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3 years ago

Find three consecutive integers whose sum is 558

1 answer:

8 0

Those are 185, 186 and 187

What you do is create this system of equations:

x+y+z=558 (three integers add up to 558)
x+1=y (they are consecutive, so that is translated as a number+1)
y+1=z (same logic as before)

And then you just resolve that system.

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Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the

SpyIntel [72]

You didn’t give us the circle lol

5 0

2 years ago

A psychologist obtains a random sample of 2020 mothers in the first trimester of their pregnancy. The mothers are asked to play

leva [86]

Answer:

First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.

In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.

According to the problem, the null hypothesis must be: $H_{o} : u = 100$ ; because it says that 100 is the normal mean that is used.

The alternative hypothesis must be: $H_{a} : u > 100$ ; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.

Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: $Z=\frac{x-u}{\frac{o}{\sqrt{n} } }$ ; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.

Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.

Applying all values to the formula: $Z=\frac{104.3 - 100}{\frac{14}{\sqrt{20} } } = \frac{4.3}{\frac{14}{ 4.5} }=\frac{4.3}{3.1}=1.4$

Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.

In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.

Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).

5 0

3 years ago

20 POINTS! Please help, best answer will recessive brainliest answer points as well as 5 stars and a thank you. :)

Vitek1552 [10]

Answer:

3): 14

Step-by-step explanation:

The problem states that ABC and DEF are similar. Therefore, dsue to similar triangles, we have 7x/7=4/x, so x^2=4. Therefore, x=2 (because x cannot be negative). Therefore, AB = 7x = 7*2=14

6 0

3 years ago

A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.75 , with a standard

bulgar [2K]

Answer:

Following are the solution to the given choices:

Step-by-step explanation:

Using chebyshev's theorem :

$\to P(|(x-\mu)|\leq k \sigma)\geq 1- \frac{1}{k^2}\\\\here \\ \to \mu=28.75\\\\ \to \sigma=4.44$

In point a)

$\to |(x-\mu)|= |20.17-28.75|=8.58 and \sigma=4.44 \\\\so, \\k= \frac{ |(x-\mu)| }{\sigma}$

$= \frac{8.58}{4.44} \\\\ =1.9 \\\\ =2$

$value= (1- \frac{1}{k^2}) \times 100 \% =75\%$

In point b)

$\to (1- \frac{1}{k^2}) \times 100 \% =84\% \\\\\to (1- \frac{1}{k^2})=0.84 \\\\\to \frac{1}{k^2} =0.16 \\\\\to \frac{1}{k}=0.4\\\\ \to k=2.5 \\\\\to |(x-\mu)| \leq k \sigma \\\\= |(x-\mu)|\leq 2.5 \times 4.44 \\\\ = |(x-\mu)|\leq 1.11 \\\\ = (28.75\pm 11.1) \\\\\to \text{fares lies between}(17.65,39.85)$

In point c)

$\to 99.7 \% \\ lie \ between=28.75 \pm z(.03)\times \sigma \\\\ =28.75\pm 2.97 \times 4.44\\\\=(28.75\pm 13.1)\\\\=(15.65,41.85)\\$

In point d)

using standard normal variate

$x=20.17\\\\ z=-2 \\\\x=37.13\\\\ z=2\\\\\to P(20.17$

8 0

3 years ago

Use the definition mtan=lim

Leokris [45]

(a) mtan refers to the slope of the tangent line. Given f(x) = 9 + 7x ², compute the difference quotient:

$\dfrac{f(x+h)-f(x)}h = \dfrac{(9+7(x+h)^2)-(9+7x^2)}h = \dfrac{(9+7x^2+14xh+7h^2)-9-7x^2}h = \dfrac{14xh+7h^2}h$

Then as h approaches 0 - bearing in mind that we're specifically considering h near 0, and not h = 0 - we can eliminate the factor of h in the numerator and denominator, so that

$m_{\rm tan} = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{14xh+7h^2}h = \lim_{h\to0}(14x+7h) = 14x$

and so the slope of the line at P (0, 9), for which we take x = 0, is 0.

(b) The equation of the tangent line is then y = 9.

4 0

2 years ago