In a lottery game, a player picks six numbers from 1 to 28. If the player matches all six numbers, they win 20,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

Answer:

Since the equation can be written in the form  

y

=

k

x

,  

y

varies directly with  

x

and  

k

. The constant of variation,  

k

, is  

3

4

.

3

4

Step-by-step explanation:

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The general form of the equation of the hyperbola with the given information is \(9x^2 - 16y^2 - 36x + 160y - 508 = 0\). The equation can be determined by first finding the center of the hyperbola, which is (2, 5), and the distance between the foci, which is 4.

The general form of the equation of a hyperbola can be determined from the given information. The vertices of the hyperbola are given as (-2, 5) and (6, 5). The foci of the hyperbola are given as (-3, 5) and (7, 5). The first step in finding the equation of the hyperbola is to determine the center of the hyperbola. The center of the hyperbola can be calculated by taking the average of the x-coordinates of the vertices and then the average of the y-coordinates of the vertices. The center of the hyperbola is then (2, 5). The distance between the foci of the hyperbola is 4. This distance can be calculated by subtracting the x-coordinates of the foci and then subtracting the y-coordinates of the foci. The standard equation for a hyperbola can then be formed by substituting the center coordinates and the distance between the foci into the equation. The resulting equation is \(9x^2 - 16y^2 - 36x + 160y - 508 = 0\). This equation is the general form of the equation of the hyperbola with the given

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

y=−128(x+6)2+12

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

..........................

Answer:

Step-by-step explanation:

In a dilatation for find the new coordinates we have to multiply the initial value for the the scale factor

A’(-3, 12)

B’(9,6)

C’(-9,-3)

so the general rule is:

(x,y) -> (3x, 3y)

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

What is the POTW clubhouse.

120x120x100= your answer.

the answer is 1,440,000. hope I helped

Answer:

120x120x100= your answer.

the answer is 1,440,000

Step-by-step explanation:

Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:

x = 4

Step-by-step explanation:

By intersecting tangent and secant theorem:

\( {(x + 2)}^{2} = x(x + 5) \\ \\ {x}^{2} + 4x + 4 = {x}^{2} + 5x \\ \\ 4x + 4 = 5x \\ \\ 4 = 5x - 4x \\ \\ 4 = x \\ \\ x = 4\)

Answer:

x = 4

Step-by-step explanation:

When a secant and a tangent are drawn to a circle from a point outside the circle, the lengths are related this way:

The square of the length of the tangent equals the product of the length of the secant and the length of the segment of the secant outside the circle.

(x + 2)² = x(x + 5)

x² + 4x + 4 = x² + 5x

x = 4

Answer:

137,280 feet

Step-by-step explanation:

1 mile = 5280 feet

26 * 5280 = 137280

Best of Luck!

Answer:

A marathon is about 26 miles long. Which of these shows how to convert 26 miles to feet?

Step-by-step explanation:

Pretty sure thats the answer

Answer:

Step-by-step explanation:

The two angles must add to 180

(4x-2)+(3x+14)=180

7x+12=180

7x=168

x=24

After solving the equation the value of x is x = 17

What do you mean by co interior angle?

Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary. The interior angles of Co are similar to the shape of a 'C' and both angles are unequal.

Common interior angles are also called continuous interior angles or equilateral interior angles.

In the given figure, line a is parallel to line b. Therefore, these two angles are co interior angle and sum of co interior angle is 180 degree

2x + 5 + 8x + 5 = 180 degree

10x + 10 = 180 degree

10x = 180 - 10

10x = 170

x = 170/10 = 17

Therefore, x = 17

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Answer:

1 1/6

Step-by-step explanation:

First convert 1/2 into twelfths.

1/2= 6/12

Then add:

6/12 + 8/12= 14/12= 7/6= 1 1/6

Hope this helps! :)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(\frac{7}{6}\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\frac{8}{12}+ \frac{1}{2}\\\rule{150}{0.5}\\\rightarrow \frac{8}{12}=\frac{8/4}{12/4}=\frac{2}{3}\\\\\rightarrow\frac{2}{3}+ \frac{1}{2}\\\\rule{150}{0.5}\\\rightarrow LCM(3,2): 6\\\\\rightarrow \frac{2}{3} =\frac{2*2}{3*2} =\frac{4}{6}\\\\\rightarrow \frac{1}{2}=\frac{1*3}{2*3}=\frac{3}{6} \\\rule{150}{0.5}\\\rightarrow \frac{4}{6} +\frac{3}{6}\\\\\rightarrow\boxed{\frac{7}{6}}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Perimeter = 33.4 units.

Step-by-step explanation:

The 2 horizontal lines are 10 and 3 units long.

The vertical line is 9 units long.

By Pythagoras the length of the sloping line

= sqrt(9^2 + 7^2)

= sqrt(130)

= 11.4017.

Perimeter = 10 + 3 + 9 + 11.4

= 33.4 units.

The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

x is -1/b yw

Step-by-step explanation:

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer: 0.03$ per container or 3 cents per container.

Step-by-step explanation: 2.70/90=0.03.

Answer:

It's either 0.03 or 2.70

Step-by-step explanation:

The five key points of the parent function are:

The function is given as:

y = -2 sin[2(x - 45)] + 1

The above function is a sine function, and the parent function of a sine function is

y = sin(x)

The properties of the above function are:

The transformed function is given as:

y = -2 sin[2(x - 45)] + 1

A sine function is represented as:

y = A sin[Bx + C] + D

Where:

Using the above representations, we have:

See attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1

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In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:

Step 1: Plot the data on a scatterplot.

Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.

Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.

Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.

Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.

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The equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the female population is related to time t by;

\(t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP\)

Now, to do partial fraction;

(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)

P + S = A((r-1)P -S) + PB

if P = 0, then:

A = -1

If (r-1)P - S = 0

p = S/(r-1)

B = 1 + r - 1

B = r

Therefore,

\(t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP\)

t = -ln|P| + ln|(r-1)P-S| + 1/r-1 x integral((r-1)/[(r-1)P-S])

t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)

t = -ln|P| + (r/r-1)ln|(r-1)P-S|

Now substituting known constants then;

t = -ln|P|-1/9(ln|-0.9P - 900|)

t = -ln|P| - 1/9(ln|-0.9P -900|)

t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))

t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)

as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value

Therefore, the equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)

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After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.

A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.

In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.

According to the normal distribution curve:

"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.

Area from a value (Use to compute p from Z)

Value from an area (Use to compute Z for confidence intervals)

Let the parameters be

Mean 64

Standard deviation 2.75

Above 1.96

Below 1.96

Between 64 and 69.5

Outside -1.96 and 1.96

Area (probability) 0.4772

And that value is 95 % of the whole data

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Answer:

79

Step-by-step explanation:

↓ Define Prime number ↓

Prime number ⇒ A positive integer that has no positive integer divisors other than 1 and itself. To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number.

Solve:

76 is not a prime number. The number 76 is divisible by 1, 2, 4, 19, 38, 76.

79 is a prime number. The number 79 is divisible only by 1 and the number itself.

100 is not a prime number. The number 100 is divisible by 1, 2, 4, 5, 10, 20, 25, 50, 100.

66 is not a prime number. The number 66 is divisible by 1, 2, 3, 6, 11, 22, 33, 66.

Hence 79 is a prime number

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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