Sophie earns 6% interest from her bank. If she has $456 in the bank, how much interest will she earn?

A coin is tossed 10 times. True or false, and explain: (a) The chance of getting 10 heads in a row is 1/1,024. (b) Given that th

Llana [10]

Answer:

a and b both are true.

Step-by-step explanation:

Given : A coin is tossed 10 times.

To find : True or false, and explain ?

Solution :

(a) The chance of getting 10 heads in a row is $\frac{1}{1024}$

Coin has two face head and tail.

The probability of getting head is $P(H)=\frac{1}{2}$

The probability of getting 10 heads in a row is

$P=(P(H))^{10}$

$P=(\frac{1}{2})^{10}$

$P=\frac{1}{1024}$

The chance of getting 10 heads in a row is $\frac{1}{1024}$ is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is $\frac{1}{2}$ .

The probability of getting 10 heads in a row is $P_1=(\frac{1}{2})^{10}$

The probability of getting 9 tosses were heads is $P_2=(\frac{1}{2})^{9}$

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,

$P=\frac{P_1}{P_2}$

$P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}$

$P=(\frac{1}{2})^{10-9}$

$P=\frac{1}{2}$

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is $\frac{1}{2}$ is true.

3 0

4 years ago

Yeah I’m not good at this

levacccp [35]

For the given triangle, x = 5.1 cm and y = 6.1 cm.

Step-by-step explanation:

Step 1:

In the given triangle, the angle is 50°. It is given that the opposite side has a length of y cm and the adjacent side has a length of y cm. The hypotenuse of the triangle measures 8 cm.

To determine the length of the opposite side of the triangle, we use the sin of the given angle.

To determine the length of the adjacent side of the triangle, we use the cos of the given angle.

$sin \theta = \frac{oppositeside}{hypotenuse} , cos \theta = \frac{adjacentside}{hypotenuse}.$

Step 2:

In the given triangle,

The length of the opposite side = y cm,

The length of the adjacent side = x cm,

The length of the hypotenuse = 8 cm,

The angle of the triangle = 50°.

$sin \theta = \frac{oppositeside}{hypotenuse} , sin 50 = \frac{y}{8}.$

$y = 0.7660 (8) = 6.128.$

$cos \theta = \frac{adjacentside}{hypotenuse} , cos 50 = \frac{x}{8}.$

$x = 0.6427 (8) = 5.1416.$

So x = 5.1416 cm and y = 6.128 cm. Rounding these off to one decimal place, we get x = 5.1 cm and y = 6.1 cm.

8 0

4 years ago

Point R is located at (1, 2) on a coordinate grid. Point S is located at (4, 5) on the same

Aleksandr-060686 [28]

Answer:

4.2 units

most likely answer choice B

Step-by-step explanation:

(1, 2) and (4, 5)

To find the distance between two points, we use the distance formula:

$d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }$

Let's plug in what we know.

$d = \sqrt{(4 - 1)^2 + (5 - 2)^2 }$

Evaluate the parentheses.

$d = \sqrt{(3)^2 + (3)^2 }$

Evaluate the exponents.

$d = \sqrt{(9) + (9) }$

Add.

$d=\sqrt{18}$

Evaluate the radical.

d = 4.24

Round to the nearest tenth.

d = 4.2 units

*note: The answer choice is 4.6. I'm not sure if that is a typo on someone's end, but the distance between these two points is exactly 4.24264068712 units.

Hope this helps!

6 0

3 years ago

Suppose the total cost for n tickets is $36 what's is the total cost of one more ticket is purchased

arsen [322]

$36/n because since there are n amount of tickets, you should divide $36 by n. I feel like you won't get me. For instance, let's say n is 6 tickets. So if 6 tickets are for $36, you should divide $36 by 6 tickets to find the unit rate. Hope this helps.

7 0

4 years ago

PLEASE HELP PLEASE

Contact [7]

Answer:

3024 in^3

Step-by-step explanation:

Think of the dimensions of this prism as being 18 in by 12 in by 14 in:

V = (18 in)(12 in)(14 in) = 3024 in^3

3 0

4 years ago