Which angles are congruent to each other? Select all that apply.

To order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

If we consider each "drop-in" guest as half a guest, then the total number of guests becomes:

40 + 0.5x, where x is the number of "drop-in" guests.

To determine how much of each food item to order, we can use the recommended amounts as a guide and scale them up based on the total number of guests:

So, to order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

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1. 13 cm

2. 27.2 in

3.24x

4. 7 m

radius is half of the diameter

diameter is twice of the radius so

radius=diameter/2,diameter =2x radius

The scores of the maths students recorded by their tutor presented in three suitable groups are 1 - 10, 11 - 20, 21 - 30.

Math test scores: 15, 24, 6, 8, 29, 6, 12, 17, 24, 22, 25, 30, 18, 3, 11, 7, 18, 27, 28, 27

The group of scores when divided into 3;

Group frequency

1 - 10 5

11 - 20 6

21 - 30 9

Therefore, the groups 1 - 10, 11 - 20, 21 - 30 have the frequency 5, 6 and 9 respectively.

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The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.

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Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.

Let C, P and G denotes the number of children, parents and the grandparents in the function.

We get the system of equations,

C + P + G = 400 [equation 1]

P = 2G  ⇒ G = P/2 [equation 2]

C = P + 50 [equation 3]

Substituting 2 and 3 in 1,

(P + 50) + P + (P/2) = 400

2P + P/2 = 350

5/2 P = 350

P = 140

C = P + 50 = 140 + 50 = 190

G = P/2 = 140/2 = 70

Hence the number of parents = 140, grandparents = 70 and children = 190.

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True. The total interest expense on the bond over its eight-year life is $400,000.

The total interest expense on the bond is calculated as follows;

Annual interest payment = face value of bond x annual interest rate

= $500,000 x 10%

= $50,000

Semi-annual interest payment = Annual interest payment / 2

= $50,000 / 2

= $25,000

The total interest expense over the bond's life is then calculated as:

Total interest expense = Semi-annual interest payment x Number of semi-annual periods

= $25,000 x 16

= $400,000

Therefore, the statement is true.

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The number of times the Team Olympus could have tied is not given in the below options

Given data ,

Let's use "W" for the number of victories and "T" for the number of ties. The information available indicates that Team Olympus played 19 games and earned a total of 28 points.

Team Olympus receives three points for each victory, so three victories would result in a total of nine points.

Team Olympus receives one point for each tie, making the sum of the tie-related points (T) equal to one times the number of ties.

We may construct the following equation using the information provided:

3W + 1T = 28   be equation (1)

Now , Since Team Olympus played 19 games in total, the total number of games (W + T) should be equal to 19.

W + T = 19   be equation (2)

Subtracting equation (2) from equation (1) , we get

2W = 9

Divide by 2 on both sides , we get

W = 4.5 wins

And , the supplied possibilities (3, 4, 2, 5, 0) do not add up to a total of 28 points, hence none of them are acceptable answers for Team Olympus.

Hence , in this situation, Team Olympus could not have tied many times

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The two x-values where the sculpture at sea-level are x = 2.581 and x = -0.581

From the question, we have the following parameters that can be used in our computation:

y = 2x^2 - 4x - 3

When the sculpture at sea-level, the value of y is 0

So, we have

2x^2 - 4x - 3 = 0

When solved graphically, we have

x = 2.581 and x = -0.581

Hence, the x values are x = 2.581 and x = -0.581

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Answer:

Step-by-step explanation:

4992223553535

your in school ask a teacher

Answer:

  (a)  x = -4y +19

Step-by-step explanation:

You want to know a good first step for solving the system of equations in an efficient manner.

One way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.

Here, a useful first step is to solve the second equation for x:

  x = -4y +19

__

Additional comment

Then the solution proceeds with substitution for x:

  3(-4y +19) +2y = 17

  -10y +57 = 17

  -10y = -40

  y = 4

  x = -4(4) +19 = 3

The solution is (x, y) = (3, 4).

Another reasonable first step is to subtract the second equation from twice the first:

  2(3x +2y) -(x +4y) = 2(17) -(19)

  5x = 15

  x = 3

  3 +4y = 19 . . . . . . substitute for x in the second equation

  y = (19 -3)/4 = 4

The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.

The best graphical representation to display the data would be a Histogram. This is appropriate because it will display the distribution and frequency of the grades, thus making it easy to compare the classes. To create the graph, you will use bars to depict the range of figures. This is on the x-axis while the y-axis will contain the frequency of occurrence.

Designing a histogram requires an understanding of the range of values, the frequency of occurrence, and the general picture that the graph is meant to paint in the mind of the reader.

So, for the histogram above, you can have a title like The distribution of 7th graders' breakfast over a 30-day period. Next, you label the x and y axis and plot the figures based on the information provided.

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Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: [tex]V=\frac{1}{2} (bh) (l)[/tex]
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
[tex]V = \frac{1}{2} (6x6)(8)[/tex]

[tex]V=\frac{1}{2} (36)(8)[/tex]

[tex]V=(18)(8)[/tex]

[tex]V=144[/tex]

Your answer, because it is a 3D shape, should be cubed, so:
[tex]V=144ft^{3}[/tex]

With a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

When calculating the circumference (C) of a circle, the formula 2 * π * radius (R) is employed.

Taking into consideration R = 20 feet, we shall arrive at the following figure:

C = 2 * π * 20

C ≈ 2 * 3.14159265359 * 20

C ≈ 125.66 feet

If we use this calculation to determine the total distance covered after running 10 laps around a track, our equation morphs into Circumference (C) multiplied by the Number of laps (L).

When L equals 10, it follows that:

Total distance ≈ 125.66 feet * 10

Total distance ≈ 1256.6 feet

Therefore, with a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

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What is the total distance covered after running 10 laps around a circular track with a radius of 20 feet?

8.) The inequality that describes the possible number of calories X, you can eat during the rest of the day would be < 1200. That is option A.

9.) The value of X would be = 3.

For question 8.)

The quantity of calories for each day < 2200. That is;

1 day < 2200

The calories consumed for breakfast = 350

The calories consumed for lunch = 650

The total calories consumed = 350+650 = 1000 calories.

The amount of calories needed to be consumed the more = 2200-1000 = 1200

Therefore the quantity of calories needed more < 1200 calories.

For question 9.)

t(X) = 3x - 5

where;

t(X) = 4

That is;

4 = 3x - 5

3x=4+5

3x = 9

X = 9/3 = 3

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A line on the graph which could represent this scenario is: C. g(x), the third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Janelle when she woke up, the temperature can be modeled by this equation:

y = mx + c

y = 2x + (-3)

y = 2x - 3

Therefore, the table of values can be generated as follows;

x      y

0     -3

1       -1

2       1

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Answer:

2x2+x+5

Step-by-step explanation:

By using the head to tail, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5).

In Geometry, a vector is typically composed of two end points. First, is the starting point which is commonly known as a "tail" and the second (ending) point that is commonly known as a "head."

Additionally, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

Next, we would add the two (2) vectors algebraically as follows;

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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The exponential function in this problem represents a decay, with a percentage rate of 6%.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function is classified as growth or decay as follows:

The function in this problem is defined as follows:

y = 15(0.94)^x.

As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:

1 - r = 0.94

r = 1 - 0.94

r = 0.06

r = 6%.

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Answer:

12 + 3 + 12 + (1/2)π(3) = 27 + (3/2)π ft

= 31.71 ft

The requried, there is only 1 possible lineup of 6 songs from a list of 6 songs.

To determine how many different lineups are possible, we can use the formula for combinations, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items being selected, and the exclamation mark denotes the factorial function.

In this case, we have n = 6 (the total number of songs) and k = 6 (the number of songs to be selected). So we can plug these values into the formula:

6C6 = 6! / (6!(6-6)!) = 6! / (6!0!) = 1

Therefore, there is only 1 possible lineup of 6 songs from a list of 6 songs.

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If the number of bacteria triples every 4 hours, then after 1 day (24 hours), the number of bacteria will triple 6 times.

Tripling a number 6 times is the same as multiplying it by 3 raised to the power of 6, or 3^6.

So, if there are 25 bacteria to start, the number of bacteria after 1 day will be:

25 x 3^6 = 25 x 729 = 18,225 bacteria.

Answer:

Step-by-step explanation:

It is not possible to accurately determine the number of bacteria in the glass after 4 hours without additional information such as the rate of bacterial growth, the environmental conditions, and whether any bacteria were removed or added during that time.

a) For Super Home, the superior (or dominant) tactic is to magnify the size of the store and parking lot. This is, regardless of what Great Home does, Super Home's payoff is amplified when it expands its size ($1m vs $0.4m if Great Home amplifies; $3.2m vs $2m if Great Home passes).

Similarly, for Great Home, the logical (or dominant) strategy is also to expand the size of the store and parking lot. This is because, although unrelated to Super Home's decision, Great Home's payoff is augmented when it enlarges its size ($1.5m vs $0.6m if Super Home magnifies; $3.4m vs $2.5m if Super Home disallows).

b) If both stores implement their authoritative plan, Great Home will witness an annual profit growth of $1.5 million, and Super Home will observe an annual profit growth of $1 million.

A Nash Equilibrium comprehends a state wherein each player chooses their finest ploy given the stratagems selected by the other participant(s), and no player can modify their consequence through exclusively adapting their strategy. In this case, the Nash Equilibrium exists in (Increase, Increase), which spans over the payoffs ($1.5m, $1m).

c) The conjunctive approach both stores should commit to would be for Great Home to amplify the size of its store and parking lot, and Super Home to renounce increasing its size.

Under this harmonized approval, the annual profit growth for Great Home will come out at $3.4 million, and for Super Home, it will arrive at $0.4 million. This system gives rise to a higher collective gain compared to the Nash Equilibrium.

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Answer:      

    |

    |  3/4 kg    

    |     x          

    |              

    |     x          

    |           x    

    |     x          

    |  x              

    |        x        

    |     x          

    |_________

       1 kg 1 1/2 kg 2 kg 2 1/2 kg

Two students brought 3/4 kg of soil.

Four students brought less than 1 1/2 kg of soil (the ones who brought 3/4 kg and the one who brought 1 kg).

Eight students brought 1 kg or more of soil.

Two fewer students brought 1 kg than 2 kg (two students brought 1 kg and four students brought 2 kg).

Two students brought more than 1 1/2 kg but less than 2 1/2 kg (the ones who brought 2 kg).

The total amount of soil brought by all the students is:

Copy code

1 1/2 kg + 3/4 kg + 1 1/2 kg + 1 kg + 2 kg + 3/4 kg + 2 kg + 2 kg + 2 kg + 2 1/2 kg + 3/4 kg

= 19 3/4 kg

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is timed by 1 1/2kg

Applying the formula for the area of triangle using sine, we have:

sin A = 1/3 (A ≈ 19.5°).

Given that a triangle has the following parameters:

Area of triangle ABC = 21 square units

Side b = 14 units

Side c = 9 units

Thus, applying the area of a triangle using the sine rule, we have the following formula:

Area = 1/2 * b * c * sin A

Plug in the values:

21 = 1/2 * 14 * 9 * sin A

2 * 21 = 126 * sin A

42 = 126 * sin A

42/126 = sin A

sin A = 1/3

A = sin^(-1)(1/3)

A ≈ 19.5°

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Answer:

relation 1-function

relation 2-not a function

relation 3-function

relation 4-funtion

Answer:

Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.

The crate of bananas is heavier than the bag of apples by 53 1/4 pounds.

An apple and a banana are both kinds of fruits. They both weigh differently.

Weight of a bag of apple = 8 7/8 pounds

Weight of a crate of bananas = 6 times as heavy as the apples

= 6 × 8 7/8

= 6 × 71 /8

= 426 / 8

= 53 1/4 pounds

Therefore, the weight of a crate of bananas is 53 1/4 pounds

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The magnitude of the vector 4v is 4 times the magnitude of v, which is equal to 4 √29.

Given the vector v = 5i - 2j, we can find the magnitude or norm of the vector ||v|| using the formula:

||v|| = √(v · v)

where · denotes the dot product of the vector with itself.

Substituting the values of the vector v, we have:

||v|| = √((5i - 2j) · (5i - 2j))

Expanding the dot product using the distributive law, we get:

||v|| = √(25i² - 20ij + 4j²)

Since i² = j² = 1 and ij = ji = 0, we can simplify this expression to:

||v|| = √(25 + 4) = √29

Thus, the magnitude of the vector v is √29.

Now, we need to find the magnitude of the vector 4v. Using the property that ||kv|| = |k| ||v|| for any scalar k and vector v, we have:

||4v|| = |4| ||v|| = 4 √29

In summary, the magnitude of the vector v is √29, and the magnitude of the vector 4v is 4 √29.

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The areas of the figures are 36 square units & 9 square units and the scale factor of dilation is 1/2

From the question, we have the following parameters that can be used in our computation:

The composite figures

The areas of the figure is calculated using the sum of the individual areas

So, we have

Figure 1 = Rectangle + Triangle

Using the area formulas, we have

Figure 1 = 5 * 4 + 1/2 * 8 * 4

Evaluate

Figure 1 = 36

The second figure is not clear

However, from the question text we have the area to be

Figure 2 = 9

So, the scale factor from figure 1 to 2 is

Scale factor = √[Figure 2/Figure 1]

This gives

Scale factor = √[9/36]

Evaluate

Scale factor = 1/2

Hence, the scale factor is 1/2

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