You are constructing a box for your cat to sleep in. The plush material for the square bottom of the box costs $7/ft2 and the ma
2 answers:
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Remember:
-When multiplying numbers with decimals just forget about the decimals for a second and pretend you are multiplying a 3 digit number times a 2 digit number.
-one digit at a time. Multiply going from right to left.
First:
-Multiply the 3 with the top numbers.
-Pretend you are seeing this:
5.72 (3)
- 2*3=6. 7*3=21. (carry the 2). 5*3 +2=17. (leave the 1).
Second:
-write below and move a digit to the left.
-pretend you are seeing this: 5.72(6).
- 2*6 =12. (carry the 1). 7*6 +1=43. (carry the 4) 5*6+4=34. (leave the 3).
Third: since in the problem the decimal is placed in the hundredths only once, place the decimal in the hundredths as your solution.
Your solution should be 360.36
Answer:
And the p value would be given by:
And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
System of hypotheses.
We need to conduct a hypothesis in order to check if the true mean is 33.7 mpg or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
And the p value would be given by:
And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.
By factorizing, we have
so that
or
Answer:
The simplest form is x/(x + 3)
Step-by-step explanation:
* To simplify the rational Expression lets revise the factorization
of the quadratic expression
* To factor a quadratic in the form x² ± bx ± c:
- First look at the c term
# If the c term is a positive number, and its factors are r and s they
will have the same sign and their sum is b.
# If the c term is a negative number, then either r or s will be negative
but not both and their difference is b.
- Second look at the b term.
# If the c term is positive and the b term is positive, then both r and
s are positive.
Ex: x² + 5x + 6 = (x + 3)(x + 2)
# If the c term is positive and the b term is negative, then both r and s
are negative.
Ex: x² - 5x + 6 = (x -3)(x - 2)
# If the c term is negative and the b term is positive, then the factor
that is positive will have the greater absolute value. That is, if
|r| > |s|, then r is positive and s is negative.
Ex: x² + 5x - 6 = (x + 6)(x - 1)
# If the c term is negative and the b term is negative, then the factor
that is negative will have the greater absolute value. That is, if
|r| > |s|, then r is negative and s is positive.
Ex: x² - 5x - 6 = (x - 6)(x + 1)
* Now lets solve the problem
- We have two fractions over each other
- Lets simplify the numerator
∵ The numerator is
- Factorize its denominator
∵ The denominator = x² + 2x - 3
- The last term is negative then the two brackets have different signs
∵ 3 = 3 × 1
∵ 3 - 1 = 2
∵ The middle term is +ve
∴ -3 = 3 × -1 ⇒ the greatest is +ve
∴ x² + 2x - 3 = (x + 3)(x - 1)
∴ The numerator =
- Lets simplify the denominator
∵ The denominator is
- Factorize its denominator
∵ The denominator = x² - 2x
- Take x as a common factor and divide each term by x
∵ x² ÷ x = x
∵ -x ÷ x = -1
∴ x² - 2x = x(x - 1)
∴ The denominator =
* Now lets write the fraction as a division
∴ The fraction = ÷
- Change the sign of division and reverse the fraction after it
∴ The fraction =
* Now we can cancel the bracket (x + 2) up with same bracket down
and cancel bracket (x - 1) up with same bracket down
∴ The simplest form =