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Bad White [126]
3 years ago
10

Sue wrote a doubles fact. It has a sum less than 10 and greater than 4. The addends are each less than 5. What fact might she ha

ve written?
Mathematics
1 answer:
harina [27]3 years ago
6 0
2×4=8 because 2 and 4 would be the addends and their less than 5 and it equal an answer between 4 and 10
You might be interested in
Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combination value of $8.85. How many of each
stepan [7]

Answer: he has 32 quarters and 17 nickels.

Step-by-step explanation:

The worth of a quarter is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of quarters that he has in her wallet.

Let y represent the number of nickels that she has in her wallet.

He has 49 coins total. This means that

x + y = 49

the total value of the coins is $8.85. This means that

0.25x + 0.05y = 8.85 - - - - - - - - - - 1

Substituting x = 49 - y into equation 1, it becomes

0.25(49 - y) + 0.05y = 8.85

12.25 - 0.25y + 0.05y = 8.85

- 0.25y + 0.05y = 8.85 - 12.25

0.2y = 3.4

y = 3.4/0.2

y = 17

x = 49 - y = 49 - 17

x = 32

7 0
2 years ago
A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha
8_murik_8 [283]
To model this situation, we are going to use the decay formula: A=Pe^{rt}
where 
A is the final pupolation
P is the initial population 
e is the Euler's constant
r is the decay rate 
t is the time in years

A. We know for our problem that the initial population is 1,250, so P=1250; we also know that after a year the population is 1000, so A=1000 and t=1. Lets replace those values in our formula to find r:
A=Pe^{rt}
1000=1250e^{r}
e^{r}= \frac{1000}{1250}
e^{r}= \frac{4}{5}
ln(e^{r})=ln( \frac{4}{5} )
r=ln( \frac{4}{5} )
r=-02231

Now that we have r, we can write a function to model this scenario:
A(t)=1250e^{-0.2231t}.

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C. 
- The function is decreasing
- The function doe snot have a x-intercept 
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0: 
A(0)=1250e^{(-0.2231)(0)
A_{0}=1250e^{0}
A_{0}=1250
- Over the interval [0,10], the function will have a minimum at t=10:
A(10)=1250e^{(-0.2231)(10)
A_{10}=134.28

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: m= \frac{A(0)-A(10)}{10-0}
where 
m is the rate of change 
A(10) is the function evaluated at 10
A(0) is the function evaluated at 0
We know from previous calculations that A(10)=134.28 and A(0)=1250, so lets replace those values in our formula to find m:
m= \frac{134.28-1250}{10-0}
m= \frac{-1115.72}{10}
m=-111.572
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0
2 years ago
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
2 years ago
Paul plans to buy a movie that has a regular price of $19.99. It is on sale for 25% off, but Paul will have to pay 6% sales tax.
d1i1m1o1n [39]

Answer:

16.00

Step-by-step explanation:

19.99 - 25% + 6% = 15.89 =16.00

8 0
2 years ago
What does a rational number plus an irrational number equal?
galben [10]
The sum must be irrational in contradiction to it being rational
3 0
2 years ago
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