Is 2 a solution of the inequality -2x < -6? example.

The probability that between 8 and 18 of the 100 randomly selected adolescents are alcoholics is approximately 0.0745 or 7.45%.

To solve this problem, we will use the binomial probability formula:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
P(x) = probability of x successes
n = number of trials
x = number of successes
p = probability of success
(1-p) = probability of failure
In this case, n = 100 and p = 0.04 (since 4% of adolescents are alcoholic).
(a) To find the probability that between 8 and 18 of them are alcoholics, we need to sum the probabilities of getting 8, 9, 10, ..., 18 alcoholics out of 100. This can be written as:
P(8<=x<=18) = P(x=8) + P(x=9) + ... + P(x=18)
Using the binomial probability formula, we can calculate each of these individual probabilities and add them up. The final answer will be the sum of these probabilities.
P(8<=x<=18) = Σ (nCx) * p^x * (1-p)^(n-x), where x ranges from 8 to 18.
Using a calculator or software, we can find that:
P(8<=x<=18) ≈ 0.0745

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The sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age is of 11, and this measure was found using a system of equations.

The variables for the system of equations in this problem are given as follows:

Joey is one year older than Chloe, hence:

x = y + 1.

Zoe is exactly one year old, hence:

z = 1.

The difference between the ages of Chloe's and Zoe's have 9 factors. Numbers with nine factors have the following format:

x² x y² , with different x and y.

These numbers have to be different of 1, due to Zoe's age, hence the smallest number is given as follows:

2² x 3² = 4 x 9 = 36.

Since the difference is of 36 years old, so the ages are as follows:

The next time this will happen is in 36 years, hence Joey's age will be of:

36 + 38 = 74 years old.

The sum of the digits will be of:

7 + 4 = 11.

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Answer:

35.34 and 16.66

Step-by-step explanation:

Given data

let the numbers be x and y

the smaller number = x

the larger number = y

x+y=52--------1

The larger number is 2 less than twice the smaller number

y=2x-2-------2

put y= 2x-2 in eqn 1

x+2x-2=52

3x-2=52

3x=52-2

3x=50

x= 50/3

x= 16.66

put x=16.66 in eqn 1 to find y

x+y=52

16.66+y= 52

y=52-16.66

y= 35.34

Hence the numbers are

35.34 and 16.66

Check

35.34+16.66= 52

Answer:

The first blank is ‘the same’ the second blank is ‘proportional’

Step-by-step explanation:

how can i explain when the answer is already an explanation

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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After ten years, you will have approximately $34,448.12.

To calculate the future value of an amount invested at a certain interest rate, we can use the compound interest formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, we will receive $15,500 in three years and then invest it for seven more years at a 9% interest rate.

Step 1: Calculate the future value after three years.

Future Value after three years = $15,500 * (1 + 0.09)^3

Step 2: Calculate the future value after ten years (three years plus the additional seven years).

Future Value after ten years = Future Value after three years * (1 + 0.09)^7

Let's calculate the future value using the given values:

Future Value after three years = $15,500 * (1 + 0.09)^3

= $15,500 * (1.09)^3

= $15,500 * 1.295029

= $20,045.45

Future Value after ten years = $20,045.45 * (1 + 0.09)^7

= $20,045.45 * (1.09)^7

= $20,045.45 * 1.71899

= $34,448.12

Therefore, after ten years, you will have approximately $34,448.12.

It's important to note that this calculation assumes that the interest is compounded annually. If the interest is compounded more frequently (e.g., semi-annually or quarterly), the calculation would be slightly different.

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The two linear equations are:

1)  y = -x + 5

2) y = (-1/2)*x - 1

Remember that two linear equations are parallel if and only if have the same slope and different y-intercept.

So to find a linear equation:

y = m*x + b

Parallel to:

x + y = 4

y = -x + 4

The slope needs to be m = -1 and the y-intercept b ≠ 4

So our line will be:

y = -x + b

To find the value of b, we use the fact that this line passes through (2, 3), replacing the values of the point in the line we get:

3 = -2 + b

3 + 2 = b

5 = b

The linear equation is y = -x + 5

For the second case, we want to find a line perpendicular to:

2x - y = 5

y = 2x - 5

Two lines are perpendicular if the product of the slopes is -1, then:

m*2 = -1

m = -1/2

So the perpendicular line is something like:

y = (-1/2)*x + b

To find the value of b we use the fact that this line needs to pass through (6, -4)

Replacing these values we get

-4 = (-1/2)*6 + b

-4 = -3 + b

-4 + 3  =b

-1 = b

The line is:

y = (-1/2)*x - 1

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The required perimeter of the new rectangle is 66 inches.

A quadrilateral with all of its angles equal, or right angles, is a rectangle.

In addition to having all equal angles, a square also has all equal sides.

Therefore, a particular case of a square is a rectangle.

To put it another way, a rectangle can also be a square (when all sides to are equal).

Because every square is a quadrilateral with all four angles at right angles, every square is also a rectangle.

To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.

So, a perimeter equals 2(l+b).

50 is the circumference and 17 is the length here.

Suppose the breadth is x.

50 = 2(17+x)

50 = (2*17)+(2*x)

50 = 34 + 2x

50 - 34 = 2x

16 = 2x

16/2 = x

8 = x

The first triangle's width is eight inches.

We know that the length of the other rectangle is 17.

And that the width is two times that of the first triangle.

Length = 17, width = 2*8 = 16, etc.

For the border:

p = 2(l+b)

p =  2(17+16)

p =  (2*17)+(2*16)

p =   34+32

p  =   66

Therefore, the required perimeter of the new rectangle is 66 inches.

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Complete question:

Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches. He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle?

To estimate the area under the graph of f(x) = 3√x from x = 0 to x = 4 using four approximating rectangles, we can divide the interval [0, 4] into four subintervals of equal width and calculate the area of each rectangle using either the right endpoints or the left endpoints.

(a) Using right endpoints:

The width of each rectangle is Δx = (4 - 0) / 4 = 1.

The right endpoints for the four subintervals are x = 1, 2, 3, and 4.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the right endpoints:

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

f(4) = 3√4 = 6

The area of each rectangle is then the product of the width and the height.

R1 = 1 * 3 = 3

R2 = 1 * f(2)

R3 = 1 * f(3)

R4 = 1 * 6

To estimate the total area, we sum up the areas of the four rectangles:

R4 = R1 + R2 + R3 + R4

(b) Using left endpoints:

Similar to part (a), the width of each rectangle is Δx = (4 - 0) / 4 = 1.

The left endpoints for the four subintervals are x = 0, 1, 2, and 3.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the left endpoints:

f(0) = 3√0 = 0

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

The area of each rectangle is the product of the width and the height.

L1 = 1 * 0 = 0

L2 = 1 * f(1)

L3 = 1 * f(2)

L4 = 1 * f(3)

To estimate the total area, we sum up the areas of the four rectangles:

L4 = L1 + L2 + L3 + L4

Now, to determine whether the estimates are underestimates or overestimates, we compare them to the actual area under the curve.

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Answer:

\(\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}\)

Step-by-step explanation:

\(\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}\)

\(\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}\)

\(\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\)

\(x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1\)

\(\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4\)

The complete flow proof is:

We have:

\(\angle 5 = 40^o\)

\(\angle 2 = 140^o\)

The proof of \(a ||b\) is as follows:

The first statement is:

\(\angle 5 = 40^o\) ---- Given

The next statement is:

\(\angle 2 = 140^o\) ---- Given

Supplementary angles add up to \(180^o\).

So, the third statement is:

\(\angle 5 + \angle 2 = 180^o\) ----- \(\angle 5\) and \(\angle 2\) are supplementary angles

Same side of interior angles add up to \(180^o\).

So, the fourth statement is:

\(\angle 5 + \angle 2 = 180^o\) ----- \(\angle 5\) and \(\angle 2\) are same-side interior angles

Because the angles are supplementary angles and also same-side interior angles, then it means that line a is parallel to line b

So, the last statement is:

\(a ||b\) ----- Proved

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Answer:

to solve what

Step-by-step explanation:

Answer:

1*2

Step-by-step explanation:

Uno por dos es igual a dos y, por lo tanto, es uno mayor (el sucesor) de uno.

The transaction would affect the company's equity accounts by increasing contributed capital by $14,400 and earned capital by $19,200. The correct answer is option C.

Equity accounts are a component of the balance sheet that represents the net worth of a business. The equity accounts include contributed capital and earned capital. Contributed capital, also referred to as paid-in capital, is the value of cash or other assets contributed to a company by investors in exchange for shares of ownership in the company. Contributed capital represents the long-term financial interests of owners in the business.

Earned capital is the amount of money that a business earns through its operations. It is also referred to as retained earnings. The difference between a business's assets and liabilities is its equity. It represents the total value of the assets that a company owns after all liabilities have been settled. According to the question, the owner contributed cash of $14,400 and a delivery truck with a fair value of $19,200 to the company. This transaction will increase contributed capital by $14,400 (the cash contribution) and increase earned capital by $19,200 (the delivery truck contribution).Therefore, option C: Increase contributed capital by $14,400 and earned capital by $19,200 is the correct answer.

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Answer:

71.4

Step-by-step explanation:

you wiil plus it by 30.4+27+14 that is how i got71.4

the answer is 8=8

Step-by-step explanation:

it just is

Answer:

Each item costs $6.46 dollars rounded to the nearest cent.

Step-by-step explanation:

All I did was divide 3133 divided by 482 is 6.45850622407.

But since this number is too big, I rounded it to the nearest cent.

So, the answer should be 6.46

Hope this helps! :)

Answer:

neither, neither, terminating, repeating

9514 1404 393

Answer:

  -13 < x ≤ 4

Step-by-step explanation:

The round bracket means the lower limit is not included in the interval. The square bracket means the upper limit is included.

  -13 < x ≤ 4

Answer:

We can do it by using the format tab

Step-by-step explanation:

We can change the background of a group of cells by selecting the cell or range of cells we want to format. We should Click Home > Format Cells dialog launcher, or press Ctrl+Shift+F from the keyboard. Then on the Fill tab, under Background Color, we pick the color we want. To use a pattern with two colors, we pick a color in the Pattern Color box, and then pick a pattern in the Pattern Style box. In this tab we can also select gradient or single color

Answer:

1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x ← is in slope- intercept form

with slope m = 1

Answer:

1

Step-by-step explanation:

Answer:

check: 2,3,5,8

Step-by-step explanation:

Answer:

30.25 feet

Step-by-step explanation:

set up a proportion and cross-multiply:

let 'x' = height of building

11/x = 8/22

8x = 242

x = 242/8 = 30 1/4

In this case, the machine has an initial cost of $26,000, a life of 12 years, and an annual operating cost of $13,000 for the first 4 years, increasing by 10% per year thereafter. With an interest rate of 10% per year, the present worth of all costs for the machine is determined to be $.

To calculate the present worth of all costs for the machine, we will use the shifted gradients method. We start by calculating the present worth of the initial cost, which is simply the initial cost itself since there is no trade-in value.

Next, we calculate the present worth of the annual operating costs. The operating costs for the first 4 years are $13,000 per year. Using the formula for the present worth of a gradient, we can calculate the present worth of these costs as follows:

PW = A * (1 - (1 + i)^(-n)) / i,

where PW is the present worth, A is the annual amount, i is the interest rate, and n is the number of years. Plugging in the values, we get:

PW = $13,000 * (1 - (1 + 0.10)^(-4)) / 0.10.

After calculating the present worth of the operating costs for the first 4 years, we need to account for the increasing costs. From the 5th year onwards, the annual operating costs increase by 10% each year. We can calculate the present worth of these increasing costs using the shifted gradient method.

By summing up the present worth of the initial cost and the present worth of the operating costs, we can determine the total present worth of all costs for the newly acquired machine. However, since the specific value is missing in the question, it is not possible to provide an exact answer without the value.

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Answer:

it takes 36 minutes to fill the bathtub using just hot water.

Answer:

I think ur answer is 10.

Step-by-step explanation:

Answer:

Number of $20 bills = 8

Number of $10 bills = 4

Explanation:

Let x be the number of $20 bills.

Let y be the number of $10 bills.

From the question, we'll have the two equations below;

From the 2nd equation, y = 12 - x.

Let's put (y = 12 - x) into the 1st equation and slove for x;

Since x = 8, let's substitute the value of x into (y = 12 - x) and find x;

Answer:

each person gets 32 papers and  there are 4 left over

Step-by-step explanation:

Answer:

z=-\(\frac{2}{3}\)

Step-by-step explanation: