All categories

3 years ago

Given that 2^x = 7, find the value of 4^x-1.

Mathematics

1 answer:

Helga [31]3 years ago

4 0

$4=2^2\\\\4^x=(2^2)^x=(2^x)^2=7^2=49\\\\4^x-1=49-1=48$

$If\ is\ 4^{x-1},\ then\\\\4^{x-1}=\dfrac{4^x}{4}=\dfrac{49}{4}=12\frac{1}{4}$

$Used:\\\dfrac{a^n}{a^m}=a^{n-m}$

You might be interested in

Which is faster 80km/h or 60mi/h

Vilka [71]

60 Mi/h is faster than 80 km/h

8 0

2 years ago

The graph shows the commission earned for each week of employment.

frozen [14]

Answer:

A, B, D

Step-by-step explanation:

A is true. From week 5 to week 11, the curve goes down.

B is true. After week 11, the curve goes up.

C is false. The curve passes $320 twice in the first ten weeks, not three times.

D is true. The curve starts at about $110.

E is false. As time increases, the graph goes up. As time decreases, the graph goes down.

8 0

3 years ago

What’s the correct answer

kolezko [41]

An increase from 1950 to 200 means the orange bar needs to be taller than the blue bar.

An increase from 2000 to 2050 means the gray bar needs to be taller than the orange bar.

There are 3 countries that have this, Australia, Canada and Egypt.

The answer is C. three.

8 0

3 years ago

The "off-peak” weekly average cost of hiring a caravan in England is £480.

valina [46]

Answer:

77.08%

Step-by-step explanation:

850 - 480 = 370

(370 / 480 ) × 100 = 77.08333333%

8 0

3 years ago

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 72 type K batteries and a sample of 49

rewona [7]

Answer:

Given:

For battery k(sample 1):

Sample size, n = 75

Sample mean, X' = 9.41

Standard deviation = 0.723

Mean u1 =???

For battery Q(sample 2):

Sample size, n = 49

Sample mean, X' = 9.69

Standard deviation = 0.257

Mean u2 =???

Significance level = 0.05

1) The null and alternative hypotheses, will be given as:

H0 : u1 - u2 = 0

H1 : u1 - u2 ≠ 0

2) This is a two tailed test.

For the test statistic, we have :

$Z_o = \frac{X'_1 - X'_2}{\sqrt{\frac{(\sigma_1)^2}{n_1} + \frac{(\sigma_2)^2}{n_2}}}$

$= \frac{9.41 - 9.69}{\sqrt{\frac{(0.723)^2}{75} + \frac{(0.257)^2}{49}}} = - 3.018$

≈ 3.02

The Zo = - 3.02

3) For the p value, using excel, we have:

2 * P(Z > (-3.018))

= 2 * NORMDIST (-3.018, 0, 1, true)

= 0.00254

For critical value:

Zcritical = Za/2 = 0.05/2

Zcritical = 0.025

We have alternative hypothesis,

H1 : u1 - u2 ≠ 0.

Therefore we reject null hypothesis H0 if Zo > Zcritical

4) We reject null hypothesis H0 if Zo > Zcritical. At 0.05 level of significance, there is not enough evidence to conclude that mean u1 and mean u2 are different.

4 0

2 years ago