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2 years ago

I will give Brainliest to whoever can get here first!

Mathematics

1 answer:

USPshnik [31]2 years ago

5 0

Answer:

The answers would be as follows:

Step-by-step explanation:

We can tell that the first two have an infinite number of solutions because when we try to solve, we get a true statement. The first one is done for you below.

-6x + 7 = -6x + 7 ------> Add 6x to both sides

7 = 7 (TRUE STATEMENT)

We can tell the next two have no solution due to the fact that they develop a false statement when trying to solve.

-3x + 7 = 3x + 7 ----> Subtract 7 from both sides

-3x = 3x ---> Divide by 3

-x = x (UNTRUE STATEMENT)

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What is 1 3/5 × 2 1/7

MakcuM [25]

Answer:

$\large\boxed{1\dfrac{3}{5}\times2\dfrac{1}{7}=3\dfrac{3}{7}}$

Step-by-step explanation:

Step 1:

Convert the mixed numbers to the improper fractions:

$1\dfrac{3}{5}=\dfrac{1\cdot5+3}{5}=\dfrac{8}{5}\\\\2\dfrac{1}{7}=\dfrac{2\cdot7+1}{7}=\dfrac{15}{7}$

Step 2:

We multiply the numbers remembering about simplifying:

$1\dfrac{3}{5}\times2\dfrac{1}{7}=\dfrac{8}{5\!\!\!\!\diagup_1}\times\dfrac{15\!\!\!\!\!\diagup^3}{7}=\dfrac{8\times3}{1\times7}=\dfrac{24}{7}=\dfrac{21+3}{7}=\dfrac{21}{7}+\dfrac{3}{7}=3\dfrac{3}{7}$

7 0

2 years ago

a pet store donated 50 pounds of food for adult dogs , puppies and cats to an animal shelter. 19 and 3/4 pounds was adult dog fo

ddd [48]

Answer: 10 3/8

Step-by-step explanation:

= 50 - 19 3/4 - 19 7/8

= 10 3/8

5 0

2 years ago

The thickness of the dictionary containing 350 pages is 15 mm. Find out the thickness of one page in mm.

damaskus [11]

Answer:

The thickness of each page of a 300-page novel is 3/20 cm. If the 2 covers are each 7/8 cm thick, find the total thickness of the book.

Well it seems to me that a 300 page novel only realy has 150 peices of paper to it.

odd pages on the front side and even pages on the back side.

24.25 cm : My goodness those pages are very think!

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Ten items are to be sampled from a lot of 60. If more than one is defective, the lot will be rejected. Find the probability that

stellarik [79]

Answer:

(a) The probability of that the lot will be rejected is 0.1904.

(b)The probability of that the lot will be rejected is 0.5315 .

(c)The probability of that the lot will be rejected is 0.7026.

Step-by-step explanation:

The formula of Hypergeometric distribution is

$P(X=x)=\frac{(^{R}C_x)( ^{N-R}C_{n-x})}{^NC_n}$

N= number of population

R= The number of success event

n= sample of size

(a)

Given that, N= 60, R=5 and n=10

More than 1 is defected, the lot will be rejected.

X is random variable and defined the number of rejected item.

P(X>1)=1-P(X≤1)

=1 - P(X=0) - P(X=1)

$=1- \frac{(^5C_0)(^{60-5}C_{10-0})}{^{60}C_{10}}-\frac{(^5C_1)(^{60-5}C_{10-1})}{^{60}C_{10}}$

=1 - 0.3879 - 0.4217

=0.1904

The probability of that the lot will be rejected is 0.1904.

(b)

N= 60, R=10 and n=10

X is random variable and defined the number of rejected item.

P(X>1)=1-P(X≤1)

=1 - P(X=0) - P(X=1)

$=1- \frac{(^{10}C_0)(^{60-10}C_{10-0})}{^{60}C_{10}}-\frac{(^{10}C_1)(^{60-10}C_{10-1})}{^{60}C_{10}}$

=1-0.1362-0.3323

=0.5315

The probability of that the lot will be rejected is 0.5315 .

(c)

N= 60, R=20 and n=10

X is random variable and defined the number of rejected item.

P(X>1)=1-P(X≤1)

=1 - P(X=0) - P(X=1)

$=1- \frac{(^{20}C_0)(^{60-20}C_{10-0})}{^{60}C_{10}}-\frac{(^{20}C_1)(^{60-20}C_{10-1})}{^{60}C_{10}}$

=1 -0.2249 - 0.0725

=0.7026

The probability of that the lot will be rejected is 0.7026.

4 0

2 years ago

Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are nor

evablogger [386]

Answer:

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the population mean for group 1 is significantly different than the population mean for group 2.

The 95% confidence interval is given by (0.756;7.243), since the interval not contain's the 0 we can reject the null hypothesis that the means are equal.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=76$ represent the mean for 1

$\bar X_{2}=72$ represent the mean for 2

$s_{1}=8$ represent the sample standard deviation for 1

$s_{2}=6.5$ represent the sample standard deviation for 2

$n_{1}=40$ sample size for the group 1

$n_{2}=40$ sample size for the group 2

$\alpha=0.05$ Significance level provided

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the population means differs, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}= 0$

Alternative hypothesis: $\mu_{1} - \mu_{2}\neq 0$

We don't have the population standard deviation's, we can apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$t=\frac{(76-72)-0}{\sqrt{\frac{8^2}{40}+\frac{6.5^2}{40}}}}=2.454$

P value

We need to find first the degrees of freedom given by:

$df=n_1 +n_{2}-2=40+40-2=78$

Since is a two tailed test the p value would be:

$p_v =2*P(t_{78}>2.454)=0.016$

Confidence interval

The critical value for this case can be calculated like this. $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are 78 so we can use this code in excel to find the critical value for the interval "=-T.INV(0.025,78)" and we got $t_{\alpha/2}=1.99$

The confidence interval for this case would be given by this formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}$

And if we replace the values given we have:

$(76 -72) - 1.99\sqrt{\frac{8^2}{40}+\frac{6.5^2}{40}}}=0.756$

$(76 -72) +1.99\sqrt{\frac{8^2}{40}+\frac{6.5^2}{40}}}=7.243$

The 95% confidence interval is given by (0.756;7.243), since the interval not contain's the 0 we can reject the null hypothesis that the means are equal.

5 0

3 years ago