Tamala’s school day is 7 1/2 hours. She has six classes that are 7/6 of an hour long each. How many hours is Tamala not in class while she is at school?

Answer:

book c has 130 pages

Step-by-step explanation:

let book a = x pages

book b      = 2x

book c      = 2x + 30

according to the question:

x + 2x +2x + 30 = 280

5x + 30 = 280

5x = 280-30

5x = 250

x = 250/5

x = 50

thus book c has 2(50) + 30 = 130 pages

Answer:

[tex]x = 3, -1[/tex]

Explanation:

math

Answer:

c

...................

Answer:

the answer is the option C

After 25 years, Sample left will be 100g if nearest hundred...ig...

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”

Using concepts of percentage,

3 is 16.63% of 22.

22 is 13.41% of 164.

0.88 is 4% of 22.

8 is 22% of 36.36.

1.1 is 5% of 22.

A percentage is a number or ratio expressed as a fraction of 100.

Let 3 be x% of 22.

=x/100*22=3

=x=3*100/22=13.63

3 is 13.63% of 22.

Let 22 be y % of 164.

=y/100*164=22

=y=22*100/164=13.41

13.41% of 164 is 22.

4% of 22 = 0.88

=4/100*22=0.88

Let 8 is 22% of z.

=22/100*z=8

=8*100/22=36.36

5% of 22 = 1.1

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The doubling period of a bacterial population is 15 minutes. the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.

y = total amount of bacteria

a = initial bacterial at time 0

b = growth factor

t=120 minutes =15 minutes 8 times

So,

t=8

90000 =  a (2)^8

90000 = a (256)

90000/256 = a

351.56 = a (initial population)

Equation:

y = 351.56 (2)t

After 3 hours (15 minutes 10 times), or at t = 10

y = 351.56 (2)^10

y= 359,997.44

Therefore the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.

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Answer:

Target

Step-by-step explanation:

$4.40/8 is 0.55 and $7.08/12 is 0.59

Answer:

  1/3log₂(x) +1/3log₂(y) +1/3log₂(z)

Step-by-step explanation:

You want the complete expansion of ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}[/tex]

The rules of logs and exponents relevant to this expansion are ...

  [tex]\log_b{(xy)}=\log_b{(x)}+\log_b{(y)}\\\\\log_b{(x^a)}=a\cdot\log_b{(x)}\\\\\sqrt[n]{\vphantom{b}a}=a^{\frac{1}{n}}[/tex]

Applying these rules to the given expression, we get ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}=\log_2{((xyz)^{\frac{1}{3}})}=\dfrac{1}{3}\log_2{(xyz)}\\\\=\boxed{\dfrac{1}{3}\log_2{(x)}+\dfrac{1}{3}\log_2{(y)}+\dfrac{1}{3}\log_2{(z)}}[/tex]

There are total 42,072,307,200 different passwords are possible .

What are combinations ?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

Combinations can be confused with permutations. However, in permutations, the order of the selected items is essential. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.

Given: A password is required to log into a system that only recognizes numbers and letters of the alphabet

Since , there are total 26 letters and 10 numbers are possible that can be used to create a password . Hence , there are 36 character in total to be used.

Also , repetition of character is not allowed. Therefore , the chance of selecting every character decreases by 1 in comparison to its preceding character .

Chance of selecting first character = 36

Chance of selecting second character = 35

Similarly for seventh = 30

Thus , different passwords that are possible  using 7 numbers or letters, without reusing any of them = 36*35*34*33*32*31*30 = 42,072,307,200 .

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The rate of change is 7 more of function A than the slope of function B.

Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.

Since y=8x+3,

The rate of change in equation A is equal to the slope m m=8.

The rate of change, m=1, is given in equation B.

y=mx+ is the solution to equation B.

By substituting the values we get,

y=x+4

Calculate the difference between the rates of change of function A and function B.

8-1=7

Therefore, the rate of change is 7 more of function A than the slope of function B.

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Answer: 5.25>1 3/4>-5/2>-8.345

Step-by-step explanation:

The equation of the line that is normal to the curve y² + ln(x) = 19 at the point (e³, -4) is given as follows:

y + 4 = -8e³(x - e³).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The derivative of the function is found applying implicit differentiation, as follows:

2y dy/dx + 1/x = 0

dy/dx = -1/(2xy).

At x = e³, y = -4, the numeric value of the derivative is given as follows:

dy/dx = e^(-3)/8.

The normal line is perpendicular to the tangent line, hence it's slope is calculated as follows:

m x e^(-3)/8 = -1.

m = -8e³.

Then the equation of the line normal to the curve at the point is given as follows:

y + 4 = -8e³(x - e³).

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Answer: n=11 m=3

Step-by-step explanation:

2n+2=3n-9

n=11

3m+6=n+4

3m+6=11+4

3m+6=15

3m=9

m=3

Answer: 02

Step-by-step explanation: w

Present Value of Annuity = $4,000 × 26.1948  = $104779.2

What is a present value?

The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.

Here, we have

Where , Annuity Amount = $4,000            

n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,

Then, n = 31 when considered for PVAF

r  = 5.4% / 4 quarters = 1.35%,

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)

PVAF(n₀,r) when the first payment is at beginning of n i.e.

n₀ = 1 + { [1-(1+r)^ -n ]/r }

= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }

= 1 + [ (1 - 0.65987 ) ] / 0.0135]

= 1 + 25.1948

= 26.1948

PVAF(32,35%) = 26.1948

Hence, Present Value of Annuity = $4,000 × 26.1948  = $104779.2

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82.9 score should be assigned for A’s and 74.4 should be assigned for B’s

In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.

It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.

We need to find what scores should be assigned A’s and B’s.

μ = 70, σ = 10

Using standard normal table,

P(X > x) = 10%

P(X > x) = 0.10

1 - P(X ≤ x) = 0.10

P(X ≤ x) =1−0.10

             =0.90

Using standard normal z table,

(x - 70)/10 = 1.29

x = 82.9 (score for A’s)

Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)

P(X>x) = 0.33

1 - P(X ≤ x) = 0.33

P(X ≤ x) = 1 - 0.33

             = 0.67

Using standard normal z table,

(x - 70)/10 = 0.44

x = 74.4 (score for B’s)

Therefore, the score for A = 82.9 and the score for B = 74.4

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Being a female and participating in sports are independent events for the provided data because P(girl) = P(girl participates in sports)

These are the occurrences that are independent of other occurrences.

Occurrences A and B are independent events when the likelihood of one occurring is unaffected by the occurrence of the other.

Probability of independent events formula:

"P(A∩B) = if A and B are independent occurrences P(A).P(B)

Finding the chance that an event will occur is the focus of this area of mathematics."

P(A) = n(A)/n(S), where n(A) is the number of positive outcomes and n(S) is the total number of possible outcomes for an event A.

For given question,

We have been given a table that shows the results broken down by gender.

            Play sports         Do not play sports       Total

Boy            95                          45                        140

Girl             76                           59                       135

Total          171                            104                     275

Using the definition of probability:

⇒ P(girl)  = Number of girls/ Number of students

⇒ P(girl) = 135/275

⇒ P(girl) = 0.49                    ....................(1)

Now we find the probability of girls that play a sport.

Using the definition of probability:

P(girl plays a sport)

= Number of girls who plays a sport/ number of students who plays a sport

= 76/ 171

= 0.44                                    ......................(2)

From (1) and (2),

P(girl) = P(girl plays a sport)

Thus, being a girl and playing a sport are Independent events.

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Step-by-step explanation:

chances of winning $20=7/20

chances of winning $30=3/20

chances of winning $15=1/2

The equation of the line is y = x - 2.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have,

y-intercept(c) = −2 and

the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ

but the angle between the axes is 90°

2θ = 90° ⇒ θ = 45°

As slope and y-intercept are given.

The equation of a line is y = mx + c

c = -2 and

m = tan45°

as the line is equally inclined to the axes.

c = -2 and m = 1

Hence, the equation of the line is y = x - 2.

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Answer:

1120

Step-by-step explanation:

Given the information below:

The Relative Frequency of selling a pan style pizza =

Therefore, if Valentino's Pizzeria were to sell 4000 pizzas, the expected number of Pan style pizza sold will be:

Number of Pan Style Pizza Sold = Relative Frequency of pan Style Pizza Purchase X Total Number of Sales

They should expect to sell 1120 pan Style pizzas.

f(x) = x² + 2x + 2

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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What is a NPV  net present value ?

The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.

Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.

1.

NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]

=$18.11

2.

NPV of project B  = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]

= $13.95

Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)

= 15.03% is the IRR for A.

Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)

= 22.26% is the IRR for B.

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Answer:

  a.  18.5 million

  b.  2002

Step-by-step explanation:

Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.

The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.

  A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5

The population in 2000 was 18.5 million.

We can solve for t to find the year in which the population reached 26.6 million:

  26.6 = 18.5·e^(0.1708t)

  26.6/18.5 = e^(0.1708t)

  ln(266/185) = 0.1708t

  t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000

The population will reach 26.6 million in the year 2002.

__

Additional comment

The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.

(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)

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Answer:

y=3x^2 - 2x + 5

Step-by-step explanation:

The easiest way to find the answer to this question would be to just plug the different x values into the equations. If you take the equations and plug in x and it gives out the correct f(x) value, then the answer would be correct.

For example, plugging -3 into y=3x^2 - 2x + 5 gives you 10. Plugging in 0 gives 5. Plugging in 2 gives 13.

Answer: Slants upwards.

Step-by-step explanation:

     This is a positive slope, so the line with this given slope will slant upwards. For every increase of one in y, there is a positive change of 2 in x. See attached for a visual example, if the graph was y = ½x.

Answer:-1.34

Step-by-step explanation:

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]

so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.

so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]