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3 years ago

Simplify to the extent possible (logx16)(log2x)

Mathematics

1 answer:

sasho [114]3 years ago

7 0

Answer:

${ \tt{ = ( log_{x}16)( log_{2}x) }}$

Change base x to base 2:

${ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}$

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A village fete has a children’s running race each year, run in heats of up to ten children. For each heat the first three contes

bekas [8.4K]

Answer: 1) 1/3,654 2) 3/406 3) 72,684,900,288,000 4) 120

<u>Step-by-step explanation:</u>

1) First and Second and Third

$\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}$

2) First and Second

$\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}$

$3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}$

$4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}$

8 0

3 years ago

Please help me!! i know u saw this so help me

storchak [24]

Answer:

I think 8

Step-by-step explanation:

9/2 and 5/8

here 8 is the LCM.

so, 9/2 × 4/4

5/8 × 1/1

which gives: 36/8 and 5/8

7 0

3 years ago

Read 2 more answers

X² – 2x - 15 / x² - 6x+5

Nuetrik [128]

Answer:

all work is pictured/shown

7 0

3 years ago

A publisher reports that 344% of their readers own a particular make of car. A marketing executive wants to test the claim that

inysia [295]

Answer:

No, there is not enough evidence at the 0.02 level to support the executive's claim.

Step-by-step explanation:

We are given that a publisher reports that 34% of their readers own a particular make of car. A random sample of 220 found that 30% of the readers owned a particular make of car.

And, a marketing executive wants to test the claim that the percentage is actually different from the reported percentage, i.e;

Null Hypothesis, $H_0$ : p = 0.34 {means that the percentage of readers who own a particular make of car is same as reported 34%}

Alternate Hypothesis, $H_1$ : p $\neq$ 0.34 {means that the percentage of readers who own a particular make of car is different from the reported 34%}

The test statistics we will use here is;

T.S. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ~ N(0,1)

where, p = actual % of readers who own a particular make of car = 0.34

$\hat p$ = percentage of readers who own a particular make of car in a

sample of 220 = 0.30

n = sample size = 220

So, Test statistics = $\frac{0.30 -0.34}{\sqrt{\frac{0.30(1- 0.30)}{220} } }$

= -1.30

Now, at 0.02 significance level, the z table gives critical value of -2.3263 to 2.3263. Since our test statistics lie in the range of critical values which means it doesn't lie in the rejection region, so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the actual percentage of readers who own a particular make of car is same as reported percentage and the executive's claim that it is different is not supported.

3 0

3 years ago

(i) 3 (a + 5b) + a (a + 4) (ii) y (10 - y) + 3 (y - 2) (iii) 2 (8a - 5b) + 3 (5a - 12) (iv) 3 (y - 3) + ( 8 - 6y + x) (v) a (a -

AveGali [126]

Answer:

$3 (a + 5b) + a (a + 4) = a^2 + 7a + 15b$