Out of 32 students, 25% are absent. How many students are absent?

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} } \\\)

From the question the points are

F(6, 9) and G(4, 14)

The distance between them is

\( |FG| = \sqrt{ ({6 - 4})^{2} + ({9 - 14})^{2} } \\ = \sqrt{( { - 2})^{2} + ({ - 5})^{2} } \\ = \sqrt{4 + 25} \\ = \sqrt{29} \: \: \: \: \: \: \: \: \\ = 5.3851...\)

We have the final answer as

Hope this helps you

Answer:

m = 2, c = -8.

Step-by-step explanation:

The general form of a straight line equation is

y = mx + c    where m = the slope and c is the y-intercept.

We are given the line

y = 2x + 4

Comparing this with the general form we see that the slope of this line  = 2 and the y-intercept C is 4.

Now the given line y = mx + c is parallel to y = 2x + 4 which means that their slopes are the same so we conclude that m = 2.

Now we need to find the value of c which is the y intercept of y = mx + c.

Consider the points A and B:

A is the point where the line y = 2x + 4 intersects the x axis so y = 0 at this point , So substituting in the equation:

0 = 2x + 4

-4 = 2x

x = -2.

So the point A is (-2, 0)

B  is the point where y = 2x + c cuts the x axis so here y = 0:

0 = 2x + c

2x = -c

x = -c/2.

Now we are given that the 2 intercepts are 6 units apart, so:

-c/2 - (-2) = 6

-c/2 + 2 = 6

-c/2 = 4

-c = 8

c = -8.

The original amount of the loan is approximately $6,605.45, and the balance after the 30th payment can be calculated using the remaining number of payments, interest rate, and the original loan amount

The original amount of the loan can be calculated using the monthly payment amount and the interest rate. The balance after the 30th payment can be determined by considering the remaining number of payments and the interest accrued on the loan.
To find the original amount of the loan, we need to calculate the present value (PV) using the monthly payment amount, interest rate, and the loan term. In this case, the loan term is five years, or 60 months, and the monthly payment is $200.38.
Using the formula for the present value of an ordinary annuity:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods (number of months in this case).
First, we need to convert the annual interest rate to a monthly interest rate. The annual interest rate is 7.5%, so the monthly interest rate is 7.5% / 12 = 0.075 / 12 = 0.00625.
Next, we can substitute the values into the formula to find the present value (original amount of the loan):
PV = $200.38 × [(1 - (1 + 0.00625)^(-60)) / 0.00625]
  ≈ $200.38 × 32.9536
  ≈ $6,605.45
Therefore, the original amount of the loan is approximately $6,605.45.
To find the balance after the 30th payment, we need to consider the remaining number of payments and the interest accrued on the loan. Since each monthly payment reduces the loan balance, we need to calculate the remaining loan balance after 30 payments.
Using the formula for the remaining balance of a loan:
Balance = PV × (1 + r)^n - PMT × [(1 + r)^n - 1] / r
Where PV is the present value (original loan amount), r is the monthly interest rate, n is the remaining number of periods (remaining number of months), and PMT is the monthly payment.
Substituting the values into the formula:
Balance = $6,605.45 × (1 + 0.00625)^(60 - 30) - $200.38 × [(1 + 0.00625)^(60 - 30) - 1] / 0.00625
Calculating the expression will give the balance after the 30th payment.

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The function is increasing on the intervals (0, 2π/3) and (4π/3, 2π), while it is decreasing on the interval (2π/3, 4π/3). The relative maximum is (4π/3, 2 - √3), and the relative minimum is (2π/3, 2 + √3).

To determine the open intervals on which the function f(x) = x + 2 sin x is increasing or decreasing, we need to find the critical points by setting the derivative equal to zero and identifying the sign changes. Taking the derivative of f(x), we get f'(x) = 1 + 2 cos x.

To find the critical points, we set f'(x) = 0:

1 + 2 cos x = 0

cos x = -1/2

x = 2π/3 or 4π/3.

Next, we determine the sign changes around the critical points.

For x < 2π/3, f'(x) is positive, so f(x) is increasing on (0, 2π/3).

For 2π/3 < x < 4π/3, f'(x) is negative, so f(x) is decreasing on (2π/3, 4π/3). Lastly, for x > 4π/3, f'(x) is positive, so f(x) is increasing on (4π/3, 2π).

Using the First Derivative Test, we can conclude that there is a relative minimum at (2π/3, 2 + √3) and a relative maximum at (4π/3, 2 - √3).

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Consider the function on the interval (0, 2pi) f(x) = x + 2 sin x Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing Apply the First Derivative Test to identify the relative extrema. Relative maximum (x, y) relative minimum (x, y)

The correct answer is the equation of the line is y = \(-\frac{2}{3} x - 2\)

Given the equation of the parallel line is 2x + 3y = 3

and the required line passes through the point (3, -4) where x is 3 and y is -4

We can write the given equation  as:

⇒ 3y = 3 - 2x

Dividing both sides by 3

\(y = 1 - \frac{2x}{3}\)

On comparing this equation with y= mx+b, thus m = \(-\frac{2}{3}\) and the slopes of parallel lines are always equal.

Using the point slope form, we will derive the equation of line

⇒ \(y-y_1 =m ( x- x_1)\)

⇒ \(y- (-4) = -\frac{2}{3} (x-3)\)

⇒ \(y+4= -\frac{2}{3} (x) - \frac{2}{3} (-3)\)

⇒ \(y = -\frac{2}{3} (x) +2-4\)

⇒ \(y = -\frac{2}{3} (x) - 2\)

Hence, the equation of the required line is \(y = -\frac{2}{3} (x) - 2\)

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Answer:

7cm

Step-by-step explanation:

Other option are not whole numbers rather they are decimal numbers

Answer:

f(-9) = -119

Step-by-step explanation:

Hello!

You can evaluate for f(-9) by substituting -9 for x in the equation f(x) = -11 + 12x.

The evaluated value is -119.

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

Answer: answer is in the ss i put

Source:trust me bro

Answer: a a a a. Aa

E s. Ss s

Step-by-step explanation:

s. S s s s. S s s s s

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

1/2

Step-by-step explanation:

Probabilty = Frequency/Total

She sold 6 flower bouquets, 3 of them were daisy bouquets.

Frequency = 3

Total = 6

3/6

3/6 can be simplified to 1/2;

P(daisy) = 1/2

The probability that both the balls drawn are white is 2/7 when two balls are drawn successively without replacement from a box which contains 4 white balls and 3 red balls.

Two balls are drawn successively without replacement from a box which contains 4 white balls and 3 red balls.

Therefore, Total number of balls in the box = 4+ 3 = 7 balls

Thus, the probability that the first ball drawn is a white is = (Total number of white balls) /  ( Total number of balls)

=4/7

The next ball is drawn without replacement thus the number of balls in the box is 6.

And if 1 ball is picked in drawn n first tie, then remaining number of white balls is 3.

Thus, the probability that the second ball drawn is a white is = (Remaining number of total white balls) /  ( Remaining number of total balls)

= 3/6 = 1/2

Therefore, the probability that both the balls drawn are white is

= (4/7)*(1/2)

= 2/7

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Answer:

6 x + 3 y = 3x+ 3(x + y)  or 3 (2 x + y)

Step-by-step explanation:

all exxpressions are equivalent

Answer: 6x + 3y & 3(x + x + y)

Step-by-step explanation:

Answer:

\(g(-2)=0\\g(4)=-4\)

Step-by-step explanation:

The intervals at the right of each number indicate what values of \(x\) you can put into the function \(g(x)\), and what answers they give.

So for \(g(-2)\), we look at where \(-2\) fits in the intervals. It cannot be the top one, because it says that \(x\) has to be less than \(-2\) for that particular value.

However, on the next interval down, it says that \(-2\) is less than or equal to \(x\), therefore \(-2\) would be allowed here. Looking at the value this interval corresponds to, we see it is 0. Therefore, \(g(-2)=0\).

Looking at \(g(4)\), it definitely will not fit in the top interval, as 4 is not mentioned there at all. Looking at the next interval down, it says \(x\) has to be less than 4, so we cannot use that. However, on the final interval, it says that 4 is less than or equal to \(x\), therefore it is allowed here. Looking at which value this interval corresponds to, we see it is -4. Therefore, \(g(4)=-4\).

Hope this helps.

a. The random variable represents the time which takes to completely tune an automobile engine.

b. The probability of tuning an engine is qual to 0.593, or 59.3%.

a. The random variable here is the time it takes to completely tune an engine of an automobile.

b. To find the probability of tuning an engine in 45 minutes or less,

Use the exponential distribution formula.

The exponential distribution is characterized by a rate parameter, which is the reciprocal of the mean.

The mean is 50 minutes,

The rate parameter (λ) can be calculated as λ

= 1/mean

= 1/50.

Using this rate parameter,

The probability of tuning an engine in 45 minutes or less by integrating the exponential probability density function (PDF) from 0 to 45 minutes,

P(X ≤ 45) = \(\int_{0}^{45}\)λ × \(e^{(-\lambda x)\) dx

Substituting the value of λ = 1/50 into the equation,

P(X ≤ 45) = \(\int_{0}^{45}\) (1/50) × \(e^{(-x/50)\) dx

Rewrite the integral:

P(X ≤ 45) = (1/50) ×  \(\int_{0}^{45}\)  \(e^{(-x/50)\) dx

Apply the integral,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-x/50)\)] evaluated from 0 to 45

Plug in the limits of integration,

P(X ≤ 45) = (1/50) × [-50 ×\(e^{(-45/50)\) - (-50 × \(e^{(-0/50)\))]

Simplify the expression,

P(X ≤ 45) = (1/50) × [-50 × \(e^{(-45/50)\)+ 50 × \(e^0\)]

Simplify further,

P(X ≤ 45) = -\(e^{(-45/50)\) + 1

Evaluate the expression,

⇒P(X ≤ 45) ≈ -\(e^{(-0.9)\) + 1

⇒P(X ≤ 45) ≈ -0.407 + 1

⇒P(X ≤ 45) ≈ 0.593

Therefore, the probability of tuning an engine in 45 minutes or less is approximately 0.593, or 59.3%.

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Answer:

N= 5, and 4

Step-by-step explanation:

I put the equation into a website calculator called math-way. com.

I told it to solve using the quadratic formula.

Answer:

He has made 42 field goals this season

Step-by-step explanation:

To find x% of number y, multiply y by \(\frac{x}{100}\) ⇒ \(\frac{x}{100}\) × y

∵  A field goal kicker makes 84% of the field goals he attempts

→ That means he makes 84% of his total attempts

∵ He has attempted 50 field goals this season

→ That means his total attempts is 50 field goals

∴ He makes 84% of 50 field goals

∵ 84% = 84 ÷ 100 = 0.84

∴ He makes 0.84 of 50

∵ He makes = 0.84 × 50

∴ He makes = 42 field goals

∴ He has made 42 field goals this season

Given:

Consider the expression is \(\sqrt{-12}\).

To find:

The value of given expression.

Solution:

We have,

\(\sqrt{-12}\)

It can be written as

\(\sqrt{-12}=\sqrt{-1\times 12}\)

\(\sqrt{-12}=\sqrt{-1}\times \sqrt{12}\)      \([\because \sqrt{ab}=\sqrt{a}\sqrt{b}]\)

\(\sqrt{-12}=i\times \sqrt{12}\)      \([\because \sqrt{-1}=i]\)

\(\sqrt{-12}=\sqrt{12}i\)

Therefore, the value of given expression is \(\sqrt{12}i\).

Note: all options are incorrect.

Given the following question:

Answer:

Divisible by none

Step-by-step explanation:

9,953 is odd

9+9+5+3 = 2 + 6 = 8 (not divisible)

53/4 is not a whole number

9,953 doesn't end with 5 or 0.

9 + 9 + 5 + 3 = 26 (not divisible by 9)

9,953 has no 0 at end.

You are welcome!

Kayden Kohl

8th Grade Student

The number 9,953 is divisible by neither of the digits 2, 3, 4, 5, 9, 10.

The importance of knowing divisibility rules is that we can determine whether a number is divisible by certain numbers generally from 1 to 20 or not without actually dividing.

Given, 9,953. Is this number divisible by 2, 3, 4, 5, 9, 10 or not.

A number is divisible by 2 if it's unit digit is divisible by 2.

A number is divisible by 3 if the sum of the digits is divisible by 3.

A number is divisible by 4 if the last two digits is divisible by 4.

A number is divisible by 5 if its unit digit is 5 or 0.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if its unit digit is 0.

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Answer:

A

Step-by-step explanation:

The student wrote a list of six consecutive integers.

The sum of the first integer and the sixth is 1.

Let the first integer be represented by n.

Then the subsequent integer will be (n + 1).

Therefore, our sequence is:

n, n + 1, n + 2, n + 3, n + 4, and n + 5.

The sum of the first and sixth is 1. Therefore:

\((n)+(n+5)=1\)

Solve for n. Combine like terms:

\(2n+5=1\)

Thus:

\(2n=-4\)

And:

\(n=-2\)

Thus, our first term is -2.

Therefore, our sequence is:

-2, -1, 0, 1, 2, 3

The least of the six integers is -2.

Our answer is A.

Answer:

A

Step-by-step explanation:

hope it helped

3(y-1)=2x+2

3(y-1)/3=2x+2/3

y-1=2x/3+2/3

y=2x/3+2/3+1

y=2x/3+5/3

m=2/3

Therefore, f(x+h) - f(x)/h is equal to 8x + 8h - 1/h, which confirms the given equation.

To show that f(x+h) - f(x)/h = 8x + 8h - 1/h, we can substitute the given function f(x) = 8x into the expression.

Starting with the left side of the equation:

f(x+h) - f(x)/h

Substituting f(x) = 8x:

8(x+h) - 8x/h

Expanding the expression:

8x + 8h - 8x/h

Simplifying the expression by combining like terms:

8h - 8x/h

Now, we need to find a common denominator for 8h and -8x/h, which is h:

(8h - 8x)/h

Factoring out 8 from the numerator:

8(h - x)/h

Finally, we can rewrite the expression as:

8x + 8h - 1/h

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Answer:

y = 1/5x - 6/5

Step-by-step explanation:

Step 1: Write out known variables

m = 1/5

y = 1/5x + b

Step 2: Find b

-1 = 1/5(1) + b

-1 = 1/5 + b

b = -6/5

Step 3: Write linear equation

y = 1/5x - 6/5

Answer:

y=px

so the answer would be $49.95

pretty sure

Step-by-step explanation:

Step-by-step explanation:

1. radius=d/2= 30/2= 15yds

diameter= 30yds

area=πr²= 22/7*(15)²

707.14yds²

circumference= 2πr=2*22/7*15

94.29yds

2.radius=8in

diameter= 2r =2(8)=16in

area=πr²= 22/7*(8)²

201.14in²

circumference= 2πr=2*22/7*13

50.29in

3.radius=d/2 =20/2=10ft

diameter= 20ft

area=πr²= 22/7*(10)²

314.29ft²

circumference= 2πr=2*22/7*10

62.86ft

The symbols x, y, and z are examples of variables in an instruction like z = x + y.

A variable is a term that signifies anything that can be varied or altered. In programming, variables are utilized to hold values that might be modified and used in later code.

A variable is a name that identifies a memory location where data is stored. It can be changed anytime. Variables are commonly used in mathematical expressions, such as those seen in algebra. For example, x + 150 = 300In this instance, x is the variable. 150 and 300 are constants.

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Answer: J. x=1/5

Explanation: So uh place the same value of x on both sides and see which value makes its equal.

(-7-4x)= -2(3x - 4)

I guess its J. x=1/5