cosx - 4 = sinx -4
(0,2pi)
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Taylor's net proceeds from the sale of his stock are $4179, after paying his broker's 0.5% commission. His capital gain on the investment is $525, calculated by subtracting the total purchase cost, including the initial broker's flat fee, from the net proceeds of the sale.

a. What were Taylor's net proceeds?

To calculate Taylor's net proceeds, we need to consider the initial cost of buying the shares, any fees paid to the broker, and the amount earned from selling the shares. Here's the breakdown:

Determine initial cost: 200 shares x $18.12 per share = $3624

Add broker's fee when buying: $3624 + $30 = $3654

Subtract broker's fee when selling: $42 (0.5% of $8400 from selling 200 shares at $21 per share)

Calculate net proceeds: $8400 - $42 = $8358

b. What was his capital gain?

To find Taylor's capital gain, subtract the total cost (initial purchase cost + fees) from the total earnings after selling the shares. The calculation is as follows:

To find the number of VHS tapes sold when 564 DVDs were sold, divide the number of DVDs by 2.

To solve this problem, we can set up a ratio comparing the number of VHS tapes sold to the number of DVDs sold. Since the ratio is given as 2 VHS tapes to every 4 DVDs, we can simplify it to 1 VHS tape to every 2 DVDs. If 564 DVDs were sold, we can divide this number by 2 to find the number of VHS tapes sold:

564 DVDs ÷ 2 = 282 VHS tapes

Therefore, 282 VHS tapes were sold.

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Answer:

Step-by-step explanation:

Answer:

6900 rounded answer -

Step-by-step explanation:

Plato users, correct.

If Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.

We have to apply the ratio which is the comparison of two quantities to determine how many times one obtains the other.

Suppose the fraction of the whole pie is each slice will be x,

x = 1/4 / 3

x = 1 /12

Thus, if Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.

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A. We are given that each person weighs 150 lb, each gear per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.

Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).

So let us say that x is the number of persons, the inequality equation is:

160 x + 200 ≤ 1200

B. There are three groups that wish to rent the boat.

> Solve the inequality equation when x = 4

160 (4) + 200 ≤ 1200

840 ≤ 1200           (TRUE)

> Solve the inequality equation when x = 5

160 (5) + 200 ≤ 1200

1000 ≤ 1200         (TRUE)

> Solve the inequality equation when x = 8

160 (8) + 200 ≤ 1200

1480 ≤ 1200         (FALSE)

So only the 4 people group and 5 people group can safely run the boat.

C. Find the maximum number of people that may safely use the boat, solve for x:

160 x + 200 ≤ 1200

160 x ≤ 1000

x ≤ 6.25

Therefore the maximum number of people that can safely use the boat is 6 people.

A mathematical inequality is created to determine that a maximum of 6 people can rent a boat based on the safety weight limit of 1200 lb. Of the groups provided, only groups with 4 or 5 people can safely rent the boat, while the group with 8 people cannot due to exceeding the weight limit.

To determine the restrictions on the number of people that can possibly fit in a rented boat given the safety weight limit, we start by creating an inequality. Let p represent the number of people, then the total weight of the people is 150 lb times p, and the total gear weight is 200 lb for the boat plus 10 lb per person. The inequality can be represented as:

150p + 10p + 200 \<= 1200

Simplifying the inequality gives us:

160p \<= 1000

Dividing both sides by 160:

p \<= 1000 / 160

p \<= 6.25

Since we cannot have a fraction of a person, the maximum number of people allowed is 6.

For part B, we evaluate if the groups mentioned can safely rent a boat:

Group 1 (4 people): 150(4) + 10(4) + 200 = 840 lb \<= 1200 lb - they can rent.

Group 2 (5 people): 150(5) + 10(5) + 200 = 1000 lb \<= 1200 lb - they can rent.

Group 3 (8 people): 150(8) + 10(8) + 200 = 1480 lb > 1200 lb - they cannot rent as it exceeds the limit.

The maximum number of people who may rent a boat based on the given restrictions and average weights is 6 people.

No, the sample design is not a simple random sample (SRS), but a stratified random sample. In an SRS, every individual in the population has an equal chance of being chosen for the sample.

The given sample design is not a simple random sample (SRS). In an SRS, every individual in the population has an equal chance of being chosen for the sample. However, in this case, the sample design is a stratified random sample. It involves dividing the population into groups (in this case, male and female engineers) and then selecting a sample from each group using a different sampling rate.

To determine if a sample design is an SRS, we need to ensure that each individual in the population has an equal chance of being chosen, and this probability is the same for every individual. In the case of the given example, the sample design does not meet these criteria, making it not an SRS.

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The slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The function graphed shows the total cost for a taxi cab ride for x miles the cost in taxi is shown in y axis and the distance covered by taxi in x axis. Now, to find put the slope we must two coordinates which  can be found out from the graph easy by observation as (0,3) and (2,8).

How using slope formula to find the slope of line :

[tex]\begin{aligned}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}&=\frac{8-3}{2-0}\\&=\frac{5}{2}\\&=2.5\end{aligned}[/tex]

It represents the cost of taxi per mile of distance travelled.

Therefore, the slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.

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Using the normal distribution and the central limit theorem, it is found that there is a:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is 1 subtracted by the p-value of Z when X = 18, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{18 - 19.32}{2.44}[/tex]

[tex]Z = -0.54[/tex]

[tex]Z = -0.54[/tex] has a p-value of 0.2946.

1 - 0.2946 = 0.7054.

0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.

Item b:

Now, we want the probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months, hence:

[tex]n = 5, s = \frac{2.44}{\sqrt{5}}[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{18 - 19.32}{\frac{2.44}{\sqrt{5}}}[/tex]

[tex]Z = -1.21[/tex]

[tex]Z = -1.21[/tex] has a p-value of 0.1131.

1 - 0.1131 = 0.8869.

0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.

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Answer:

Jake had twenty-four dollars ($24) at the beginning of the day.

Step-by-step explanation:

Jake has $11 dollars left in his pocket, after spending 3 dollars on a bus ticket, 5 dollars on lunch, and 5 more dollars on a movie. 3+5+5 is equal to 13, therefore if after spending 13 dollars Jake still has 11 dollars, which means that at the beginning of the day Jake had 24 dollars (11+13).

The value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 ​will be negative four.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4 ​

Simplify the expression, then the value of the expression will be

⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4 ​

⇒ (2) ⋅ (−7) + 14 − 4 ​

⇒ −14 + 14 − 4 ​

⇒ − 4 ​

Then the value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 ​will be negative four.

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Answer:

[tex]\frac{20+2k}{3k+12}[/tex]

Step-by-step explanation:

Since there is no equals sign here, we are not solving this.  The only way to simplify is to get a common denominator and write the expression as a single expression.  We can begin by noting that the second term has a k in the numerator and in the denominator, and those cancel each other out.  That is the first simplification we can perform.  That leaves us with:

[tex]\frac{4}{k+4}+\frac{2}{3}[/tex]

In the first term, the denominator is k + 4, in the second term it is just 3.  Therefore, the common denominator is 3(k+4).  We are missing the 3 in the denominator of the first term, so we will multiply in 3/3 by that term.  We are missing a (k + 4) in the second term, so we will multiply in (k + 4)/(k + 4) by that term:

[tex](\frac{3}{3})(\frac{4}{k+4})+(\frac{k+4}{k+4})(\frac{2}{3})[/tex]

Multiplying fractions requires that I multiply straight across the top and straight across the bottom.  That gives me:

[tex]\frac{12}{3k+12}+\frac{2k+8}{3k+12}[/tex]

Now that the denominators are the same, I can put everything on top of that single denominator:

[tex]\frac{12+2k+8}{3k+12}[/tex]

Th final simplification requires that I combine like terms:

[tex]\frac{20+2k}{3k+12}[/tex]

The solution is, 1080  = 2*2*2*3*3*3*5, is not a cube number.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

the number is 1080

Split  into prime factors

1080  = 2*2*2*3*3*3*5

so, we have,

Its not a cube

because  although there are  2 triplicates there is also a 5.

as, we know that,

Note 2*2*2*3*3*3   is a cube.

so, 1080  = 2*2*2*3*3*3*5, is not a cube number.

Hence, The solution is, 1080  = 2*2*2*3*3*3*5, is not a cube number.

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Piecewise function with 3 pieces: [tex]x^2+1, 4x-8, 2[/tex]

The piecewise function ƒ that is represented by the graph in the image is:

ƒ(x) =

[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]

[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]

[tex]5^2+1 = 26, & \text{if } x = 5[/tex]

This is because the graph of the function consists of three distinct pieces:

For 0≤x<4, the graph is a parabola with vertex at (0,1) and opening upwards. This suggests that the function is of the form [tex]ax^{2} +bx+c.[/tex]

We can find the values of a, b, and c by substituting the points (0,1), (1,1), and (4,16) into the equation.

This gives us the system of equations:

\begin{cases}

[tex]a \cdot 0^2 + b \cdot 0 + c = 1[/tex]

[tex]a \cdot 1^2 + b \cdot 1 + c = 1 \\[/tex]

[tex]a \cdot 4^2 + b \cdot 4 + c = 16[/tex]

\end{cases}

Solving this system gives us a=1, b=0, and c=1, so the equation of the function for this interval is [tex]x^{2} +1[/tex].  

For 4≤x<5, the graph is a line with slope 4 and y-intercept −8.

This suggests that the function is of the form mx+b.

We can find the values of m and b by substituting the points (4,2) and (5,25) into the equation.

This gives us the system of equations:

\begin{cases}

[tex]4m+b = 2 \\[/tex]

5m+b = 25

\end{cases}

Solving this system gives us m=4 and b=−8, so the equation of the function for this interval is 4x−8.

For x=5, the graph is a horizontal line at y=26.

This suggests that the function is of the form c.

We can find the value of c by simply looking at the graph.

This gives us c=26, so the equation of the function for this interval is 26.

Therefore, the complete piecewise function is:

ƒ(x) =

\begin{cases}

[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]

[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]

[tex]5^2+1 = 26, & \text{if } x = 5[/tex]

\end{cases}

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