Find the equation that models this data

Answer:

\(\dfrac{2}{3}\)

Step-by-step explanation:

Given that:

The number of observations is:

6, 10, 12

If we are to use a simple  random sampling without replacement, then we will have:

(6,10)  (6,12)  (10,12)

Here;

the sample size n = 2

The population size N = 3

For (6,10) ; The sample mean = \(\dfrac{6+10}{2}\)

= \(\dfrac{16}{2}\)

= 8

For (6,12) ; The sample mean = \(\dfrac{6+12}{2}\)

= \(\dfrac{18}{2}\)

= 9

For (10, 12) ; The sample mean = \(\dfrac{10+12}{2}\)

= \(\dfrac{22}{2}\)

= 11

The probability distribution of sample mean(x) is:

X           8           9          11

P(X=x)    \(\dfrac{1}{3}\)          \(\dfrac{1}{3}\)           \(\dfrac{1}{3}\)

Thus, the probability that the sample mean  is larger than 8 is:

P(X> 8) = P(X = 9) + P(X + 11)

P(X> 8) = \(\dfrac{1}{3}+\dfrac{1}{3}\)

P(X > 8) = \(\dfrac{1+1}{3}\)

P(X> 8) = \(\dfrac{2}{3}\)

Answer:  (1, -9)

Hope this helped!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-4

Answer: B aka -4

Step-by-step explanation:

edge2022 hope this helps

The equation of a line that passes through points (2,5) and (4,3) is

y = -x+7.

Finding the equation of a line:

First, we need to find out the slope for the given points.

(X1,Y1) = (2,5)

(X2,Y2) = (4,3)

formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)

substitute the points in the above formula

\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)

\(\frac{-2}{2}\) = -1

slope for the given points(m) = -1.

m = -1

The equation of a line is y-y1 = m(x-x1), where x and y are variables.

substituting the values in the above equation then :

y-5 = -1(x-2)

y-5 = -x+2

y+x = 2+5

x+y = 7

y = -x+7

Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7

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Answer:

6

Step-by-step explanation:

22 + -176 ÷ 11

b i division m a s

-176 ÷ 11 = -16

22 - 16 = 6

Answer:

points hehehhehehehe points hehehehehhehehehehehehe points hehehehe

Step-by-step explanation:

Answer:

250

5:15

true

i already helped you

Answer:

9- 4 hours 30 minutes

10- 250

11- False

An appropriate assignment of digits to the outcomes for a simulation of this random process would be:

Option 1: Let 0 and 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6, 7, 8, 9, and 0.

This option assigns two digits, 0 and 1, to represent the two possible outcomes: a student is either enrolled in the nursing program (outcome 1) or not enrolled (outcome 2-5). The digits 2-5 represent the non-nursing program outcomes, and the digits 6-9 and 0 are skipped.

Option 1 is appropriate because it assigns a unique digit to each possible outcome, and the skipped digits are not relevant to the simulation. Additionally, the proportion of digits assigned to each outcome (2 out of 10) corresponds to the proportion of students in the nursing program (20%).

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.

To determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.

Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):

Number of half-lives = (Total time elapsed) / (Half-life)

Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545

Since we can't have a fraction of a half-life, we take the integer part, which is 5.

Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:

Remaining amount = Initial amount * (1/2)^(Number of half-lives)

Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:

Remaining amount = 1000 grams * \((1/2)^5\)

Remaining amount ≈ 1000 grams * 0.03125

Remaining amount ≈ 31.25 grams

Therefore, after 2 hours, approximately 31.25 grams of francium will be left.

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Answer: ......... 14.85

Step-by-step explanation:

4.95 × 3

...

14.85

bros lazy lol

Answer:

0,3+3,10

Step-by-step explanation:

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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The simplified firm of the ratio 0.40 to 0.60 is 2 : 3

0.40 : 0.60

= 0.40 / 0.60

divide both numerator and denominator by 0.20

= 2 / 3

= 2 : 3

Therefore, the simplified form of the ratio 0.40 to 0.60 is 2 : 3

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add me on fortnite IClapYsn

Answer:

The greatest whole number: 2799

The least whole number: 2750

Step-by-step explanation:

I just went by the rule five or more round-up.

Remember that

The probability values cannot be greater than 1

so'

the fraction

55/27 > 1

therefore

Answer:

Solution:

Hi! The given fraction could never represent probability. The reason for that is: Probability cannot be greater than 1.

Remember, the formula for probability is:

\(\hfill\stackrel{\sf{Probability\:Formula}}{\boxed{\boxed{\sf{{Probability=\frac{Favourable\:Outcomes}{Total\:Outcomes}}}}}}\)

The number of favourable outcomes cannot be greater than the number of total outcomes. Therefore, probability cannot be greater than 1. Therefore, the given fraction could never represent probability.

Problem solved! It's been a pleasure helping you.

Yes, cropping a picture and then using a scale factor to resize it is a two-step process.

The image is first cropped by subtracting 2 inches from the right side, altering the image's proportions.

The image is then enlarged using a scale factor of 1.5, which increases the image's dimensions by 1.5.

The final measurements of the image would be its original measurements less 2 inches (for cropping), then multiplied by 1.5. (for the resizing).

It's vital to keep in mind that both picture cropping and image scaling change the size of the final product.

Yes, cropping a photo, then resizing it with a scale factor, is a two-step process.

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Answer:

x = 12

Step-by-step explanation:

By the property of exterior angles of a triangle,

"Exterior angle of a triangle is equal to the sum of opposite angles of the triangle"

Since, ∠HRQ is the exterior angle of ΔPRQ and ∠RPQ and ∠RQP are the opposite angles.

m∠HRQ = m∠RPQ + m∠RQP

(8 + 6x)° = 30° + (4x + 2)°

6x - 4x = 30 + 2 - 8

2x = 24

x = 12

Therefore, value of x is 12.

Answer:

x = 12

Step-by-step explanation:

Hope this helps

Answer:

9f

Step-by-step explanation:

f(9) = f * (9)

a) Multiply.

f * (9) = 9f

In a regular deck, there are 52 cards from which 4 are aces (one of these aces belongs to the diamond type) and 13 are diamond cards.

Finally, the probability of drawing an ace or a diamond card is (13+3)/52.

Answer: 30.76% (or 0.3076)

The average number of enrollments per day at the Sunnyside Daycare is 21.

An average is a result obtained by summing some numerical values and then dividing the total by the number of values or variables.

An average is the mean, which is one of the central tendency values.

Day          Number of Enrollments

Monday                 17

Tuesday                19

Wednesday         23

Thursday              14

Friday                  25

Saturday             28

Total =               126

Average enrollments = 21 (126/6)

Thus, the average number of enrollments per day at the Sunnyside Daycare is 21.

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What was the average number of enrollments per day?

The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

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The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

\((x - 3)^2\) = 2x + 29

Expand the left side:

\(x^2\) - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

\(x^2\) - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

\(y=0.00035x^{2}\)

Compute the first order derivative of y as follows:

 \(y=0.00035x^{2}\)

\(\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]\)

    \(=2\cdot 0.00035x\\\\=0.0007x\)

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

\(\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx\)

                  \(=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\\)

Now, let

\(x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u\)

\(\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u\)

                  \(={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}\)

Plug in the solved integrals in Arc Length and solve as follows:

\(\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\\)

                  \(=1245.253707795227\\\\\approx 1245.25\)

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Answer:

1. V = 15.95 (to 2 decimal places)

2. V = 107.23 (to 2 decimal places)

3. V = 560.25 (to 2 decimal places)

Step-by-step explanation:

1. y = ln 5x, y = 2, y = 3, x = 0; about the y-axis

Find volume using the disk method.

First find inverse of y=ln(5x)

5x = exp(y)

x(y)=exp(y)/5

Width of each strip = dy

length of each strip = x(y)

volume of each disk by rotation of strip about y=axis

dV = 2*pi*x(y)dy

total volume  

V = integral (dV) for y=2 to 3

= integral (2*pi*e^y/5) for y=2 to 3

= 2*pi*(e^y/5) for y=2 to 3

= 2pi(e^3-e^2)/5

= 15.95 (to 2 decimal places)

2. y2 = 2x, x = 2y; about the y-axis

Find point of intersection between  

solve y^2/2 = 2y  =>  y=4, x=2y=8, therefore

intersection is at (8,4), which is the upper integration limit

Using the disk method again

Volume of each disk

dV(y) = pi((2y)^2-(y^2/2)^2)dy

Total volume of solid  

V = integral(pi((2y)^2-(y^2/2)^2)dy) for y=0 to 4

= pi (4y^3/3 - y^5/20)  for y = 0,4

= pi (256/3 - 1024/20)

= 512pi/15

= 107.23 (to 2 decimal places)

3. y = x, y = 0, x = 2, x = 7; about x = 1

Use the shell method.

volume of each shell formed by roatation of a vertical strip about the axis of rotation (x=1)

dV = 2*pi*(x-1)*(y*dx)

Total volume of rotation

V = integral(2*pi*(x-1)*y dx for x=2 to 7

= 535pi/3

= 560.25 (to 2 decimal places)

The taxi ride was 7 miles

Mia took a taxi from her house to the airport

The taxi charged a pick up fee of $1.30

They also charged $4.25 per mile

The total fare was $31.05

The number of miles can be calculated as follows

31.05 - 1.30 = 4.25x

29.75= 4.25x

Divide both sides by the coefficient of x which is 4.25

29.75/4.25= 4.25x/4.25

x= 7

Hence the taxi ride was 7 miles

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Insured = 72%.

Uninsured = 28%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Here is a table classifying 116 thousand US households (in thousands) in

2013 by tenure and insurance status:

Insurance status      Owns home   Rents home

Insured                              71                13

Uninsured                         27               5

Total house = 71 + 13 + 5 + 27 = 116

Insured = (71 + 13)/116 = 72%.

Uninsured = (5 + 27)/116 = 28%.

Therefore, 72% = insured and 28% = uninsured.

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Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6

Answer:

2/35 * x/60

Step-by-step explanation:

the x is what you're trying to find. the 60 is how many minutes there are in an hour. when setting up this proportion, you can't put 1 for 1 hour because you have 35 minutes. if it says minutes, then keep everything in minutes. from here, you would cross multiply and solve, that should give you the answer :) hope this helps <3