How many sides does an octagon have?

sides

Answer:

20

Step-by-step explanation:

For the computation of the average number of SUVs parked in the company's lot first it is required to compute the utilization which is shown below:-

\(Utilization = \frac{p}{a\times m}\)

where p indicates activity time which is equal to 3 days = 72 hours

a indicates an interarrival time which is equal to 2.4

m indicates the number of servers which is equal to 50

now we will put the values into the above formula

\(Utilization = \frac{72}{2.4\times 50}\)

After solving the above equation we will get

u = 0.6

or

60%

now, the average cars parked in the company's lot is

\(Average\ cars = 50 - 60\%\times 50\)

= 50 - 30

= 20

The height of her eye above sea level will be equal to 33.06 kilometers.

Addition, subtraction, multiplication, and division of two or even more integers are the four basic mathematical operations. Included among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

Distance, d = 3.6√h

3.6√h = 20.7 km

√h  = 5.75 km

h = 33.0625 km above the sea level or,

Height, h = 33.06 km

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Answer:

40

Step-by-step explanation:

The value of a right angle is 90° and <SQR is a fraction of <PQR.

Hence,  <PQS, which is the other fraction of <PQR, equals 90-50 and 90-50 is 40.

Or we can do it like this;

⇒ 180-90-50

⇒ 90 - 50

⇒ 40

Thus, Answer is 40.

[RevyBreeze]

Answer:

0.1319 or 13.2%

Step-by-step explanation:

You can solve this using the binomial probability formula.

The fact that "obtaining at least two 6s" requires you to include cases where you would get three and four 6s as well.

Then, we can set the equation as follows:

P(X≥x) = ∑(k=x to n) C(n k) p^k q^(n-k)

n=4, x=2, k=2

when x=2  (4 2)(1/6)^2(5/6)^4-2 = 0.1157

when x=3  (4 3)(1/6)^3(5/6)^4-3 = 0.0154

when x=4 (4 4)(1/6)^4(5/6)^4-4 = 0.0008

Add them up, and you should get 0.1319 or 13.2% (rounded to the nearest tenth)

The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.

It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.

Since slope is the rate of change in y with respect to x;

The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;

Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.

Remarks: The complete question is such that the required slope is -2.

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Answer: the second option

Step-by-step explanation:

i took the assignment

Answer:

ifruhhwhahsjjdhwjdkk

Based on simultaneous equations, five pieces of lasagna and 3 salads would cost $28.42.

Simultaneous equations are two or more equations solved simultaneously or concurrently.

Simultaneous equations are also known as a system of equations.

                          Lasagna   Salads  Total Costs

The first order          3             2            $17.63

The second order   4              1            $18.69

Let the unit cost of Lasagna = x

Let the unit cost of Salads = y

3x + 2y = 17.63 ...Equation 1

4x + y = 18.69 ...Equation 2

Multiply Equation 2 by 2:

8x + 2y = 37.38 ...Equation 3

Subtract Equation 1 from Equation 3:

8x + 2y = 37.38

-

3x + 2y = 17.63

5x = 19.75

x = 3.95

Substitute x = $3.95 in either Equations 1 or 2:

3x + 2y = 17.63

3(3.95) + 2y = 17.63

11.85 + 2y = 17.63

2y = 5.78

y = $2.89

Total Cost of 5 Lasagna and 3 Salads:

5(3.95) + 3(2.89) =

19.75 + 8.67 = $28.42

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Distribution will be possible even if we do not know the true population distribution.

What is a frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

Here, the A5 sample size is infinite then the sample distribution becomes normal.  So as per the C.L.T n→∞  so distribution is normal.

Hence, Distribution will be possible even if we do not know the true population distribution.

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Answer:

\(j = 7 \pm \sqrt{44}\)

Step-by-step explanation:

First, move the constant term to the other side of the equation.

\(j\² + 14j + 5 = 0\)

\(j\² + 14j = -5\)

Next, add the coefficient of the first degree j term divided by 2, then squared to both sides.

\(j^2 + 14j + (14/2)^2 = -5 + (14/2)^2\)

\(j^2 + 14j + (7)^2 = -5 + (7)^2\)

\(j^2 + 14j + 49 = -5 + 49\)

\(j^2 + 14j + 49 = 44\)

Now, we can factor the left side as a square.

\((j+7)(j+7) = 44\)

\((j+7)^2 = 44\)

Finally, we can take the square root of both sides to solve for j.

\(\sqrt{(j+7)^2} = \sqrt{44\)

\(j+7=\pm\sqrt{44}\)

\(\boxed{j = 7 \pm \sqrt{44}}\)

Note that there are two solutions, as \(\sqrt{44\) could be positive OR negative because of the even root property:

if \(x^2 = a^2\),

then \(x = \pm a\)

because both \((+a)^2\) and \((-a)^2\) equal \(a^2\).

For Puzzle #1: \(log_5 2*7\) produces an integer, \(log_3 8/7\) produces an irrational number, and \(log_6 4^5\) produces a rational number. For Puzzle #2: \(log 9^8 = log 7*6 = log 1/3\), \(log 5*2 = 1 = log8*0\), \(log 4/1 = log 3*9 = log 2^7\).

For Puzzle #1, we are given three requirements for the logs we need to fill in:

We need to fill in the blanks with digits 1 to 9, using each digit only once.

To fulfill the first requirement, we need to choose two digits that, when multiplied, produce an integer. The only two digits that can do this are 2 and 7 (2 x 7 = 14). We can then choose any base for the log function. In this case, we chose 5. So \(log_{5} 2*7\) produces an integer.

To fulfill the second requirement, we need to choose two digits that, when divided, produce an irrational number. There are many pairs of digits that can do this. For example, 8 and 7 (8/7 is irrational). Again, we can choose any base for the log function. In this case, we chose 3. So \(log_3 8/7\) produces an irrational number.

To fulfill the third requirement, we need to choose two digits that, when raised to a power, produce a rational number. Again, there are many pairs of digits that can do this. For example, 4 and 5 (\(4^5 = 1024\)). We can then choose any base for the log function. In this case, we chose 6. So \(log_6 4^5\) produces a rational number.

For Puzzle #2, we are given a chart with three columns and three rows. Each box in the chart represents a logarithmic expression, with the base being 10. We need to fill in the blanks with digits 0 to 9, using each digit only once in the blue boxes and once in the red boxes.

The goal is to make sure that the logarithmic expressions in each row and column satisfy the indicated conditions. We can do this by choosing appropriate digits to fill in each blank.

We can continue this process for each blank, making sure to use each digit only once in each blue and red box. Once we have filled in all the blanks, we can check that the logarithmic expressions in each row and column satisfy the indicated conditions.

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Answer:

A)0.126775 B)0.000004325376 C) 0.07548

Step-by-step explanation:

Given the following :

A.) a. n = 15, p = 0.4, find P(4 successes)

a = number of trials p=probability of success

P(4 successes) = P(x = 4)

USING:

nCx * p^x * (1-p)^(n-x)

15C4 * 0.4^4 * (1-0.4)^(15-4)

1365 * 0.0256 * 0.00362797056

= 0.126775

B)

b. n = 12, p = 0.2, find P(2 failures),

P(2 failures) = P(12 - 2) = p(10 success)

USING:

nCx * p^x * (1-p)^(n-x)

12C10 * 0.2^10 * (1-0.2)^(12-10)

66 * 0.0000001024 * 0.64

= 0.000004325376

C) n = 20, p = 0.05, find P(at least 3 successes)

P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)

To avoid complicated calculations, we can use the online binomial probability distribution calculator :

P(X≥ 3) = 0.07548

Answer:

a) 7000 x 1.06^t

b) 11156

Step-by-step explanation:

a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.

b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.

Answer:I think you mean 2 over 12 if so its 1/6

Step-by-step explanation:

you must simplify you divide  both of them by numbes they are divisblle by

Answer:

w=4

Step-by-step explanation:

\(A=lw\)

\(40= (10)w\)

\(\frac{40}{10} = \frac{10}{10}w\\w=4\\\)

Step-by-step explanation:

x = the total money she had first.

x - x×1/4 - (x - x×1/4)×1/2 = 15

you see, first we needed to deduct 1/4 of x from x. that left us with (x - x×1/4). and from that we need to deduct 1/2.

now, we can simplify :

(x - x×1/4) = (x×4/4 - x×1/4) = x×3/4

x×3/4 - x×3/4 × 1/2 = 15

x×3/4 - x×3/8 = 15

we multiply both sides by 8 (4 is a factor of 8, so this handled both fractions perfectly) :

x×3×2 - x×3 = 120

6x - 3x = 120

3x = 120

x = $40

she had $40 at the beginning.

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

3.89 minutes

Step-by-step explanation:

Firstly, we have this in a table using the range

There are 6 ranges

We put the frequency alongside

Afterwards we calculate the midpoint of the range

For example, midpoint of range 1-4 is (1+4)/2 = 5/2 = 2.5

We multiply the midpoint by the frequency which gives another column

Then we calculate the mean, where the mean is the summation of all frequencies and their midpoints

We subtract each midpoint from the mean, square the results, then multiply each by their frequency

Lastly, we apply the standard deviation formula

Please check attachment for the tabular representation and formulas

Answer:

\(\frac{17}{28}\)

Step-by-step explanation:

I hope this helps!

Answer:

216 (if 0 does not work)

Skills needed: LCM, Cubing

Step-by-step explanation:

1) We need to find the lowest possible cube number which is exactly divisible by 4 and 6.

---> First of all, \(0^3=0\), and 0 is perfectly divisible by 4 and 6. But most likely, this case will not count, so we will move on to the next possible case.

2) Instead of trying guess and check or trying every cube number, let's think about it algebraically. When looking at an LCM, use prime factorization.

4 prime factorized is: \(2^2\)

6 prime factorized is: \(2*3\)

This means that the prime number has to have both these factors in them. When you think about it, the least possible cube would be \((2*3)^3\), as you will get a \(2*3\) and also \(2^3\) is a multiple of \(2^2\), which is a factor (meaning that \(2^2\) is included as a factor here).

Both 4 and 6 can perfectly divide into the number stated above (which is 216). 4 * 54  = 216, 6 * 36  = 216...

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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Answer:

Step-by-step explanation:

We are given that line a and b and perpendicular to line x. By definition of perpendicular lines, lines a and b form right angles at the intersection of a and x and b and x. By definition, a right angle is equal to 90 degrees, and the sum of angle 2 and 3 is equal 180 degrees, so by the Converse of Same-Side Interior Angle Theorem, line a is parallel to line b.

Note: I don't have a drawing, but we can assume that angles 2 and 3 are same-side interior.

Line m and line n have corresponding angles that are congruent, which implies that line m is parallel to line n.

Theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Proof:

Let's assume we have a plane with three lines: line l, line m, and line n. We are given that both line m and line n are perpendicular to line l. We want to prove that line m is parallel to line n.

Since line m is perpendicular to line l, the angle formed between line m and line l is 90 degrees. Let's call this angle A.

Similarly, since line n is perpendicular to line l, the angle formed between line n and line l is also 90 degrees. Let's call this angle B.

By the definition of parallel lines, if corresponding angles formed by a transversal and two other lines are congruent, then the two lines are parallel.

In our case, angle A is congruent to angle B (both are 90 degrees). Therefore, line m and line n have corresponding angles that are congruent, which implies that line m is parallel to line n.

Hence, we have proven that in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

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The possible values of x are 3 and 7

Given the rational expression below;

√60-8x = x - 9

Square both sides to have:

(60-8x)² = (x-9)²

60-8x = x²-18x+81

Equate to zero to have;

x²-18x+81 - 60 + 8x = 0

x² - 10x + 21 = 0

x² -3x-7x +21 = 0

x(x-3)-7(x-3) = 0

x = 3 and 7

Hence the possible values of x are 3 and 7

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Answer:I’m definitely for the 1first one the second one no the 3rd one I’m for everyone to have

the right to have access to guns

Step-by-step explanation:

Answer:

1.I would say i am against the legal driving age because some students can’t always get a ride from people so then they have to walk and most of the time they can be late. And yes I would want to change it. I am for the legal drinking age because more People could drink and drive and cause things to happen. And no I wouldn’t want to change it. for number three idea what to put.

Step-by-step explanation:

Answer: 5.3

Step-by-step explanation: (4/15)x20=5.3

Answer: 6/13

Step-by-step explanation:

Let the equation be represented as ANow , the value of A is Let the first number be p = 4 / 15Let the second number be q = 20And , A = p x qSubstituting the values in the equation , we getA = ( 4/15 ) x 20On simplifying the equation , we getA = ( 4/3 ) x 4A = 16/3

Because both pyramids are identical or congruent, m∡EFG is given as 128.

Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror counterpart.

Congruence has three characteristics. They are reflexive, symmetric, and transitive properties. All three qualities apply to lines, angles, and forms.

In the above case, ∠EFG is similar to ∠ABC. If ∠ABC is 128° then,  ∠EFG = 128° as well.

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Answer:

Step-by-step explanation:

y - 6 = 3(x + 5)

y - 6 = 3x + 15

y = 3x + 21