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3 years ago

7

An annual family membership pass to the science museum is discounted by the amount shown on the tag if a family membership pass

is normally $120 it will cost only $80 while the sale lasts

2 answers:

Nostrana [21]3 years ago

4 0

Answer:

33%

Step-by-step explanation:

change/original x100

40/120x100=33.33333

33%

Burka [1]3 years ago

3 0

The discount is a 33% discount

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Identify the like terms in this expression: 4x^2 + 2x - 6x + 3y

Kamila [148]

Answer:

the like terms here are the x and the + symbol.

Step-by-step explanation:

If a part of the equation appears more than once that is a like term.

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3 years ago

Which graph most closely models the data in the table

Evgesh-ka [11]

I think the answer is Graph A

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3 years ago

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Moises is determining the solution to the system of equations that is show below. Equation representing line A: mc018-1.jpg Poin

dimulka [17.4K]

Answer:
equation of line is:
y = -2x - 6

Explanation:
The general form of the line is:
y = mx + c
where:
m is the slope of the line
c is the y-intercept

(a) getting the slope of the line:
slope of the line is calculated using the following rule:
slope of line (m) = (y2-y1) / (x2-x1) = (-24--12) / (9-3) = -2
The equation now becomes:
y = -2x + c

(b) getting the y-intercept:
The two given points belong to the line. Therefore, to get the y-intercept, we will use one of the points and substitute in the equation and solve for c.
I will use the point (3,-12)
y = mx + c
-12 = -2(3) + c
-12 = -6 + c
c = -12 + 6
c = -6

Based on the above, the equation of the line is:
y = -2x - 6

Hope this helps :)

6 0

3 years ago

Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

3 years ago

Read 2 more answers

Cindy has 6 identical pink candies and 8 identical green candies. Find the number of ways that Cindy can line up her candies in

Daniel [21]

Answer:

175 ways

Step-by-step explanation:

Form a partition into 2 or 3 parts and the number of ways.

Pink candies

[1,5](2) , [2,4](2) , [3,3](1) , [1,4](3), [1,2,3](6) , [2,2,2](1)

Green candies

[1,7](2) , [2,6](2) , [3,5](2) , [4,4](1) , [1,1,6](3) , [1,2,5](6) , [1,3,4](6) , ,[2,2,4](3) , [2,3,3](3)

Number of ways will be:

(2+2+1) (2+6+6+3+3) + (3+6+1)(2+2+2+1)

Number of ways =( 5×21) + (10×7) = 175ways

4 0

3 years ago