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Semenov [28]
3 years ago
5

Which ordered pair is a solution of the equation

Mathematics
1 answer:
andrew11 [14]3 years ago
4 0
(0,-7)
-7=11(0)+4
-7=0+4
-7 is not 4 -----not a solution

(-1,-7)
-7=11(-1)+4
-7=-11+4
-7=-7 ----solution

(1,-7)
-7=11(1)+4
-7=11+4
-7=15
-7 is not 15 ----not a solution

(2,26)
26=11(2)+4
26=22+4
26=26 ----soltion

(-1, -7) & (2, 26) are solutions to the equation
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The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard
dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{106.8 - 104}{2}

Z = 1.4

Z = 1.4 has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

8 0
3 years ago
Keisha had $54 when she went to a bookstore. She
storchak [24]
54 - a = 12 i believe
4 0
3 years ago
Read 2 more answers
I'm stuck on algebra.
Rainbow [258]
Point slope form : y-y1 = m(x-x1)
slope intercept form : m=(y-y1)/(x-x1)
standard form : Ax + By = C

just pick any random points on a graph and plug the same points into all three forms.
7 0
3 years ago
Read 2 more answers
A rectangle has an area of 19.38 cm2. When both the length and width of the rectangle are increased by 1.50 cm, the area of the
Lostsunrise [7]

Answer: 5.7\ cm

Step-by-step explanation:

Given

Rectangle has an area of 19.38\ cm^2

Suppose rectangle length and width are l and w

If each side is increased by 1.50\ cm

Area becomes A_2=35.28\ cm^2

We can write

\Rightarrow lw=19.38\quad \ldots(i)\\\\\Rightarrow (l+1.5)(w+1.5)=35.28\\\Rightarrow lw+1.5(l+w)+1.5^2=35.28\\\text{use (i) for}\ lw\\\Rightarrow 19.38+1.5(l+w)=35.28-2.25\\\Rightarrow l+w=9.1\quad \ldots(ii)

Substitute the value of width from (ii) in equation (i)

\Rightarrow l(9.1-l)=19.38\\\Rightarrow l^2-9.1l+19.38=0\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{(-9.1)^2-4(1)(19.38)}}{2\times 1}\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{5.29}}{2}\\\\\Rightarrow l=\dfrac{9.1\pm2.3}{2}\\\\\Rightarrow l=3.4,\ 5.7

Width corresponding to these lengths

w=5.7,\ 3.4

Therfore, we can write the length of the longer side is 5.7\ cm

8 0
3 years ago
PLEASE HELP FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!ASAP
AveGali [126]

Answer:

x=2.50

Step-by-step explanation:

But I am not sure if its positive or negative.

6 0
3 years ago
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