There are 1,200 freshmen and 1,500 sophomores at a prep rally at noon. After 12 p.m., 20 freshmen arrive at the rally
every five minutes while 15 sophomores leave the rally. Find the ratio of freshmen to sophomores at 1 p.m.
Enter your answer as a fraction.

Answer:

m∠1 = 41°

m∠2 = 139°

Step-by-step explanation:

Set variables:

  1. ∠1 = x

  2. ∠2 = y

Make first equation:

It says "m∠2 is 16 more than 3 times m∠1."

So let's convert that into an equation:

y = 16° + 3x

Now, by looking at the photo, we can tell that its a straight line, which is equal to 180°

Derived from that, we can get m∠1 + m∠2 = 180°, which in other "words" is x + y = 180°.

Great, now we have our 2 equations, and we just have to solve.

Equations:

  1. y = 16° + 3x

  2. x + y = 180°

Let's substitute what we have for y into the second equation:

x + (16° + 3x) = 180°

Solve:

(We can take out parentheses because it's a "+" sign)

Combine like terms:

4x + 16° = 180°

Subtract 16° from both sides

4x = 164°

Isolate x by dividing both sides by 4

x = 41°

Substitute:

Now that we have x = 41°, we can substitute that in for the equation - "y = 16° + 3x"

New Equation:

y = 16° + 3(41°)

Solve:

Multiply 3 and 41°, which is 123°

y = 16° + 123°

Simplify:

y = 139°

Reminder:

m∠1 = x

m∠2 = y

Therefore,

m∠1 = 41°

&

m∠2 = 139°

Hopefully this helps!

(If you want, please mark me brainliest tomorrow)

Answer:

Basically, a straight line is equal to 180 degrees. If angle 2 is 16 more than 3 times angle 1, we get the equation of y = 16 + 3x. Put them together and you get x + 16 + 3x = 180. Then you just solve, and get x = 41. Then you put x in for the other equation and get y = 139.

Answer: $3.60

Step-by-step explanation: $30(Item Purchased)x0.12(Sales Tax)=$3.60(Sales Tax Rate for a 12% Sales Tax State.)

Answer:

63

Step-by-step explanation:

we divided 18÷2=9

and we multiply 9×7=63

Answer:

[tex]p(a) = \frac{7}{100} [/tex]

Step-by-step explanation:

Given:

7 red marbles

18 blue marbles

Total number of marbles: 7 + 18 = 25

All outcomes:

[tex]n = \frac{25 \times 24}{2 \times 1} = 300[/tex]

Let's name the event A:

A - "both marbles are red"

Event's A favorable outcomes:

[tex]m(a) = \frac{7 \times 6}{2 \times 1} = 21[/tex]

[tex]p(a) = \frac{m(a)}{n} = \frac{21}{300} = \frac{7}{100} [/tex]

Answer:

Step-by-step explanation:

r=12 in

dr=±32

A=πr²

dA=2 πr×dr=2π×12×1/32=3π/4

Possible error in computing the area=3π/4 ~square~inches.

Step-by-step explanation:

The answer is (-2, -7)

Before rotated, the coordinates of P is (7,2)

Imagine if P is rotated 360° clockwise, it will come back to the initial place (7,2).

Now it is just rotated 180° clockwise, halfway of 360° clockwise. So the coordinates should be(-7,-2) after rotated 180° clockwise.

The average annual cοst in 2014 is $4751.6.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equatiοn that represent the annual cοst in dοllars.

=> y = 83.66x+3915

Where x= number οf years

In 2004 , t = 0 years

Sο , In 2014 , t = 2014-2004 = 10 years.

Then average annual cοst in 2014 is,

=> y=83.66(10)+3915

=> y=836.6+3915

=> y = $4751.6.

Hence the average annual cοst in 2014 is $4751.6.

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The probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%.

The problem states that the probability that a Caucasian person in the U.S. has AB- blood is 1%. This means that the probability of a Caucasian person not having AB- blood is 1 - 0.01 = 0.99.

The problem asks to find the probability that none of the four unrelated Caucasian people have AB- blood. Since we are assuming that the blood types of the four people are independent, we can multiply the probabilities of each person not having AB- blood to find the probability that none of them have AB- blood.

Using the multiplication rule of probability, we can calculate the probability of no AB- blood as:

P(No AB- in 4) = P(Not AB-) * P(Not AB-) * P(Not AB-) * P(Not AB-)

P(No AB- in 4) = 0.99 * 0.99 * 0.99 * 0.99

P(No AB- in 4) = 0.9606

Therefore, the probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%. This means that there is a high likelihood that none of the four people have AB- blood.

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Answer:

-16x+28

Step-by-step explanation:

Using the 2nd and 1st term in the sequence, we can find the change.

4x+4, -x+10.  Using mental math, we can see that x decreases by 5 and 4 increases by 6.  Using this, the change is -5x + 6.

The easiest way to solve this is mental math because the 5th term is very close to the last term (the 3rd).

Solving:

-6x+16 = 3rd term, so -6x+16-5x+6 = -11x+22 | -11x+22-5x+6 = -16x+28.

Answer:

43.20 = 18x + 25.20

x = $1.00

Step-by-step explanation:

43.20 - 18x = 25.20

or

43.20 = 25.20 + 18x

Solve for x:

18x = 43.20 - 25.20

18x = 18

x = 18/18 = $1.00

Linear Scale Factor:

1) Enlargement. Scale Factor = 18/6 = 3

2) Reduction. Scale factor = 6/12 = 1/2

Answer:

Cross Sections

In this task, you will use cross section flyer, an online tool, to investigate the cross sections of cones, cylinders, pyramids, and prisms by passing different planes through such objects.

For each part of this task, you will select a three-dimensional object from the list of shapes in the bottom-left corner of the screen. A three-dimensional view of the object appears on the left, and the two-dimensional cross section formed by the intersection of the object with the chosen plane appears on the right. The bottom-right controls allow you to rotate and move the plane of intersection. By varying the intersecting plane, you can change the resulting cross section.

You can also adjust the view of the three-dimensional object by clicking and dragging anywhere inside the object window. Use the coordinate X-Y-Z axes to guide you through the views. You can verify the name of a cross section by using the Click to show identification of cross section checkbox.

For Bob: Mean =10.13,MAD = 2.66,Median =10.5 ,IQR = 5.5,Q1 = 8,Q3 = 13.5

for alan :Mean =7.25,Median = 7.5,IQR = 10,Q1 = 4,Q3 = 14

For Bob:

Mean = (8+15+10+10+10+15+7+8+10+9+12+11+11+13+7+8+9+9+8+10+11+14+11+10+9+12+14+14+12+13+5+13+9+11+12+13+10+8+7+8) / 38 = 10.13

MAD = 2.66 (calculated using the median of Bob's data)

To calculate the median and quartiles for Bob's data, we need to first sort the data in ascending order:

5, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15

Median = (10+11) / 2 = 10.5

Q1 = median of the first half of the data = (8+8) / 2 = 8

Q3 = median of the second half of the data = (13+14) / 2 = 13.5

IQR = Q3 - Q1 = 13.5 - 8 = 5.5

Therefore, for Bob:

Median = 10.5

IQR = 5.5

Q1 = 8

Q3 = 13.5

For Alan:

Mean = (2+3+4+5+7+10+12+14+15+16) / 10 = 7.25

MAD = 2.81 (calculated using the median of Alan's data)

Median = 7.5 (calculated as the average of the 5th and 6th value in Alan's sorted data)

Q1 = 4

Q3 = 14

IQR = Q3 - Q1 = 14 - 4 = 10

Therefore, for Alan:

Median = 7.5

IQR = 10

Q1 = 4

Q3 = 14

To determine if there are any outliers, we can use the following formula:

Outliers = data points outside the range [Q1 - 1.5(IQR), Q3 + 1.5(IQR)]

For Bob:

Lower outlier bound = 8 - 1.5(5.5) = -0.25

Upper outlier bound = 13.5 + 1.5(5.5) = 24.25

There are no outliers in Bob's data.

For Alan:

Lower outlier bound = 4 - 1.5(10) = -11

Upper outlier bound = 14 + 1.5(10) = 29

There are no outliers in Alan's data.

If the team needs a more consistent player with a higher median and narrower IQR, Bob might be a better choice. On the other hand, if the team needs a player who can potentially score more points, Alan might be a better choice as his mean is higher.

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The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.

What is probability?

To find the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle, we need to divide the number of bottles that meet both conditions by the total number of bottles.

Let's say Sandra examined 100 bottles, and 60 of them were properly placed, and 25 of them were Plastic #4 bottles, and 15 of those Plastic #4 bottles were also properly placed.

Then, the number of bottles that meet both conditions is 15, and the total number of bottles is 100. Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is:

P(Correctly placed and Plastic #4) = 15/100 = 0.15

So, there is a 15% chance that a randomly selected bottle is both correctly placed and a Plastic #4 bottle.

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Complete question is: Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed. The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.

The correct graph of the function [tex]y=-1\sqrt{x-2-3}[/tex] is attached as picture below.

To graph a function, we need to first determine the domain and range of the function. The domain is the set of all possible input values for the function, while the range is the set of all possible output values. Once we have determined the domain and range, we can plot the points on a graph.

To plot the graph, we can choose a set of values for the independent variable (usually denoted as x) and use the function to find the corresponding values of the dependent variable (usually denoted as y). We can then plot these points on the graph and connect them to create a curve that represents the function.

Graph using the end point and a few selected points.

x       y

2    − 3

3     −4

4     −4.41

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Answer:

The new value of the portfolio would be $207,000 - $18,180 = $188,820

Step-by-step explanation:

Using the first-order partial derivatives, we can calculate the approximate change in the portfolio value due to changes in E and S using the formula:

ΔP ≈ ∂P/∂E * ΔE + ∂P/∂S * ΔS

where ΔE is the change in the price of a Euro and ΔS is the change in the TSX stock index.

Given that ∂P/∂E = 80,000 and ∂P/∂S = -20, and the changes ΔE = -0.07 and ΔS = -629, we can plug in the values and get:

ΔP ≈ 80,000 * (-0.07) + (-20) * (-629)

≈ -5,600 - 12,580

≈ -18,180

Therefore, the portfolio value is expected to decrease by approximately $18,180 if the price of a Euro goes down by $0.07 and the TSX stock index goes down by 629 points. The new value of the portfolio would be $207,000 - $18,180 = $188,820.

Answer:

To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right triangle. Let's call the height "h" and the width "w". Then we have: w = h + 7 (since the width is 7 inches longer than the height) We also know that the diagonal measurement is 34 inches, so we can use the Pythagorean theorem to relate the height, width, and diagonal: h^2 + w^2 = d^2 Substituting the values we have: h^2 + (h+7)^2 = 34^2 Expanding and simplifying: 2h^2 + 14h - 795 = 0 Now we can solve for h using the quadratic formula: h = (-14 ± sqrt(14^2 - 4(2)(-795))) / (

The average adult weight is 79 kilοgrammes, with a standard deviatiοn οf 10 kilοgrammes.

We want tο find the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams.

An n-sample sample mean is given by: x = xi / n

where xi is the tοtal οf the sample's individual weights.

The sample mean distributiοn is apprοximately nοrmal, with mean = 79 and standard deviatiοn [tex]= 10 /\sqrt{(n)} = 10 / \sqrt{(188)0.727.}[/tex]

We can standardise the sample mean tο find the prοbability that it is greater than 80.5 kilοgrammes using the fοrmula: [tex]z = (x - ) / ( / \sqrt{(n)})[/tex]

where z is the standard nοrmal variable.

Substituting the values, we get:

[tex]z = (80.5 - 79) / (10 / \sqrt{(188)}) \approx2.14[/tex]

Using a standard nοrmal table οr calculatοr, we can find the prοbability that z is greater than 2.14:

P(z > 2.14) ≈ 0.0161

Therefοre, the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams is apprοximately 0.0161, rοunded tο fοur decimal places.

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The ladder makes an angle of approximately 19.94 degrees with the wall.

We can use trigonometry to solve for the angle between the ladder and the wall.

Let's call the angle we're looking for "theta" (θ). We can use the cosine function, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse side of a right triangle, to solve for theta:

cos(θ) = opposite/adjacent

So we have:

cos(θ) = 4.7/5

We can use a calculator to solve for theta:

cos(θ) = 0.94

Take the arc cos

θ ≈ 19.94 degrees

Therefore, the ladder makes an angle of approximately 19.94 degrees with the wall.

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Answer:

Step-by-step explanation:

The given sequence can be written as:

a_1 = 8

a_2 = 10

a_3 = 12.5

a_4 = 15.625

To find the recursive formula, we need to find the common ratio (r) between consecutive terms:

r = a_2 / a_1 = 10 / 8 = 1.25

r = a_3 / a_2 = 12.5 / 10 = 1.25

r = a_4 / a_3 = 15.625 / 12.5 = 1.25

Since the common ratio is constant, we can use the formula for a geometric sequence to find the recursive formula:

a_n = r * a_{n-1}

Substituting r = 1.25 and a_1 = 8, we get:

a_n = 1.25 * a_{n-1}

Therefore, the recursive formula for the given sequence is:

a_n = 1.25 * a_{n-1}, with a_1 = 8.

Answer:

−x2−6x+8

Step-by-step explanation:

1,Rearrange terms

2.Distribute

3.Add the numbers

4.combine like terms

hope this helps i lfet some steps for you!!!<3333

When x is -10, the value of y is 38. This means that the point (-10, 38) is on the graph of the function y = -4x - 2.

We must determine the values of x and solve for the matching value of y in order to fill in the table using the function rule y = -4x - 2. The table can then be populated with the resulting values for x and y.

An illustration table with x values ranging from -3 to 3 is shown below:

x y

-3 10

-2 6

-1 2

0 -2

1 -6

2 -10

3 -14

We may easily change x in the function rule y = -4x - 2 to -10 to find the value of y when x is -10:

y = -4(-10) (-10) - 2 \sy = 40 - 2 \sy = 38

As a result, y equals 38 when x is -10. This indicates that the point (-10, 38) is located on the y = -4x - 2 function graph.

It's vital to remember that the numbers in the table are produced by inserting various x values into the function rule, and the resulting y-values represent the corresponding locations on the function's graph. The line passing through the point on the graph of the function y = -4x - 2 has a slope of -4 and a y-intercept of -2. (-10, 38).

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The area and the circumference of the circle would be 4π square kilometers and 4π kilometers respectively.

The area of a circle with a radius r is given by:

The circumference of a circle with a radius r is given by:

Given that the radius of the circle is 2km, we can substitute r = 2 into these formulas to find the area and circumference:

In other words, the area and the circumference of the circle are 4π square kilometers and 4π kilometers respectively.

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The average cost per day is $90 and the average cost per km is $0.655.

To calculate the average cost per day, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of days.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of days is 4 (2 days for each occasion).

Therefore, the average cost per day is $360 ÷ 4 = $90.

To calculate the average cost per km, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of kilometers driven.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of kilometers driven is 550km (150km for the first occasion + 400km for the second occasion).

Therefore, the average cost per km is $360 ÷ 550km ≈ $0.655.

Correct question is " Eleni rents a car on two separate occasions. The first time, she paid $180 for 2 days and 150km. The next time, she paid $180 for 2 days and 400km. What is the average cost per day? What is the average cost per km?"

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a) The temperature decreases at a rate of -4°C per km.

b) The temperature is 0°C at a height of 8km

Here we can see the graph of a relation between the height and the temperature.

We can see that the line goes downwards from left to right, this means that as the height increases, the temperature decreases.

Notice that the horizontal squares represent 1km, while the vertical ones represent 4°C, then, the temperature is decreasing at a rate of -4°C per kilometer, your answer is correct here.

At which height is the temperature zero?

the temperature is zero at the horizontal axis, we can see that the line meets the horizontal axis at a height of 8 km, so that is the answer here.

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Answer:

3.1) Para calcular la mediana de la lista de datos, primero debemos ordenarlos de menor a mayor:

2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10

Como la lista tiene un número impar de elementos (35), la mediana es el valor central de la lista, es decir, el elemento en la posición 18. En este caso, el valor de la mediana es 6.

3.2) Para calcular la media y la mediana mediante una tabla de frecuencias, primero debemos determinar las frecuencias de cada valor en la lista:

Valor Frecuencia

2 5

4 8

6 9

8 5

10 8

La media se calcula sumando todos los valores y dividiendo entre el número total de elementos:

media = (25 + 48 + 69 + 85 + 10*8) / 35 = 5.8

Para calcular la mediana, primero debemos determinar el valor que ocupa la posición central de la lista. Como el número total de elementos es impar, ese valor es el que ocupa la posición (n+1)/2, donde n es el número total de elementos. En este caso, ese valor es el que ocupa la posición (35+1)/2 = 18.

Luego, debemos encontrar el valor que ocupa la posición 18 contando los valores de la tabla de frecuencias. Podemos hacer esto sumando las frecuencias hasta alcanzar o superar la posición 18:

Valor Frecuencia Frec. Acumulada

2 5 5

4 8 13

6 9 22

8 5 27

10 8 35

Como la posición 18 está dentro del intervalo correspondiente al valor 6, la mediana es 6.

The stem and leaves display the image and distribute information continuously. These charts are similar to histograms, but instead of using lines, they show numbers. It is a useful tool, especially when searching for statistical information.

The stem and leaf diagram, also known as the stem and leaf diagram, is a method of organizing data in a way that makes it easy to observe the frequency of importance of different species. A chart that shows numerical data arranged in a series. Each data value or number is divided into stems and leaves.

Rows and sheets are represented in the form of a special table in which each first digit or digit of the document value is divided by the stem and the last digit of the document in sheets. The letter is used to represent the stem and leaf, called stem and leaf values.

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Answer: X = 1, Y = 2

Step-by-step explanation:

X - Y = -1

X = Y - 1

2(Y - 1) - Y = 0

2Y - 2 - Y = 0

Y - 2 = 0

Y = 2

X - (2) = -1

X - 2 = -1

X = 2 - 1

X = 1

Answer:

Therefore, the height of the rectangular prism is approximately 13 meters.

Step-by-step explanation:

Let's call the height of the rectangular prism "h". We know that the base area is 54 m², which means that the product of the length "l" and the width "w" is 54. In other words:

l × w = 54

We also know that the volume of the rectangular prism is 702 m³, which means:

l × w × h = 702

We can use the first equation to solve for one of the variables, for example:

w = 54 / l

Substituting this expression for "w" into the second equation, we get:

l × (54 / l) × h = 702

Simplifying and canceling the "l" terms, we get:

54h = 702

Dividing both sides by 54, we get:

h = 702 / 54

Simplifying this expression, we get:

h ≈ 13

Therefore, the height of the rectangular prism is approximately 13 meters.

The amount of citrus juice in the combination is therefore 0.75, or 75%.

The area filled within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's potential.

If 2 gallons of 25% orange juice drink are added to 4 gallons of pure orange juice, then the total volume of the mixture will be 2 + 4 = 6 gallons.

Let's use the given function f(x) to calculate the concentration of orange juice in the mixture:

f(2) = (4 × 1.0 + 2 × 0.25) / (4 + 2)

= (4 + 0.5) / 6

= 4.5 / 6

= 0.75

Therefore, the concentration of orange juice in the mixture is 0.75 or 75%.

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1 ) Finding the difference 4/9 - ⅖:

We require a common denominator to subtract fractions. The least frequent multiple of 9 and 5 in this example is 45. So we'll recast both fractions with 45 as the denominator:

[tex]\frac{4}{9} = \frac{20}{45} \\\frac{2}{5} = \frac{18}{45}[/tex]

Now we can subtract:

[tex]\frac{20}{45} - \frac{18}{45} = \frac{2}{45}[/tex]

Therefore, the difference between 4/9 and ⅖ is 2/45.

Examine the prime factors of the denominator when the fraction is in its simplest elementary form to determine if it will have a terminating or repeating decimal. The decimal will end if they are made up of 2s and/or 5s.

2) calculating the quotient 2/9 / ⅚:

Fractions are divided by multiplying the first fraction by the reciprocal of the second fraction. So:

2/9 ÷ ⅚ = 2/9 x 6/5

Before multiplying, we can simplify:

2/9 x 6/5 = 12/45

And here's another example:

12/45 = 4/15

As a result, the quotient of 2/9 56 is 4/15.

3) Writing each terminating decimal as an integer quotient:

(a) 0.437 = 437/1000

(b) 8.2 = 82/10 = 41/5

4) Choosing whether each rational number will result in a repeated or terminating decimal:

(a) 8/15

Yes, the fraction is simplified.

The simplified denominator contains factors 2 0r 5.

It is a terminating decimal.

(b) 13/125

Yes, the fraction is simplified.

The simplified denominator contains factors other than 2 or 5.

It is a repeating decimal.

(c) 8/35

Yes, the fraction is simplified.

The simplified denominator contains factors other than 2 or 5.

It is a repeating decimal.

(d) 3/24

Yes, the fraction is simplified.

The simplified denominator contains factors other than 2 or 5.

It is a repeating decimal.

(e) 22/55

Yes, the fraction is simplified.

The simplified denominator contains factors other than 2 or 5.

It is a repeating decimal.

(f) 24/75

No, the fraction is not simplified.

The simplified fraction is = 8/25

The simplified denominator contains factors 2 or 5.

It is a terminating decimal.

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