Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.

Answer:

Explanation:

The expected value is calculated as the net result of the sum of the products of every probability times each value, less the cost.

That is: expected value = [ ∑ (probability × value)] - cost

For the game of roulette you have:

Expected value = $ 360 × 1/38 + $ 0 × 37/38 - $10 = $9.47 - $10 = - $ 0.53

Since, each time you play is independent of the others plays,  if you played 1,000 times, you would expect to lose 1,000 times 0.53, i.e 1,000 × 0.53 = $ 530.

Based on the probabilities and payoffs involved, the expected value of this roulette game is -$0.263 per game, meaning the player loses approximately $0.263 with each game. If played 1000 times, the player would expect to lose about $263.

In the game of roulette, the expected value represents an average of all possible outcomes, weighted by their corresponding probabilities. When the metal ball lands on 6, the net gain is $350 (the $10 bet returned plus the $350 winnings). However, when any other number is rolled, the player loses their $10 bet. Hence, the expected value for any single play of the game can be calculated by multiplying each outcome by its probability, and then adding these results together.

The expected value is calculated with the formula:

So, with a 1/38 chance of winning $350 and a 37/38 chance of losing $10, we get:

Therefore, the expected value is -$0.263. This means, on average, you will lose approximately $0.263 each time you play the game. If you play the game 1000 times, you would expect to lose about $263.

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Answer:

C.(x-5)²+(x+5)=9

D (x-9)²+(y+9)²=16

Step-by-step explanation:

Use a graph tool to visualize the circle.See attached

You can also see that  in the options

C. circle has center (5,-5) and radius 3 which will form in 4th quadrant

D. Circle has center (9,-9) and radius 4 which will still form in 4th quadrant

Answer:

b. 19.54 ft²

Step-by-step explanation:

Measure of the central angle made by the arc CD = 35 degrees

Measure of radius of circle = r = 8 feet

Area of the sector is calculated as:

[tex]A=\frac{1}{2}r^{2} \theta[/tex]

Where the angle [tex]\theta[/tex] is in radians.

35 degrees in radian would be = [tex]35 \times \frac{\pi}{180} = \frac{7 \pi}{36}[/tex]

Using the values in the formula, we get:

[tex]Area = \frac{1}{2} \times (8)^{2} \times (\frac{7 \pi}{36} )\\\\ Area = 19.54[/tex]

Thus, the area of the sector bounded by arc CD would be 19.54 ft²

Answer:

S

Step-by-step explanation:

If the dilation is of magnitude 3, then the lenghts of all segments must be thriced.

The center of dilation is at point P. If you have to find image of point Q, you should connect points Q and P (pre-image point and center of dilation) and thrice this segment.

So,

PQ→PS,

because PQ=1,

PS=PQ+QR+RS=1+1+1=3

Hence, the image point is point S

Answer:

  see below

Step-by-step explanation:

Attached is the output of a computer program that picked two different numbers at random from the set 1-52, then converted those numbers to a suit and value.

Such a program could be written in a spreadsheet or any of a variety of computer languages.

Answer:

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Step-by-step explanation:

step 1

In the right triangle DOC

Find the measure of side DO

Applying the Pythagoras Theorem

[tex]DC^{2}=DO^{2}+OC^{2}[/tex]

substitute the given values

[tex]7^{2}=DO^{2}+5^{2}[/tex]

[tex]DO^{2}=7^{2}-5^{2}[/tex]

[tex]DO^{2}=49-25[/tex]

[tex]DO^{2}=24[/tex]

[tex]DO=2\sqrt{6}\ in[/tex]

step 2

In the right triangle DOC

Find the sine of angle ∠ODC

sin(∠ODC)=OC/DC

substitute

[tex]sin(ODC)=5/7[/tex] -----> equation A

step 3

In the right triangle DOP

Find the sine of angle ∠ODP

sin(∠ODP)=OP/DO

substitute

[tex]sin(ODP)=x/2\sqrt{6}[/tex] -----> equation B

step 4

Find the value of x

In this problem

∠ODC=∠ODP

so

equate equation A and equation B

[tex]5/7=x/2\sqrt{6}[/tex]

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Answer:

P (sum of two numbers is < 5) =2/9

Step-by-step explanation:

There are two numbers that can be picked such that the first number odd and less than 5:  1 and 3.

Then, the numbers that can be drawn with these numbers should be from: 1, 2, 3, 4, 5, 6, 7, 8 or 9.

The number of total possibilities = 18

Out of these, the following are the four possible options to have a sum which is less than 5 and 1:

1 and 1

1  and 2

1 and 3

3 and 1

So P (sum of two numbers is < 5) = [tex]\frac{4}{18}[/tex] = 2/9

Answer:

Step-by-step explanation:

2/9 is right because i just took it and got a 5/5

Answer:

y = 4

Step-by-step explanation:

2 ( - 6 y + 29 ) - 4 y = - 6

⇒ Expand brackets

-12 y + 58 - 4 y = -6

Simplify

-16 y + 58 = -6

⇒ -58 from to isolate - 16 y

-16 y = - 64

⇒ ÷ -16 from both sides to isolate y

y = 4

Answer:

(S+7)/4 = T

Step-by-step explanation:

S=4T-7

We want to solve to T

Add 7 to each side

S+7=4T-7+7

S+7 = 4T

Divide each side by 4

(S+7)/4 = 4T/4

(S+7)/4 = T

Answer:

He will need 38 more blueberries

Step-by-step explanation:

If each cupcake will have 6 blueberries and he wants to make 17 cupcakes he will need a total of 102 blueberries (found by multiplying 17 and 6 together). If he already has 64 he will just need to buy 38 more (found by subtracting 64 from 102). I hope this helped, if not then I apologize.

Answer:

p=6

Step-by-step explanation:

4p+12=36

(subtract 12)

4p=24

(divide by 4)

p=6

Answer: 6

Step-by-step explanation:

edge 2023

Answer:

Simplifying

0x =-2, 1

0 * x =-2.1

Apply rule () *a = 0

0=-2.1

Step-by-step explanation:

Therefore, the zeroes of the function [tex]\( f(x) = x^2 - x - 2 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -1 \).[/tex]

To find the zeroes of the quadratic function [tex]\( f(x) = x^2 - x - 2 \),[/tex] we need to solve for [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex]. This means we need to find the values of [tex]\( x \)[/tex]that make the function equal to zero.

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

For a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex], the solutions [tex]\( x \)[/tex] are given by:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

For our equation [tex]\( f(x) = x^2 - x - 2 \)[/tex], we have [tex]\( a = 1 \), \( b = -1 \)[/tex], and [tex]\( c = -2 \)[/tex]. Substituting these values into the quadratic formula:

[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \][/tex]

[tex]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm 3}}{2} \][/tex]

So, the solutions are:

[tex]\[ x_1 = \frac{{1 + 3}}{2} = 2 \][/tex]

[tex]\[ x_2 = \frac{{1 - 3}}{2} = -1 \][/tex]

Answer:

  see the attachment

Step-by-step explanation:

f(x) is increasing for x > 0.

g(x) is increasing for x < 4.

Both functions are increasing on the open interval (0, 4). It will be graphed with a solid line between 0 and 4, and with open circles at 0 and 4. See the black line on the x-axis of the attachment for an example of such a graph.

Answer:

The correct answer would be option D, Events in which neither event is dependent upon the other.

Step-by-step explanation:

Mutually exclusive events are the events which cannot occur at the same time. If there are two events, then in mutually exclusive situation, both events can not happen at the same time. One event will happen at a time. Mutually exclusive events are also called disjoint. Both events are not dependent upon one another. The occurrence of one event would not change the occurrence of the other event. The most appropriate and suitable example of mutually exclusive events is the tossing of a coin. Either tails will come or heads. Both events can't happen at the same time, and also not both events are dependent upon each other.

Answer:

Events in which neither event is dependent upon the other

Step-by-step explanation:

Events that are independent and cannot happen at the same time.

Answer:

612 times does the clock chime

Step-by-step explanation:

Given data

two times 15 minutes after the hour

four times 30 minutes after the hour

six times 45 minutes after the hour

clock chimes 8 + 2 = 10 times

to find out

how many times does the clock chime in a 24-hour period

solution

we can say clock chimes from 12:05 - 1:05  is for this 1 hour

2 +4+6+8 = 20 + 1

and clock chimes from 1:05 - 2:05  is for this 1 hour is 20 +2

and we know for 24 hours clock chimes  is 20 × 24 i.e

= 480 + 2 × ( 1 +2 + ...  +11 )     .....................1

we know

2 × ( 1 +2 + ...  +11 ) will be  = 2 × (n) × (n+1) / 2

here n is 11 so

= 2 × (n) × (n+1) / 2

= 2 × (11) × (11+1) / 2

= 132

so now put this in equation 1

we get

clock chime in a 24-hour period = 480 + 132

clock chime in a 24-hour period = 612

so 612 times does the clock chime in a 24-hour period

Answer:

636

Step-by-step explanation:

Look at the picture for explanation:)

Answer:

[tex]\large\boxed{y=4x+3}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of aline:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points:

(-2, -5)

y-intercept (0, 3) → b = 3

Calculate the slope:

[tex]m=\dfrac{3-(-5)}{0-(-2)}=\dfrac{8}{2}=4[/tex]

Put the value of the slope and the y-intercept to the equation of a line:

[tex]y=4x+3[/tex]

The equation of the line through (-2, -5) and (0, 3) is y = 4x + 3, obtained using the point-slope form with the calculated slope and one of the given points.

To find the equation of the line passing through the given coordinates (-2, -5) and (0, 3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line, and m is the slope.

First, calculate the slope (m) using the given coordinates:

m = (y2 - y1) / (x2 - x1)

m = (3 - (-5)) / (0 - (-2)) = 8 / 2 = 4

Now, choose one of the points, let's use (-2, -5), and substitute the values into the point-slope form:

y - (-5) = 4(x - (-2))

y + 5 = 4(x + 2)

Simplify the equation:

y + 5 = 4x + 8

Isolate y:

y = 4x + 3

Therefore, the equation of the line passing through the points (-2, -5) and (0, 3) is y = 4x + 3.

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Answer:

first Let's find the common difference

an=a1+(n-1)d

let's take A2 that is 18

so 18=7+(2-1)d

18=7+d

d=11

so the next term is going to be 40+11 that is 51

Answer:

y = 1/2 x

Step-by-step explanation:

We have the slope of 1/2 and a point of (4,2)

We can use point slope form

y-y1 = m(x-x1)

y-2 = 1/2(x-4)

Distribute

y-2 = 1/2x -2

Add 2 to each side

y-2+2 = 1/2 x -2+2

y = 1/2 x

This is in slope intercept form

Answer:

  24.15 feet

Step-by-step explanation:

The shadow is opposite the specified angle, and the distance from its tip to the building edge is the hypotenuse of the relevant right triangle. Then the applicable relation is ...

  Sin = Opposite/Hypotenuse

  (25 ft)sin(75°) = Opposite = shadow length

  24.15 ft = shadow length

Answer:

29

Step-by-step explanation:

I'm going to write both of this as improper fractions.

That is the mixed fraction [tex]a\frac{b}{c}[/tex] can be written as the improper equivalent fraction of [tex]\frac{ca+b}{c}[/tex] assuming [tex]a[/tex] is positive.

So we are going to write [tex]-3\frac{1}{3}[/tex] as [tex]-\frac{3(3)+1}{3}[/tex].

Simplifying that gives us [tex]-\frac{10}{3}[/tex].

Now for [tex]-8\frac{7}{10}=-\frac{10(8)+7}{10}=-\fraC{87}{10}[/tex].

Now we are ready to find the product which just means multiply:

[tex]\frac{-10}{3} \cdot \frac{-87}{10}[/tex]

To multiply fractions you just multiply straight across on top and straight across on bottom unless you see a common factor on and bottom to cancel (and I do; I see 10)

[tex]\frac{-1}{3} \cdot \frac{-87}{1}[/tex]

[tex]\frac{87}{3}[/tex]

Negative times negative is positive.

Anyways time to write 87/3 as a mixed fraction.

How many 3's are in 87?  29  with no remainder

Answer:

29

Step-by-step explanation:

its close... ish

Answer:

Step-by-step explanation:

x-intercept is for y = 0.

4x - 8y = 16

Put y = 0 to the equation, and solve for x:

4x - 8(0) = 16

4x - 0 = 16

4x = 16          divide both sides by 4

x = 4

The x-intercept of a line is where it crosses the x-axis. By setting y to 0 in the equation 4x-8y=16 and solving for x, we find that the x-intercept is 4.

The x-intercept of a line is the point at which it crosses the x-axis. This is determined by setting the equation equal to zero and solving for x. In the line equation 4x-8y=16, to find the x-intercept, we set y equal to 0 and solve for x. The equation becomes 4x-8*0=16, which simplifies to 4x=16. Dividing each side of the equation by 4, we find that x=4. So, the x-intercept of the line 4x-8y=16 is 4.

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Answer:

false

Step-by-step explanation:

It's false. Entirely. No hesitation.

The sec(X) = 1 / Cos(X)

Cos(x) = y / z

1/cos(x) = 1//y/z

1/cos(X) = 1/1 * z/y

1/cos(X) = z/y

sec(X) = z/y

Yea it's false

I know I'm late but I hope it helped a little haha

Answer:

A student finds a​ 95% confidence interval of​ (16.34,18.69) for the mean number of species counted. This is a valid interval because the mean number of species or any population mean does not necessarily have to be a whole number, as stated by the student.

This given confidence interval of (16.34,18.69) helps us to simply estimate the mean species counted.

Answer:

There are 40 band members including the band director that were notified of the new starting point

Step-by-step explanation:

The diagram below shows the band director at the top, then the three band members he called, then the next band members, and so forth.

Answer: i got 19

Step-by-step explanation:

Answer:

  $858

Step-by-step explanation:

You pay for 11 of the 12 months, so the average monthly payment is ...

  (11/12)×$936 = $858

Answer:

FE=7.1 units

Step-by-step explanation:

we know that

In the right triangle DEF

The tangent of angle of 55 degrees is equal to divide the opposite side to the angle of 55 degrees (FE) by the adjacent side to angle of 55 degrees (DE)

so

tan(55°)=FE/DE

FE=(DE)tan(55°)

substitute the given value

FE=(5)tan(55°)

FE=7.1 units

Answer:

y < 2/3 x - 1 is the linear inequality which represented by the graph ⇒ 4th answer

Step-by-step explanation:

* Lets explain how to solve the problem

- At first lets find the equation of the line

∵ The line passes through points (3 , 1) and (-3 , -3)

∵ The form of the equation is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The rule of the slope of any line passes through points (x1 , y1) and

  (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the intersection between the line and the

  y-axis at point (0 , c)

∵ (3 , 1) and (-3 , -3) are two points on the line

- Let (x1 , y1) is (3 , 1) and (x2 , y2) is (-3 , -3)

∴ The slope of the line m = (-3 - 1)/(-3 - 3) = -4/-6 = 2/3

∵ The line intersects the y-axis at point (0 , -1)

∴ c = -1

∵ The equation of the line is y = mx + c

∴ The equation of the line is y = 2/3 x + -1

∴ The equation of the line is y = 2/3 x - 1

- If the shaded part is over the line then the sign of inequality is ≥ or >

- If the shaded part is under the line then the sign of inequality is ≤ or <

- If the line represented by solid line (not dashed), then the sign of

 inequality is ≥ or ≤

- If the line represented by dashed line (not solid), then the sign of

 inequality is > or <

∵ The shading part is under the line

∵ The line is dashed

∴ The sign of the inequality is <

∴ y < 2/3 x - 1

* y < 2/3 x - 1 is the linear inequality which represented by the graph

The linear inequality represented by the graph is y < (2/3) * x - 1

To solve the problem, we can follow these steps:

Find the equation of the line that passes through the points (3, 1) and (-3, -3). The equation of a line is in the form y = mx + c, where "m" is the slope and "c" is the y-intercept.

Use the slope formula to calculate the slope (m) of the line. The slope formula is given by m = (y2 - y1) / (x2 - x1), where (x1, y1) is (3, 1) and (x2, y2) is (-3, -3).

Calculate the slope (m):

m = (-3 - 1) / (-3 - 3) = -4 / -6 = 2/3

Determine the y-intercept (c), which is the point where the line intersects the y-axis. In this case, it's at point (0, c).

Since the line passes through (3, 1), we can use this point to find the y-intercept:

1 = (2/3) * 3 + c

1 = 2 + c

c = -1

Now that we have the slope (m) and the y-intercept (c), we can write the equation of the line:

y = (2/3) * x - 1

Determine the direction of the shading in the inequality. If the shaded region is under the line, the sign of the inequality is "<."

Determine the style of the line on the graph. If the line is dashed, the sign of the inequality is also "<."

Combine the information to form the linear inequality:

y < (2/3) * x - 1

So, the linear inequality represented by the graph is:

y < (2/3) * x - 1

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Answer:

See below.

Step-by-step explanation:

52 inches - 41 inches = 11 inches

She needs to be at least 11 inches taller to be at least 52 inches tall.

Statements that describe how much taller she must be:

(The correct answers are in bold and checked with the square root symbol, √.)

at least 11 inches √

no more than 11 inches

a maximum of 11 inches

a minimum of 11 inches √

fewer than 11 inches

at most 11 inches

Answer:

Step-by-step explanation:

at least 11 inches

a minimum of 11 inches

Answer:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

Step-by-step explanation:

The given ellipse has equation:

[tex]\frac{(y-2)^2}{64}+\frac{x^2}{9}=1[/tex].

The center of this ellipse is (h,k)=(0,2)

We use the equation: [tex]a^2-b^2=c^2[/tex] to determine the foci.

[tex]\implies 64-9=c^2[/tex]

[tex]\implies 55=c^2[/tex]

[tex]\implies c=\pm \sqrt{55}[/tex]

The directrices are given by [tex]y=k\pm\frac{a^2}{c}[/tex]

[tex]y=2\pm\frac{64}{\sqrt{55}}[/tex]

[tex]y=2\pm8.6[/tex]

[tex]y=2-8.6[/tex] and [tex]y=2+8.6[/tex]

The equation of the directrices are:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

The correct answer is D

Answer:

10x^2-25x-35

Step-by-step explanation:

FOIL means first, outer, inner, and last.

The first term of each pair is 2x and 5x.

The outer term of each pair is 2x and 5.

The inner term of each pairs are -7 and 5x.

The last term of each is -7 and 5.

Now we just have to multiply the terms I pairs above:

First:   (2x)(5x)=10x^2

Outer: (2x)(5)=10x

Inner: (-7)(5x)=-35x

Last:   (-7)(5)=-35

------------------------------Add the terms:

10x^2-25x-35