The number π is A. Rational B. Irrational

Answer:

The probability that two of them

die is 0.257

Step-by-step explanation:

From the question, we have that the mortality rate is 0.1

So the probability that they will survive is 1-0.1 = 0.9

Now, we want to check that two will die

We are going you use the Bernoulli approximation of the Binomial theorem as follows

= nCr * p^n * q^(n-r)

where n = 16

r = 2

P = 0.1

q = 0.9

Substituting these values;

14 C 2 * 0.1^2 * 0.9^12

= 0.257

Answer:

0.0000175631 or \(\frac{175631}{10000000000}\)

Step-by-step explanation:

\(\frac{(1.6)(10^{-7})}{(9.11)(10^{-3})}\)

Solve Numerator

\((1.6)(10^{-7})=(1.6)(\frac{1}{10000000})=\frac{16}{100000000} =0.00000016\)

Solve Denominator

\((9.11)(10^{-3})=(9.11)(\frac{1}{1000} )=\frac{911}{100000} =0.00911\)

Divide

\(0.00000016/0.00911\)

0.0000175631 or \(\frac{175631}{10000000000}\)

Given:

A line has a slope = -9

The line passing through the point (-4 , -2)

the general form of the equation of the line in point - slope form is :

Where: m is the slope, and ( h,k) is the point

So,

So, the equation of the line will be:

The answer is option C. y + 2 = -9 ( x + 4 )

The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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Answer:

1) 4

2) 1

3) -7

4) 13

Step-by-step explanation:

Instructions:

a) Subtract or add the slope from each side

( it doesn't matter which one you pick )

b) Subtract or add the # next to the slope from each side

( it doesn't matter which one you pick )

c) Divide Each number by the slope

d You have you answer

____________________________________________

1) 9x - 35 = - 7x + 29

+7x + 7x

_____________________

16x - 35 = 29

+ 35 +35

_____________________

16x = 64

_____________________

16 16

x = 4

2). - 2x - 2 = 9x - 13

+2x +2x

_____________________

- 2 = 11x - 13

+ 13 + 13

_____________________

11 = 11x

_____________________

11 11

1 = x

3). 3x + 29 = - 5x - 27

+5x + 5x

_____________________

8x + 29 = - 27

-29 -29

_____________________

8x = -56

_____________________

8 8

x = -7

4). x - 11 = 3x - 37

- x - x

______________________

-11 = 2x - 37

+37 +37

______________________

26 = 2x

_______________________

2 2

13 = x

Hope this helps! (:

Answer:

90 I am guessing. if it's like a square or rectangle

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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Multiple regression analysis assumes certain underlying statistical assumptions are met, such as linearity, independence of errors, homoscedasticity, and normally distributed errors.

A statistical method that would be best to use in this situation is Multiple Regression Analysis.

Multiple Regression Analysis is a statistical method used to identify the relationships between a dependent variable and multiple independent variables.

The dependent variable is the grade point average (GPA) of students, and the independent variables are the factors that may be affecting how well the students are doing.

Multiple regression can be used to model the relationships between these variables and to identify which factors are most strongly associated with differences in GPA.

Multiple regression analysis is a useful tool for exploring the complex relationships between multiple variables and can help identify which factors are most important in predicting GPA.

By analyzing the relationships between the various independent variables and GPA, school districts can identify areas where they may need to focus their efforts to improve academic performance.

It's also important to use caution when interpreting the results of regression analysis, as correlation does not necessarily imply causation, and other factors not included in the model may also be influencing GPA.

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Answer:

3×2-2x + 6 + 3x - 4

-2x +3x + 3 × 2 +6-4

Answer:

\(\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )\).

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

\(x=4cos (t)\)

\(\dfrac{dx}{dt}=-4sin (t)\)

\(y=4sin (t)\)

\(\dfrac{dy}{dt}=4cos (t)\)

Now,

\(\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}\)

\(\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}\)

\(\dfrac{dy}{dx}=-\cot t\)

So, slope of the curve is \(-\cot t\).

\(-\cot t=\dfrac{1}{2}\)

\(-\tan t=2\)

\(\tan t=-2\)            ...(1)

Using \(\sec^2t=1+\tan^2t\), we get

\(\sec^2t=1+(-2)^2\)

\(\sec^2t=1+4\)

\(\sec t=\pm \sqrt{5}\)

\(\cos t=\pm \dfrac{1}{\sqrt{5}}\)

Now,

\(\sin^2t=1-cos^2t\)

\(\sin t=\pm \sqrt{1-\dfrac{1}{5}}\)

\(\sin t=\pm \sqrt{\dfrac{4}{5}}\)

\(\sin t=\pm \dfrac{2}{\sqrt{5}}\)

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If \(\sin t= \dfrac{2}{\sqrt{5}}\), then \(\cos t=- \dfrac{1}{\sqrt{5}}\).

\(x=4cos (t)=-\dfrac{4}{\sqrt{5}}\)

\(y=4sin (t)=\dfrac{8}{\sqrt{5}}\)

If \(\sin t=- \dfrac{2}{\sqrt{5}}\), then \(\cos t= \dfrac{1}{\sqrt{5}}\).

\(x=4cos (t)=\dfrac{4}{\sqrt{5}}\)

\(y=4sin (t)=-\dfrac{8}{\sqrt{5}}\)

Therefore, the two points are \(\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )\).

Answer:

the perimeter is simply 2L + 2W

So lengthy 8.3

2(8.3) + 2(w) =22.4

16.6=2(w) =22.4

2(w) = 5.8

w = 5.8 divide by 2

The width is 2.9

The value of x = 50 degrees.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

 ΔABC∼ΔDEF

∠A=∠D

 ,  ∠B=∠E

 &  ∠C=∠F

But given that  ∠A=47∘

 ,  ∠E=83∘=∠B

hence, in  ΔABC

the sum of interior angles must be  180∘

∴∠A+∠B+∠C=180∘

47∘+83∘+∠C=180∘

∠C=180∘−130∘

=50∘

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Step-by-step explanation:

To answer this, we need to find the scale factor which is to find how much one individual car is worth.

So we need to divide 3.84 and 4.

3.84 ÷ 4 = 0.96

So each car is $0.96.

To find 20 toy cars, we need to multiply 0.96 and 20.

The answer is:

$19.20

The answer is: A) seasonal variations, Seasonal variations in time-series data refer to regularly repeating upward or downward movements tied to recurring events. hese patterns occur over fixed periods, such as daily, weekly, monthly, or yearly cycles.

In time-series data, seasonal variations are regularly repeating upward or downward movements in series values that can be tied to recurring events.

These variations occur over a fixed period, such as daily, weekly, monthly, or yearly cycles. Seasonal variations can be observed in various phenomena, including sales data, weather patterns, and economic indicators.

By identifying and analyzing seasonal variations, patterns and trends can be detected, helping to make predictions and informed decisions.

Seasonal variations are commonly represented using seasonal indices or seasonal adjustment techniques to remove the effects of seasonality and better understand the underlying trends in the data.

Understanding and accounting for seasonal variations are crucial for accurate forecasting and decision-making in various fields.

Hence, the correct option is (A) seasonal variations.

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Isolate y by dividing by e^x: y(x) = (1/7)e^(6x) + C*e^(-x). This is the general solution of the given differential equation.

The given differential equation is of the form dy/dx + y = e^(6x). To find the general solution, we can first solve the homogeneous equation dy/dx + y = 0, which has a solution y = Ce^(-x), where C is a constant. To find the particular solution, we can use the method of variation of parameters, which gives us y = (1/7)e^(6x) - (1/7)Ce^(-x), where C is again a constant. Therefore, the general solution of the given differential equation is y = Ce^(-x) + (1/7)e^(6x), where C is any constant. This solution satisfies the differential equation for any value of C. This explanation is 99 words. The given differential equation is dy/dx + y = e^(6x). This is a first-order linear differential equation. To find the general solution, we first determine the integrating factor (IF) by calculating e^(∫1 dx) = e^x. Now, multiply both sides of the equation by the IF: e^x(dy/dx) + e^x*y = e^(7x). The left side is now the derivative of a product, i.e., d/dx(y*e^x).
Next, integrate both sides with respect to x: ∫[d/dx(y*e^x) dx] = ∫[e^(7x) dx]. This results in y*e^x = (1/7)e^(7x) + C, where C is the constant of integration. Finally, isolate y by dividing by e^x: y(x) = (1/7)e^(6x) + C*e^(-x). This is the general solution of the given differential equation.

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The total amount of money in her account at the end of 3 years is, $80.7

We have,

Lesly deposits $65 into a new savings account. The account earns 7. 5% interest per year.

We can use the formula,

For final amount,

A = P (1 + r%)ⁿ

Here, P = 65

r = 7.5% = 0.075

n = 3

Substitute all the values,

A = 65 (1 + 0.075)³

A = 65 (1.075)³

A = 65 × 1.24

A = $80.7

Therefore, The total amount of money in her account at the end of 3 years is, $80.7

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Answer:

it is a right angle

Step-by-step explanation:

25+65=90

90 degrees is a right angle

The inequality that represents all x values is \(x \ge 4\)

The expression is given as:

\(\sqrt{x - 4} \cdot \sqrt{x + 1}\)

Set the radicands to >=0

\(x - 4 \ge 0\) or \(x + 1 \ge 0\)

Solve for x in both inequalities

\(x \ge 4\) or \(x \ge -1\)

When \(x \ge -1\), the first radicand is irrational from some x values

Hence, the inequality that represents all x values is \(x \ge 4\)

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Answer:-22

Step-by-step explanation:

g(x)=g(-2) means that, x=-2:

so, we have to write -2 instead of every x,

5*(-2)-12=-10-12=-22

Answer: 1<x<3

Step-by-step explanation:

There are 3  rules in one that are needed for this problem

1st:  you can never get a 0 at the bottom of a denominator so x \(\neq\) 1

\(\sqrt{x-1}=0\\ x-1=0\\x=1\) would make a value of 0 on the bottom of a denominator which is not allowed.

2nd:  you can never get a - under the square root so x cannot be less than 1

3rd.  you can never get a log that is equal to 0 or less than 0 so x

3-x=0

-x=-3

x=3

so x cannot =3 or be greater than 3

the values that x CAN be are  1<x<3

Answer:

w = 1.5m + 8

Step-by-step explanation:

Basically what the question says is that the weight of a baby is equal to 8  plus the weight he gained. So then we can make the following equation...  

w = (weight he gained) + 8

(the weight gained is equal to the age in months times 1.5 pounds, so now the formula becomes.....)

w = 1.5m + 8

Answer:

15 ft

Step-by-step explanation:

If every 1/4 of an inch is a foot, than every inch is 4 feet.

1 inch = 4ft

3 inches = 12ft

1/4 + 1/4 + 1/4 = 3/4

3/4=3 ft

12+3=15ft

Answer: Elevation is going to be greater than 5.71059°

Step-by-step explanation: 60/600 = tan∅ = 0=5.71059°,   so 0> 5.71059°

Answer:

$699.52

Step-by-step explanation:

Theres two ways to solve this.

(1) You can either find 7 percent of 653.76 and then add it on

or

(2) You can just multiply the tax with the 653.76

Option (1)

You find 7 percent of 653.76. Now percent means out of a hundred so 7 percent is really 7/100 or 0.07

Now you multiply 653.76 by 0.07 which is 45.76 (rounded to nearest cent)

Now add it up to the total.

653.76+45.76= $699.52

Option (2)

This is the easier method in my opinion. SInce you want to find the total of the product including tax. The tax is technically multiplying the total. The total of course is 653.76 and total means everything. Everything means 100%. So you can add 100% to the tax cause technically thats what your doing becuase you grinding 7percent of the total which is 100 percent. So in this case your price is increasing by 107 percent.

(Example)

So If you want to find 100 percent of a product it would be the same exact result. Like 100 percent of 653.76 is 654.76… So using that we can just add the amount of tax to the 100%. 100+7=107%

Proof that this works is this

usually when you want to find a percentage of something, you turn the percentage into a decimal then multiply. So 100 percent of 653.76 is 653.76*1.00 which is 653.76. So the 100 percent is a place holder to prevent you from doing more steps. Now just add 7 percent since your increasing the total by 7 percent (tax). Now its 653.76*1.07 which when solved you would get $699.52. The same exact result. Less steps same result.

Final answer: $699.52

\(\\ \rm\longmapsto a^3-a+b^3-b\)

\(\\ \rm\longmapsto a(a^2-1)+b^3-b\).

Take out b common

\(\\ \rm\longmapsto a(a^2-1)+b(b^2-1)\)

\(\\ \rm\longmapsto (a+b)(a^2-1)(b^2-1)\)

Step-by-step explanation:

a^3-a+b^3-b = a³+b³-a-b

= a³+b³ - (a+b)

= (a+b)(a²-ab+b²) - (a+b)

= (a+b) (a²-ab+b²-1)

Step-by-step explanation:

8-1,2,4,8

12-1,2,3,4,6,12

15-1,3,5,15

20-1,2,4,5,10,20

Answer

What is the question?

Explanation

Thanks for the free points

Have a great day/night ❤

The intercept of a function are the values of the function when the graph crosses the x or y axes.

The function is given as:

\(\mathbf{f(x) = \frac 1{25}(|7x| + 5x)}\)

Set x to 0, to calculate the y-intercept

\(\mathbf{f(0) = \frac 1{25}(|7 \times 0| + 5\times 0)}\)

\(\mathbf{f(0) = \frac 1{25}(|0| + 0)}\)

\(\mathbf{f(0) = \frac 1{25}(0)}\)

\(\mathbf{f(0) = 0}\)

Set f(x) to 0, to calculate the x-intercept

\(\mathbf{ \frac 1{25}(|7x| + 5x) = 0}\)

Multiply through by 25

\(\mathbf{ |7x| + 5x = 0 \times 25}\)

\(\mathbf{ |7x| + 5x = 0}\)

Remove absolute bracket

\(\mathbf{ 7x + 5x = 0}\)

\(\mathbf{ 12x = 0}\)

Divide through by 12

\(\mathbf{ x = 0}\)

Hence, the intercepts are 0

This interpretation is that:

Isaiah's starting position is on the ground (a step before the staircase)

Because he can move up and down the staircase, where the up and down movements represent negative and positive direction

The appropriate domain is: \((-\infty, \infty)\)

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)