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3 years ago

three times the sum of a number x and 3 is 10 plus twice the difference of the number x and another number y

Mathematics

1 answer:

Nadya [2.5K]3 years ago

4 0

Step-by-step explanation:

We have 3(x + 3) = 10 + 2(x - y).

=> 3x + 9 = 10 + 2x - y

=> x = 1 - y

=> y = 1 - x.

(Rewritting it as a mathematical statement is the 1st line)

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Sam read 60 pages, which is 3/4 of the book. How many pages are there in the book?

Elenna [48]

Divide the pages read by the portion read:

60/ 3/4 = 60 x 4/3 = 240/3 = 80

The book has 80 pages.

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3 years ago

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Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minute

valkas [14]

Solution :

We know that

$H_0: \mu_1 = \mu_2=\mu_3$

$H_1 :$ At least one mean is different form the others (claim)

We need to find the critical values.

We know k = 3 , N = 35, α = 0.05

d.f.N = k - 1

= 3 - 1 = 2

d.f.D = N - k

= 35 - 3 = 32

SO the critical value is 3.295

The mean and the variance of each sample :

Goust Jet red Cloudtran

$\overline X_1 =50.5$ $\overline X_2 =50.07143$ $\overline X_3 =55.71429$

$s_1^2=19.96154$ $s_2^2=14.68681$ $s_3^2=36.57143$

The grand mean or the overall mean is(GM) :

$\overline X_{GM}=\frac{\sum \overline X}{N}$

$=\frac{51+51+...+49+49}{35}$

= 52.1714

The variance between the groups

$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$

$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$

$=\frac{127.1143}{2}$

= 63.55714

The Variance within the groups

$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$

$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$

$=\frac{669.8571}{32}$

= 20.93304

The F-test statistics value is :

$F=\frac{s_B^2}{s_W^2}$

$=\frac{63.55714}{20.93304}$

= 3.036212

Now since the 3.036 < 3.295, we do not reject the null hypothesis.

So there is no sufficient evidence to support the claim that there is a difference among the means.

The ANOVA table is :

Source Sum of squares d.f Mean square F

Between 127.1143 2 63.55714 3.036212

Within 669.8571 32 20.93304

Total 796.9714 34

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3 years ago

0.3 of what number is 36

steposvetlana [31]

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2 years ago

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3 years ago

On Tuesday Conrad had 3 times as many sales as on Monday. On Wednesday, he had 9 times as many sales as on Monday. Over the thre

Vlad1618 [11]

Answer:

Conrad had 56 sales on Monday , 168 sales on Tuesday and 504 sales on Wednesday.

Step-by-step explanation:

Let x be the no. of sales on Monday

We are given that On Tuesday Conrad had 3 times as many sales as on Monday.

So, Conrad had sales on Tuesday = 3x

We are also given that On Wednesday, he had 9 times as many sales as on Monday.

So, Conrad had sales on Wednesday = 9x

Over the three days, he had a total of 728 sales

So, x+3x+9x=728

13x=728

$x=\frac{728}{13}$

x=56

Conrad had sales on Tuesday = 3x =3(56)=168

Conrad had sales on Wednesday = 9x=9(56)=504

Hence Conrad had 56 sales on Monday , 168 sales on Tuesday and 504 sales on Wednesday.

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3 years ago