A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:





How many students are in the class?

The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem

Given data ,

Let the two triangles be represented as ΔMDA and ΔMBC

Now , the measure of side MD ≅ MB ( given )

And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )

Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

So , ΔMDA ≅ ΔMBC by ASA theorem

Hence , the congruent triangles are solved

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According to Jean-Claude Maleuvre's book "Museum Memories: History, Technology, Art," Gauguin's views on Polynesian women were complex and contradictory. On the one hand, he was fascinated by their exotic beauty and saw them as a source of artistic inspiration. On the other hand, he objectified and exoticized them, portraying them as primitive and sexually available. Gauguin's depictions of Polynesian women have been criticized as perpetuating colonialist stereotypes and promoting a Westernized gaze.

The sum of all the number is found to be 630 which is not given in the options.

Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.

The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.

Therefore, we have,

9x = 220 + x + 340

Simplifying and solving for x, we get,

8x = 560

x = 70

Therefore, the sum of all the numbers is 9x = 970 = 630.

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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?

a) 112

b) 504

c) 144

d) 560

d) 122

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

There are two distinct y values satisfying the given equation.

First, we rewrite the equation as |y-3| = 5 - x² + 8x - 18. Then, we express |y-3| as two cases: y-3 and -(y-3).

Case 1: y - 3 = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 16.

Case 2: -(y - 3) = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 10.

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

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Step-by-step explanation:

x = -2 or x = 2

x + 2 = 0 or x - 2 = 0

(x + 2) (x - 2) = 0

x² - 4 = 0

The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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

[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]

From the above expression, we can see that the different expression in each term is

9/n

So, we introduce a variable

Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

When represented using the sigma notation, we have

[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).

Expected number of dog owners who brush their dog's teeth = 639 x 0.18

= 115.02 (rounded to the nearest whole number)

So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.

The work done in pushing the car along the level road from point A is found to be 8147 foot-pounds.

The work done in pushing a car along a level road can be calculated using the formula,

work = force × distance × cos(angle) where the angle between the force and the direction of motion is 0 degrees (since the force is parallel to the level road). The force is given as 103 pounds, and the distance is 79 feet. Therefore,

work = 103 × 79 × cos(0) = 8147 foot-pounds

Rounding to the nearest foot-pound, the work done in pushing the car from point A to point B is 8147 foot-pounds.

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The equivalent expression for the given expression 132/11 is 12.

1) Given that, 132/11

Here, the equivalent expression is 132/11 =12

2) 126/7 = 18

3) 7)98(14

      7

_______

     28

     28

________

      0

4) Sixty-four divided by four

That is, 64/4 = 16

5) 28÷2

= 28/2

= 14

6) 28/2 = 14

7) 48/3 = 16

8) 36÷2

= 36/2

= 18

9) 36÷3

= 36/3

= 12

Therefore, the equivalent expression for the given expression 132/11 is 12.

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Jordan's account balance at the end of the month would be $143.85.

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.

Initial balance: $92.66

Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)

Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)

To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:

Account balance at the end of the month = Initial balance + Deposits - Withdrawals

= $92.66 + $185.60 - $134.41

= $143.85

Hence, Jordan's account balance at the end of the month would be $143.85.

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Answer: The coordinates of F' are (14, 21).

Step-by-step explanation:

       Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.

               (21, -14) ➜ (14, 21)

               The coordinates of F' are (14, 21).

Answer:

(x-3)(x+4)

Step-by-step explanation:

This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49

χ1,2=-1+-7^2=3

=-4

Answer:

26

Step-by-step explanation:

The probability of needing fewer than 4 rolls to get doubles is 13/25.

Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.

This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).

Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:

P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4

P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4

The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.

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Complete questions as follows-

Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.

The total area of the front of the figure is 21 [tex]feet^{2}[/tex].

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

To find the total area we need to add the area of the refrigerator and the area of the freezer.

The top part i.e refrigerator has a height of 5 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 5 * 3

                                                       = 15 [tex]feet^{2}[/tex]

The bottom part i.e freezer has a height of 2 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 2 * 3

                                                       = 6 [tex]feet^{2}[/tex]

The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section

                                                                   = 15 + 6 = 21[tex]feet^{2}[/tex]

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Answer:

Step-by-step explanation:

actual area : 60 x 12 = 720

1/2 = 0.5

60 + 0.5 = 60.5        12 + 0.5 = 12.5  -max area = 60.5 x 12.5 = 756.25

60 - 0.5 = 59.5         12 - 0.5 = 11.5    -min area =  59.5 x 11.5 = 684.25

absolute error :  1/2(756.25-684.25) = 36

relative error : 36/720 = 0.05

 ... your welcome  

a) The future value of the account after 30 years can be calculated using the formula:

FV = P * ((1 + r/n)^(n*t))

where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:

FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60

So you will have $150,505.60 in the account after 30 years.

b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:

$300 * 360 = $108,000

c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:

$150,505.60 - $108,000 = $42,505.60

Answer:

a) you will have approximately $133,381.85 in the account in 30 years.

b) a total of $108,000 into the account over 30 years.

c) a total of $25,381.85 in interest over 30 years.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).

To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:

0.3 * sqrt(100) = 3

So the margin of error in terms of the number of vehicles is ±3.

Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.

So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.

Answer:

Step-by-step explanation:

8,800x0.09=792. The salesperson earns $792 in commission.

Answer:

$792

Step-by-step explanation:

8800×0.09= 792

9÷100=0.09

commission =$792

The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.

To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.

The volume of a cylinder is given by the formula  [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.

Container A has a radius of  [tex]4[/tex] feet and a height of 18 feet, so its volume is:

[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet

Container B has a radius of 5 feet and a height of 15 feet, so its volume is:

[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex]  cubic feet

When the water from Container A is transferred to Container B, the volume of water in Container B will be:

V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet

The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:

V(empty in  [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet

To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:

Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]

[tex]= (87\pi / 375\pi) \times 100[/tex]

[tex]= 23.2[/tex]%

Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

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For the given vector v = 2i - 3j, the value of the vector magnitude ||2v|| is 2√13.

To find the norm, or magnitude, of a vector, we use the Pythagorean theorem in the following way:

||v|| = √(v₁² + v₂² + ... + vn²)

In this case, we have v = 2i - 3j, so:

||v|| = √((2)² + (-3)²)

= √(4 + 9)

= √13

So the norm of the vector v is √13.

To find ||2v||, we simply double the vector and then find its norm:

2v = 2(2i - 3j)

= 4i - 6j

||2v|| = √((4)² + (-6)²)

= √(16 + 36)

= √52

= 2√13

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Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.

Using a standard normal distribution table or   calculator, we can find the z   scores corresponding to 35,000 miles and 40,000 miles...

z 1 = ( 35,000 - 40,000) / 3,700 = -1.35

z 2 = (40,000 -   40,000) / 3,700 = 0

Then, we can find the area between these z  scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:

P( -1.35  < Z < 0) = 0.4119 or 41.19%

What it means is that , about 41.19% of the tires would qualify for a free replacement.

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Answer:

5%

Step-by-step explanation:

Percent error equation is:

(Absolute value of experimental value - actual value / actual value) * 100

Experimental Value: 315

Actual Value: 300

315 - 300 / 300 = 0.05

0.05*100 = 5

Percent error is 5%

Answer: the percent error is 5%

Step-by-step explanation:

Answer:

To find the product of matrices AB, we need to multiply the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and then sum these products.

Since matrix A is a 2x2 matrix and matrix B is a 2x3 matrix, we can perform the multiplication as follows:

AB = | 1 2 |   | 1 2 3 |   | (1*1)+(2*4)  (1*2)+(2*5)  (1*3)+(2*6) |

    | 3 4 | x | 4 5 6 | = | (3*1)+(4*4)  (3*2)+(4*5)  (3*3)+(4*6) |

                          |              |              |              |

    |  9 12 15 |          |  9  12  15 |

Therefore, the product of matrices AB is a 2x3 matrix, and the answer is C) 2x3.

Answer:

3

Step-by-step explanation:

3 * 3 = 6

1/2 * 6 = 3 not 4.5

Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.

The 3 x 3 part turns into 9

So we have 1/2 x 9 or 9/2

Use long division to find that 9/2 gives a quotient of 4 and remainder 1

Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.

The "remainder 1" then leads to 1/2 = 0.5

quotient = 4

remainder = 1 ---> decimal portion = 1/2 = 0.5

So that's how we get to 4+0.5 = 4.5

You can use a calculator to see that 9/2 = 4.5

The decimal - 2. 97 is the solution to the subtraction problem of D.  - 6. 1  - ( - 3. 13 ).

When subtracting decimal numbers, the effective method is to align their decimal points and begin removing each corresponding digit from one another. You may extend any decimals with fewer digits by appending zeros on the right-hand side as required for parity.

= - 6. 1  - ( -3. 13 )

= - 6. 1  + 3. 13

= - 2. 97

The decimal 2.97 is the solution to the subtraction problem - 6. 61 - (- 3. 13).

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a. The radius of circle is 4 units.

b. The diameter of the circle is 2 x 4 = 8 units.

c. The area of the circle to be around 31 to 32 square units.

A circle is a geometrical shape consisting of all points that are at an equal distance from a central point.

The distance from the center to any point on the circle is called the radius of the circle.

a. To find the radius of the circle, we need to measure the distance from the center point N to any point on the circumference of the circle.

Using the grid, we can count the number of squares from N to the edge of the circle.

In this case, we can count 4 squares horizontally and 4 squares vertically.

b. The diameter of the circle is twice the radius. Therefore, the diameter of the circle is 2 x 4 = 8 units.

c. To estimate the area of circle using the grid, we can count the number of complete squares that are either fully inside the circle or partially covered by the circle.

In this case, we can count 31 complete squares. We can also see that there are some squares that are partially covered by the circle, so we can estimate that the total area of the circle is slightly more than 31 square units. Therefore, we can estimate the area of the circle to be around 31 to 32 square units.

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Our table looks like this:
x | y
--|--
1 | 3
2 | 6
-2 | -6
0 | 0

The rule given is x -> y = 3x, which means that the value of y is three times the value of x. To fill in the table with at least 4 points, we can choose any four values of x and calculate their corresponding values of y using the rule.

Let's start with x = 1. Plugging this value into the rule, we get y = 3(1) = 3. So the first point in our table is (1, 3).

Next, let's try x = 2. Using the rule, we get y = 3(2) = 6. So the second point in our table is (2, 6).

Moving on, let's choose x = -2. Using the rule, we get y = 3(-2) = -6. So the third point in our table is (-2, -6).

Lastly, let's try x = 0. Using the rule, we get y = 3(0) = 0. So the fourth point in our table is (0, 0).
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