to calculate, but there isn't so just use a calculator

tan 31° = x ÷ 10

Answer:

Step-by-step explanation:

The total number of outcomes that is sample space is 8.

As 4 flavors each with 2 more options to go

4x2=8

Answer:

3x - 5y = -20

Step-by-step explanation:

Jorge will receive 9 hours in time off from work.

How many hours will Jorge get to take time off?

It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.

Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.

As a result, the time off he receives from work = \(1\frac{1}{2} (6)\) hours

\(=\frac{3}{2}(6) = 9 hours\)

Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.

What is Fair Labor Standards Act?

The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.

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Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

To find the speed of the movement of the spotlight along the shore, we need to determine the rate at which the distance between the light and the point where the beam meets the shore is changing.

Let's consider a right triangle formed by the light, the point where the beam meets the shore, and the shoreline. The hypotenuse of the triangle represents the distance between the light and the point on the shore where the beam meets. The angle between the hypotenuse and the shoreline is 60°.

Using trigonometry, we can relate the distance between the light and the shore to the angle of the beam. The distance is given by the formula:

distance = hypotenuse = 4 km

The rate of change of the distance is given by the derivative of the distance with respect to time:

d(distance)/dt = d(hypotenuse)/dt

Since the light rotates at a constant angular speed of 3.5 rad/min, the rate of change of the angle is constant:

d(angle)/dt = 3.5 rad/min

Using the chain rule, we can relate the rate of change of the distance to the rate of change of the angle:

d(distance)/dt = d(distance)/d(angle) * d(angle)/dt

Since the angle is 60°, we can calculate the rate of change of the distance:

d(distance)/dt = (4 km) * (π/180 rad) * (3.5 rad/min)

Simplifying the expression, we get:

d(distance)/dt = 2π km/min

Therefore, the speed of the movement of the spotlight along the shore when the beam is at an angle of 60° with the shoreline is 2π km/min.

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Answer:

38° I think it is just because with you add it

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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Answer:

2.5

Step-by-step explanation:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline.

The distance from the highest most point to the lowest point vertically is 5, meaning that the midpoint is 2.5 units from either end.

Answer:

156

Step-by-step explanation:

The answer is D in other cases it is 156.

If you get it right can you leave a like.

Answer:

-10, square root of 100, square rout of 220, 11.5

Step-by-step explanation:

Answer:

2,1 .     4,4 .     5,2

Step-by-step explanation:

Answer:

a' (2,1)

b'(4,4)

c'(5,2)

(x,y)→(x+1,y+4)

Step-by-step explanation:

So the <a'b'c' is <abc translated 1 unit to the right and 4 units up. Whenever it says to move to the right or the left it has to do with the x axis. When you move to the left its subtraction and when you move to the right you addition.

When ever is say to move up or down it has to do with the y-axis. when you move up its addition and when you move down its subtraction. Sooo since the question said to move it to the right and up theyre both going to be addition. Thats why in the translation theyre both addition sign.

Im really bad at explaining things but hope this helps:)

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Given the expression:

To factor the given expression, we need two numbers the product of them = 100 and the sum of them = 20

We will factor the number 100

100 = 1 x 100 ⇒ 1 + 100 = 101

100 = 2 x 50 ⇒ 2 + 50 = 52

100 = 4 x 25 ⇒ 4 + 25 = 29

100 = 5 x 20 ⇒ 5 + 20 = 25

100 = 10 x 10 ⇒ 10 + 10 = 20

So, the suitable numbers are 10, 10

so, the factorization will be as follows:

The given expression is a complete square.

So, the answer will be (u+10)(u+10)

Or can be written as (u+10)²

Answer:

Each card will have a value of $15 when they equal after 600 days which also is 20 30-day periods.

Step-by-step explanation:

Card1: \(85 - \frac{3.50}{30} x\)

Card2: \(75 - \frac{3}{30} x\)

x is number of days

\(85 - \frac{3.50}{30} x = 75 - \frac{3}{30} x\)

2550 - 3.50x = 2250 - 3x

2550 - 0.50x = 2250

-0.50x = -300

x = 600 days

Card1: \(85 - \frac{3.50}{30} (600)\)

         85 - 70 = 15 dollars

Card2: \(75 - \frac{3}{30} (600)\)

         75 - 60 = 15 dollars

The value of each card will be when they have equal value is $15.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now, Let x be the number of time periods for which the gift card is not used, then

For the gift card $ 85 if it is not used for x periods, then the amount that will be lost is

85 - 3.50 x---------------------(1)

For the gift card $ 75 if it is not used for x periods, then the amount that will be lost is

75 - 3x---------------------- (2)

Now when both the amount lost is equal

85 - 3.50 x = 75 - 3x

solving the equation, we get

or, 3.50 x - 3x = 85 -75

or, 0.50 x = 10

or,  x = 20

Thus the value of gift cards will be equal for 20 ,30 day periods.

Now,the value of each card be when they have equal​ value

The two cards  will have equal value after 20, 30 day periods, this denotes that at this time, the value of each card will be equal.

Then

85 - 3.50 x = 75 - 3x

substituting  x = 20, we get

85 - 3.50*20 = 75 - 3*20

85 - 70  = 75 - 60

15  = 15

So, when they have equal​ value, the value of each card will be $15.

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Answer:

=

Because = usually means relation

Answer:

Step-by-step explanation:

The ratio of blue flowers to red flowers is five to eight. If 40 flowers were red how many were blue?

5b : 8r is the ratio

solve with an equation

5 : 8 = x : 40

x = 5 * 40 : 8

x = 25

Answer:

Ewan

Step-by-step explanation:

ewan ko na po sorry po at

kasi hindi kopo maintindihan

tapus hindi naman po ako

magaling

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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the function \(1/(1 + sin^2(x))\) can be expressed as the geometric series Σ [infinity] \(n=0 (sin^2(x))^n.\)

To apply this identity, we need to rewrite the given function in the form of (1 - y), where y is a variable. Let's start by rearranging the expression:

\(1/(1 + sin^2(x)) = 1 - sin^2(x)\)

Now we can see that y = sin^2(x), and we want to express\(1 - sin^2(x)\)as a geometric series. Using the identity, we have:

\(1 - sin^2(x) = 1/(1 - y)\)

This geometric series representation provides a useful way to manipulate and evaluate the original function 1/(1 + sin^2(x)). It allows us to express the function as an infinite sum, which can be helpful in various mathematical calculations and analyses.

Substituting y = sin^2(x) into the identity, we get:

\(1 - sin^2(x) = Σ [infinity] n=0 (sin^2(x))^n\)

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Answer:

about 6000π

Step-by-step explanation:

Answer:

1,350 square cm

Step-by-step explanation:

As we all know, we have to square a dimension of length to get the dimension of an area

So in this case, since the dimension of the length is increasing by a factor of 3, the dimension of the area will be increasing by a factor which is square the factor by which the dimension of the side is increasing

Thus, we have the area dimension increase by a factor of 3^2 = 9 times the area of the smaller

nonagon

So the area of the bigger nonagon will be :

150 * 9 = 1,350 square cm