Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width.4x+y^2=12, x=yThen find the area S of the region.

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4  for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

[tex]P(6)=\dfrac{1}{6}[/tex]

The probability of getting a 5 is:

[tex]P(5)=\dfrac{1}{6}[/tex]

The probability of getting a 4 is:

[tex]P(4)=\dfrac{1}{6}[/tex]

The probability of getting other numbers (1,2,3) is:

[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]

[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]

We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]

[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]

[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]

[tex]E(x)=\dfrac{10+7+4}{6}[/tex]

[tex]E(x)=\dfrac{21}{6}[/tex]

[tex]E(x)=3.5[/tex]

Therefore, the expected winnings for this game are $3.50.

Answer:

A.

D needs to be equal or more to 260

Answer:

The correct option is A

Step-by-step explanation:

Given:

In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].

To find:

The length of the hypotenuse.

Solution:

It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the given triangle,

[tex]\sin A=\dfrac{a}{c}[/tex]

Substituting the given values, we get

[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]

By cross multiplication, we get

[tex]1\times c=4\times 2[/tex]

[tex]c=8[/tex]

Therefore, the length of the hypotenuse is 8 units.

Answer:

20 glasses a day

Step-by-step explanation:

2.5litres equals 2500millilitres

2500÷125=20

Answer:

x = 1.9

Step-by-step explanation:

Thanks to a theorem we can use this proportion

10.47 : 4.44 = 4.44 = x

x = (4.44^2)/10.47 = 1,882865 = 1.9

Answer:

3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

just did it

Answer:

x=50

Step-by-step explanation:

The solution to the equation x – 25 = 25 is x = 50. The axiom used to solve the equation is the addition property of equality.

To solve the equation x - 25 = 25, we want to isolate the variable x to find its value.

Adding 25 to both sides of the equation, we get:

x - 25 + 25 = 25 + 25

Simplifying, we have:

x = 50

Therefore, the solution to the equation is x = 50.

In this case, the axiom used to solve the equation is the addition property of equality. According to this axiom, if two expressions are equal, adding the same value to both sides of the equation preserves the equality.

In the given equation, we add 25 to both sides of the equation to maintain equality and obtain the solution x = 50. The addition property of equality allows us to perform this operation and determine the value of x.

To learn more about axioms click on,

https://brainly.com/question/33725824

#SPJ2

Answer:

(a) By converting to decimal:

2:3=23=0.6¯

4:5=45=0.8

As 0.6¯<0.8,2.:3<4:5.

(b) By converting to fractions:

Ratios can be compared by converting them to like fractions.

2:3=23=2(5)3(5)=1015

4:5=45=4(3)5(3)=1215

As 1015<1215,2:3<4:5.

Answer: The length of DC is 3 units

Step-by-step explanation:

The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.

The given image is attached below.

From the BPT theorem, we can say that:

[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]

We are given:

AE = 12 units

EB = 4 units

AD = 9 units

Putting values in above equation, we get:

[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]

Hence, the length of DC is 3 units

Answer:

The answer is 3 units

Step-by-step explanation:

9514 1404 393

Answer:

  29)  1/5

  30)  independent; 64/225 ≈ 0.284

Step-by-step explanation:

In general, a "spinner" is considered to be a (mathematically ideal) device that returns one of the values with which it is marked, with a probability according to the area of the sector in which the mark resides. Usually, sectors are presumed to have equal areas. The result of one spin is generally considered to be independent of the result from any other spin. In the real world, an operator familiar with a given spinner can often ensure that the results do not have equal probability and are not independent. We ignore that possibility in math problems.

__

29) Of the numbers 1 to 15, there are three numbers less than 4. The probability of spinning one of them is 3/15 = 1/5.

__

30a) We have defined our spinner so that the events are independent. (See above.)

30b) In the set of numbers 1 to 15, 8 are odd and 7 are even. The probability of getting an odd number on any spin is 8/15. Because the results of successive spins are independent, the probability of any given sequence is the product of the probabilities of the numbers in that sequence.

  P(2 odd) = P(odd)×P(odd) = (8/15)(8/15) = 64/225 ≈ 0.284

Answer:

Last one.

Step-by-step explanation:

[tex]\sqrt{3}[/tex] is used in 30-60-90 triangles

[tex]\sqrt{2}[/tex] is used in 45-45-90 triangles

Base is x, leg is x[tex]\sqrt{3}[/tex], hypotenuse is 2x

Answer:

x = 20 ; y= 10√3

Step-by-step explanation:

30, 60 , 90 triangle ratio is

Side opposite to 30 is a

a = AC = 10

Side opposite to 60 is a[tex]\sqrt{3}[/tex]

AB = a[tex]\sqrt{3}[/tex] = 10√3

Side opposite to 90 is  2a

BC = 2a = 2* 10 = 20

Answer:

= 21i

Step-by-step explanation:

√-9 = 3i

= 7 . 3i

Multiply the numbers: 7 . 3 = 21

= 21i

Hope this helps!

Answer:

7.65 or 7.7 rounded to 1 DP

Step-by-step explanation:

To find the length of the side of a cube we do the inverse of finding the volume.

one side= x

If x³ = volume, therefore ∛448 is how to find the length of one side.

∛448= 7.65

I hope this helps you.

Answer:

Step-by-step explanation:

P = 4 + 6 + (3y - 2)      Remove the brackets

P = 10 + 3y - 2            Combine

P = 8 + 3y

Note 3y must be less than 8. That's because 2 sides of any triangle must be larger than the 3rd side or else you don't have a triangle.

Answer:

The domain of a function is the input numbers that, when plugged into a function, the result is defined. In simple words, we can define the domain of a function as the possible values of x that will make an equation true.

The range of a function is defined as a set of solutions to the equation for a given input. In other words, the range is the output or y value of a function. There is only one range for a given function.

hope this helps!

Step-by-step explanation:

Since there is a fixed number of trials and the trials are independent, it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Thus, the binomial distribution is appropriate.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

Answer:

- 2+8x/x

Step-by-step explanation:

See image below:)

FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free

Answer:

(8x-2) / (x-8)

Step-by-step explanation:

8x/x-8 - 2/x-8

Since the denominator is the same, we can add the numerators

(8x-2) / (x-8)

Answer:

3

Step-by-step explanation:

[tex]\sqrt{9}=\sqrt{3*3} = 3[/tex]

Answer:

The additional deposit to be made in one year should be $ 301.81.

Step-by-step explanation:

Given that I need to save $ 1,300 to go overseas in two years, and I deposit $ 800 in a savings account today, that earns 10% interest, and I will make an additional deposit in one year, to determine how much must I deposit in one year in order to have enough to go on the trip, the following calculation must be performed:

800 x 1.1 = 880

(880 + X) x 1.1 = 1300

1300 / 1.1 = 1,181.81

1,181.81 - 880 = X

301.81 = X

Therefore, the additional deposit to be made in one year should be $ 301.81.

Answer:

10π in.

Step-by-step explanation:

circumference of a circle = 2πr

=2*π*5

=10π in.

I dont think I can be answered with just the given info... is some of the q missing still?

Closest we can do with above is dress cost = 120+ c

Answer:

use this formula(a+b+c) a,b,c are the 3 sides of a triangle this will help you to find the perimeter of a triangle

6+T=1

Try T=-5

6+(-5) = 1

Correct, So...

T=-5

Answer:

i think its 13

Step-by-step explanation:

you are supposed to measure the lowest point of the liquid.

Answer:

y = -2x + 2

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (2, -1)

Points on the y-axis (y1, y2) = (-2, 4)

To find the equation of line in slope intercept form;

First of all, we would determine the slope of the line.

Mathematically, slope is given by the formula;

[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]

[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

Substituting into the equation, we have;

[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]

[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]

[tex] Slope, m = \frac {6}{-3} [/tex]

Slope, m = -2

Next, we would use the following formula to find the equation of the line;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - (-2) = -2(x - 2)

y + 2 = -2x + 4

y = -2x + 4 - 2

y = -2x + 2 = mx + c

Answer:

500 kilometers

Step-by-step explanation:

The fuel (y) Karl has in his car is a function of the distance (x) Karl travelled. The amount of fuel (y) is dependent on the distance (x) Karl travelled.

On the y-axis, we have amount of fuel.

On the x-axis, we have distance travelled.

At the time Karl travelled when he had 200 liters of fuel (y) remaining in his car, he had travelled a distance (x) of 500 kilometers.

We know this by looking at the graph given. When x (distance) = 500, y (fuel) = 200.

Answer:

121x+y²

Your Welcome

BIFFY OUT!!!

Answer:

y=-x-3

Step-by-step explanation: