13

Write

as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

9

let's firstly convert the mixed fractions to improper fractions and them sum them up.

[tex]\stackrel{mixed}{7\frac{5}{12}}\implies \cfrac{7\cdot 12+5}{12}\implies \stackrel{improper}{\cfrac{89}{12}}~\hfill \stackrel{mixed}{11\frac{2}{3}} \implies \cfrac{11\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{35}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{89}{12}+\cfrac{35}{3}\implies \cfrac{(1)89~~ + ~~(4)35}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{89+140}{12}\implies \cfrac{229}{12}\implies {\Large \begin{array}{llll} 19\frac{1}{12} \end{array}}[/tex]

Answer:

6x-4y=18

-x-6y=7

-x-6y=7

-x=7+6y

x=-7-6y

6x-4y=18

6(x-7-6y)-4y=18

-42-40y=18

-40y=18+42

-40y=60

y=-60/40

y=-3/2

x=-7-6y

x=-7-6(-3/2)

x=-7+9

x=2

(x,y) = (2,-3/2)

Answer:

[tex]\dfrac{x}{x + 1}\\\\\text{which is the first answer choice }[/tex]

Step-by-step explanation:

We are given
[tex]f(x) = x^2 - x\\g(x) = x^2 - 1\\\\\text{and we are asked to find $ \left(\dfrac{f}{g}\right)\left(x\right)$}[/tex]

[tex]\left(\dfrac{f}{g}\right)\left(x\right) = \dfrac{f(x)}{g(x)}\\\\\\= \dfrac{x^2-x}{x^2 - 1}[/tex]

[tex]x^2 - x = x(x - 1)\text{ by factoring out x}\\\\x&2 - 1 = (x + 1)(x - 1) \text{ using the relation $a^2 - b^2 = (a + 1)(a - 1)$}[/tex]

Therefore,

[tex]\dfrac{x^2-x}{x^2 - 1} = \dfrac{x(x-1)}{(x + 1)(x - 1)}[/tex]

x - 1 cancels out from numerator and denominator with the result
[tex]\dfrac{x}{x+1}[/tex]

So

[tex]\left(\dfrac{f}{g}\right)\left(x\right)$} = \dfrac{x}{x + 1}[/tex]

the length of the actual kitchen wall is 144 inches.

The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

Given, On a scale drawing, a kitchen wall is 6 inches long. The scale factor is 1/24

If the scale factor is 1/24, it means that every 1 inch on the drawing represents 24 inches in real life.

Let's set up a proportion:

1 inch on the drawing : 24 inches in real life = 6 inches on the drawing : x inches in real life

where x is the length of the actual wall.

To solve for x, we can cross-multiply:

1 inch on the drawing * x inches in real life = 6 inches on the drawing * 24 inches in real life

x = 6 inches on the drawing * 24 inches in real life / 1 inch on the drawing

x = 144 inches in real life

Therefore, the length of the actual kitchen wall is 144 inches.

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The value of the machine after 4 years can be calculated using the formula:
V = P * (1 - r) ^ n
Where:
V = value after n years
P = initial purchase price
r = annual depreciation rate
n = number of years

In this case, P = 3,000.00, r = 0.10 (10%), and n = 4.
Plugging these values into the formula, we get:
V = 3,000.00 * (1 - 0.10) ^ 4
V = 3,000.00 * 0.90 ^ 4
V = 3,000.00 * 0.6561
V = 1,968.30

Therefore, the value of the machine after 4 years is $1,968.30.

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The height of the container if it's a cylinder with a radius of 3 cm is 5 cm.

The cost of coffee is $2.83.

The height of the container if it's a cylinder with a radius of 5 cm is 1.8 cm.

The cost of hot chocolate powder is $9.90.

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Picking a volume of 45π cm³, the height of this container is given by:

h = V/πr²

Height, h = 45π/π3²

Height, h = 5 cm.

For the cost of coffee, we have:

Cost of coffee = 45π cm³ × $0.02

Cost of coffee = $2.83.

When the radius is 5 cm, the height of this container is given by:

h = V/πr²

Height, h = 45π/π5²

Height, h = 1.8 cm.

For the cost of hot chocolate powder, we have:

Cost of hot chocolate powder = 45π cm³ × $0.07

Cost of hot chocolate powder = $9.90.

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48500 has been invested in total. Total invested at the end: $289,279.40. This exemplifies the need to allow your savings to increase over time.

An investments is a procurement made with both the intention of making money or increasing capital. Appreciate seems to be the term for just an asset's value growing over time. When someone invests in something, they do it with the intention of using it to generate cash later on instead of for current consumption.

Investing is a wise method to use your money and may possibly increase your wealth. When your make intelligent investment choices, your cash can increase in value and outpace inflation.

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The cost of the desktop computer was $2100, and the cost of the laptop computer was $2350.

A finance charge is a fee or interest payment that a borrower is required to pay to a lender for the use of credit or a loan. It represents the cost of borrowing money and is typically calculated as a percentage of the outstanding balance.

Finance charges can take many forms, including interest rates, annual fees, late payment fees, balance transfer fees, and cash advance fees. The specific amount of the finance charge depends on a variety of factors, such as the loan amount, the interest rate, the repayment period, and the borrower's credit history.

Let the cost of the desktop computer be x. Then, the cost of the laptop computer would be x + 250.

The finance charge for the desktop would be 8.5% of x, which is 0.085x.

The finance charge for the laptop would be 5% of (x + 250), which is 0.05(x + 250) = 0.05x + 12.5.

The total finance charges for one year were $296, so we can write the equation:

0.085x + 0.05x + 12.5 = 296

Combining like terms and solving for x, we get:

0.135x = 283.5

x = 2100

Therefore, the cost of the desktop computer was $2100, and the cost of the laptop computer was $2350.

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If p-hat is equal to 0.65, then the complement (q-hat) is equal to 0.35.

We must deduct p-hat from 1 to obtain the complement q-hat when p-hat is known. The complement is the probability that the event won't occur, which is the same as the likelihood of every other scenario that isn't the one we're interested in.

Take p-hat out of 1 to get:

q-hat = 1 - p-hat

The value of p-hat is 0.65, therefore replace it as follows:

q-hat = 1 - 0.65

Condense the phrase:

q-hat = 0.35

As a result, the complement q-hat is 0.35 if the p-hat is 0.65.

It's critical to keep in mind that the probabilities p-hat and q-hat are complimentary and always sum up to 1. The equation q-hat = 1 - p-hat can be used to quickly compute the other if the first is known.

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Answer:

13

an example:In words: 103 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed"

Trust me its 13

10 + 3³/⁹ answer is  11.4422495703074083.

An algebraic expression is a combination of variables, constants, and mathematical operations. It represents a mathematical relationship between quantities and can be used to model real-world situations or solve problems.

Algebraic expressions can contain variables, which are symbols that represent unknown values, constants, which are fixed values, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.

We can simplify the expression step by step as follows:

10 + 3³/⁹ = 10 + 3^(1/3) (since 3^(3/9) = (3^3)^(1/9) = 27^(1/9) = (3^3)^(1/3) = 3^(3/3) = 3^1 = 3)

= 10 + 1.4422495703074083 (using a calculator to evaluate 3^(1/3) to about 15 decimal places)

= 11.4422495703074083

Therefore, 10 + 3^(3/9) = 11.4422495703074083.

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a)0.1359, or 13.59%

b)85,100,115

c)0.0062, or 0.62%.

d)0.9705, or 97.05%

a. The probability of a randomly selected person's IQ being over 120 is 0.1359, or 13.59%.

b. Q1 for IQ is 85, Q2 is 100, and Q3 is 115.

c. The probability of an outlier for IQ for a single person is 0.0062, or 0.62%.

d. The probability of the average IQ of 10 randomly selected people being over 105 is 0.9705, or 97.05%.

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Since, 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

To determine whether a value of x is a solution to the inequality 13 < 2x+3, we need to substitute the value of x into the inequality and see if it is true or false.

Let's try x = 5. Then: 13 < 2x+3

13 < 2(5)+3

13 < 10+3

13 < 13

This is not true, since 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

Note that if we had found 13 < 13 instead, then we would have concluded that x = 5 is not a solution to the inequality. But since the inequality is strict (i.e., "less than"), we need to have a strict inequality when we substitute the value of x to determine whether it is a solution.

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A) The probability of getting 3 or fewer students who play a sport in your sample is 0.014, or 1.4%.

B) The probability of getting 3 or fewer students who play a sport in your sample is much lower than the expected probability of 0.4 (40%). This suggests that your estimate of 40% of students in the whole school playing a sport may be too high.

C) There are 1140 different combinations of 3 students who play sports and 17 students who don't in your sample.

A) To find the probability of getting 3 or fewer students who play a sport in your sample, you can use the binomial probability formula:

P(X = x) = nCx * p^x * (1-p)^(n-x)

where n is the sample size, x is the number of successes, p is the probability of success, and nCx is the number of combinations of x successes in n trials.

For x = 0, 1, 2, and 3, the probabilities are:

P(X = 0) = 20C0 * 0.4^0 * 0.6^20 = 0.000006
P(X = 1) = 20C1 * 0.4^1 * 0.6^19 = 0.00016
P(X = 2) = 20C2 * 0.4^2 * 0.6^18 = 0.0019
P(X = 3) = 20C3 * 0.4^3 * 0.6^17 = 0.012

Adding these probabilities gives:

P(X <= 3) = 0.000006 + 0.00016 + 0.0019 + 0.012 = 0.014



C) The number of different combinations of 3 successes and 17 failures is given by:

20C3 = 20! / (3! * 17!) = 1140


D) The formula for the number of combinations of x successes in n trials is:

nCx = n! / (x! * (n-x)!)

For 20C2 and 20C17, the formulas are:

20C2 = 20! / (2! * 18!)
20C17 = 20! / (17! * 3!)

Since 2! * 18! = 17! * 3!, these two formulas are equivalent and give the same result. This is why 20C2 = 20C17.

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a. The point estimate for the birth weights is 2714.58, b. the value of tq is 1.70814, and c. the margin of error for the confidence interval is 124.3. d. The confidence interval for birth weights is (2503, 2927). e. No conclusions can be drawn since the confidence interval contains 2500.

a. The point estimate for the birth weights is 2714.58. This is the average of the sample data and is used as an estimate for the population mean.

b. The value of tq is 1.70814. This is the t-value associated with the given confidence level and degrees of freedom.

c. The margin of error for the confidence interval is 124.3. This is calculated using the formula ME = tq * (s/√n), where tq is the t-value, s is the sample standard deviation, and n is the sample size.

d. The confidence interval for birth weights is (2503, 2927). This is calculated by taking the point estimate and subtracting and adding the margin of error to get the lower and upper bounds of the interval.

e. No conclusions can be drawn since the confidence interval contains 2500. This means that the true population mean could be less than 2500, greater than 2500, or equal to 2500.

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a) The domain of (f o g)(x) is [-5/3, ∞).

b) The domain of (g o f)(x) is [0, ∞).

c) The domain of (f o f)(x) is [0, ∞).

d) (f o g)(x) = f(g(x)) = f(3x+5) = √(3x+5).

e) The domain of this composite function is all real numbers.

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

3x+5 ≥ 0

3x ≥ -5

x ≥ -5/3

Therefore, the domain of (f o g)(x) is [-5/3, ∞).

(b) (g o f)(x) = g(f(x)) = g(√x) = 3√x + 5

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

√x ≥ 0

x ≥ 0

Therefore, the domain of (g o f)(x) is [0, ∞).

(c) (f o f)(x) = f(f(x)) = f(√x) = √(√x)

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

√x ≥ 0

x ≥ 0

Therefore, the domain of (f o f)(x) is [0, ∞).

(d) (g o g)(x) = g(g(x)) = g(3x+5) = 3(3x+5) + 5 = 9x + 20

The domain of this composite function is all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (g o g)(x) is (-∞, ∞).

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To obtain 400 liters of 11% acid solution, you need to mix  390 liters of the 10% acid solution and 10 liters of the 50% acid solution to obtain 400 liters of 11% acid solution.

Let x be the number of liters of 10% acid solution and y be the number of liters of 50% acid solution.

We can set up a system of two equations to represent the given information:

x + y = 400 (total volume of the mixture is 400 liters)

0.10x + 0.50y = 0.11(400) (the amount of acid in the mixture is 11% of the total volume)

Simplifying the second equation:

0.10x + 0.50y = 44

We can now use either substitution or elimination method to solve for x and y.

Using substitution, we can solve for y in terms of x from the first equation:

y = 400 - x

Substituting this into the second equation:

0.10x + 0.50(400-x) = 44

Simplifying and solving for x:

0.10x + 200 - 0.50x = 44

-0.40x = -156

x = 390

So the chemist needs 390 liters of the 10% acid solution and 10 liters of the 50% acid solution to obtain 400 liters of 11% acid solution.

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We have the solve using the quadratic equation as;

Step 2:

a = 1

b = -5

c = -14

Step 3:

What 1: (-5)²

What 2: 1

What 3: -14

What 4: 1

The quadratic equation is expressed as;

ax² + bx + c = 0

x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex]/2a

From the information given, we have that;

x² -5x - 14 = 0

Now, substitute the values, we get;

x = - (-5) ± [tex]\sqrt{(-5)^2 - 4 * 1 * -14}[/tex]/ 2(1)

find the square and substitute the values, we have;

x = 5 ± [tex]\sqrt{25 + 56}[/tex]/2

Add the values, we have;

x = 5 ± √81/2

Find the square root

x = 5 ±9/2

x = 5 ± 4. 5

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The given expression -5x⁶-7x³+7x²+4 is a polynomial.

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. The terms in a polynomial are called monomials, and they can be either constants or variables with a coefficient.

In the given expression, there are four terms: -5x⁶, -7x³, 7x², and 4. Each of these terms is a monomial. Since there are four terms in the expression, it is classified as a polynomial with four terms, also known as a quadrinomial.

Therefore, the given expression -5x⁶-7x³+7x²+4 is a quadrinomial, which is a type of polynomial.

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Answer: To determine the effective rate of Zoe's loan, we can use the formula:

Effective rate = (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1

Since the nominal rate is compounded monthly, the number of compounding periods is 12.

Plugging in the values, we get:

Effective rate = (1 + (0.039/12))^12 - 1

Effective rate = 0.0407 or 4.07%

Therefore, the effective rate of Zoe's loan is 4.07%, rounded to the nearest hundredth. The correct response is 3.97%.

Step-by-step explanation:

The probability is 4/8 = 1/2. The probability that the student answered True at least two times is 1/2.

The number of residents in a city is a discrete variable because it is a countable number of people. The level of measurement is a ratio level because there is a true zero point (no residents in a city) and the difference between values is meaningful. Therefore, the correct answer is discrete, ratio level.

The sample space for the three True (T) or False (F) questions is: {TTT, TTF, TFT, FTT, FTF, FFT, TFF, FFF}

The outcomes corresponding to the event "The student answered True at least two times" are: {TTT, TTF, TFT, FTT}

To evaluate the probability of the event "The student answered True at least two times", we need to divide the number of favorable outcomes by the total number of possible outcomes. The number of favorable outcomes is 4 (TTT, TTF, TFT, FTT) and the total number of possible outcomes is 8 (TTT, TTF, TFT, FTT, FTF, FFT, TFF, FFF). Therefore, the probability is 4/8 = 1/2. The probability that the student answered True at least two times is 1/2.

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b.4+3cos²x is the simplification of the given trigonometric identity

Explanation:
Using the identity sin²x + cos²x = 1, we can simplify the expression:

4-4sin²x/(cot²x) + 7cos²x
= 4 (1-sin²x)/(cot²x) + 7cos²x
= 4 cos²x/cot²x + 7cos²x
= 4sin²x + 7cos²x

= 4sin²x + 4cos²x + 3cos²x

=4+3cos²x

Hence, the answer is b. 4 + 3cos²x

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Solving a quadratic equation we can see that the 3 consecutive numbers are:

4, 5, and 6.

First, we can write 3 consecutive integers as:

x, (x + 1), and (x +2 )

The square of the first increased by the last is 22, then we can write:

x^2 + (x + 2) = 22

x^2 + x + 2 - 22 = 0

x^2 +x  - 20 = 0

Using the quadratic formula we will get the solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-20} }{2} \\\\x = \frac{-1 \pm 9}{2}[/tex]

We know that x is positive, then the solution is:

x = (-1 + 9)/2 = 4

The 3 consecutive numbers are:

4, 5, and 6.

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By answering the above question, we may infer that The answer is yes, equation and Kaylee now has 26 nickels. Option B, or 50, is the correct response, therefore.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Hence, she has twice as many nickels and quarters as normal.

The combined worth of Kaylee's coins is $30. This may be expressed as an equation:

[tex]0.05(2x) + 0.10x + 0.25(4x) = 30\\0.10x + 0.10x + 1.00x = 30\\2.20x = 30\sx = 13.64[/tex]

Kaylee has 2x = 28 nickels and 4x = 56 quarters if x = 14. These coins are worth 0.05(28), 0.10(14), and 0.25(56), for a total of $7.70.

This does not equal $30, hence the suggested solution is invalid.

Kaylee has 2x = 26 nickels and 4x = 52 quarters if x = 13. These coins are worth [tex]0.05(26) + 0.10(13) + 0.25(52) = $30.[/tex]

The answer is yes, and Kaylee now has 26 nickels.

Option B, or 50, is the correct response, therefore.

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\[ \left[\begin{array}{rr}-35 & 7 \\ 5 & -1\end{array}\right] \]

In Exercises 1-12, use the Gauss-Jordan method to compute the inverse, if it exists, of the matrix.

1. \( \left[\begin{array}{ll}7 & 3 \\ 5 & 2\end{array}\right] \)

To find the inverse of this matrix, we need to use the Gauss-Jordan method. We begin by writing the augmented matrix:

\[ \left[\begin{array}{cc|cc}
7 & 3 & 1 & 0 \\
5 & 2 & 0 & 1
\end{array}\right]\]

Next, we subtract 5 times the first row from the second row to obtain:

\[ \left[\begin{array}{cc|cc}
7 & 3 & 1 & 0 \\
0 & -11 & -5 & 1
\end{array}\right]\]

Now, we divide the second row by -11 to obtain:

\[ \left[\begin{array}{cc|cc}
7 & 3 & 1 & 0 \\
0 & 1 & 5 & -1
\end{array}\right]\]

Finally, we subtract 7 times the second row from the first row to obtain:

\[ \left[\begin{array}{cc|cc}
1 & -20 & -35 & 7 \\
0 & 1 & 5 & -1
\end{array}\right]\]

Therefore, the inverse of the given matrix is:

\[ \left[\begin{array}{rr}-35 & 7 \\ 5 & -1\end{array}\right] \]

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Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.

To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:

There were n1 squirrels in the first group.

Second sample's fox count is equal to n2.

Second sample's total number of labelled squirrels is m2.

The following provides the Lincoln-Petersen index:

=> n1 * n2 / m2

Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.

=> n1 * n2 / m2 = 100 * 200 / 20 = 1000

Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.

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Answer:

Last answer choice: 4

Step-by-step explanation:

The set of inputs to the graphed function is he set of all x values for which the function has a defined value

Looking at the answer choices we see that the graph does not go the negative x region nor does it have a value for 0

So x = 4 is an input, and the resultant output y from the graph = 0

Answer

Last answer choice: 4

The time needed for the number of people infected with the flu to reach 3072 is given as follows:

4 days.

The exponential function that models the situation has the definition given as follows:

y = ab^x.

In which the parameters are given as follows:

Assume a total of 12 people have the flu as of today, hence the parameter a is given as follows:

a = 12.

Each day the total number people who have the flu quadruples, hence the parameter b is given as follows:

b = 4.

Hence the function giving the number of people with the flu after x days is given as follows:

y = 12(4)^x.

The number of days needed for the number to reach 3072 is obtained as follows:

12(4)^x = 3072

4^x = 3072/12

4^x = 256.

2^(2x) = 2^(8)

Hence the value of x is obtained as follows:

2x = 8

x = 4.

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Answer:

376, and 122

Step-by-step explanation:

To solve for the surface area, we add up the areas for each side together.

([8×6] × 2) + ([8×10] × 2) + ([10×6] × 2) = 376

376 is the surface area for the 1st shape.

(10 × 5) + (4×3) + ([3×10] ×2)= 122

122 is the surface area for the 2nd shape

Answer:

9)376ft^2 10)132ft^2

Step-by-step explanation:

the first one is pretty easy use the formula 2(l*w+l*b+w*b) where l is length b is breadth and w is the width, l=10 b=8 w=6

2(10*6+10*8+6*8)

=376ft^2

the second one is also not that hard, first find out the area of the triangles in which the base is 3 and height is 4 so 4*3/2

=6

since there are two triangles, the surface area of the triangles combined is 12

now lets move the base where the width is 3 and the length is 10 as it also corresponds, now l*w is the formula to find the surface area of a rectangle so 10*3 is 30 now lets find the surface area of the square on the front which is just 10*5 which equals to 50 and lastly the rectangle at the back, for which we know that the width is 4 and length is 10 so 10*4 is 40 now simply just add all ofn these areas, 12+50+40+30

=132ft^2