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Ad libitum [116K]

3 years ago

6

joe spent $68 on shirts. Tee shirts cost $2 and long sleeve shirts cost $14. If he bought a total of 10, then how many of each k

ind did he buy?

1 answer:

Ulleksa [173]3 years ago

4 0

The answer will be 84 because your just adding all of it together

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Fine the exact value. <br> tan(60°)+tan(225°)

Harman [31]

$1+ \sqrt{3}$
tangent 60 is √3 on the unit circle and tangent 225 is 1. So 1+√3 is the exact value of tan 60 plus tan 225

7 0

3 years ago

Read 2 more answers

Factor by grouping (sometimes called the ac-method).

lesya692 [45]

Answer:

Step-by-step explanation:

The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.

Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything. Now, a = 8, b = 2 and c = -3. a*c = -24 so now we want to find all the factors of that.

-1 and 24

1 and -24

-2 and 12

2 and -12

-3 and 8

3 and -8

-4 and 6

4 and -6

And after that they repeat. It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be and 12 as well as -1 and -12.

Now we want to look at all the factor pairs and find one that add together to equal 2 because b = 2. -4 + 6 does it, so there's our choice. Now we can rewrite the original quadratic as 8x^2-4x+6x-3. You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3. Anyway, now we can factor.

8x^2-4x+6x-3 You can imagine there being two sets of parenthesis.

( 8x^2-4x)+(+6x-3) Now from here we can factor something out of each parenthesis. e can factor out 4x fromt he first and 3 from the second.

4x(2x-1)+3(2x-3) Now, it may not be obvious but you can factor 2x-3 from each term. If that's not clear pretend 2x-3 = u

4xu + 3u Now hopefully it is clear you can factor out this u

u(4x+3) Then we know u = 2x-3 so

(2x-3)(4x+3) And it's factored.

I do want to mention you could have done this with 8x^2+6x-4x-3 with the +6 and -4 switched. I won't go through it here but it may help to do it yourself if you still don't quite understand. Let me know if there is something I can further explain though.

3 0

3 years ago

Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of

forsale [732]

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

$n = 120, \pi = \frac{58}{120} = 0.4833$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001$

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

8 0

3 years ago

1) The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x-3 and g(x) = 3x+8. Find f(x) multiplied by g(x). 2

Elena-2011 [213]

Answer:

1)6x^2+7x-24

2) x-4

3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7

f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15

4)f'(x)=(x-7)/3

Step-by-step explanation:

1) f(x)=2x-3 g(x)=3x+8

f(x)*g(x)=m(x)=(2x-3)(3x+8)=6x^2+16x-9x-24=6x^2+7x-24

2) f(x)=x^2+x-20 g(x)=x+5

f(x)/g(x)=p(x)=(x^2+x-20)/(x+5)=> by finding the roots of f(x) we obtain =

(x-4)(x+5)/(x+5)--->f(x)/g(x)=p(x)=(x-4)

3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7

f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15

4) If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back x

y=3x+7

(y-7)/3=x=--> f'(x)=(x-7)/3

3 0

4 years ago

I NEED HELP ASAP

beks73 [17]

The answer is in the attached picture.

6 0

4 years ago