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3 years ago

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A player on the school baseball team reaches first base 3/10 of the time he is at-bat. Out of 80 times at bat, about how many ti

mes would you predict that he will make it to first base?

1 answer:

k0ka [10]3 years ago

7 0

Answer:

24 times

Step-by-step explanation:

3/10 of 80 is 24

3*8=24

10*8=80

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In 2012, the population of New Zealand was approximately 4.43

mrs_skeptik [129]

Answer: 6.71 × 10^6 people

Step-by-step explanation:

Given that the population of New Zealand was approximately 4.43million people. In the same year, the population of Belgium was approximately 11.14 million people.

The difference in number of population will be

(11.14 - 4.43) millions

= 6.71 millions people

Expressing the answer by using scientific notation will be

6.71 × 10^6 people.

Therefore, 6.71 × 10^6 people live in Belgium than in New Zealand

8 0

3 years ago

P(k)=a^k=2 3 4 find value of a that makes this is a valid probability distribution

Vesna [10]

Sounds like you're asked to find $a$ such that

$\displaystyle\sum_{k=2}^4\mathbb P(k)=\mathbb P(2)+\mathbb P(3)+\mathbb P(4)=1$

In other words, find $a$ that satisfies

$a^2+a^3+a^4=1$

We can factorize this as

$a^4+a^3+a^2-1=a^3(a+1)+(a-1)(a+1)=(a+1)(a^3+a-1)=0$

In order that $\mathbb P(k)$ describes a probability distribution, require that $\mathbb P(k)\ge0$ for all $k$ , which means we can ignore the possibility of $a=-1$ .

Let $a=y+\dfrac xy$ .

$a^3+a-1=\left(y+\dfrac xy\right)^3+\left(y+\dfrac xy\right)-1=0$
$\left(y^3+3xy+\dfrac{3x^2}y+\dfrac{x^3}{y^3}\right)+\left(y+\dfrac xy\right)-1=0$

Multiply both sides by $y^3$ .

$y^6+3xy^4+3x^2y^2+x^3+y^4+xy^2-y^3=0$

We want to find $x\neq0$ that removes the quartic and quadratic terms from the equation, i.e.

$\begin{cases}3x+1=0\\3x^2+x=0\end{cases}\implies x=-\dfrac13$

so the cubic above transforms to

$y^6-y^3-\dfrac1{27}=0$

Substitute $y^3=z$ and we get

$z^2-z-\dfrac1{27}=0\implies z=\dfrac{9+\sqrt{93}}{18}$
$\implies y=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}$
$\implies a=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}-\dfrac13\sqrt[3]{\dfrac{18}{9+\sqrt{93}}}$

6 0

3 years ago

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the g

PIT_PIT [208]

H=P/mg is the solution

8 0

3 years ago

Read 2 more answers

An architect created the blueprints for the Chin's house. The scale factor is 1 inch: 40 inches. The length and width of the liv

Gnoma [55]

Step 1: Find the area of the living room on the blueprint with the formula Area = length x height

A = 4 x 8

A = 32

Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in the 32 inches is times 40 <<< Does that make sense?), so...

40 x 32 = 1,280

Hope this helped!

8 0

3 years ago

Read 2 more answers

When you were born, your uncle put $1000 into a bank account for you. According to the terms of the account, your investment

kompoz [17]

Answer:

D. Time; amount; $2800

I hope this is right because I was looking for the answer to the same question and this is the solution I came up with.

Step-by-step explanation:

Time is the independent variable because it is the variable that is changed.

The Amount (dollars) is the dependent variable because it is effected by the independent variable.

4 0

3 years ago