16. A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.

Last year, Kim read a total of 30 fiction and non-fiction books. The number of non-fiction books was 5 less than 4 times the num

VashaNatasha [74]

Answer:

10

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Help me asap please <br> I'll mark you as brainliest

Viefleur [7K]

Answer:

2b/ab+3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6. respectively. All 10 dice we

kompoz [17]

Answer:

C) a sample distribution of a sample mean with n = 10

$\mu_{{\overline}{X}} = 3.5$

and $\sigma_{{\overline}{Y}} = 0.38$

Step-by-step explanation:

Here, the random experiment is rolling 10, 6 faced (with faces numbered from 1 to 6) fair dice and recording the average of the numbers which comes up and the experiment is repeated 20 times.So, here sample size, n = 20 .

Let,

$X_{ij}$ = The number which comes up on the ith die on the jth trial.

∀ i = 1(1)10 and j = 1(1)20

Then,

$E(X_{ij})$ = $\frac {1 + 2 + 3 + 4 + 5 + 6}{6}$

= 3.5 ∀ i = 1(1)10 and j = 1(1)20

and,

$E(X^{2}_{ij}$ = $\frac {1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2}}{6}$

= $\frac {1 + 4 + 9 + 16 + 25 + 36}{6}$

= $\frac {91}{6}$

$\simeq$ 15.166667

so, $Var(X_{ij}$ = $(E(X^{2}_{ij} - {(E(X_{ij})}^{2})$

$\simeq 15.166667 - 3.5^{2}$

= 2.91667

and $\sigma_{X_{ij}}$ = $\sqrt {2.91667}[/tex [tex]\simeq 1.7078261036$

Now we get that,

$Y_{j} = \frac {\sum_{j = 1}^{20}X_{ij}}{20}$

We get that $Y_{j}'s$ are iid RV's ∀ j = 1(1)20

Let, ${\overline}{Y} = \frac {\sum_{j = 1}^{20}Y_{j}}{20}$

So, we get that $E({\overline}{Y}) = E(Y_{j})$

= $E(X_{ij}$ for any i = 1(1)10

= 3.5

and,

$\sigma_{({\overline}{Y})} = \frac {\sigma_{Y_{j}}}{\sqrt {20}} = \frac {\sigma_{X_{ij}}}{\sqrt {20}} = \frac {1.7078261036}{\sqrt {20}} [tex]\simeq 0.38$

Hence, the option which best describes the distribution being simulated is given by,

C) a sample distribution of a sample mean with n = 10

$\mu_{{\overline}{X}} = 3.5$

and $\sigma_{{\overline}{Y}} = 0.38$

6 0

3 years ago

From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E

belka [17]

Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: $y=a(b)^x$

where a=initial value aka when x=0

in this case, b can be expressed as: $1+r$ , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: $y=16(1.0213)^x$

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: $1.0213(16)$ , which can be expressed as a 2.13% increase from year 0

When x=2, we get: $1.0213(1.0213(16))$ , which can be expressed as a 2.13% increase from year 1

when x=3, we get: $1.0213(1.0213(1.0213(16)))$ , which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

We get the following equation: $y=16(1.0213)^7$

Using a calculator this simplifies to approximately: $18.5436$

Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million

4 0

1 year ago

A jewelry prism with a length of 9 inches and a height of 4 1/4 inches. The volume of the jewelry box is 283 1/2 cubic inches. W

masha68 [24]

Answer:

volume = (length × Width × height)

(567/2) = (9×) × (17/4) × (w)

283.5 = 38.25w

w= 7.41inches

4 0

3 years ago