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3 years ago

Solve the equation 4(2^m+1)-16^m=0

Mathematics

2 answers:

Karolina [17]3 years ago

7 0

M=2
That’s the answer

Otrada [13]3 years ago

6 0

$\\ \rm\longmapsto 4(2^m+1)-16^m=0$

$\\ \rm\longmapsto 8^m+4-16^m$

take 4common

$\\ \rm\longmapsto 4(2^m+1-4^m)=0$

$\\ \rm\longmapsto 2^m-4^m+1=0$

$\\ \rm\longmapsto 2^m=4^m$

$\\ \rm\longmapsto 2^m=2^{2^m}$

$\\ \rm\longmapsto 2^m=m$

$\\ \rm\longmapsto m=\dfrac{1}{2}$

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What is the area to this shape ?

Dafna1 [17]

Answer:

249.42 units²

Step-by-step explanation:

Given only the apothem of an n-sided regular polygon, the area can be computed as ...

... A = n·a²·tan(180°/n)

For n=3 and a=4√3, this is ...

... A = 3·(4√3)²·tan(60°)

... A = 3·48·√3 = 144√3 . . . . units²

... A ≈ 249.42 units²

4 0

3 years ago

At a university, 60% of the 7,400 students are female. The student newspaper reports the results of a survey of a random sample

omeli [17]

Given Information:

Population mean = p = 60% = 0.60

Population size = N = 7400

Sample size = n = 50

Required Information:

Sample mean = μ = ?

standard deviation = σ = ?

Answer:

Sample mean = μ = 0.60

standard deviation = σ = 0.069

Step-by-step explanation:

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

50*0.60 ≥ 10

30 ≥ 10 (satisfied)

n(1 - p) ≥ 10

50(1 - 0.60) ≥ 10

50(0.40) ≥ 10

20 ≥ 10 (satisfied)

The mean of the sampling distribution will be same as population mean that is

Sample mean = p = μ = 0.60

The standard deviation for this sampling distribution is given by

$\sigma = \sqrt{\frac{p(1-p)}{n} }$

Where p is the population mean that is proportion of female students and n is the sample size.

$\sigma = \sqrt{\frac{0.60(1-0.60)}{50} }\\\\\sigma = \sqrt{\frac{0.60(0.40)}{50} }\\\\\sigma = \sqrt{\frac{0.24}{50} }\\\\\sigma = \sqrt{0.0048} }\\\\\sigma = 0.069$

Therefore, the standard deviation of the sampling distribution is 0.069.

4 0

3 years ago

Amanda needs to make a garden plot which has an area less than 18 sq. feet. The length should be 3 feet longer than the width. W

SCORPION-xisa [38]

Answer:

<em>Any width less than 3 feet</em>

Step-by-step explanation:

<u>Inequalities</u>

The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:

A = L.W

The first condition can be written as follows:

LW < 18

The length should be 3 feet longer than the width, thus:

L = W + 3

Substituting in the inequality:

(W + 3)W < 18

Operating and rearranging:

$W^2 + 3W - 18 < 0$

Factoring:

(W-3)(W+6)<0

Since W must be positive, the only restriction comes from:

W - 3 < 0

Or, equivalently:

W < 3

Since:

L = W + 3

W = L - 3

This means:

L - 3 < 3

L < 6

The width should be less than 3 feet and therefore the length will be less than 6 feet.

If the measures are whole numbers, the possible dimensions of the garden plot are:

W = 1 ft, L = 4 ft

W = 2 ft, L = 5 ft

Another solution would be (for non-integer numbers):

W = 2.5 ft, L = 5.5 ft

There are infinitely many possible combinations for W and L as real numbers.

6 0

3 years ago

How old am I if 400 reduced by 2 times age is 244

zalisa [80]

440- 2x= 244 // simplify the equation given

3 0

3 years ago

mr. duc asked perry to set up 450 chairs in a large hall. perry puts 20 chairs in each row. he has already set up 15 rows of cha

Brums [2.3K]

The number of chairs that still need to be set up are 150.

6 0

4 years ago

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Solve the equation 4(2^m+1)-16^m=0​

Solve the equation 4(2^m+1)-16^m=0