a class has eight girls and two boys. if the teacher randomly picks eight students, what is the probability that she will pick all girls? find the probability of the event.

The owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.

a) To get the regression equation for the relationship between time and trees remaining, we need to use linear regression. We can use the data given in the table to create a scatterplot and then find the line of best fit. Using a calculator or Excel, we can find that the regression equation is:
Trees remaining = 1177.38 - 36.25(time)
where "Trees remaining" is the number of trees remaining and "time" is the number of years since harvesting began.
b) To find during which year the owners of the farm will stop harvesting when only 1000 trees remain, we can substitute "1000" for "Trees remaining" in the regression equation and solve for "time":
1000 = 1177.38 - 36.25(time)
Solving for "time", we get:
time = (1177.38 - 1000) / 36.25
time ≈ 4.89 years
Therefore, the owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.

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Answer:

A

≈

50.27

ft²

Step-by-step explanation:

when the radius is 4 ft the area is 50.27 ft squared

Answer:

50.24

Step-by-step explanation:

Because i know

Answer:

Step-by-step explanation:

x + 4 + 2x - 6 + 10 > 50

4 - 6 + 10 = 8

x + 2x = 3x

3x + 8 > 50

Subtract 8 from both sides

3x > 50 - 8

3x > 42

Divide 3 from both sides

42/3 = 14

x > 14

The total area of all six faces of the tunnel is \(614.197\pi\) square centimeters.

The surface area of the solid (\(A\)) used to represent the tunnel for a toy train is the sum of its six faces (two semicircular sections, inner semicircular arc section, outer semicircular arc section, two rectangles).

We calculate the surface area as following:

\(A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)\)

\(A = 614.197\pi\,cm^{2}\)

The total area of all six faces of the tunnel is \(614.197\pi\) square centimeters. \(\blacksquare\)

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Answer:

(6,7)

Step-by-step explanation:

Let B(x,y).

By the midpoint formula,

So, the coordinates of B are (6,7).

The distance Sam traveled is 1.15 miles.

Given: Sam road his bike 2/5 of a mile and walked another 3/4 of a mile.

To find the total distance Sam traveled,

we need to add the distance he traveled while riding his bike to the distance he traveled on foot.

To do that, we need to find a common denominator for 2/5 and 3/4.

The smallest common multiple of 5 and 4 is 20.

So, we'll rewrite 2/5 and 3/4 with a denominator of 20.2/5 = 8/20 (multiply the numerator and denominator by 4)

3/4 = 15/20 (multiply the numerator and denominator by 5).

Now, we can add these two fractions together: 8/20 + 15/20 = 23/20.

So, Sam traveled 23/20 of a mile, which is equivalent to 1 3/20 miles or 1.15 miles (rounded to the nearest hundredth).

Therefore, the distance Sam traveled is 1.15 miles.

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1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes. 2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

An equation in mathematics is a claim made regarding the equality of two expressions. It comprises of two expressions that express the same value or amount and are joined by an equal sign. The objective is to solve for the unknown value by modifying the equation in accordance with predetermined rules and principles when one side of the equation is typically unknown. From straightforward arithmetic operations to intricate differential equation systems, equations are used to model and solve a wide range of issues in many branches of mathematics, science, and engineering.

1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes.

2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

3. (6x + 3)(x - y + 4) = 6x² - 15xy + 18x + 3y - 12. This product is not a sum or difference of two cubes.

4. (x² - 2)(x² + 3x - 1) = x⁴ + 3x³ - x² - 6x - 2. This product is a difference of two cubes: x^6 - 2^3.

5. (x - 3)(3x + 1) (4x (2)) = 12x⁴ - 32x³ - 9x² + 27x. This product is not a sum or difference of two cubes.

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1 millimetre is dependent variable and 5 seconds are independent variable.

What is independent nd dependent variable?

In scientific research, variables are any property that can take on different values, such as height, age, temperature, or experimental results.

Researchers often manipulate or measure independent and dependent variables in research to test cause and effect relationships.

The reason is the independent variable. Its value is independent of other variables in your study.

The dependent variable is the effect. Its value depends on changes in the independent variable.

For example, you are designing a study to test whether changes in room temperature affect the results of a math test.

Your independent variable is room temperature. Change the temperature of the room, making half the participants cooler and the other half warmer.

Your dependent variable is math test scores. You measure the math skills of all participants using a standardized test and see if they differ based on room temperature.

Here given expression is 1 milliliter per 5 seconds.

That means length of any perticular thing change 1 millimetre per 5 seconds.

So, it is clear that length of that object is dependent on time.

Therefore, here 1 millimetre is dependent and 5 seconds are independent variable.

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Answer:

.8

Step-by-step explanation:

Answer:

7.75 x ? = 1/24

___         ____

7.75         7.75

x= 1/186

Answer:

7

Step-by-step explanation:

2x-3=11

14=2x

x=7

the answer is 7.

x=-4

Step-by-step explanation:

|2x-3|= 11

-2x+3 = 11

-2x = 8

x = 8/-2

x= -4

Hope it helps you

Answer:

70 is the right answer....

Answer:

70 ways

Step-by-step explanation:

8 C 4 =   8 ! / ( 4! * 4!) = 70 ways

Answer:

I have no idea

Step-by-step explanation:

I can barely see the screen

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible.

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible. So, we need to minimize the sum of and . Now, let's use calculus to find the minimum value of the sum.To find the minimum value, we have to find the derivative of the sum of and , i.e. f(x) with respect to x, which is given by f '(x) as shown below:

f '(x) = 1/x^2 - 1/(1-x)^2

We can see that this function is defined on the closed interval [0, 1]. The reason why we are using the closed interval is that x is a positive number, and both endpoints are included to ensure that we cover all positive numbers. Therefore, the problem requires optimization over a closed interval. This means that the minimum value exists and is achieved either at one of the endpoints of the interval or at a critical point in the interior of the interval.

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\(3x+4y=12\implies 4y=-3x+12\implies y=\cfrac{-3x+12}{4} \\\\\\ y = \cfrac{-3x}{4}+\cfrac{12}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{4}}x+\stackrel{\stackrel{b}{\downarrow }}{3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ 5 } \implies 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 1}(x-\stackrel{x_1}{3}) \\\\\\ y-4=x-3\implies {\Large \begin{array}{llll} y=x+1 \end{array}}\)

The RT is 8 units long.

Given that ePoint S is between points R and T. This means that R is located on one side of S while T is located on the other side of S. We can represent this relationship between points R, S, and T on a number line as follows:

R---------S---------TThe distance from R to S is denoted as RS, and the distance from S to T is denoted as ST.

We can also represent the distance from R to T as RT. Therefore, we can say that:RT = RS + ST

This is known as the segment addition postulate, which states that if three points A, B, and C are collinear and B is between A and C, thenAB + BC = ACIn this case, the collinear points are R, S, and T, and S is between R and T.

Hence, we can apply the segment addition postulate to find the value of RT when we know the lengths of RS and ST. If the units of measurement are not specified, then the answer will be in arbitrary units.Let us suppose thatRS = 5 unitsandST = 3 units.Then,RT = RS + ST= 5 + 3= 8 units

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The dot product of a constant tensor D and the position vector x is equal to the constant tensor D.

Let us first write out the dot product of x and D:

(x ⋅ D) = (xi eˆi ⋅ D) = xi (eˆi ⋅ D)

Since D is a constant tensor whose components do not depend upon the coordinates, the dot product between D and any vector eˆi will also be constant and not depend on the coordinates. Therefore, we can simplify the above equation as:

(x ⋅ D) = xi (eˆi ⋅ D) = xi Di

But since Di is a constant for all i, we can write:

(x ⋅ D) = xi Di = D(ij) xi = D

Therefore, the dot product of a constant tensor D and the position vector x is equal to the constant tensor D.

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Z-score of given data comes to be -5.30.

It is given that

Population mean μ= 310

Standard deviation σ= 20

Mean of sample data X= 295

Sample size n= 50

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

For a hypothesis test

Z-score = (X-μ)/(σ/√n)

Where, X = observed value

μ= mean

σ = standard deviation

n =sample size

Z-score of above data = (295-310)/(20/√50)

Z-score = -5.30

Therefore, the Z-score of the given data comes to be -5.30.

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Answer:

A = 51°   b = 15.3858...   c = 24.448

Step-by-step explanation:

Given: B= 39°

a = 19

and that it's a right triangle

so that means the other 3rd angle is

A+39+90=180

A= 51°

use SOH CAH TOA to remember how sin cos and tan fit on the triangle

Sin(x)=Opp/Hyp    Cos(x)=Adj/Hyp  Tan(x)=Opp/Adj

Let's use  Tan to find b

Tan(b) = Opp / Adj

Tan(39) = b / 19

19*Tan(39) = b

15.38589... = b

use Pythagoras to find c

c = \(\sqrt{a^{2} +b^{2} }\)

c = \(\sqrt{19^{2} +15.3858^{2} }\)

c = 24.448....

The probability that the small business owner's annual profit will not exceed $100,000 is about 0.0571

We can use the central limit theorem to approximate the distribution of the annual profit. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed.

Let X be the daily profit, then the annual profit, Y, is given by Y = 105X. The mean of Y is:

μY = 105μX = 105(975) = 102375

The variance of Y is:

σY^2 = 105σX^2 = 105(129)^2 = 2244385

The standard deviation of Y is:

σY = sqrt(2244385) ≈ 1498.12

We want to find the probability that the annual profit will not exceed $100,000, which is equivalent to finding the probability that Y ≤ 100000. We can standardize Y using the formula:

Z = (Y - μY) / σY

Substituting the values, we get:

Z = (100000 - 102375) / 1498.12 ≈ -1.58

We can use a standard normal distribution table or calculator to find the probability that Z ≤ -1.58. This probability is approximately 0.0571.

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The given question is incomplete, the complete question is:

A small business owner estimates his mean daily profit as $975 with a standard deviation of $129. His shop is open 105 days a year. What is the probability that his annual profit will not exceed $100,000?

Answer:

6. -4x+3   7. 2x+24   8. 4x+3

Step-by-step explanation:

The formula to find slope is y2-y1/x2-x1.  With y2 serving as any y value on the table that is not whatever you decide as your y1 value, same goes for the x values.

y2 and x2 should be from the same line in the table, same goes for x values.

Explaining #6: I used point (2,-5) and (1,-1).

y2=-5, y1=-1, x2=2, x1=1

Plug values into slop equation--> (-5-(-1)/(2-1)= -4

To find the y-intercept you would either take the formula y=mx+b and plug in a point from the table and slop you just found to find b. Or when x=0 on the table the y value is your b/y-intercept.

Hope this helped and you can understand!

Answer:

r/2 -6

Step-by-step explanation:

less than means it comes after

half of r

r/2

6 less than means subtract

r/2 -6

The solution to the differential equation dy/dt = y^2(1 - t), with the initial condition y = 2 when t = 1, is: y = -1 / (t - (t^2)/2 - 3/2)

To find the solution to the differential equation dy/dt = y^2(1 - t) with the initial condition y = 2 when t = 1, we can use separation of variables and integrate.

First, let's separate the variables by moving all the terms involving y to one side and all the terms involving t to the other side:  dy/y^2 = (1 - t) dt

Now, we integrate both sides of the equation: ∫(dy/y^2) = ∫(1 - t) dt

Integrating the left side:-1/y = t - (t^2)/2 + C1

Next, we solve for y: y = -1 / (t - (t^2)/2 + C1)

Now, we can use the initial condition y = 2 when t = 1 to find the value of the constant of integration C1. Substituting these values into the equation, we have:

2 = -1 / (1 - (1^2)/2 + C1)

2 = -1 / (1 - 1/2 + C1)

2 = -1 / (1/2 + C1)

Multiplying both sides by (1/2 + C1):

2(1/2 + C1) = -1

1 + 2C1 = -1

2C1 = -3

C1 = -3/2

Now, we substitute the value of C1 back into the equation for y:

y = -1 / (t - (t^2)/2 - 3/2)

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A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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y=47,916.666 dollar after 25 years

librarian salary =25000 dollar in 2000

librarian salary=30500 dollar in 2006

in 6 years increment is 30500 - 25000= 5500dollar

in one year increment is 5500/6= 916.666

m= 916.666 each year

b= 25000

y=mx+b

y=916.666*25+25000      given x=25

y=47,916.666 dollar after 25 years

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Answer:

x=48

Step-by-step explanation:

Answer:

X=48

Step-by-step explanation:

.5(x+20)= 6+ .25(x+64)

.5x +10 = 6 + .25x +16

.5x+10= 22+ .25x

-.25x -.25x

_______________

0.25x + 10 = 22

-10 = -10

_____________

.25x = 12

Divide both side by .25

X= 48

The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In \(2^4 = 2\times 2\times 2 \times 2\), here, 2 is multiplied by itself 4 times.

If  \(a^m = a\times a\times a \times.....\times a\) (m times), a is the base and m is the index.

The laws of index are

\(a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m\)

Here,

For first option

\(\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1\)

For second option

\((5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1\)

For the third option,

\((2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1\)

For the fourth option
\(\frac{(3^5)^2}{3^4}\)

\(\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1\)

Fourth option does not have an expression greater than 1

Fourth option is correct.

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Juan bought 4.5 lbs for $7.98 per lb

This implies that 1 lb is sold at the rate of $7.98

1 lb -------- $7.98

4.5lb ------ $x

Introduce cross multiplication

1 * x = 7.98 x 4.5

x = $35.91

Therefore, 4.5lbs is sold at the rate of $35.91

The tax sales is 6%

Total amount = original price + 6% of original price

Total amount = 35.91 + 6/100 x 35.91

= 35.91 + 0.06 x 35.91

= 35.91 + 2.1546

= $38.0646

The total amount Juan paid is $38.0646