Which are solutions of the equation 4x2 - 7x = 3x + 24? Check all that apply.

Solve the logarithmic equation

vichka [17]

$\text{We know:}\\\\\log_ab=c\iff b=a^c\\\\y=\log_{10}0.0001\\\\y=\log_{10}10^{-4}\to\boxed{y=-4}$

8 0

3 years ago

Tell whether each set of events is independent or dependent (problems 1 - 4).

tatyana61 [14]

Answer:

1 dependent

234 independent

Step-by-step explanation:

7 0

3 years ago

What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the uni

puteri [66]

Answer:

We have two rates, A and B.

If we want that the units of A can be converted into the units of B, then we must have that the units of A represent the same measure that the units of B.

What does this mean?

For example, if A is written in distance over time, then B must also must have units of distance over time.

An example would be:

units for distance = meter, kilometer, feet, etc.

units for time = hour, minute, second, etc-

Then we could have:

[A] = [km/h]

[B] = [m/min]

Then the units of A could be converted into the ones of B, because both of them have the same physical meaning.

Concluding, you only can convert units that represent the same physical quantity, for example, if you have one quantity in meters, for example:

10m

You only can convert this to other units of distance, remember to do the correct conversion, if we would want to write this in cm, you should remember that:

1m = 100cm

Then, 10 times one meter is 10 times 100 cm

10m = 10*(1m) = 10*(100cm) = 1000cm

7 0

3 years ago

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that $n = 3900, \pi = \frac{1911}{3900} = 0.49$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032$

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

3 0

2 years ago

8/f = 56/105 what is f?

svetlana [45]

8/15 = 56/105

This may be solved using proportion.
a/b = c/d
ad = bc where cross products are equal.

a = 8
b = f
c = 56
d = 105

ad = bc
8*105 = f*56
840 = 56f
840/56 = 56f/56
f = 15

56 ÷ 7 = 8
105 ÷ 7 = 15

6 0

3 years ago

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