how do you calculate the area and perimeter of a slope triangle?

The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.

The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.

Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.

The following formula gives the likelihood that we will discover a value for X between c and d,

\(P(c\leq X\leq d)=\frac{d-c}{b-a}\)

Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.

Then,

\(P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%\)

The answer is 14.29%.

The complete question is -

The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?

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The correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,

it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.

The expression x² + x - 72 can be factored as follows:

x² + x - 72

= x² + 9x - 8x - 72

=x(x+9) -8(x+9)

= (x + 9)(x - 8)

Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

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The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer:

7.75

Step-by-step explanation:

7 is a whole so stays as such, 1/4 is 0.25 so 3/4 is 0.75

Answer: 12

Step-by-step explanation:

     A straight line has a measurement of 180° so these two angles added together will equal 180°.

     (10x - 20)° + (6x + 8)° = 180°

     10x° + 6x° + 8° - 20° = 180°

     16x° -12° = 180°

     16x° = 192°

     x = 12

Supplementary angles

the first four nonzero terms of the Taylor series for the given function centered at 0 are 1, 5x, -2x^2, and x^3/3.

To find the Taylor series centered at 0 for a function, we can use the concept of derivatives evaluated at 0. The Taylor series expansion of a function f(x) centered at 0 is given by f(x) = f(0) + f'(0)x + (f''(0)x^2)/2! + (f'''(0)x^3)/3! + ...

For the given function, we need to compute the first four nonzero terms of its Taylor series centered at 0. Let's denote the function as f(x) = x^3 - 2x^2 + 5x + 1.First, we evaluate f(0) which is simply f(0) = 1.Next, we calculate the first derivative of f(x) and evaluate it at 0. The first derivative is f'(x) = 3x^2 - 4x + 5. Evaluating at 0, we get f'(0) = 5.Then, we find the second derivative f''(x) = 6x - 4 and evaluate it at 0, yielding f''(0) = -4.Finally, we compute the third derivative f'''(x) = 6 and evaluate it at 0, giving f'''(0) = 6.Now, we can substitute these values into the Taylor series expansion to obtain the first four nonzero terms:

f(x) = 1 + 5x - (4x^2)/2! + (6x^3)/3! + ...

Simplifying this expression, we have f(x) = 1 + 5x - 2x^2 + x^3/3 + ...

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The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Answer:

a, e, u, o, q, r, s, t, u is the union

Answer:

32

Step-by-step explanation:

plug in the values of the variables then simplify

Answer:

\(\boxed{32}\)

Step-by-step explanation:

Hey there!

Well given the expression,

6p - 2q

and p and q we need to plug them in.

6(3) - 2(-7)

Simplify

18 - -14

18 + 14

= 32

Hope this helps :)

The vertex of the graph is (h, k) = (- 2, 36).

In this question we have a quadratic equation of the form f(x) = a · (x - r₁) · (x - r₂) and we need to transform the expression into its vertex form of determine the coordinates of the vertex. First, we need to exprand the expression:

f(x) = - 4  · (x - 1) · (x + 5)

f(x) = - 4 · (x² + 4 · x - 5)

f(x) = - 4 · x² - 16 · x + 20

Now we proceed to complete the square:

f(x) = - (4 · x² + 16 · x - 20)

- f(x) = 4 · x² + 16 · x - 20

- f(x) = (2 · x)² + 8 · (2 · x) - 20

- f(x) + 36 = (2 · x)² + 8 · (2 · x) + 16

- f(x) + 36 = (2 · x + 4)²

- f(x) + 36 = 4 · (x + 2)²

f(x) - 36 = - 4 · (x + 2)²

The vertex of the graph is (h, k) = (- 2, 36).

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Answer:

should be 3/7 I think that's right

Answer:

The way I would tackle these types of problems would be to make a table, then graph the points using the results I get.

Step-by-step explanation:

So explaining the table is kinda hard since I suck at explaining, so I've attached a file showing the table I've made for number 1.

First Step:

Make the table. Make it a 3x4 table. For the top row, put y, the equation (I put 'y=2x' as shown in number 1), then x. Then for the left column, go down by one box, then put: -1, 0, 1. Really, you can put any numbers, but to make it easy for yourself, just write the numbers I've listed. These will be your y-values you'll be substituting.

Second Step:

a.) Plugging in the numbers. For the middle column, I've put down y=2x in each box, as shown in my table. Then for each of those boxes, plug in the numbers to the left of them and substitute them for the y-value. For example, look at the second row. The left box has '-1', so I replaced the 'y' in the equation and got '(-1)=2x'.

b.) After substituting the y-values, solve for x. For this case, you'll need to divide both sides by 2. If it doesn't make much sense, think about a seesaw. If you have 5 pounds on both sides, the seesaw will stay balanced. Add an additional 5 pounds to one side, then the seesaw will start tipping towards the heavier sides. So in order to keep an equation balanced, you must do any action to both sides of the equation. After diving both sides by 2, you'll get the value for x.

Final Step:

After finding the x-values for each of the y-values, it's time to graph the equations. Remember, x is left to right and y is down to up. To graph them, let's use the second row for example. y=-1 and x=-0.5. So all you need to do is to start from the origin (0,0), then go half a unit to the left, as x is negative, then go a unit down, as y is negative, then make a point. The rest should be pretty straight forward.

After making all three points, just get a ruler or any straight edge, then align it along those three points, then just make a line, and boom! You've solved number 1! For the purpose of saving my time, I'm pretty sure you can solve the rest using what I've just told you. Good luck!

Answer:

181

Step-by-step explanation:

Emily = 62

Collin = 3 years + Emily = 3 + 62 = 65

Dan = Emily - 8 years = 62 - 8 = 54

So, for finding the combined age,

=> 62 + 65 + 54

=> 181

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

The coordinates of the quadrilateral

A(5,6)

B(10,6)

C(8,1)

D(3,1)

Part A.

The rule for a rotation counterclockwise of 180°

A'=(-5,-6)

B'=(-10,-6)

C'=(-8,-1)

D'=(-3,-1)

Then we will draw the quadrilateral

the original is the red

and the rotate is the blue

Part B

the coordinate change as the given rule seen previously for rotation of 180° counterclockwise

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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Therefore, on average, a customer arriving during the morning rush would wait approximately 2.17 hours to be served.

To determine the average waiting time for a customer arriving during the morning rush at the coffee shop, we need to consider the arrival rate and the capacity of the shop.

Given that 100 customers per hour arrive at the coffee shop during the two-hour morning rush, and the shop has a capacity of 80 customers per hour, we can conclude that there will be more customers arriving than the shop can accommodate.

To calculate the average waiting time, we need to account for the time spent by customers who have to wait due to the shop being at full capacity. For simplicity, let's assume that customers arrive uniformly throughout the two-hour period.

During the first hour (8 a.m. to 9 a.m.), there will be 100 customers arriving, but the shop can only serve 80 customers. Therefore, 20 customers will have to wait for their turn to be served.

During the second hour (9 a.m. to 10 a.m.), again, 100 customers will arrive, but since the shop is already at full capacity, all 100 customers will have to wait for their turn.

In total, during the two-hour morning rush, there will be 20 customers who wait for one hour and 100 customers who wait for the entire two hours.

To calculate the average waiting time, we can sum up the waiting times and divide by the total number of customers:

Average waiting time = (20 * 1 hour + 100 * 2 hours) / (20 + 100) = (20 + 200) / 120 = 2.17 hours

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Answer:

(25 ÷ 5 ) ÷ 4

Step-by-step explanation:

solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.

Answer:

C

Step-by-step explanation:

the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so

4 × (25 ÷ 5 ) → C

The mean crack size is 1.25 mm.

(a) To sketch the PDF and CDF, we can plot the given probability density function (PDF) on a graph paper.

The PDF f_X(x) is defined as follows:

f_X(x) = {

x/8 for 0 < x ≤ 2,

1/4 for 2 < x ≤ 5,

0 elsewhere

}

First, let's plot the PDF on the graph paper:

        |       .     .

   1/4  |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

   0.2  |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

        |       .     .

   0.1  |   .   .   .   .

        | . . . . . . . .

        +----------------

          0   2   4   6

The height of the PDF corresponds to the probability density at a given value of x.

Next, let's calculate the cumulative distribution function (CDF) to sketch it on the graph paper.

The CDF is obtained by integrating the PDF from negative infinity to x:

F_X(x) = ∫[0,x] f_X(t) dt

For 0 ≤ x ≤ 2:

F_X(x) = ∫[0,x] (t/8) dt = (1/8) * ∫[0,x] t dt = (1/8) * (t^2/2)|[0,x] = (1/8) * (x^2/2) = x^2/16

For 2 < x ≤ 5:The height of the PDF corresponds to the probability density at a given value of x.

Next, let's calculate the cumulative distribution function (CDF) to sketch it on the graph paper.

The CDF is obtained by integrating the PDF from negative infinity to x:

F_X(x) = ∫[0,x] f_X(t) dt

For 0 ≤ x ≤ 2:

F_X(x) = ∫[0,x] (t/8) dt = (1/8) * ∫[0,x] t dt = (1/8) * (t^2/2)|[0,x] = (1/8) * (x^2/2) = x^2/16

For 2 < x ≤ 5:The height of the PDF corresponds to the probability density at a given value of x.

Next, let's calculate the cumulative distribution function (CDF) to sketch it on the graph paper.

The CDF is obtained by integrating the PDF from negative infinity to x:

F_X(x) = ∫[0,x] f_X(t) dt

For 0 ≤ x ≤ 2:

F_X(x) = ∫[0,x] (t/8) dt = (1/8) * ∫[0,x] t dt = (1/8) * (t^2/2)|[0,x] = (1/8) * (x^2/2) = x^2/16

For 2 < x ≤ 5:F_X(x) = ∫[0,2] (t/8) dt + ∫[2,x] (1/4) dt = (1/8) * ∫[0,2] t dt + (1/4) * ∫[2,x] dt = (1/8) * (t^2/2)|[0,2] + (1/4) * (t)|[2,x] = (1/8) * 2 + (1/4) * (x-2) = 1/4 + (1/4) * (x-2) = 1/4 + (x-2)/4 = (x+1)/4

For x > 5:

F_X(x) = 1

Now, let's plot the CDF on the same graph paper:

        | . . . . . . . .

   1    | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

   0.8  | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

   0.6  | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

        | . . . . . . . .

   0.4  | . . . . . . . .

        |

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Answer:

40.4026226 aka 40.403

Step-by-step explanation:

tan 22 degrees = h/100

After 13 years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old iddm women, if the incidence rate remains constant over time.

In this question we have been given the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

We need to find the number of years after which we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time.

Let n be the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females.

The probability of becoming blind over n years is 0.10

Given that the annual incidence rate of blindness per year was 0.74% IDDM females.

This means the rate r = 0.0074

For n years the annual incidence rate of blindness  0.0074n

We need to find the value of n,

0.0074n = 0.10

n = 13.51

n ≈ 13 years

Therefore, the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females = 13

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The complete question is:

A study [12] of incidence rates of blindness among insulin-dependent diabetics reported that the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time?

Answer:

k = 5/6

Step-by-step explanation:

The √ can be rewrite as a power, and this power is 1/2

So √a = a^1/2, and it is multiplying a, so we add the powers: a¹•a^1/2 = a^(1+1/2) = a^3/2

And the ³√ can be rewrite as the power 1/3, but the a inside the ³√ is to the power of 2, so we can rewrite it like this: (a²)^1/3

And to evaluate this we have to multiply the powers, so we will have: a^2/3

Now we have this fraction:

\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } \)

A fraction with powers in the same base can be rewrite like a subtraction of the powers, so let's do that:

\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } = {a}^{ \frac{3}{2} - \frac{2}{3} } = {a}^{ \frac{5}{6} } \)

Answer: B is correct

Step-by-step explanation:

The answer is m<D=14*

The given equation [−10. 74=u−(−11)] yields the value of u as "-21.74".

The equation is [−10. 74=u−(−11)]

In order to solve this equation simple mathematical operations are perfromed. Steps by step solution is given here:

[−10. 74=u−(−11)]

[-10.74 = u + 11]

To determine the value of u, it is required to take constants to one side the equation, so

[-10.74 - 11 = u]

[-21.74 = u]

The value of u is -21.74.

So after solving the given equation which is [−10. 74=u−(−11)] , the value of u to be determined is "-21.74."

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Answer:

if x is the number of years she is working that the equation would be: 24,500+x*((3/100)*24,500)

Step-by-step explanation:

For her 4th year x would be 4, so for the equation above x=4:

24500+4*((3/100)*24500)=27440

Answer:

The answer could be 40. I might be wrong.

Step-by-step explanation:

15 divided by 3/8 = 40

First one is -1. The second one is 1/2.

The possible 4-digit numbers are 1,680.

Probability that 4-digit number ends up being an odd number greater than or equal to 6000 is 57.14%.

a) The number of possible 4-digit numbers that can be formed using the given digits without repetition is given by the permutation formula:

P(8,4) = 8! / (8 - 4)! = 8 x 7 x 6 x 5 = 1,680

Therefore, there are 1,680 possible 4-digit numbers using the given digits.

b) The total number of 4-digit numbers that can be formed from the given digits is 1,680, as calculated in part a).

To find the probability that the 4-digit number is odd and greater than or equal to 6000, we need to calculate the number of odd 4-digit numbers in the range [6000, 6999] and the number of odd 4-digit numbers greater than or equal to 7000, and divide each by the total number of 4-digit numbers.

Number of odd 4-digit numbers in [6000, 6999]:

The last digit must be 1, 3, 5, or 7 (4 choices). The first three digits can be any of the remaining 7 digits (7 choices for the first digit, 6 choices for the second digit, and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers in [6000, 6999] is:

4 x 7 x 6 x 5 = 840

Number of odd 4-digit numbers greater than or equal to 7000:

The first digit must be 7 (1 choice). The last digit must be 1, 3, 5, or 7 (4 choices). The second and third digits can be any of the remaining 6 digits (6 choices for the second digit and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers greater than or equal to 7000 is:

1 x 4 x 6 x 5 = 120

The total number of odd 4-digit numbers is 840 + 120 = 960.

Therefore, the probability that the 4-digit number is odd and greater than or equal to 6000 is: 960 / 1,680 = 0.5714 or approximately 57.14%.

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