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2 years ago

Need help l don’t understand

Mathematics

2 answers:

andreyandreev [35.5K]2 years ago

8 0

Answer:

x = 12

Step-by-step explanation:

9(x - 11) = 9 ( divide both sides by 9 )

x - 11 = 1 ( add 11 to both sides )

x = 12

Diano4ka-milaya [45]2 years ago

6 0

Step-by-step explanation:

open brackets and work out

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I need help with 2,3 and 6! Please Help!

Georgia [21]

2. If you already know Faulhaber's formula, which says

$\displaystyle\sum_{k=1}^nk^2=\dfrac{n(n+1)(2n+1)}6$

then it's just a matter of setting $n=4$ . If you don't, then you can prove that it works (via induction), or compute the sum by some other means. Presumably you're not expected to use brute force and just add the squares of 1 through 4.

Just to demonstrate one possible method of verifying the formula, suppose we start from the binomial expansion of $(k-1)^3$ , do some manipulation, then sum over $1\le k\le n$ :

$(k-1)^3=k^3-3k^2+3k-1$
$\implies k^3-(k-1)^3=3k^2-3k+1$
$\implies\displaystyle\sum_{k=1}^n(k^3-(k-1)^3)=\sum_{k=1}^n(3k^2-3k+1)$

The left side is a telescoping series - several terms in consecutive terms of the series will cancel - and reduces to $n^3$ . For example,

$\displaystyle\sum_{k=3}^2(k^3-(k-1)^3)=(1^3-0^3)+(2^3-1^3)+(3^3-2^3)=3^3$

Distributing the sum on the right side across each term and pull out constant factors to get

$\displaystyle n^3=3\sum_{k=1}^nk^2-3\sum_{k=1}^nk+\sum_{k=1}^n1$

If you don't know the formula for $\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2$ , you can use a similar trick with the binomial expansion $(k-1)^2$ , or a simpler trick due to Gauss, or other methods. I'll assume you know it to save space for the other parts of your question. We then have

$\displaystyle n^3=3\sum_{k=1}^nk^2-\frac{3n(n+1)}2+n$
$\implies\displaystyle\sum_{k=1}^nk^2=\dfrac{n(n+1)(2n+1)}6$

and when $n=4$ we get 30.

3. Each term in the sum is a cube, but the sign changes. Recall that $(-1)^n$ is either 1 if $n$ is even or -1 if $n$ is odd. So we can write

$1^3-2^3+3^3-4^3+5^3=\displaystyle\sum_{k=1}^5(-1)^{k-1}k^3$

( $k+1$ as the exponent to -1 also works)

6. If $0\le k\le n$ , and $i=k+1$ , then we would get $1\le k+1\le n+1\iff1\le i\le n+1$ . So the sum with respect to $i$ is

$\displaystyle\sum_{k=0}^n\frac{k^2}{k+n}=\sum_{i=1}^{n+1}\frac{(i-1)^2}{i+n-1}$

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3 years ago

Find the X intercept show work

Natali [406]

Answer = D; 1, -5

i’m not sure how to explain it, sorry!

5 0

3 years ago

While dining at yet another 5 star restaurant, which is my normal, I received the bill for $95.11 which by the way included an a

viktelen [127]

Answer:

$16.54

Step-by-step explanation:

First step we need to do is to find the bill without the 15% tips:

95.11 = 1.15x

x = $82.70 is the original bill

Now we can add the 20% tips and multiply it into the original:

82.70 x 1.2 = $99.24 is the new bill

To find out how much you tipped:

99.24 - 82.7 = $16.54 is your new tip

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4 years ago

Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The

sattari [20]

Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) $\sqrt{\frac{pq}{n} }$

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value ± 1.28.

We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) $\sqrt{\frac{pq}{n} }$

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 $\sqrt{\frac{0.8*0.2}{200} }$

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region we reject the null hypothesis.

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3 years ago

What is the length of side x,y, and z

Bezzdna [24]

Answer:

X = $\sqrt{2}$ , Y = 3 , Z = 10

Step-by-step explanation:

using Pythagoras' identity in all 3 right triangles

X² = 1² + 1² = 1 + 1 = 2 ( take square root of both sides )

X = $\sqrt{2}$

middle triangle

Y² = 1² + X² = 1 + ( $\sqrt{2}$ )² = 1 + 2 = 3

triangle on right

Z² = 1² + Y² = 1 + 3² = 1 + 9 = 10

4 0

2 years ago