What company should he rent from

We can conclude that exists 211680 ways.

We know that the three research department is have 8, 10, and 7 members.

We choose a delegate and an alternate to represent the department.

First case: department have 8 members.

So, for a delegate, we have 8 options, and for a alternate 7, so a total of

\(8 \times 7 = 56 \ \text{options}\)

Second case: department have 10 members.

So, for a delegate, we have 10 options, and for a alternate 9, so a total of

\(10\times 9 =90 \ \text{options}\)

Third case: department have 7 members.

So, for a delegate, we have 7 options, and for a alternate 6, so a total of

\(7\times6 = 42 \ \text{options}\)

Therefore, we get:

\(56 \times 90 \times 42 = \bold{211680}\)

Hence, we conclude that exists 211680 ways.

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To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).

Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)

where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.

First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:

\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)

Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:

\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)

Now, we can calculate the approximate volume using the Midpoint Rule:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)

Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

Sure, here are the questions and solutions for module 3 page 330 in Carnegie textbook:

If the cost of goods sold is 65% of sales and sales are $720,000, what is the cost of goods sold?

To find the cost of goods sold, we need to multiply the sales by the percentage of the cost of goods sold, expressed as a decimal:

Cost of goods sold = 0.65 × $720,000

Cost of goods sold = $468,000

Therefore, the cost of goods sold is $468,000.

At a cost of $110 each, how many calculators can be purchased with a budget of $8,800?

To find the number of calculators that can be purchased, we need to divide the budget by the cost per calculator:

Number of calculators = $8,800 ÷ $110

Number of calculators = 80

Therefore, 80 calculators can be purchased with a budget of $8,800.

a is the cost of adult tickets.

s is the cost of students tickets.

The cost of each type of ticket is $10.

The solution of an equation differ from the solution of a linear system of equations because because it only satisfies a single equation.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of adult tickets sold and cost of student tickets sold, and then translate the word problem into an algebraic equation as follows:

The total amount of money that Ashley charged the first person is represented by this linear equation:

2a + 2s = 40

For the second person, we have:

a + 3s = 40

By solving the system of linear equations simultaneously, we have:

2(40 - 3s) + 2s = 40

80 - 6s + 2s = 40

4s = 40

s = $10.

For the value of adult ticket (a), we have:

a = 40 - 3s = 40 - 3(10) = $10.

For the third person, we have:

Cost = 3a + 5s

Cost = 3(10) + 5(10) = $80.

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Answer:

\(-2\sqrt{2}-2 < a < 2\sqrt{2}-2,\;\;a\neq0\)

Step-by-step explanation:

Given quadratic equation:

\(ax^2 + (2a + 2)x + a + 3 = 0\)

To find the possible values of "a" such that the given equation has two roots and the distance between them on the number line is greater than 1, use the quadratic formula.

\(\boxed{\begin{minipage}{4 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)

Comparing the coefficients:

Substitute the coefficients into the quadratic formula:

\(x=\dfrac{-(2a+2) \pm \sqrt{(2a+2)^2-4a(a + 3)}}{2a}\)

Simplify the discriminant (the part under the square root sign):

\(x=\dfrac{-(2a+2) \pm \sqrt{-4a+4}}{2a}\)

Factor out 4 from the discriminant:

\(x=\dfrac{-(2a+2) \pm \sqrt{4(-a+1)}}{2a}\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(x=\dfrac{-(2a+2) \pm \sqrt{4}\sqrt{-a+1}}{2a}\)

Therefore:

\(x=\dfrac{-(2a+2) \pm 2\sqrt{-a+1}}{2a}\)

Factor out the common term 2:

\(x=\dfrac{-(a+1)\pm \sqrt{-a+1}}{a}\)

Therefore, the two solutions are:

\(x=\dfrac{-a-1+\sqrt{-a+1}}{a},\;\;x=-\dfrac{a+1+\sqrt{-a+1}}{a}\)

As both solutions have "a" as their denominator, a ≠ 0.

Note: When substituting a = 0 into the original equation, we are left with a linear equation, which only has one root. Therefore, this confirms that a ≠ 0.

Now we have found expressions for the two roots, we can set the distance between them to greater than 1:

\(\dfrac{-a-1+\sqrt{-a+1}}{a}-\left(-\dfrac{a+1+\sqrt{-a+1}}{a}\right) > \:1\)

\(\dfrac{-a-1+\sqrt{-a+1}}{a}+\dfrac{a+1+\sqrt{-a+1}}{a} > \:1\)

Simplify:

\(\begin{aligned}\dfrac{-a-1+\sqrt{-a+1}+a+1+\sqrt{-a+1}}{a}& > 1\\\\\dfrac{2\sqrt{-a+1}}{a}& > 1\\\\2\sqrt{-a+1}& > a\\\\(2\sqrt{-a+1})^2& > a^2\\\\4(-a+1)& > a^2\\\\-4a+4& > a^2\\\\a^2+4a-4& < 0\\\\(a+2)^2-8& < 0\\\\(a+2)^2& < 8\end{aligned}\)

\(\textsf{For\;\;$u^n < a$,\;\;if\;$n$\;is\;even\;then\;\;$-\sqrt[n]{a} < u < \sqrt[n]{a}|$:}\)

\(-\sqrt{8} < a+2 < \sqrt{8}\)

Therefore:

\(-\sqrt{8} -2 < a < \sqrt{8}-2\)

\(-2\sqrt{2}-2 < a < 2\sqrt{2}-2\)

So the possible values of "a" such that ax² + (2a + 2)x + a + 3 = 0 has two roots and the distance between them on the number line is greater than 1 are:

\(\large{\boxed{-2\sqrt{2}-2 < a < 2\sqrt{2}-2,\;\;a\neq0}\)

Answer:

The student whose measurement had the greatest percent error was student 5. Their measurement was 27 mm, and the actual length of the nail was 25 mm. To find the percent error, we use the formula:

percent error = |(measured value - actual value) / actual value| x 100%

Plugging in the values we get:

percent error = |(27 - 25) / 25| x 100% = 8%.

So student 5's measurement had a percent error of 8%.

Answer:

Step-by-step explanation:

Layne:26:4%

Tenicia:23:8%

Juan:25:0%

Answer:

Step-by-step explanation:

-2-2=x/4

x/4=-4

x=(-4)x4= -16

Answer: 1/9

Step-by-step explanation:

There are 3 possibilities of it landing on 7 (greater than 6), is 1/3 alone. Then adding on landing on 5, right after, you have 1/9.

Answer:

tough one

Step-by-step explanation:

sorry goodluck

Answer:

-2.72

Step-by-step explanation:

-8.16 / 3 = -2.72

Extra:

3(-2.72) = -8.16

Answer:

8

Step-by-step explanation:

1.08 x total equal

108% of total

(100+8%)

total    tax

Answer: 12 degrees or 11 5/5 or 60/5

Step-by-step explanation:

Since the temperature is rising 2 2/5 per 1/5 of an hour we just need to multiply 2 2/5 times 5 because 5/5 would equal the whole hour. In order to multiply easier you can change 2 2/5 to an improper fraction by multiplying the whole number with the denominator and then adding the numerator. Which you should get 12/5 next change 5 to a fraction which would be 5/1. 5 times 12 is 60 and 5 times 1 is 5. You get 60/5 which if divided is 12.

For the number line you just have to find 1/5 and 2 2/5 on it and mark it.

Answer:

a

Step-by-step explanation:

Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true? A line has points A, D, B, K, C. AD = One-thirdAC AC = 4DB AB + DC =

B is right

Answer:

k = 5.25

Step-by-step explanation:

y is directly proportional to x

y∝x

y = kx where k is the constant

if y is 84 and x is 16,

84 = 16k

k = 84/16 = 5 4/16 = 5.25

k = 5.25

Answer:

Diameter = 3.81 Cm

Step-by-step explanation:

Given as in the pic...

Thank you!

Answer:

84-85

Step-by-step explanation:

you out them in order from greatest to least

82 83 __ __ 86 87 88

^ ^

84 85

i hope this work for you

Frequency for the interval 86 - 88 in the given histogram is equals to 10.

" Frequency is defined as the representation of occurrence of any particular event repeatedly in fixed time interval."

According to the question,

Given histogram shows,

Students with weight between 80 - 82 = frequency 2

Students with weight between 83 - 85 = frequency 6

Students with weight between 86 - 88 = frequency 10

10 students are there having weight between 86 - 88 pounds.

Hence, Option(C) is the correct answer.

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Answer:

There is only one x intercept: x = -0.5 or -1/2

Step-by-step explanation:

To find the x-intercepts of the graph of the function, we need to find the values of x where y = 0. In other words, we need to solve the equation 4x^2 + 4x + 1 = 0 for x.

4x^2 + 4x + 1 = 0

(2x+1)^2 = 0

2x + 1 = 0

2x = 0 -1

x = -1/2

Answer:

Let's start by using variables to represent the ages of the three people:

Let L be Liz's age.

Let D be Debbie's age.

Let F be Freya's age.

From the problem, we know that Liz's age is two-thirds of Debbie's age, so we can write:

L = (2/3)D

We also know that Debbie's age is half of Freya's age, so we can write:

D = (1/2)F

To find the ratio of Liz's age to Freya's age, we need to express Liz's age and Freya's age in terms of a common variable. Since we have an equation relating Debbie's age to Freya's age, we can use that as the common variable. From the equation D = (1/2)F, we can solve for F in terms of D:

F = 2D

Now we can substitute this expression for F into the equation for Liz's age:

L = (2/3)D = (2/3)(1/2)F = (1/3)F

So Liz's age is one-third of Freya's age. The ratio of Liz's age to Freya's age is therefore 1:3.

Answer:

First, we know that:

1 1/3 = 4/3

10 2/3 = 32/3

15 minutes = 0.25 hours

Let's imagine that x (hours) is the time it takes Lee to type 32/3 pages.

From the information, we can tell that:

Lee can type:

4/3 pages in 0.25 hours

32/4 pages in x hours

So x should be:

x = (32/4 . 0.25)/4/3 = 2 (hours)

So it takes Lee 2 hours ro type 10 2/3 pages

Step-by-step explanation:

Answer:

y = 21

x = 8

Step-by-step explanation:

AB = 180

27 + 3y = 90°

-27           -27

-----------------------

3y = 63

÷3     ÷3

--------------

y = 21

x + 27 + 3y + 8x + 18 = 180

9x + 45 + 3(21) = 180

9x + 45 + 63 = 180

9x + 108 = 180

      -108   -108

-----------------------

9x = 72

÷9    ÷9

----------------

x = 8

I hope this helps!

Answer:

Step-by-step explanation:

They are (1.5, 0).

Answer:

The answer is 11 becasue 66 divided by 6 equals 11

Step-by-step explanation:

Hope this helped

Answer:

The third and fourth ones are functions.

Step-by-step explanation:

How that helped.

Answer:

3rd and 4th

Step-by-step explanation:

.

Answer:

25

Step-by-step explanation:

To solve for UC, you can subtract the length of CN from UN.

UN=40

CN=15

40-15=25