please help!!!!!!!!!!

Answer:

17/25

Step-by-step explanation:

68/100

divided by 2

34/50

divided by 2

17/25

and 17/25 is as simplified as it's going to get.

Answer: y = -(5/3)x + 8

I assume (6,-2)(6,−2) is actually just (6,−2).

Step-by-step explanation:

A parallel line will have the same slope as the reference line.  Rewite the reference line equation into y=mx+b format:

5x+3y=6

3y = -5x+6

y = -(5/3)x + 6

The parallel line we want will have the same slope, -(5/3):

y = -(5/3)x + b

b will be different since we want this new, parallel, line to go through point (6,-2), so it must be moved to accomodate this point.  Find the value of b we need by entering the point into the new equation and solving for b.

y = -(5/3)x + b  for point (6,-2)

-2 = -(5/3)(6) + b

-2 = -10 + b

b = 8

y = -(5/3)x + 8

Therefore, option a and d are Independent events and the correct answer.

Two events are independent if the occurrence of one event has no effect on the likelihood of the occurrence of the other event.

So, let's go through each of the given options to determine which pairs of events are independent:

a. Having a large shoe size and using blue pens:

These two events are completely unrelated to each other, so they are independent. Thus, option a is the correct answer.

b. Driving on ice and having an accident:

Driving on ice increases the likelihood of having an accident, so these two events are dependent.

c. Being pregnant and being female: These two events are not independent since being pregnant is only possible for females. Thus, they are dependent.

d. Drawing a spade from a deck of cards and getting tails on a flip of a coin: These two events are completely unrelated, so they are independent.

e. A father being blonde and his daughter being blonde: These two events are dependent since the father passes on his genes to his daughter. Thus, they are dependent.

f. Getting a raise in salary and buying a new car: These two events are dependent since getting a raise would make buying a car more likely.

Therefore, option a and d are independent events and the correct answer.

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The amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

The amount to which $800 will grow under each of these conditions is as follows:a) 8% compounded annually for 9 years

When compounded annually for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years

Compounded annually = n = 1 Amount = $1,447.91 (rounded to the nearest cent)

b) 8% compounded semiannually for 9 years Compounded semiannually for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded semiannually = n = 2 Amount = $1,471.16 (rounded to the nearest cent)

c)  8% compounded quarterly for 9 years Compounded quarterly for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded quarterly = n = 4 Amount = $1,491.03 (rounded to the nearest cent)

d) 8% compounded monthly for 9 years Compounded monthly for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded monthly = n = 12 Amount = $1,505.91 (rounded to the nearest cent)

e) 8% compounded daily for 9 years Compounded daily for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded daily = n = 365Amount = $1,511.74 (rounded to the nearest cent)

The observed pattern of FVs (future values) occurs due to compounding. Compounding is the process of earning interest not only on the principal amount invested but also on the interest earned from the principal. This results in an increase in the interest earned and the future value of the investment. The more frequent the compounding, the higher the future value of the investment. Hence, the amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

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Answer:

  3800 tickets sold

Step-by-step explanation:

We know the number of people seated, and we know the percentage of total ticket sales that represents. So, we can find the total number of tickets sold.

  seated + not-arrived = total sold

  228 + 0.94 × total sold = total sold

  228 = 0.06 × total sold . . . . . . . . . . . . subtract 0.94 × total sold

  228/0.06 = total sold = 3800

There were 3800 tickets sold for the performance.

Research on aging uses a **longitudinal** design.

A longitudinal design is a research design in which the same participants are studied over time. This is in contrast to a **cross-sectional** design, in which different participants are studied at different times.

Because age cannot be manipulated as an independent variable, research on aging must use a longitudinal design. This allows researchers to track changes in participants' behavior, cognition, and other factors as they age.

Longitudinal studies can be expensive and time-consuming to conduct, but they can provide valuable insights into the aging process. For example, longitudinal studies have shown that cognitive decline is not inevitable with age, and that certain lifestyle factors, such as exercise and social engagement, can help to protect against cognitive decline.

Here are some examples of longitudinal studies on aging:

* The Baltimore Longitudinal Study of Aging, which has been following a group of adults for over 70 years.

* The Framingham Heart Study, which has been following a group of adults for over 70 years.

* The Study of Adult Development and Aging, which has been following a group of adults for over 80 years.

These studies have provided valuable insights into the aging process, and they continue to be an important source of information for researchers and policymakers.

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Answer:

The probability of winning the bet is approximately 0.4238, or about 42.38%.

Step-by-step explanation:

We can solve this problem using the normal approximation to the binomial distribution. Let X be the number of heads in 100 tosses of a fair coin. Then X follows a binomial distribution with n = 100 and p = 0.5. The mean of X is µ = np = 100 × 0.5 = 50, and the standard deviation of X is σ = sqrt(np(1-p)) = sqrt(100 × 0.5 × 0.5) = 5.

Now, we want to calculate the probability that |X - 50| ≥ 4. This is equivalent to calculating the probability that |(X - 50)/5| ≥ 4/5, which is the probability that a standard normal variable Z = (X - 50)/5 is less than -4/5 or greater than 4/5. Using a standard normal distribution table or a calculator, we can find:

P(Z ≤ -4/5) ≈ 0.2119

P(Z ≥ 4/5) ≈ 0.2119

Therefore, the probability of winning the bet is:

P(|X - 50| ≥ 4) = P(|(X - 50)/5| ≥ 4/5)

≈ P(Z ≤ -4/5 or Z ≥ 4/5)

≈ P(Z ≤ -4/5) + P(Z ≥ 4/5)

≈ 0.2119 + 0.2119

≈ 0.4238

So the probability of winning the bet is approximately 0.4238, or about 42.38%.

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Answer:

3/16 miles/minute

Step-by-step explanation:

A rate of change describes how an output quantity changes relative to the change in the input quantity.

Points given:

Input        Output

  2            1/6

  3          17/48

  4          13/24

  5          35/48

  6          11/12

Here input values describe the time in minutes from 2 to 6 and output values describe the distance in miles from 1/6 to 11/12

Calculating the rate of change using the first two pairs of input-output values

We will get the same result if we take any other ordered pair of input and output values.

Answer:

it is 3/16 miles per minute

Step-by-step explanation:

...

Answer:

x = ±9

Step-by-step explanation:

x² - 55 = 26

   +55   + 55

     x² = 81

     x = √81

     x = ± 9

Answer:

x = 9, -9

Step-by-step explanation:

x^2 - 55 = 26

x^2 = 81.

Now, you might think that x = 9, but don't be fooled. -9 squared is also equal to 81.

So, x = 9, -9

Answer:

3/5

Step-by-step explanation:

15x+9y+189

9y=-15x+189

y=-5/3x+21

Answer:

Step-by-step explanation:

the slope its -1/15

the whole equation is:

15x+9y=189

subtract 15 on both sides

9y= 15x +189

divide 9 on 15 and 189

y= -9/15x +21

Answer: the slope is -7

Step-by-step explanation: by finding the difference between 14/2 and 7/3, then 7/3 and 0/4, you find that the difference is a negative 7/1 which simplifies to -7.

Two standards $6$-sided dice are rolled. The probability that the sum rolled is a perfect square 7/36.

Likelihood is the part of math concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a suggestion is valid. Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a recommendation is valid. Likelihood and measurements, the parts of science worried about the regulations administering arbitrary occasions, including the assortment, investigation, understanding, and show of mathematical information. While calculation and variable based math were concentrated on by old Greek mathematicians over long time back, the ideas of likelihood just arose in the seventeenth and eighteenth 100 years.

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Given that kareem deposits $500 into an account that pays simple interest at a rate of 3% per year.

We have to find the interest got in the first 6 years.

The formula to find the interest on P at an interest rate of R for T years is given by:

So, the interest is:

Thus, the interest is $90.

Hello,

\(( \frac{1}{3} ) {}^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1 {}^{3} }{3 {}^{3} } = \frac{1}{27} \)

Hi! ⋇

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\sf\color{darkblue}{( \frac{1}{3}) ^{3} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1} {27} }\)

The tabular data shown in the image attached does not represent a function.

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find which of the given tables represent a function.

For a table to represent a function, for every unique value of {x}, there should be only one possible value of {y}. This means that if for a function f(x), at {x} = 1, there exists two or more values of {y}, then it is not a function. From the image, it can be seen that the relations given in tables does not represent a function. This is because -

Table {1} -

for {x} = - 3, there exists two values of y

Table {3} -

for {x} = 0, there exists two values of y

Therefore, the tabular data shown in the image attached does not represent a function.

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Answer:

y=11.5x

he rides 11.5 miles every hour

A total of 23, 950, 080 results are possible.

We are given;

10 women

12 men

5 men and 5 women, chosen and pared off, how many results in total?

Thus;

[10 choose 5] x [12 choose 5]=252 x 792 = 199584 ways

We then need to know how many ways there could put into pairs i.e. For the first woman, there will be 5 choices of men. For the second woman, there will be 4 choices remaining of men. For the third woman, there will be 3 choices remaining. For the fourth woman, there will be only 2choices remaining, and only 1 choice left for the last woman.

Therefore, there are 5x4x3x2x1 = 120 ways.

 In total there are 199584x120 = 23950080 total  ways

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Answer:

x=176.78

y=262.28

z=176.77

Answer:

10,000

Step-by-step explanation:

when rounding to the thousands u go one space to the left of the place your rounding (so since its thousands i look at the hundreds place.) My teacher taught me 4 or less let it rest meaning make it a zero. 5 or more raise the score meaning round it. since its more then 5 i rounded it and make it 10,000.

Answer:

10,000

Step-by-step explanation:

To obtain the least common multiple of (l.c.m) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

\(\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{32 \ \ \ 42 \ \ \ 48}\\ 16 \ \ \ 21 \ \ \ 24\\ \ 8 \ \ \ 21 \ \ \ 12\\ \ 4 \ \ \ 21 \ \ \ \ 6\\ \ 2 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ \ 7 \ \ \ \ 1\\ \ 1 \ \ \ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 2\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}\)

              \(\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2\times2\times2\times2\times2\times3\times7} \end{gathered}$}\)

                       \(\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2^{5} \times3\times7} \end{gathered}$}\)

                            \(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=672} \end{gathered}$}}}\)

Therefore, the least common multiple of 32, 42, and 48 is 672.

\(\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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The given expression c(x)=4x2-30x 500 represents the total cost of producing x items. This expression is a quadratic function, and it has a parabolic shape.

The coefficient of the x^2 term is positive, indicating that the parabola opens upward. This means that the cost initially increases as the number of items produced increases, but eventually, the cost starts decreasing as the production level becomes too high.
To find the minimum cost of production, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively. In this case, a=4 and b=-30, so the x-coordinate of the vertex is x=30/8=3.75.
To find the minimum cost, we need to substitute this value of x into the expression c(x). c(3.75) = 4(3.75)^2 - 30(3.75) + 500 = $281.25. Therefore, the minimum cost of producing x items is $281.25.
In conclusion, the given expression c(x)=4x2-30x 500 represents the total cost of producing x items. The minimum cost of production is $281.25, and this occurs when 3.75 items are produced.

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Answer:

$77.39

Step-by-step explanation:

170/2    230/3     290/4      

take all three answers and add together, then divide by 3  :)

Answer: 8575/2

Step-by-step explanation:

c = 9 + 3n (option A)

Explanation:

when n = 0, c = $9

This means $9 is the initial price

We need to find the cost pre toppings. To do that, we calculate the change in cost divided by the change in topping.

rate of Change = (12-9)/(1-0) = (15-12)/(2-1)

rate of change = 3/1 = 3

If the number of toppings = n

The cost = initial cost + (rate of change × number of toppings)

The cost = $9 + (3× n)

The equation best represents the relationship between the cost and the number of toppings: c = 9 + 3n (option A)

The quadratic equation are equations that have an axis of symmetry

passing through the vertex.

Reasons:

2. The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

3. The points through which the quadratic equation passes are;

(-4, 2) and (1, 2)

The value at the vertex = Maximum value

Taking the vertex as the point midway between the two given points, we have;

\(\displaystyle Coordinates \ of \ the \ vertex = \left( \frac{-4 + 2}{2} , \, k \right) = \left(-1, \, k)\)

The coordinates of the vertex, (h, k) = (-1, y)

The vertex form of a quadratic equation is presented as follows;

(y - k) = a·(x - h)²

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1))² + k = a·(x + 1)² + k

y = a·(x + 1)² + k

At the point (-4, 2), we have;

2 = a·((-4) + 1)² + k = 9·a + k

2 = 9·a + k

Taking the value of k as 11, we have;

(h, k) = (-1, 11)

2 = 9·a + 11

\(\displaystyle a = \frac{2 - 11}{9} = -1\)

Which gives;

y = -1·(x + 1)² + 11 = -x² - 2·x + 10

y = -x² - 2·x + 10

When x = -4, we have;

y = -(-4)² - 2·(-4) + 10 = 2

When x = 2, we have;

y = -(2)² - 2·(2) + 10 = 2

4. The points through which the graph passes are; (-4, 2) and (1, 2)

The x-coordinate of the minimum vertex is given by the equation;

\(\displaystyle Coordinates \ of \ the \ vertex, \ (h, \, k) = \left( \frac{-4 + 1}{2} , \, k\right) = \left(-1.5, \, k)\)

(h, k) = (-1.5, y)

The vertex form of the equation of a quadratic equation is presented as follows;

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1.5))² + k

y = a·(x + 1.5)² + k

\(\displaystyle a = \mathbf{\frac{y - k}{\left(x + 1.5\right)^2}}\)

At the point (1, 2), we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - k}{6.25}\)

When k = -4.25, we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - \left(-4.25 \right)}{6.25} = 1\)

The equation is therefore;

y = 1·(x + 1.5)² - 4.25 = x² + 3·x - 2

y = x² + 3·x - 2

At the point where x = -4, we have;

y = (-4)² + 3·(-4) - 2 = 2

At the point where x = 1, we have;

y = (1)² + 3·(1) - 2 = 2

Therefore;

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