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3 years ago

Identify the x- and y-intercepts of f(x) and the x- and y-intercepts of g(x). f(x) =3x−1;g(x)=2f(x)−4

1 answer:

6 0

F(x)=3x-1

y-intercept:
y=3(0)-1
y=-1

x-intercept:
0=3x-1
1=3x
1/3=x

g(x)=2f(x)-4

y-intercept:
y=2f(0)-4
y=2(-1)-4
y=-6

x-intercept:
0=2f(x)-4
0=2(3x-1)-4
0=6x-2-4
0=6x-6
0=x-1
1=x

Hope I helped :)

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Let Y1 and Y2 have the joint probability density function given by:

Ann [662]

Answer:

a) k=6

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

Step-by-step explanation:

a) if

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 = ∫∫k(1 − y2) dy1*dy2 = k ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)- (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)= 9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

8 0

3 years ago

Pete and Teegan each put the same amount of money in a new bank account. Teegan's account earns 2.75% simple interest, and she e

ss7ja [257]

Answer:

Step-by-step explanation:

Let us assume that Pete and Teegan each put an amount of $P in a new bank account.

Teegan's account earns 2.75% simple interest and she earned $2.20 in interest after one year.

P = $80

Now, this $80 in Pete's account earns 5% simple interest.

Then after one year Pete will earn as interest 80x5/100 = 4 Dollars.

Therefore your answer is $4.

3 0

3 years ago

How do you find x? and how do you round to the nearest tenth?

expeople1 [14]

Hey there!

In order to solve this problem, we can use the Pythagorean Theorem, which is $c^2 = a^2 + b^2$ . Since the Pythagorean Theorem would find only half of the length of x, we'll need to double it in the end.

First, let's plug in what we know to the Pythagorean Theorem: $2.1^2 = 1.4^2 + b^2$

Next, we'll simplify to that $b^2$ is by itself:

$b^2 = 2.45$

Then, we'll find the square root of 2.45, multiply that by 2 and round to the nearest tenth:

$2(\sqrt{2.45} ) = 3.1$

Therefore, x = 3.1 ft.

How to round to the nearest tenth:

In a decimal, the tenth is the first number after the decimal point. To round to the tenth, if the number in the hundredth place is less than 5, you keep the number as it is, but if the number in the hundredth place is more than 5, you increase the number in the tenth place by 1.

Hope this helps!! :)

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3 years ago

1.) The check number on a check:

ziro4ka [17]

Answer:

D) Identifies the transaction and is located at the top right corner of the check

Step-by-step explanation:

The check number on a check is the number located at the top right corner of the check, and it can also be found at the bottom of the check, located in lower right corner after the routing number and the account number

The check number aids in the tracking and identifying bank transactions such as to identify checks that the bank has processed and to know outstanding checks that are yet to be processed.

The check number also aids in balancing of the checkbook.

Therefore, the check number on a check identifies the transactions and is located at the top right corner of the check.

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2 years ago

If the sphere shown above has a radius of 5 units, then what is the approximate volume of the sphere? (Use 3.14 for .) A. 261.67

Olenka [21]

Answer:

B. 523.33 cubic units

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 (3.14) 5^3

V =523.3333333

V = 523.33 units^3

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3 years ago