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2 years ago

QUESTION: Determine if the statement is true or false? if false give an counterexample.

Mathematics

1 answer:

Jobisdone [24]2 years ago

5 0

Answer:

False

Step-by-step explanation:

Actual question is:

logf 4(3d) + log4 1 = log4 3d

Solution:

logf 4 + logf (3d) + 0 = log4 (3d)
logf 4 + logf (3d) = log4 (3d)

If we assume f = 4, then

log4 4 + log4 (3d) = log4 (3d)
log4 4 = 0

but log4 4 = 1

1 = 0 is impossible

Therefore the statement is False

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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

3/4(x + 3) = 9 How do I solve this

Sonbull [250]

Answer:

x = 10

Step-by-step explanation:

so first distribute the 3/4 to everything on the inside

3/4x + 1 1/2 = 9

now subtract 1 1/2 on both sides

3/4x = 7 1/2

Now divide both sides by 3/4

x = 7 1/2 divided by 3/4

x = 15/2 divided by 3/4

x = 15/2 times 4/3

x = 5/1 times 2/1

x = 10

4 0

2 years ago

A cheetah's speed was timed over a set distance. The cheetah was clocked running 60 miles per hour. Which equation is the relati

Troyanec [42]

Answer:

D. y=70x

Step-by-step explanation:

The cheetah was clocked running 70 miles per hour.

i.e. in 1 hour cheetah covered 70 miles

in 2 hours cheetah covered 140 miles

in 3 hours cheetah covered 210 miles

in general, in n hour cheetah covered 70n miles

If y denote the distance covered

and x denotes the time cheetah runs

Then, y=70x

Hence, the equation which shows the relationship between the distance, y, and time, x, the cheetah runs is:

D y=70x

8 0

3 years ago

Hi can you help !!!???

GalinKa [24]

Answer:

Step-by-step explanation:

4 1/3 can be separated into 4, and 1/3.

half of 4 is 2.

Half of 1/3 is 1/6.

Add 2 and 1/6, and you get 2 and 1/6. Answer is C

5 0

2 years ago

Read 2 more answers

Find the compound amount on an investment of $8,500 at 7.5% compounded daily for 3.5 years.

Leto [7]

Answer:

Accrued Amount: 10955.51, Total Interest: 2455.51

Step-by-step explanation:

A = P(1+r/n)nt

CI = A-P

Where,

CI = Compounded interest

A = Final amount

P = Principal

t = Time period in years

n = Number of compounding periods per year

r = Interest rate

7 0

2 years ago