Two people can sit at the long side of a cafeteria table, and one person can sit at the short side. Tables are pushed together as shown to seat more people. Arrangements for one and two tables are shown. Make a chart to find how many tables will need to be pushed together to seat 16 people.

A. 4 tables
B. 5 tables
C. 6 tables
D. 7 tables​

Answer:

7. 9

8. 6.7

9. 12.2

10. 7.6

11. 7.3

12. 6.3

Step-by-step explanation:

7. 8^2+4^2=x^2

64+16=x^2

80=x^2

√80=√x^2

8.9=x

Round up

9=x

8. 6^2+3^2=x^2

36+9=x^2

45=x^2

√45=√x^2

6.7=x

9. 7^2+10^2=x^2

49+100=x^2

149=x^2

√149=√x^2

12.2=x

10. 3^2+7^2=x^2

9+49=x^2

58=x^2

√58=√x^2

7.6=x

11. 7^2+2^2=x^2

49+4=x^2

53=x^2

√53=√x^2

7.28=x

Round up

7.3=x

12. 6^2+2^2=x^2

36+4=x^2

40=x^2

√40=√x^2

6.3=x

Hope this helps

Answer:

7) X = a^2 + b^2 = c^2

X = (4^2) + (8^2) = c^2

X = 80^2 = c^2

X = √80 = 8.944

X = 8.9 = c^2

8) X = a^2 + b^2 = c^2

X = (6^2) + (3^2) = c^2

X = 45^2 = c^2

X = √45 = 6.708

X = 6.7 = c^2

9) X = a^2 + b^2 = c^2

X = (7^2) + (10^2) = c^2

X = 149^2 = c^2

X = √149 = 12.206

X = 12.2 = c^2

10) X = a^2 + b^2 = c^2

X = (3^2) + (7^2) = c^2

X = 58^2 = c^2

X = √58 = 7.615

X = 7.6 = c^2

11) X = a^2 + b^2 = c^2

X = (7^2) + (2^2) = c^2

X = 53^2 = c^2

X = √53 = 7.280

X = 7.3 = c^2

12) X = a^2 + b^2 = c^2

X = (2^2) + (6^2) = c^2

X = 40^2 = c^2

X = √40 = 6.324

X = 6.3 = c^2

Step-by-step explanation:

X = a^2 + b^2 = c^2

X and c^2 = missing side

a^2 and b^2 = the two legs of the triangle (the mesurments of the sides that are given)

c^2 = hipatanouse

The formula is called Pythagromtherom (a^2 + b^2 = c^2)

Answer:

18.42

Explanation:

15+3=18

0.4+0.02=0.42

18+0.42=18.42

We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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Answer:

Using the digits 1 to 10 at most one time each to fill the given boxes, the value that makes the expression closest to 1 is;

Explanation:

Given the question in the attached image.

To make sure the result of the expression is closest to 1, we must make sure the value of the denominator and the numerator of the fraction is as close as possible.

Picking a set of values for the numerator, we must also try to select a separate set of values for the denominator that gives a result that is almost equal to the numerator.

Using this method we can arrive at a possible solution;

Let us simplify this expression to confirm;

Therefore, Using the digits 1 to 10 at most one time each to fill the given boxes, the value that makes the expression closest to 1 is;

Answer:

The equation is 4 1/3(2/5+1)

Step-by-step explanation:

So, it's 4 1/3+1 11/15=

65/15+26/15=91/15

6 1/15

2/5x4 1/3

Which is 2/5 x 13/3

Which is 26/15

Which is 1 11/5

X is a geometric random, its variable is constant and equal to p.

To show that if X is a geometric random variable, its failure rate is constant and equal to p, we will use the definition of the geometric distribution and the failure rate formula.

As the expression for z(x) does not depend on x, the failure rate is constant and equal to p/(1-p). However, we need to show that it is equal to p.
Recall that p is the probability of success. Since failure and success are complementary events, the probability of failure is q = 1-p.

Observe that the failure rate z(x) equals the probability of success p when divided by the probability of failure q. Since the failure rate for a geometric random variable only depends on the probability of success p and the probability of failure q, it is constant and equal to p.

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The matrix given is:```
-3  8 -8
8 -7  2
-3 10  3
2  2  3
-1 -10 -10
```a) Add -3 times row 2 to row 3This operation means the new row 3 is the sum of row 3 and (-3)*row 2. The matrix obtained after this operation is:```
-3  8 -8
8 -7  2
3 16 -7
2  2  3
-1 -10 -10
```b) Multiply row 2 by -3This operation replaces row 2 by (-3)*row 2. The matrix obtained after this operation is:```
-3  8 -8
-24 21 -6
3 16 -7
2  2  3
-1 -10 -10
```c) Interchange rows 1 and 3This operation replaces row 1 by row 3 and row 3 by row 1. The matrix obtained after this operation is:```
3 16 -7
-24 21 -6
-3  8 -8
2  2  3
-1 -10 -10
```Thus, the resulting matrices obtained after performing the given 3 elementary row operations are:Matrix obtained after adding (-3)*row 2 to row 3:```
-3  8 -8
8 -7  2
3 16 -7
2  2  3
-1 -10 -10
```Matrix obtained after multiplying row 2 by -3:```
-3  8 -8
-24 21 -6
3 16 -7
2  2  3
-1 -10 -10
```Matrix obtained after interchanging rows 1 and 3:```
3 16 -7
-24 21 -6
-3  8 -8
2  2  3

-1 -10 -10```

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Answer:

F=0.46N

Step-by-step explanation:

\(F\)∝\(\frac{1}{d^{2}}\),

\(F=\frac{k}{d^{2} } \\\)

\(F=0.35N, d=8m\\\)

\(0.35=\frac{k}{8^{2} }\)

\(k=0.35\times 8^{2} \\\\k=22.4\\F=\frac{22.4}{d^{2} } \\d=7m, F=\frac{22.4}{7^{2} } =0.46N\)

The correct proportion regarding the similar polygons is given as follows:

x/19.2 = 48/8.

Similar polygons are polygons that share these two features listed as follows:

For this problem, we have that the two rectangles are similar, as they both have the same angle measures, and the side lengths form a proportional relationship.

The proportional relationship for the equivalent side lengths of the rectangles is given as follows:

x/19.2 = 48/8.

Meaning that the fourth option is the correct option.

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The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is -

10 - 1/2x < -18

Solve the inequality to get the value for x.

First collect all the like terms -

-1/2x < -18 + (-10)

Then use arithmetic operation of addition -

-1/2x < -28

Multiply (-1) to both the sides -

-1/2x × (-1) < -28 × (-1)

1/2x < 28

Then move the coefficient of variable to right hand side of the equation -

x < -1 / (2 × (-28))

Then use arithmetic operation of multiplication and division-

x < 1/56

Therefore, the inequality is 0 < x < 1/56.

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Answer:

A. mB = 40°

Step-by-step explanation:

In geometry, congruent figures are identical in form, coinciding exactly when superimposed.

From the diagram,

<CAB = 80°; <EFG = 40° and <FGE = 60°

From triangle ️ EFG,

<GEF + <EFG + <FGE = 180°

》<GEF = 180° - (<EFG + <FGE)

<GEF = 180° - (40° + 60°)

<GEF = 180° - 100°

<GEF = 80°

》<GEF = <CAB = 80°

Also,

》<ACB = <EGF = 60°

<ABC = <EFG = 40°

NB. <ABC = mB

Answer: 1/2

Step-by-step explanation : change in y over change in x 14-10/ -5 - (-3)

4/8 = 1/2

Given \(-6x-20\)

Proof that it is equal to the \(-2x + 4(1 - 3x)\) or not

\(-2x + 4(1 - 3x)\)

Distribute

\(-2x+ 4-12x\)

\(4-14x\)

Not equal to the \(-6x-20\) \(\neq\) \(4-14x\)

So, it is false

What is Distribute in math?

To "distribute" anything is to divide it up or to give someone a piece of it.

What does the mathematical distributive property mean then?

The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.

Distributive property: What Is It?

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.

This characteristic also holds for subtraction.

A(B-C) = AB-AC

This demonstrates that the other two operands share operand A.

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The tangent line DC is perpendicular to the radius of the park

The length of AC is 245 feet

To calculate the distance AC, we start by calculating the length of AB using:

DC^2 = (BC + AB) * BC

So, we have:

105^2 = (45 + AB) * 45

Evaluate the exponent

11025 = (45 + AB) * 45

Divide both sides by 45

245 = 45 + AB

Rewrite as:

AB + 45 = 245

From the figure, we have:

AC = AB + 45

Substitute AB + 45 = 245

AC = 245

Hence, the length of AC is 245 feet

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At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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Answer:

Step-by-step explanation:

Let width be x

Let lenght be 25 + x

Total ax = (25+x) * x

Square with 5in long are cut from the four corner formed = 750in

(25+x-10) * (x-10) * 5 = 750

(15+x) (x-10) = 150

15x-150+x^2-10x =150

15x -150-150+x^2-10x+0

x^2+15x-300=0

(ax^2+bx+c=0)

Answer:

99 and 33

Step-by-step explanation:

let x and y be the 2 numbers, with x being the larger of the 2, then

x + y = 132 → (1)

x - y = 66 → (2)

add (1) and (2) term by term to eliminate y

(x + x) + (y - y) = 132 + 66

2x + 0 = 198

2x = 198 ( divide both sides by 2 )

x = 99

substitute x = 99 into (1) and solve for y

99 + y = 132 ( subtract 99 from both sides )

y = 33

the 2 numbers are 99 and 33

Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

The probability that Angela will roll the die an odd number of times to get three consecutive rolls in order can be calculated by considering the possible outcomes and their probabilities.

To start, let's look at the possible outcomes for Angela to roll the die an odd number of times. For her to achieve three consecutive rolls in order, she needs to roll the die either 1, 3, 5, 7, or any other odd number of times.

Next, let's consider the probability of each of these outcomes:

1. If Angela rolls the die once, she has a 1/6 probability of getting the desired sequence in one roll.

2. If Angela rolls the die three times, she needs to calculate the probability of getting the desired sequence on the third roll. The first two rolls can be any number, but on the third roll, she needs to roll the specific sequence. The probability of getting the desired sequence on the third roll is 1/6.

3. If Angela rolls the die five times, the first four rolls can be any numbers, but on the fifth roll, she needs to roll the specific sequence. The probability of getting the desired sequence on the fifth roll is 1/6.

We can see a pattern here: for Angela to roll the die an odd number of times and achieve the desired sequence, the last roll must be the specific sequence. Therefore, the probability for each odd number of rolls will always be 1/6.

Now, let's calculate the overall probability:

Since Angela can roll the die 1, 3, 5, 7, or any other odd number of times, we need to add up the probabilities for each of these cases. The probability of rolling the die an odd number of times is equal for each case, which is 1/6. Since there are infinitely many possible odd numbers of rolls, we can represent this as the sum of an infinite geometric series.

The probability of rolling the die an odd number of times to get three consecutive rolls in order is therefore:

1/6 + 1/6 + 1/6 + ... (infinitely many terms)

To find the sum of this infinite geometric series, we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

In this case, a = 1/6 (the first term) and r = 1/6 (the common ratio).

Sum = (1/6) / (1 - 1/6)
Sum = (1/6) / (5/6)
Sum = 1/5

So, the probability that Angela will roll the die an odd number of times and get three consecutive rolls in order is 1/5.

In summary, the probability of rolling the die an odd number of times and achieving three consecutive rolls in order is 1/5.

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If an observation yields a Z-score of -3, this indicates that the observed value is 3 standard deviations below the mean.

The Z-score measures the number of standard deviations an observation is away from the mean of a distribution. A Z-score of -3 means that the observed value is 3 standard deviations below the mean. In a standard normal distribution (with a mean of 0 and a standard deviation of 1), a Z-score of -3 indicates that the observed value is 3 standard deviations below the mean. This means the observed value is relatively far from the mean in the negative direction. For example, if the mean of a dataset is 50 and the standard deviation is 10, an observation with a Z-score of -3 would have a value of:

Value = Mean + (Z-score * Standard Deviation)

Value = 50 + (-3 * 10)

Value = 50 - 30

Value = 20

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The linear equation representing Mia's situation is y = 3x + 12.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two points given are - (4,24) and (6,30)

The slope-intercept form of a linear equation is - y = mx + b, where m is the slope and b is the y-intercept.

To find the slope use the formula -

m = (y2 - y1)/(x2 - x1)

m = (30 - 24)/(6 - 4)

m = 6/2

m = 3

So, now the equation becomes - y = 3x + b

To find the y-intercept substitute the equation with x and y values -

24 = 3(4) + b

24 = 12 + b

b = 24 - 12

b = 12

So, now the equation becomes - y = 3x + 12.

Therefore, the linear equation y = 3x + 12.

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A bathtub has some water in it. Mia turns on the faucet and add more water. The total amount of water in gallons, y, is a function of the time in minutes since Mia turned on the faucet, x. The graph of a linear function passes through the points (4,24) and (6,30) What is the equation of the function?

Answer:

x = 5

Step-by-step explanation:

First, break it down:

Two is eight less than twice a number

2 = 2x - 8

+8       + 8

10 = 2x

5 = x

Hope this helps :)

Answer:

Student B did the problem corectly

Step-by-step explanation:

Student a did 3*4 while student B did 3*3*3*3 which would equal 27

Answer:

D

Step-by-step explanation:

Answer:

6/pi isn't greater than 2

Step-by-step explanation:

for the inequality to be true 6 would have to be divided by something less than 3 because 6/3 is two. And we know that pi is greater than 3 and we also know that the more the denominator increases, the less value the fraction has, so 6/pi is actually less than 2, its around 1.91

In the given scenario, in order to calculate an 88% confidence interval, the z statistics that fall at each line marking the middle 88% of scores in the distribution would be +/- 1.555 (from the table).

Hence the z score = 1.5550

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If a man had put $26 in the bank in 1828 at a 3% interest rate compounded continuously, it would have been worth $ in 2000.

To determine the future value of $26 deposited in the bank in 1828 at a 3% interest rate compounded continuously, we can use the formula for continuous compound interest: A = P * e^(rt), where A is the future amount, P is the principal, r is the interest rate, t is the time in years, and e is Euler's number, approximately 2.71828.

In this case, the principal (P) is $26 and the interest rate (r) is 3% or 0.03. We want to find the future amount (A) in the year 2000, which is 2000 - 1828 = 172 years later.

Substituting the given values into the formula, we have A = 26 * e^(0.03 * 172).

To calculate this value, we can use the natural logarithm (ln) function, which is the inverse of the exponential function. The formula ln(A/P) = rt can be rearranged to t = ln(A/P) / r.

In this case, we want to find t, so t = ln(A/26) / 0.03.

Using a calculator or a mathematical software, we can determine the value of A/26 by evaluating e^(0.03 * 172). Then, we can take the natural logarithm of that value and divide it by 0.03 to find t.

The result is the exact length of time in years, which can be rounded to the nearest dollar.

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Answer: It would be about 10 cents an ounce.

Step-by-step explanation:

1.25/12 = ~.10

The number of bacteria  After 3 hours, in the petri dish would be approximately 823,542,481.

To calculate the number of bacteria in the petri dish after a certain number of hours, you can use the formula:

Number of bacteria = Initial number of bacteria × (growth factor)^(number of hours)

In this case, the initial number of bacteria is 500,500,500 and the growth factor is 1.21.21, point, 2.

Let's calculate the number of bacteria after 1 hour:

Number of bacteria after 1 hour = 500,500,500 × (1.21.21, point, 2)^1

Number of bacteria after 1 hour ≈ 500,500,500 × 1.21.21, point, 2 ≈ 605,662,605

After 1 hour, the number of bacteria in the petri dish would be approximately 605,662,605.

If you want to calculate the number of bacteria after multiple hours, you can simply raise the growth factor to the power of the number of hours. For example, to calculate the number of bacteria after 3 hours:

Number of bacteria after 3 hours = 500,500,500 × (1.21.21, point, 2)^3 ≈ 500,500,500 × 1.21.21, point, 2 × 1.21.21, point, 2 × 1.21.21, point, 2 ≈ 500,500,500 × 1.64642042 ≈ 823,542,481

After 3 hours, the number of bacteria in the petri dish would be approximately 823,542,481.

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