Is it rational or irrational

Answer to your question is:

B. 4

Explanation:

2 + 5 + 4 + 1 + 8 = 20

20 ÷ 5 = 4

The mean is found out by adding the scores given and dividing the total by the number of scores.

In the given question the mean of the scores is 4.

The mean is calculated to get an average about something that is given.

Here

n= number of scores= 5

Sum of scores = ∑x= 2+5+4+1+8= 20

Mean = x bar=  ∑x/n= 20/5= 4

For different distributions mean may or may not be the middle value.

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Answer:

Vicky's take home pay per month will be $1,580

Step-by-step explanation:

Given that her salary per annual i.e salary for the year = $24,000

Therefore salary per month would be $24,000/12 = $2,000.

From this, she must pay 15% income tax.

i.e 15% of salary

15/100 * 2000

= 0.15*2000

= $300.

Salary after paying tax = $2,000 - $300= $1,700.

Since, she must repay a loan at a rate of $120 per month we will reduct the loan from her salary,

$1,700 - $120 = $1,580

Vicky's take home pay per month will be $1,580

Answer: Vicky's take home pay per month is $1,580

Step-by-step explanation: If Vicky's annual gross salary (salary before any deductions) is given as 24000, then her monthly gross salary is derived as;

Salary Per month = 24000/12

Salary per month = 2000

She must pay 15 percent income tax and this derived as follows;

Income tax = 2000 x 0.15

Income tax = 300

Therefore her salary after tax deduction is derived as follows;

Salary after tax = 2000 - 300

Salary after tax = 1700

However, she must repay a loan (after tax deduction) at a rate of 120 per month, which is now derived as follows;

Salary after loan repayment = 1700 - 120

Salary after loan repayment = 1580

Therefore the calculations show that her take home pay after all adjustments comes down to $1,580 per month.

Hope this will help u....

The transit and passenger trains will pass each other at 5:00 PM, considering their combined speed and the distance between New York and Boston.

The question involves using relative speed to determine the time at which two trains traveling towards each other will meet. The transit train travels from Boston to New York at a speed of 80 mph, and the passenger train travels from New York to Boston at a speed of 60 mph. Since both trains start at the same time and move towards each other, their combined speed is the sum of their individual speeds, which is 80 mph + 60 mph = 140 mph. To find the time taken for the trains to meet, we divide the total distance by their combined speed.

The distance between New York and Boston is 280 miles. Therefore, the time taken to meet is calculated by dividing the distance by the combined speed, which is 280 miles / 140 mph = 2 hours. Given that they departed at 3:00 PM, they will pass each other at 3:00 PM + 2 hours = 5:00 PM.

Answer:

32.1869

Step-by-step explanation:

multiply 20 by 1.609

multiplying miles by 1.609  will give you the answer

Answer:

20 miles =32.1869

Step-by-step explanation:

For an approximate result multiply the length value by 1.609.

Answer:

20 t shirt

Step-by-step explanation:

Step-by-step explanation:

[tex]m(arc \: JN) = 360 \degree - (60 \degree + 150 \degree) \\ \hspace{57pt}= 360 \degree - 210 \degree \\ \hspace{57pt} = 150\degree \\ \\ m \angle K = \frac{1}{2} \times m(arc \: JN) \\ \hspace{30pt}= \frac{1}{2} \times 150\degree \\ \hspace{30pt} = 75\degree \\ [/tex]

Answer:

33 1/3%

Step-by-step explanation:

When you roll a die, the possible outcomes are 1,2,3,4,5,6

getting a number less than 5: 1,2,3,4

P( getting a number less than 5)

         = number of outcomes that meet conditions / total outcomes

         =4/6

           = 2/3                                            

Then we flip a coin  heads or tails

We want heads

P (heads)  = number of outcomes that meet conditions / total outcomes

    = 1/2

Since the event outcomes do not depend on each other

P( getting a number less than 5) *P (heads) = 2/3 * 1/2 = 1/3

as a percent

= 33 1/3%

Answer:

sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex]

Step-by-step explanation:

See the attachment.

Cosine is adjacent over hypotenuse, so since cos(θ) = 3/8, then the adjacent side of the triangle is 3 and the hypotenuse is 8.

Since is opposite divided by hypotenuse. To find the opposite side, which is the unlabelled side on the graph, we need to use the Pythagorean Theorem:

x = [tex]\sqrt{8^2-3^2} =\sqrt{64-9} =\sqrt{55}[/tex]

So, sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex].

Hope this helps!

Answer:

A

Step-by-step explanation:

Given the exponential function

f(t) = 228[tex](0.975)^{t}[/tex] ← where t is time in years

Substitute t = 20 into f(t), that is

f(20) = 228 × [tex](0.975)^{20}[/tex] = 228 × 0.60268.... ≈ 137 → A

Similar triangles are defined as two triangles having equal B. corresponding angles, shown by the congruence of vertical angles, alternate interior angles, and the application of the AAA theorem.

Similar triangles are two triangles with equal corresponding angles. According to the question, in the figure, two triangles named triangle ABC and triangle FCE are observed to be similar because they have three sets of congruent angles - vertical angles (Angle ACB \\<=\ Angle FCE), alternate interior angles (Angle CAB \\<=\ Angle CFE), and another set of alternate interior angles (Angle CBA \\<=\ Angle CEF).

This is summed up by the AAA (Angle Angle Angle) theorem which states that two triangles are similar if all their corresponding angles are congruent. An example will be two right triangles which are equal when the hypotenuse and an acute angle of one are equal, respectively, to the hypotenuse and an acute angle of the other. These principles help us understand the similarity of triangles in geometry.

If we use v for Vidya's age, then the expression (24v)+6

Answer:

Width 4 Length 5

Step-by-step explanation:

4+4+5+5=18

4*5=20

Answer:if your talking about a square or rectangle then two sides would 5 and the other two four

Step-by-step explanation:area equals base times height

Base=5

Height=4

5*4=20 which is area

5+5+4+4=18 which is perimeter

Answer:

its

40 192 cm

Step-by-step explanation:

Answer:

40.192cm

Step-by-step explanation:

the circumference of a circle = ?

radius = 6.4cm

recall that,

circumference of a circle = 2πr

circumference of a circle = 2 x 3.14 x 6.4cm

circumference of a circle = 40.192cm

therefore the circumference of a circle whose radius is 6.4cm is evaluated to be equals to 40.192cm.

the answer to your question is option B 40.192cm

Answer:

B

Step-by-step explanation:

If you set x to hours and y to the amount of miles, you can multiply the hours to the numbers and equal out your miles. So, if 8 hours is multiplied to 50, it equals out the 400 miles.

Answer:

The bakery made a profit of $8,013 during the summer months

Step-by-step explanation:

A profit is made when income is greater than expenses while a loss is made when expenses are greater than income

A loss is a negative profit

In June

Income = $750

Expense:

rent = $890

Operating costs = $975

Total expense = $1,865

Profit = income - expense

profit = $750 - $1865

= -$1115

Therefore, a loss of $1115 was made in June

July

Income = $ 925

Expenses:

Rent = $890

Operating costs = $721

Total expenses = 1611

Profit = $925 - $1611

= -$686

A loss of $686 was made in July

August

Income = $11,250

Expenses:

Rent = $890

Operating costs= $546

Total expense = $1436

Profit = $11,250 - $1436

= $9,814

A profit of $9,814 was made in August

Now let's find the difference between the profit and losses that were made during the summer months. This will be the addition of the profit and losses of all three months

Remember that losses carry a negative sign

$9,814 -$686 -$1115 = $8,013

Therefore, the bakery made a profit of $8,013 during the summer months

Answer:

A' (-3,7)

B' (0,10)

C' (12,10)

D' (-2,-4)

Step-by-step explanation:

A' (-6+3 , 3+4) = (-3,7)

B' (-3+3 , 6+4) = (0,10)

C' (9+3 , 6+4) = (12,10)

D' (-5+3 , -8+4) = (-2,-4)

Answer:

Step-by-step explanation:

51,480 is the answer.

Answer:

51,480

Step-by-step explanation:

66 x 26 = 1,716

1,716 x 60 = 102,960

102,960 x 1/2 = 51,480

Answer:

[tex]9 \times 2 - 16 \\ 18 - 16 = 2[/tex]

Answer:

Omar

Step-by-step explanation:

to find the base, which i am to assume they want to find the triangle base based on the formula they are using,

you should multiply base * height, then divide by 2, since it is a triangle, you not solving for a rectangle.

dividing by 2 and multiplying by 1/2 is the same thing!

so,

1/2 (7* 24) is the right answer to finding the base!

Kari looked at he direct base of 7*28, however, that shape is actually a rectangle... so Kari is wrong because he multiplied that dimension by 1/2, which is the formula for a triangle.

Omar is correct because he chose the dimensions of a triangle, and properly used the triangle formula!

i hope this helped you out!

stay safe!

:)

Answer:

a + b = 16 or -16.

Step-by-step explanation:

a - b =  4

ab = 60  so a = 60/b

Substituting for a in the first equation:

60/b - b = 4

60 - b^2 = 4b

b^2 + 4b - 60 = 0

(b + 10)b - 6) = 0

b = 6, -10.

Therefore, from the first equation:

When b = -10 . a + 10 =4 giving a = -6 or

When b = 6, a -  6 = 4 giving a = 10.

So  when a = -6, b = -10  and

when a = 10, b = 6.

So a + b is either 16 or -16.

Answer:

16

Step-by-step explanation:

the perimeter of the given rhombus is 8√5.

To find the perimeter of a rhombus, we need to calculate the sum of the lengths of all four sides.

Given the coordinates of the points touching the graph: (-5,-3), (-1,-1), (3,-3), and (-1,-5), we can calculate the distances between these points to find the lengths of the sides.

Let's calculate the lengths of the sides:

1. Side 1: Distance between (-5,-3) and (-1,-1)

Length = √[(x2 - x1)^2 + (y2 - y1)^2]

Length = √[(-1 - (-5))^2 + (-1 - (-3))^2]

Length = √[4^2 + 2^2]

Length = √[16 + 4]

Length = √20

Length = 2√5

2. Side 2: Distance between (-1,-1) and (3,-3)

Length = √[(x2 - x1)^2 + (y2 - y1)^2]

Length = √[(3 - (-1))^2 + (-3 - (-1))^2]

Length = √[4^2 + (-2)^2]

Length = √[16 + 4]

Length = √20

Length = 2√5

3. Side 3: Distance between (3,-3) and (-1,-5)

Length = √[(x2 - x1)^2 + (y2 - y1)^2]

Length = √[(-1 - 3)^2 + (-5 - (-3))^2]

Length = √[(-4)^2 + (-2)^2]

Length = √[16 + 4]

Length = √20

Length = 2√5

4. Side 4: Distance between (-1,-5) and (-5,-3)

Length = √[(x2 - x1)^2 + (y2 - y1)^2]

Length = √[(-5 - (-1))^2 + (-3 - (-5))^2]

Length = √[(-4)^2 + 2^2]

Length = √[16 + 4]

Length = √20

Length = 2√5

Now, we can calculate the perimeter by adding the lengths of all four sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

Perimeter = 2√5 + 2√5 + 2√5 + 2√5

Perimeter = 8√5

Therefore, the perimeter of the given rhombus is 8√5.

Answer:

3124

Step-by-step explanation:

Answer: -273

Step-by-step explanation: To determine the 72nd term, we will want use our explicit formula which is shown below.

[tex]^{a}n = ^{a}1 + (n - 1)d[/tex]

Since we want to find the 72nd term, the [tex]^{a}n[/tex]

in the formula will be changed to [tex]^{a} 72[/tex].

Also, the 72 will be substituted in for the n

that is inside the set of parentheses.

Then [tex]^{a} 1[/tex] will be the 1st term given in our sequence or 11.

Lastly, the d outside the parentheses is the difference between

each of the terms in the sequence which is -4.

So we now have [tex]^{a} 72 = 11 + (72 - 1)(-4)[/tex].

Now we have all the information we need.

Now we can simplify from here.

Make sure to apply your order of operations because

this is where a lot of students make mistake.

Start simplifying inside the parentheses!

(72 - 1) is going to be 70.

So we have [tex]^{a} 72 = 11 + (71)(-4)[/tex].

Then, we have to multiply before we add.

So (71)(-4) is going to be -284.

So we have [tex]^{a} 72 = 11 + (-284)[/tex].

Solving from here, 11 + (-284) simplifies to -273.

This means that the 72nd term of this sequence is -273.

The graph of the quadratic function g(x) = -x^2 + 9x - 20 will be a downward opening parabola with vertex at (4.5, 0.25), x-intercepts at (4, 0) and (5, 0), and a y-intercept at (0, -20). To graph it, label the axes as 'f(x)' and 'x' and scale them to include these critical points.

The student wants to identify the graph of the quadratic function g(x) = –x2 + 9x – 20. To do this, first note that the standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants.

In this case, a = -1 (which makes the parabola open downward), b = 9, and c = -20.

The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b/(2a).

For g(x), this gives h = -9/(2 * -1) = 4.5.

We can then find the value of k by substituting h back into g(x), which gives us k = -4.52 + 9(4.5) - 20.

Therefore, k = 0.25.

The vertex of the parabola is at (4.5, 0.25), and because a is negative, the parabola opens downward. The x-intercepts (or roots) of the parabola can be found by factoring the quadratic equation or using the quadratic formula. In this case, the x-intercepts are (4, 0) and (5, 0). Lastly, the y-intercept occurs when x = 0, which for g(x) is -20.

To label the graph, we'd use 'f(x)' for the vertical axis and 'x' for the horizontal axis. The scale of the axes depends on the maximum and minimum x and y values of the graph, which in this instance would include at least the vertex, x-intercepts, and y-intercept.

Answer:

B. About 50% of the days in January had average temperatures between 66 and 75 degrees.

The box ranges from 66 to 75... meaning that most of the days were in those temperatures.

The lines mean that there were only a few days that were in those temperatures.

You're welcome if I'm correct.

The correct answer is about 50% of the days in January had average temperatures between 66 and 75 degrees.

A Box and Whisker Plot (also known as a Box Plot) is a visual representation of data distribution through quartiles.

In the graph given in the question we can clearly see that the interquartile range of the data is lying between the temperatures 66° to 75°, which means that 50% of days in January had the temperature between 66 to 75 degrees.

Hence, Option(c) is correct for the given question.

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Answer:

x=107

Step-by-step explanation:

Given:

Number of mice and frequency

Mean = 7

To find:

The value of x.

Solution:

Number of mice = X

Frequency = Y

XY = Multiply X and Y values.

X         Y            XY

5         4            20

6         13           78

7         16           112

8          x            8x

9          6            54

Sum of Y = 4 + 13 + 16 + x + 6

               = 39 + x

Sum of XY = 20 + 78 + 112 + 8x + 54

                  = 8x + 264

Mean formula:

[tex]$Mean = \frac{\Sigma XY }{\Sigma Y}[/tex]

[tex]$7=\frac{8x+264}{39+x}[/tex]

Do cross multiplication.

[tex]7(39+x)=(8x+264)[/tex]

[tex]273+7x=8x+264[/tex]

Subtract 264 from both sides, we get

[tex]9+7x=8x[/tex]

Subtract 7x from both sides, we get

[tex]9=x[/tex]

The value of x is 9.

Answer:

x=3

Step-by-step explanation:

44-29=15

5*3=15

The value of x in the equation 29 + 5x = 44 is solved by isolating x to find that x = 3.

To solve the equation 29 + 5x = 44 for x, you should start by isolating the variable on one side. Here's a step-by-step process:

Therefore, the value of x in the given equation is 3.

Answer:

73333.333

Step-by-step explanation:

100/4.5= 22.222

3300*22.222= 73333.333

The information given, y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, is not enough to calculate the area of an object unless its shape is known. If it's a rectangular prism, the volume can be calculated. But without further information, we cannot provide a specific area calculation.

The type of area an object will have depends on its shape. For example, the area of a rectangle is given by width times height (w * h). Similarly, the volume of a rectangular prism would be length times width times height (l * w * h). However, the given dimensions in the question (y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches) are not enough to determine the shape of the object. We need additional information on how these dimensions are related to the shape of the object before we can calculate the area.

If for instance, this object is a rectangular prism, then we could calculate its volume. That volume would be y (depth) * z (width) * h (height). In this case with the provided values, the volume would be 11 inches * 14 inches * 7 inches = 1078 cubic inches.

Without more information on the object’s shape, we can’t make assumptions and provide a definitive calculation of the area.

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