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makvit [3.9K]
3 years ago
11

You can represent an odd integer whith the expression 2n+1, where n is any integer . Write and solve an equation to find three c

onsecutive odd that have a sum of 63
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0
Any odd number can be expressed by 2n+1.

For example,  

2n+1=111
2n=110
n=110/2=55

means that 111 is 2n+1 for n=55


Thus if an odd number is 2a+1, the next few numbers are as follows:

2a+1, 2a+2, 2a+3, 2a+4, 2a+5

So 2a+1, 2a+3 and 2a+5 are 3 consecutive odd numbers.


Back to our problem: 

three consecutive odd numbers whose sum is 63 are:

(2n+1)+(2n+3)+(2n+5)=63

6n+9=63

6n=63-9=54

n=54/6=9


2n+1=2*9+1=18+1=19, the 2 next odd numbers are 21 and 23


Answer: 19, 21, 23



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A Rasmussen Reports survey of 1,000 US adults found that 42% believe raising the minimum wage will help the economy. Construct a
vitfil [10]

Answer:

(0.3798, 0.4602)

Step-by-step explanation:

Let p be the true proportion of US adults who believe raising the minimum wage will help the economy. A point estimate for p is \hat{p}=0.42 and a good aproximation (because we have a large sample) for the standard deviation of \hat{p} is \sqrt{\hat{p}(1-\hat{p})/n}=\sqrt{0.42(0.58)/1000}=0.0156. Therefore, a 99% confidence interval for p is given by \hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} where \alpha=0.01 and z_{\alpha/2} is the \alpha/2th quantile of the standard normal distribution, so we have, 0.42\pm z_{0.005}0.0156, i.e., 0.42\pm(-2.5758)(0.0156) or equivalently (0.3798, 0.4602).

6 0
3 years ago
After John worked at a job for 10 years, his salary doubled. If he started at $x, his salary after 10 years is _____.
VARVARA [1.3K]
After ten years his salary is x2
6 0
3 years ago
Read 2 more answers
write 6.847 in word form is the answer 6 + 0.8 + 0.04 + 0.007 or do they want six and eight hundred and 47 thousandths?
Alex787 [66]

Answer:

six and eight hundred fourty-seven thousandths

Step-by-step explanation:

6 + 0.8 + 0.04 + 0.007 is called extended form, six and eight hundred fourty-seven thousandths is called word form.

4 0
3 years ago
If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)
krok68 [10]

Tan(x-\frac{\pi }{4}) = \frac{-17}{31}

<u>Step-by-step explanation:</u>

Here we have ,  sin ⁡x=7/25( given sin x = 725 which is not possible ) , 0 . Let's find tan (x - pi/4):

⇒ Tanx = \frac{sinx}{cosx}

⇒ Tanx = \frac{sinx}{\sqrt{1-(sinx)^{2}}}

⇒ Tanx = \frac{\frac{7}{25}}{\sqrt{1-(\frac{7}{25})^{2}}}

⇒ Tanx = {\frac{7}{25}}{\sqrt{(\frac{625}{625-49})^{}}}

⇒ Tanx = {\frac{7}{25}}(\frac{25}{24} )

⇒ Tanx = {\frac{7}{24}}

Now , Tan(x-\frac{\pi }{4}) = \frac{Tanx - Tan(\frac{\pi }{4} )}{1+ Tanx(Tan(\frac{\pi }{4} )}

⇒ Tan(x-\frac{\pi }{4}) = \frac{Tanx -1}{1+ Tanx(1)}

⇒ Tan(x-\frac{\pi }{4}) = \frac{\frac{7}{24}  -1}{1+\frac{7}{24} }

⇒ Tan(x-\frac{\pi }{4}) = \frac{\frac{7-24}{24} }{\frac{7+24}{24} }

⇒ Tan(x-\frac{\pi }{4}) = \frac{-17}{24} (\frac{24}{31} )

⇒ Tan(x-\frac{\pi }{4}) = \frac{-17}{31}

7 0
3 years ago
PLEASE HELP PLA
aleksley [76]

Answer:

y = -x+8

Step-by-step explanation:

The side that is parallel to BC is EF

Find the slope of EF:

m = \frac{2-4}{6-4} =\frac{-2}{-2} =-1

Easiest way is just put the formula in point-slope form and simplify.

Let's use point F, which is (6,2)

y -2=-(x-6)

Simplify:

y-2=-x+6

Add 2 on both sides:

y = -x+8

Hope this helped

5 0
2 years ago
Read 2 more answers
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