A number is 3 1/3 greater than another. If the sum of the numbers is doubled, the result in 19 1/2. What is the smaller number?

Isabel has scored 22, 20, and 20 points in her three basketball games so far. How many points does she need to score in her next

Semenov [28]

Answer: 18

Step-by-step explanation:

To average 20 in 4 games, she would need 80 points in total. In her 3 games, she gets 62 points.

80 - 62 = 18

7 0

3 years ago

How do I find the complement?

likoan [24]

Let A be some subset of a universal set U. The "complement of A" is the set of elements in U that do not belong to A.

For example, if U is the set of all integers {..., -2, -1, 0, 1, 2, ...} and A is the set of all positive integers {1, 2, 3, ...}, then the complement of A is the set {..., -2, -1, 0}.

Notice that the union of A and its complement make up the universal set U.

In this case,

U = {1, 2, 3, 6, 10, 13, 14, 16, 17}

The set {3, 10, 16} is a subset of U, since all three of its elements belong to U.

Then the complement of this set is all the elements of U that aren't in this set:

{1, 2, 6, 13, 14, 17}

6 0

3 years ago

A local gym had 490 members last quarter. This quarter, with a change in its rates, it has 686 members. What is the percent of i

sergij07 [2.7K]

Given:

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

To find:

The percent of increase in the number of members.

Solution:

We have,

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

Now, the percent of increase in the number of members.

$\%\text{ of increase}=\dfrac{{Members in this month - Members in last month}}{\text{Members in last month}}\times 100$

$\%\text{ of increase}=\dfrac{686-490}{490}\times 100$

$\%\text{ of increase}=\dfrac{196}{490}\times 100$

$\%\text{ of increase}=\dfrac{2}{5}\times 100$

$\%\text{ of increase}=2\times 20$

$\%\text{ of increase}=40$

Therefore, the gym members increased by 40%.

4 0

3 years ago

Convert 0.33333...in to a fraction

erik [133]

Step-by-step explanation:

Let x = 0.3333333...

Then 10x = 3.3333333....

We have 9x = 3, so x = 3/9 or 1/3.

6 0

4 years ago

A spring with a spring constant k of 100 pounds per foot is loaded with 1-pound weight and brought to equilibrium. It is then st

shutvik [7]

Answer:

Equation of movement y(t)

$y(t)=sin(10t-\pi/2)$

Amplitude: 1 inch

Period: 0.628 seconds

Step-by-step explanation:

If there is no friction, the amplitude will be the length it was streched from the equilibrium. In this case, this value is 1 inch

$A=1\,inch$

The period depends on the mass and the spring constant.

The formula for the period is:

$T=\frac{1}{f} =\frac{2/pi}{\omega} =2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{1}{100}}=2\pi*0.1=0.628\, s$

The model y(t) for the movement of the mass-spring system is

$y(t)=A\cdot sin(\omega t +\phi)\\\\A=1\\\\\omega=\sqrt{k/m} =\sqrt{100/1}=10\\\\y(0)=Asin(\phi)=-A\\\\ \phi=arcsin(-1)=-1.571=-\pi/2\\\\\\y(t)=sin(10t-\pi/2)$

8 0

3 years ago