A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.

Finding the area of irregular shapes can be challenging, as they do not have a regular geometric formula to calculate their area. However, there are a few methods you can use depending on the shape and available information. Here are three common approaches:

It's important to note that these methods provide approximations and may not yield exact results, especially for highly complex irregular shapes. Additionally, there may be specialized techniques for specific types of irregular shapes. In some cases, using computer software or online tools designed for area calculations can also be helpful.

Remember to carefully assess the shape and available information to choose the most suitable method for finding the area of an irregular shape in your specific situation.

Hello !

Answer:

[tex]\Large \boxed{\sf length=13cm}[/tex]

Step-by-step explanation:

The volume of a pyramid is given by [tex]\sf V_{pyramid}=\frac{1}{3} \times B\times h[/tex] where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where [tex]\sf B=l\times w[/tex] l is the length and w is the width (breadth).

So [tex]\sf V_{pyramid}=\frac{1}{3} \times l\times w\times h[/tex]

Given :

Let's replace h, w, l, [tex]\sf V_{pyramid}[/tex] with their values in the previous formula :

[tex]\sf 728=\frac{1}{3} \times x\times 8 \times 21\\728=56x[/tex]

Let's solve for x !

Divide both sides by 56 :

[tex]\sf \frac{56x}{56} =\frac{728}{56}\\ \boxed{\sf x=13cm}[/tex]

Have a nice day ;)

The side and angles of the right triangle are as follows:

1. 5 units

2. 5 units

3. tan ∅ = 4 / 5

The side of a right triangle can be found using Pythagoras's theorem and the angles of a right angle triangle can be found using trigonometric ratios as follows:

c² = a² + b²

where

Therefore,

1.

c² = 4² + 3²

c = √16 + 9

c = √25

c = 5 units

2.

a² = 13² - 12²

a = √169 - 144

a = √25

a = 5 units

3.

tan ∅ = opposite / adjacent

tan ∅ = 4 / 5

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Answer: Please See attached file for answers and work for problems 1-2.

1. a= 7

  b= 70 degrees

2. a= 6

  b= 19pi/20

Step-by-step explanation:

Use the rule(s):

[tex]z_{1} z_{2} =r_{1} r_{2} cis[/tex](θ[tex]_{1}[/tex]+θ[tex]_{2}[/tex])

[tex]\frac{z_{1} }{z_{2}} =\frac{r_{1} }{r_{2}}cis[/tex](θ[tex]_{1}[/tex]-θ[tex]_{2}[/tex])

and isolate it to standard form: a (cos b + i sin b)

you can also rewrite that as a (cis b)

The required area of the given parallelogram is 156 square yards.

Given that, the base of the parallelogram is 12 yd and height of the given parallelogram is 13 yd.

To calculate the area of the parallelogram by using the formula,

Area of parallelogram = base × height.

That implies, Area of given parallelogram(A) = base × height.

A = 12 × 13.

A = 156 square yards.

Therefore, the required area of the given parallelogram is 156 square yards.

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Mbhalati's statement is valid.

The charge of R180 is less than the total value of his deposit is R2000.

To determine whether Mbhalati's statement is valid, we need to calculate the total value of his deposit and compare it to the stated charge.

Given information:

Value of notes deposited: R1500

Value of coins deposited: R500

Charge for the deposit: R180

To calculate the total value of Mbhalati's deposit, we add the value of the notes and the value of the coins:

Total deposit value = Value of notes + Value of coins

Total deposit value = R1500 + R500

Total deposit value = R2000

Now, let's compare the total deposit value to the stated charge:

Total deposit value = R2000

Stated charge = R180

Mbhalati's statement would be valid if the stated charge (R180) is equal to or less than the total deposit value (R2000).

Let's check:

Is R180 ≤ R2000?

Yes, R180 is less than R2000.

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Answer:

B. 33

Step-by-step explanation:

Step 1:  Find total measure of ∠R:

Step 2:  Find total measure, m, of ∠Q:

m∠P + m∠Q + m∠R = 180

m∠Q = 180 - (m∠P + m∠R)

m∠Q = 180 - (60 + 76)

m∠Q = 180 - 136

m∠Q = 44°

Since QA bisects ∠Q into two congruent angles, we divide 44 by 2 to find the measures of each angle made by the bisector:  44/2 = 22.

Step 3:  Find x by setting the sum of the 38° angle, the 22° angle, and angle C equal to 180:

38 + (3x + 21) + 22 = 180

60 + 3x + 21 = 180

81 + 3x = 180

3x = 99

x = 33

Thus, x equals 33.

The correct match are;

1 - 0.25

2 - 0.5

3 - 0.8

1) We must first evaluate the probability of each event before multiplying them together in order to predict the likelihood of receiving heads on a coin and an even number on a die.

Chance of flipping a coin heads:

The probability of receiving heads is 1/2 (or 0.5) because a fair coin has two equally likely outcomes (heads or tails).

Probability of rolling a die for an even number:

The probability of rolling an even number is 3/6 (or 1/2 or 0.5) since three of a fair die's six sides are even numbers (2, 4, and 6).

We sum the probabilities of the different events to determine the total probability:

P(Heads and Even) is defined as P(Heads) x P(Even) = 0.5 x 0.5 = 0.25, or 25%.

Therefore, the chance of rolling an even number on a die and receiving heads on a coin is 0.25, or 25%.

2) There are 26 red cards in a regular deck of cards out of a total of 52

As a result, the likelihood of earning a red card is:

P(Red card) = Red card count / total cards = 26 / 52 = 0.5 (or 50%).

Therefore, the chance of drawing one red card from a regular deck of cards is 0.5, or 50%.

3) The total number of marbles in the bag of 2 green, 8 yellow, 4 red, 3 blue, and 3 orange marbles is 2 + 8 + 4 + 3 + 3 = 20.

One can compute the likelihood of drawing a red marble as follows:

P(Red marble) = Red marble count / Total marble count = 4 / 20 = 0.2 (or 20%).

However, we are interested in determining the likelihood of NOT drawing a red marble.

Therefore, we deduct from 1 the likelihood of drawing a red marble:

Red marble: P(Not drawing one) = 1 - P(Red marble) = 1 - 0.2 = 0.8, or 80%.

Therefore, 0.8 or 80% of the time, no red marble will be drawn from the specified bag.

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Answer:

Step-by-step explanation:

The expression x-3 is a factor of P(x)=x²-x2-2x-12 because the remainder is zero. P(x) written as a product of two factors is (x-3)(x²+2x+4).

Answer:

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.

The commutative rule of addition, the commutative rule of multiplication, the associative rule of addition, the associative rule of multiplication, and the distributive property of multiplication make up the fundamental rules of the algebra.

ps. i copy from the internet

The domain, the range, and the intervals over which the function is increasing, decreasing, or constant is  [-2, -1],  [-1, 1] and  [1, 3].

We are given that;

The graph of the function

Now,

From the graph, we can see that:

The domain of the function is [-2, 3], since these are the smallest and largest x-values that the graph covers.

The range of the function is [-1, 2], since these are the smallest and largest y-values that the graph covers.

The intervals of the function are:

Increasing on [-2, -1], since the graph is rising on this interval.

Constant on [-1, 1], since the graph is flat on this interval.

Decreasing on [1, 3], since the graph is falling on this interval.

Therefore, we can write:

Domain: [-2, 3]

Range: [-1, 2]

Intervals:

Increasing: [-2, -1]

Constant: [-1, 1]

Decreasing: [1, 3]

Therefore, by the function the answer will be [-2, -1],  [-1, 1] and  [1, 3].

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Answer:

50

Step-by-step explanation:

The angles of a triangle add up to 180°

So

53+77+x=180

x=180-130

x=50

Answer:

k = - 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given equation of PQ is

3x - 2y = 12 ( subtract 3x from both sides )

- 2y = - 3x + 12 ( divide through by - 2 )

y = [tex]\frac{3}{2}[/tex] x - 6 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

now calculate the slope of PQ using the slope formula and equate to [tex]\frac{3}{2}[/tex]

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = P (6, 3 ) and (x₂, y₂ ) = Q (- 2, k )

m = [tex]\frac{k-3}{-2-6}[/tex] = [tex]\frac{k-3}{-8}[/tex]

equating the slopes of PQ

[tex]\frac{k-3}{-8}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2(k - 3) = - 8 × 3 = - 24 ( divide both sides by 2 )

k - 3 = - 12 ( add 3 to both sides )

k = - 9

One way to show a function is 1-1 is to show that if two outputs are the same, then the inputs had to have been the same as well:

   If f(a) = f(b), then a=b.

If you can show this, you've shown that each output is paired with a unique input, so the function is 1-1.

For this function, we'd first start assuming that f(a) = f(b):

              f(a) = f(b)

         -3a+5 = -3b+5

Now we'll solve this for a:

        -3a + 5 = -3b + 5

   -3a + 5 - 5 = -3b + 5 - 5

               -3a = -3b

      -3a ÷ (-3) = -3b  ÷ (-3)

                   a = b

This shows that the only way the outputs are the same is if the inputs are the same, which means each output comes from a unique input, so the function is 1-1.

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  [tex]x\leq 2[/tex]

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer: The rental cost of each movie is $2 and each video game is approximately $5.5

Step-by-step explanation:

Let's assume the rental cost per movie is "m" and the rental cost per video game is "v". We can set up a system of linear equations based on the given information.

From the first month:

5m + 2v = 21 ----(1)

From the second month:

3m + 8v = 50 ----(2)

To solve the system of equations:

5m + 2v = 21 ----(1)

3m + 8v = 50 ----(2)

We can multiply equation (1) by 4 to make the coefficients of "m" the same:

4(5m + 2v) = 4(21)

20m + 8v = 84 ----(3)

Now, subtract equation (2) from equation (3):

(20m + 8v) - (3m + 8v) = 84 - 50

20m - 3m + 8v - 8v = 34

17m = 34

Divide both sides of the equation by 17:

m = 34 / 17

m = 2

Now that we have the value of "m," we can substitute it back into either equation (1) or (2) to solve for "v." Let's use equation (1):

5(2) + 2v = 21

10 + 2v = 21

2v = 21 - 10

2v = 11

v = 11 / 2

v = 5.5

Therefore, the solution to the system of equations is:

m = 2 and v = 5.5

Hello!

BC // AB => Thalès

AB/AC = AE/AD = BE/CD

3/(3+8) = AE/(AE+10)

3/11 = AE/(AE+10)

3/11 = AE/(AE+10)

3/11 * (AE+10) = AE/(AE+10) * (AE+10)

(3AE + 30)/11 = AE

(3AE + 30)/11 * 11 = AE * 11

3AE + 30 = 11AE

30 = 11AE - 3AE

30 = 8AE

AE = 30/8

AE = 3.75

AE ≈ 3.8

Answer:

Here is an example of a dot plot (in text, did as best as I could to represent it) that matches the description you provided:

Number of Minutes Spent on Math Homework Problem

 |

10|    o

9| o

8|

7|       o

6|

5|          o

4|

3|             o

2|

1|                o

0|___________________

  1  2  3  4  5  6  7  8  9  10

  Students

This dot plot shows the number of minutes spent on a math homework problem by ten students. The mean amount of time is represented by the dot at the y-value of 9, and the MAD (Mean Absolute Deviation) is represented by the spread of the data around the mean.

If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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There were 14 games played in total during April and May of 2022.

To determine the total number of data values (games played) represented in the frequency table,

Add all of the frequencies indicated in the table.

So, we have:

0 goals scored in 1 game

3 games with a single goal scored 2 goals scored in 2 games

4 games with three goals

2 games with four goals 1 game with 7 goals

And 1 game with 9 goals

Adding up all of these frequencies,

We get,

⇒ 1 + 3 + 2 + 4 + 2 + 1 + 1 = 14

Therefore,

There were 14 games played.

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Answer:

Step-by-step explanation:

According to the sources I found, cows consume an average of 3 to 30 gallons of water per day. One gallon is equivalent to 3.78541 liters. Therefore, a cow drinks between 11.35623 liters and 113.5623 liters per day.

If we assume that each cow drinks 30 gallons (113.5623 liters) per day, then a full trough would have enough water for 2.37 cows per day (226.8 liters / 113.5623 liters per cow). Therefore, Zipho’s statement is incorrect if we assume that each cow drinks 56 liters per day.

Based on the given information, the average annual salary for all US teachers is $48,000 with a standard deviation of $5,700. So, you should feel good about your $52,000 offer, as it is above the average salary for US teachers and places you in a relatively higher earning position compared to your peers.

If you apply for a teaching position and were offered $52,000, let's determine your relative position in the salary distribution using a z-score.

The z-score is calculated as (X - μ) / σ, where X is your salary, μ is the mean salary, and σ is the standard deviation. Plugging in the values, we have:
Z = ($52,000 - $48,000) / $5,700 = $4,000 / $5,700 ≈ 0.70
A z-score of 0.70 indicates that your salary is 0.70 standard deviations above the mean salary. Based on a normal distribution table, about 24% of teachers would earn more than you, and 76% would earn less.

Considering the probability result, you should feel good about your $52,000 offer, as it is above the average salary for US teachers and places you in a relatively higher earning position compared to your peers.

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The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

We have,

To find the angle opposite to side BC in triangle ABC, we can use the Law of Cosines.

The Law of Cosines states that in a triangle with sides of lengths a, b, and c, and the angle opposite to side c being denoted as C, the following equation holds:

c² = a² + b² - 2ab x cos(C)

In this case,

Side a is BC with length 12, side b is AC with length 20, and side c is AB with length 11. We want to find the angle C, which is opposite to side BC.

Plugging the given values into the Law of Cosines equation:

11² = 12² + 20² - 2 x 12 x 20 x cos C

121 = 144 + 400 - 480 x cos C

121 = 544 - 480 x cos C

480 x cos C = 544 - 121

480 x cos C = 423

cos C = 423/480

Now, we can find the angle C by taking the inverse cosine (arccos) of (423/480):

C = arccos(423/480)

Using a calculator, we find that C is approximately 38.213 degrees.

Therefore,

The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

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Answer:

2 x 2

Step-by-step explanation:

Given the dimensions of the first matrix are 2x3 and the dimensions of the second matrix are 3x2, then the dimensions of the product will be 2x2.

Remember that the dimensions of a matrix are read by rows*columns.

The product of an m×n matrix and an n×k matrix is an m×k matrix

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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To find the value of f^(-1)(7), we need to determine the inverse function of f(x) = 0.5(3)^x.

To find the inverse function, we interchange the roles of x and y and solve for y.

Let's start with the original function:

y = 0.5(3)^x

Now, let's interchange x and y:

x = 0.5(3)^y

Next, solve for y:

x = 0.5(3)^y

2x = 3^y

log base 3 (2x) = y

So, the inverse function of f(x) = 0.5(3)^x is:

f^(-1)(x) = log base 3 (2x)

Now, we can find the value of f^(-1)(7):

f^(-1)(7) = log base 3 (2 * 7)

= log base 3 (14)

Using a calculator, we can approximate the value of log base 3 (14) to be approximately 2.264.

Therefore, the value of f^(-1)(7) is approximately 2.264.

Answer:

p=7.5 or 7 1/2

Step-by-step explanation:

To solve this equation you need to isolate the P

1) We can multiply P and the numerator (In this case 2) since it is the same thing. The rewritten equation is 2p/3=5.

2) Now we can multiply both sides by 3 to isolate 2p. The equation is now 2p=15

3) The next step is to divide both sides by 2 so we can isolate the p. We now have p=7.5 or 7 1/2

                                          Hope this helps :)

keeping in mind that the sum of all exterior angles in a polygon always add up to 360°, then

[tex]58+39+50+48+59+x+x~~ = ~~360\implies 254+2x=360 \\\\\\ 2x=106\implies x=\cfrac{106}{2}\implies x=53[/tex]

Answer:

X is 53 because 106 divide by 2 is equal to 53

Answer:

To find the experimental probability of not spinning a 1, we need to determine the total number of spins and the number of spins that resulted in not landing on 1.

From the bar graph, we can see that the bar labeled "1" ends at 8, indicating that the spinner landed on 1 a total of 8 times.

To find the total number of spins, we sum up the values at the end of each bar:

Total number of spins = 8 + 6 + 9 + 11 + 9 + 7 = 50

The number of spins that did not result in landing on 1 is the sum of the values at the ends of the bars labeled 2, 3, 4, 5, and 6:

Number of spins not landing on 1 = 6 + 9 + 11 + 9 + 7 = 42

Now, we can calculate the experimental probability of not spinning a 1 by dividing the number of spins not landing on 1 by the total number of spins:

Experimental probability of not spinning a 1 = Number of spins not landing on 1 / Total number of spins

Experimental probability of not spinning a 1 = 42 / 50

Experimental probability of not spinning a 1 = 0.84 or 84%

Therefore, the experimental probability of not spinning a 1 is 84%.

Step-by-step explanation:

Answer: 21/25 or 0.84

Step-by-step explanation:

8+6+9+11+9+7=50

50-8=42

42/50=21/25=0.84