What is 0.015625 as a fraction

stiv31 [10]

Since it's a right triangle you can use the Pythagorean theorem or Trig (Soh Cah Toa).

I'll just use the Pythagorean theorem : a² + b² = c²
a = 9
b = x
c = 18

9² + x² = 18²
81 + x² = 324
x² = 324 - 81
x² = 243
x = √(243)

factor 243 to find a perfect square

x = √(3*81)
x = 9√(3)

5 0

3 years ago

Simplify the expression: 14x-5(6x-7)+18

USPshnik [31]

Answer:

−16x+53

Step-by-step explanation:

Distribute

14−5(6−7)+18

↓

14−30+35+18

Add

14−30+35+18

↓

14−30+53

Combine like terms

14−30+53

↓

−16+53

8 0

3 years ago

Find the next 3 terms in the geometric sequence -36, 6, -1, 1/6, ...

timama [110]

we are given

geometric sequence -36, 6, -1, 1/6, ...

first term is -36

$a_1=-36$

now, we can find common ratio

$r=\frac{6}{-36}$

$r=-\frac{1}{6}$

now, we can find nth term

$a_n=a_1(r)^{n-1}$

now, we can plug values

and we get

$a_n=36(-\frac{1}{6})^{n-1}$

now, we can find 5th term , 6th term, 7th term

fifth term:

$a_5=36(-\frac{1}{6})^{4}$

$a_5=\frac{1}{36}$

sixth term:

$a_6=36(-\frac{1}{6})^{5}$

$a_6=-\frac{1}{216}$

seventh term:

$a_7=36(-\frac{1}{6})^{6}$

$a_7=\frac{1}{1296}$

so, next terms are

$a_5=\frac{1}{36}$ , $a_6=-\frac{1}{216}$

, $a_7=\frac{1}{1296}$ .............Answer

6 0

3 years ago

Multiply each polynomial (x + 5)(x+4) teach me step by step

lara [203]

Answer: x^2 + 9x + 20

Step-by-step explanation:

Foil Method: (a + b) (c + d) = ac + ad + bc + bd

Lets say:

a = x

b = 5

c = x

d = 4

Plugging in the numbers: xx + 4x + 5x + 5*4

Combine like terms:

xx = x^2

4x + 5x = 9x

5 * 4 = 20

You're then left with: x^2 + 9x + 20

6 0

3 years ago

Suppose that you are in charge of evaluating teacher performance at a large elementary school. One tool you have for this evalua

Strike441 [17]

Answer:

a) Standard error = 2

b) Range = (76.08, 83.92)

c) P=0.69

d) Smaller

e) Greater

Step-by-step explanation:

a) When we have a sample taken out of the population, the standard error of the mean is calculated as:

$\sigma_m=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{25}}=\dfrac{10}{5}=2$

where n is te sample size (n=25) and σ is the population standard deviation (σ=10).

Then, the standard error of the classroom average score is 2.

b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.

The population standard deviation is know and is σ=10.

The population mean is M=80.

The sample size is N=25.

The standard error of the mean is σM=2.

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_M=1.96 \cdot 2=3.92$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 80-3.92=76.08\\\\UL=M+t \cdot s_M = 80+3.92=83.92$

The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).

c) We can calculate this by calculating the z-score of X=79.

$z=\dfrac{X-\mu}{\sigma}=\dfrac{79-80}{2}=\dfrac{-1}{2}=-0.5$

Then, the probability of getting a average score of 79 or higher is:

$P(X>79)=P(z>-0.5)=0.69146$

The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.

d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.

e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.

6 0

3 years ago