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3 years ago

14

Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ...

...... is a factor of every number. ing with Numbers

1 answer:

solong [7]3 years ago

5 0

Answer:

i.)1,2,3,4,6,12

ii).the number itself

iii.)1

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Chang will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $50 and costs an add

oksano4ka [1.4K]

Answer:

450 miles
$117.50

Step-by-step explanation:

The difference in fixed cost is $9; the difference in per-mile cost is $0.02. The difference in per-mile cost will equal the difference in fixed cost for a distance of ...

$9.00/($0.02/mi) = 450 mi

At that distance, the rental cost is ...

$50 +450×$0.15 = $50 +67.50 = $117.50

Both plans will cost $117.50 for 450 miles of driving.

5 0

3 years ago

Which system of equations does not have a real solution?

dolphi86 [110]

Answer:

It's A.

Step-by-step explanation:

Let's look at option A:

From the second equation y = -10 - x. Substituting in the first equation:

-10 - x = x^2 + 3x - 5

x^2 + 4x + 5 = 0

Checking the discriminant b^2 - 4ac we get 16 - 4*1*5 = -4 so there are no real roots. (A negative discriminant means no real roots).

So A has no real solution.

B.

x^2 + 3x - 5 = (20 - 4x)/5 = 4 - 0.8x

x^2 +3.8x - 9 = 0

b^2 - 4ac = (3.8)^2 - 4*1*-9 = 50.44 (positive) so there are real roots.

C.

x^2 + 3x - 5 = -9 - x

x^2 + 4x + 4 = 0

b^2 - 4ac = 4^2 - 4*1*4 = 0 so there are real roots.

7 0

3 years ago

Read 2 more answers

As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to its surfa

Soloha48 [4]

Answer:

Option A)

$\dfrac{dV}{dt} = k(4\pi r^2)$

Step-by-step explanation:

We are given the following in the question:

The rate of evaporation of rainfall drop is proportional to surface area.

Volume of rainfall drop =

$\text{Volume of sphere} = V = \displaystyle\frac{4}{3}\pi r^3$

Surface area of rainfall drop =

$\text{Surface area of sphere} = S =4\pi r^2$

$\displaystyle\frac{dV}{dt} \propto 4\pi r^2\\\\\frac{dV}{dt} = k(4\pi r^2)\\\\\text{k is a constant of proportionality}$

Now,

Rate of evaporation =

$\displaystyle\frac{dV}{dt} = \frac{d}{dt}(\frac{4}{3}\pi r^3) = 4\pi r^2\frac{dr}{dt}$

Equating the two values we get,

$k(4\pi r^2) = 4\pi r^2\displaystyle\frac{dr}{dt}\\\\\frac{dr}{dt} = k$

Thus, the radius radius of the raindrop decreases at a constant rate. Because the evaporation is proportional to,

Option A)

$\dfrac{dV}{dt} = k(4\pi r^2)$

5 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

sammy [17]

if the line is parallel then that means it has the same slope, jjust a different y-intercept. so you'd have to substitute both the x and y value into the equation and keep the y-intercept a variable then solve for it, you'll get 4. so the equation is y=x/3 +4

8 0

4 years ago

What is the minimum number of clients the travel agent should survey? Note that z=1.96 for a 95% confidence interval.

slega [8]

Answer:

121

Step-by-step explanation:

Given data as per the question

Standard deviation = $\sigma$ = 840

Margin of error = E = 150

Confidence level = c = 95%

For 95% confidence, z = 1.96

based on the above information, the minimum number of clients surveyed by the travel agent is

$n = (\frac{z\times \sigma}{E})^2$

$= (\frac{1.96\times 840}{150})^2$

= 120.47

= 121

hence, the 121 number of clients to be surveyed

Therefore we applied the above formula to determine the minimum number of clients

4 0

3 years ago