The measures of the 3 sides of a triangle can be represented by algebraic expressions x, 3x-1, and 4x＋2.the perimeter of the triangle is 81inches. What are the lengths of the sides of the triangle?

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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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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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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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:

Answer:

6900 rounded answer -

Step-by-step explanation:

Plato users, correct.

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:

b. A checking account, or a savings account for other expenses (predictable), and emergencies.

Step-by-step explanation:

Peggy needs to pay car insurance 2 times every year.

She has divided the payment by 6 and saves that amount each month.

So, the best account in which she can save this money is - A checking account, or a savings account.

Other options are irrelevant as a 401-K retirement fund is some other type of account. It is not used for daily or monthly expenses.

Options C and D are also not correct.

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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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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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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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).

To find the side of a square with a given diagonal length, apply the Pythagorean theorem. With a diagonal of 8 miles, the side length is calculated to be 4√2 miles.

To find the side of a square whose diagonal is given, we can use the Pythagorean theorem. In a square, the diagonal creates two right-angled triangles, each with the square's sides as the legs.

Let the side of the square be s, and the given diagonal is 8 miles. According to the Pythagorean theorem, the diagonal (d) is calculated as d = √(s² + s²). Simplifying, this becomes d = √(2 * s²) or s = d / √2. Substituting the value of the diagonal, we get s = 8 / √2. To get rid of the radical in the denominator, we can multiply both the numerator and denominator by √2, giving us s = (8√2) / 2, which simplifies to s = 4√2 miles. Therefore, the side of the square is 4√2 miles.

Answer:

Step-by-step explanation: