Student Manual
College Readiness Mathematics. Unit 1. Lesson 3
Independent Practice:
School Lunches & Movie Tickets
Find the cost of school lunches (adult and student) for three different area schools. Then create a table
of values. Also find the number of students and teachers at each school.
Write an expression based on the table for each of the following:
Schools
Student
Adult
A

The total number of different combinations of classes there are, based on the classes that Jimmy can choose are 47, 520 combinations

First, find the total combinations as a whole, per subject.

For math, the total combinations will be:

= 3! / (3 - 1) !

= 3 combinations for math

For science, the combinations are:

= 4! / ( 4 - 2)!
= 12

For electives:

= 12! / ( 12 - 3)!

= 1, 320

The total different combination of classes is the product of these combinations:

= 3 x 12 x 1, 320

= 47, 520 combinations

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Answer:

81

Step-by-step explanation:

1/2 -7. Is that what your looking for?

Answer:

10 is 10 times as much as 1 because if you were to multiply 1 x 10, you would get 10.

Answer:

6 < x

Step-by-step explanation:

4(3x + 2) <5(3x - 2)

Distribute

12x +8 < 15x -10

Subtract 12 x from each side

12x +8-12x < 15x-12x -10

8 < 3x - 10

Add 10 to each side

8+10 < 3x-10+10

18 < 3x

Divide by 3

18/3 < 3x/3

6 < x

Answer:

16pi km² / 8pi km

Step-by-step explanation:

r = 4

A = pi(r²)

4² = 16

A = 16pi km²

C = 2r(pi)

2r = 8

C = 8pi km

Answer:2

20/10=2/1=2

Step-by-step explanation: Rise over run

find a point were you can measure the squares I used 30 to 50

count the squares going up;2 and each square represents 10 so that equals 20

count the square(s) over; 1 and each square equals 10 so that equals 10

20 over 10 reduced is 2 over 1 and if a fraction is over 1 then it is a whole.

I hope this was good enough for you:

Answer:

52 metros.

Step-by-step explanation:

En este caso debemos usar las identidades trigonométricas. La información por medio del enunciado es:

*Sombra proyectada, que mide 20 metros y sería el cateto adyacente

*Ángulo de inclinación que son 69°

Con estos datos podemos calcular el cateto opuesto que sería altura, por medio de la identidad de la tangente:

tan α = CO/CA

CO = tanα * CA

CO = tan(69) · 20 m

CO = 52 metros

Lo que quiere decir que la altura del edificio es de 52 metros.

Comparing experiment data to public opinion polls helps evaluate media accuracy, detect biases, and understand the influence on public opinion, while describing data trends and comparing theoretical and empirical probabilities aids in making informed decisions.

In conclusion, comparing the data collected from experiments to public opinion polls allows for the assessment of media accuracy and biases, while analyzing data trends and comparing theoretical and empirical probabilities provides valuable insights for decision-making.

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The intercept is 3 and 5

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

To find x- intercept, y=0

x² + 2x -15=0

x² -5x + 3x -15=0

x(x-5) - 3(x-5) = 0

(x-5)(x-3)=0

Hence, the x- intercept is 3 and 5.

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The cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

To determine the required number of revolutions per second for the cylinder in order for the clothes to lose contact with the wall at a specific angle, we can use the concept of centripetal acceleration.

The centripetal acceleration experienced by an object moving in a circular path of radius r at a speed v is given by the formula:

\(a = v^2 / r\)

In this case, when the clothes lose contact with the wall, the net force acting on them is the gravitational force pulling them downward, which can be expressed as:

mg = m * g

Since the gravitational force provides the centripetal force for the clothes, we can equate the centripetal acceleration to the gravitational acceleration:

v^2 / r = g

To solve for the speed v, we need to find the circumference of the circular path. The circumference C can be calculated as:

C = 2πr

Substituting this into the equation above, we have:

v^2 / (2πr) = g

Now, we need to find the required speed v when the clothes lose contact with the wall at an angle of θ = 54.0°. We can use the angle θ to find the arc length traveled by the clothes on the circular path.

The arc length s can be calculated as:

s = θ * r

Substituting the given values, we have:

s = (54.0°) * (0.512 m)

Next, we can calculate the time it takes for the clothes to traverse the arc length s at the required speed v. The time t can be calculated as:

t = s / v

Now, since we want to find the number of revolutions per second, we need to convert the time t into seconds per revolution (s/rev). Since each revolution covers the circumference C, the time for one revolution is:

t_rev = C / v

Finally, the number of revolutions per second is given by the reciprocal of the time for one revolution:

Rev/s = 1 / t_rev

Let's calculate the required number of revolutions per second using the given values. Assuming the acceleration due to gravity is approximately 9.8 m/s²:

r = 0.512 m (radius)

θ = 54.0° (angle)

g = 9.8 m/s² (acceleration due to gravity)

First, calculate the arc length s:

s = (54.0°) * (0.512 m) = 27.648 m

Next, calculate the required speed v using the centripetal acceleration equation:

v^2 / (2πr) = g

v^2 / (2π * 0.512 m) = 9.8 m/s²

v^2 = (2π * 0.512 m) * (9.8 m/s²)

v^2 = 10.0384 m²/s²

v ≈ 3.1687 m/s

Now, calculate the time for one revolution:

t_rev = (2π * 0.512 m) / (3.1687 m/s) ≈ 3.2321 s/rev

Finally, calculate the number of revolutions per second:

Rev/s = 1 / (3.2321 s/rev) ≈ 0.3097 rev/s

Therefore, the cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

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Per year 40 squirrels are added

Any of the many statistical methods used to determine the value of a population's attribute based on observations of a sample taken from the population is known as an estimate. For instance, a point estimate is the one figure that is most likely to convey the property's value.

Estimates are created by multiplying the unit cost of the relevant goods by the amounts derived from the dimensions of the designs for various things needed to execute the project. Estimates' objectives: should be aware of the financial requirements for finishing the suggested task.

According to the given question

The birth rate is 0.06 and the death rate is 0.02 per person per year. The number of deaths per year for a population of 1000 is equal to 1000*0.02, or 20. The annual birth rate is equal to 1000 * 0.06, or 60. As a result, the population of squirrels grows by a total of 40 individuals each year

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Answer:

So using process of elimination it isnt possible for it to be AA or not similiar bc they are similiar since there vertical angles so were left with picking between SSS and SAS which I know that there is an angle that is congruent which is at the midpoint so if i were you I would put SAS similarity.

Step-by-step explanation:

I just took a test of this lesson so I hope im right.

Answer:

68%

Step-by-step explanation:

85 divided by 125 = .68 * 100 = 68

Answer: The sale price is 40 percent of the regular price

Step-by-step explanation:

Answer:

1.75 or about 1 cup of ice cream

Step-by-step explanation:

Well, we first have to figure out how many cups of ice cream are in a quart. (There are 4 cups in a quart) So know we have to divide 4 into 7 that will give you 1.75 so each family would get approximatley 1.75 cups of ice cream. That is if it is talking about specifically  how much ice cream but you could also say about a cup

The height of the cylinder is 5 m.

The surface area of a cylinder is \(28 \pi m^{2}\).

The total surface area of a cylinder is equal to the sum of the areas of all its faces. The total surface area with radius ‘r’, and height ‘h’ is equal to the sum of the curved area and circular areas of the cylinder.

Let's call the height of the cylinder "h". The surface area of a cylinder can be calculated as

Where r is the radius of the base.

Since the diameter of the base is 4 meters, the radius is 4/2 = 2 meters.

We know the surface area of the cylinder is \(28 \pi m^{2}\), so we can use this information to find h:

⇒\(28 \pi = 2 \pi(2)h + 2 \pi(2)^{2}\)

Expanding and simplifying the equation:

⇒28π = 4πh + 8π

Subtracting 8π from both sides:

⇒20π = 4πh

Dividing both sides by 4π:

⇒h = 5

Therefore, the height of the cylinder is 5 meters.

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The variance of (X + Y)/2 is 5/9. The variance of a random variable is defined as E[(X - E[X])^2], where E[X] is the expected value of the random variable.

We are given the joint probability density function of X and Y as f(x,y) = (x+y)/8 for 0 < x < 2 and 0 < y < 2.

We need to find the variance of (X + Y)/2.

Let Z = (X + Y)/2. Then, the expected value of Z is:

E[Z] = E[(X + Y)/2] = E[X]/2 + E[Y]/2

We can find E[X] and E[Y] as follows:

E[X] = ∫∫x f(x,y) dxdy = ∫∫x(x+y)/8 dxdy

= ∫0²∫0²x(x+y)/8 dydx = 2/3

Similarly, E[Y] = 2/3.

Therefore, E[Z] = 2/3.

Now, we need to find E[Z^2]:

E[Z^2] = E[(X + Y)^2/4] = E[X^2]/4 + E[Y^2]/4 + E[XY]/2

We can find E[X^2], E[Y^2], and E[XY] as follows:

E[X^2] = ∫∫x^2 f(x,y) dxdy = ∫0²∫0²x^2(x+y)/8 dydx = 2

E[Y^2] = ∫∫y^2 f(x,y) dxdy = ∫0²∫0²y^2(x+y)/8 dydx = 2

E[XY] = ∫∫xy f(x,y) dxdy = ∫0²∫0²xy(x+y)/8 dydx = 1/2

Therefore, E[Z^2] = (2/4) + (2/4) + (1/4) = 1.

Finally, we can find the variance of Z as:

Var(Z) = E[Z^2] - E[Z]^2 = 1 - (2/3)^2 = 5/9.

Therefore, the variance of (X + Y)/2 is 5/9.

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Answer: 2

Step-by-step explanation:

They are saying that x equals 2, and the question is what the function is defined at when x = 2

Going to x = 2, the y value is just 2

The answer is 4.

f(2)=4

Answer:

To find the extremes, we must see the graph.

The maximum will be the value where the value of y is the greatest.

We can see that the graph peaks at y = 3.

Then the maximum is 3.

The minimum is the value of y that is the lowest.

We can see that in the left side, when x = 0, y takes the lowest value, y = -1

Then the minimum in the interval is -1.

The easier way to see maximum/minimum value is to look at the highest/lower value in the graph.

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Answer:

Linear pairs add up to 180°

1st angle = x

2nd angle = x+24 (24° more than the first)

The equation would be

1st angle + second angle = 180 Subbing in the expressions we came up with:

x+x+24 = 180

I never en studied this stuff

Answer:

Step-by-step explanation:

If dim span{v1,v2,...,v5} = 4, it means that the span of the set of vectors {v1,v2,...,v5} can be expressed as a 4-dimensional subspace of r^2. This implies that there are only 4 linearly independent vectors in the set {v1,v2,...,v5}. Therefore, there must be at least one vector in the set that can be expressed as a linear combination of the other 4 vectors. In other words, the set of vectors {v1,v2,...,v5} is linearly dependent.

To prove this, we can assume that v5 can be expressed as a linear combination of v1, v2, v3, and v4. That is, v5 = c1v1 + c2v2 + c3v3 + c4v4 for some constants c1, c2, c3, and c4. If we substitute this expression into the equation for the span of {v1,v2,...,v5}, we get:

span{v1,v2,...,v5} = span{v1,v2,v3,v4,c1v1 + c2v2 + c3v3 + c4v4}

Since v5 can be expressed as a linear combination of the other vectors, we can remove it from the span without changing the dimension of the span. Therefore, we have:

span{v1,v2,...,v5} = span{v1,v2,v3,v4}

Since the dimension of the span is 4, we conclude that the set {v1,v2,...,v5} is linearly dependent.

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Answer:

2272.03

Step-by-step explanation:

Answer:

27  is  25 %  of  108

Step-by-step explanation:

x*25/100=27 or x=(27*100)/25=108

The present age of the Father is 35 and the age of the Son is 15 years after solving the given problem.

By examining the given problem we can solve it in the following way:

Present age:

Let x = Son's present age

x + 20 = Father's present age

5 years ago:

x - 5 = Son's age 5 years ago

x + 20 -5 = father's age 5 years ago

Father's age 5 years ago = 3( Son's age 5 years ago )

x + 20 - 5 = 3 (x - 5)

x + 15 = 3x - 15

2x = 30

x = 15

x = 15, Son's present age

x + 20 = 35 = father's present age.

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The equivalent fractions of 2/5 and 1/7 are 14/35 and 5/35

From the question, the fractions are given as

2/5 and 1/7

The denominators of the fractions are

Denominators = 5 and 7

Take the LCM of the denominators

LCM = 5 * 7

Evaluate

LCM = 35

This means that the denominators of the equivalent fractions must be 35

When this is done, we have

14/35 and 5/35

This is done by multiplying the numerator and the denominator by the same factor

Hence, the fractions are 14/35 and 5/35

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a. The utility of going to Western is 6.4/10

b. The utility of going to York would also be 5.15/10

Decision theory is a branch of mathematics that deals with decision making in the face of uncertainty.

a. If Martha accepts the early admission offer from Western, her utility would be 5/10, since that is the utility of going to Queens.

If Martha waits and gets admitted to Queens, her utility would be 5/10 as well, since that is the utility of going to Queens.

If Martha waits and gets admitted to UTM, her utility would be 9/10.

The probability of getting admitted to Queens is 1, since she is guaranteed admission. The probability of getting admitted to UTM is 6/10. The probability of accepting the early admission offer from Western is 4/10, since it is the complement of the probability of getting admitted to UTM.

Therefore, the expected utility of waiting is ⇒ (1 * 5/10) + (6/10 * 9/10) = 8.4/10. The expected utility of accepting the early admission offer is

⇒ (4/10 * 5/10) = 2/10.

Since Martha is indifferent between the two options, the utility of going to Western is 8.4/10 - 2/10 = 6.4/10

b. If Martha is indifferent between accepting an early-admissions offer from York and gambling on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens, then the utility of going to York must be the same as the expected utility of gambling.

If Martha gambles, her expected utility would be (3/4 * 6.4/10) + (1/4 * 5/10) = 5.15/10.

Therefore, the utility of going to York would also be 5.15/10.

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