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noname [10]
3 years ago
9

If the gradient of a line joining the points (-2, 6) and (5, b) is 14. Find the value of b.

Mathematics
1 answer:
babunello [35]3 years ago
3 0

Answer:

b = 104

Step-by-step explanation:

Slope is expressed as;

m = y2-y1/x2-x1

14 = b - 6/5-(-2)

14 = b - 6/5+2

14 = b-6/7

Cross multiply

b-6 = 14 * 7

b - 6 = 98

b  = 98 + 6

b = 104

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Solve the expression and find the value of x.
vovangra [49]

\large\underline{\sf{Solution-}}

\sf \dfrac{x + 1}{10}  -  \dfrac{3(x - 1)}{5}  = 2

\sf\longmapsto  \dfrac{x + 1}{10}  -  \dfrac{3x - 3}{5}  = 2

\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10}   = 2

\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10}  = 2

\sf\longmapsto  \dfrac{x + 1 - 6x + 6}{10}  = 2

\sf\longmapsto \dfrac{ - 5x + 7}{10}  = 2

\sf\longmapsto - 5x + 7 = 20

\sf\longmapsto - 5x = 20 - 7

\sf\longmapsto - 5x = 13

\sf\therefore x =  -  \dfrac{13}{5}

Hence, the value of x will be -13/5 respectively.

7 0
3 years ago
Read 2 more answers
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars
velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

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 normal distributions can be 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that \mu = 965, \sigma = 113

Sample of 57:

This means that n = 57, s = \frac{113}{\sqrt{57}} = 14.97

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

Z = \frac{972.5 - 965}{14.97}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

X = 939.6

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

Z = \frac{939.6 - 965}{14.97}

Z = -1.7

Z = -1.7 has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

3 0
2 years ago
The ground temperature at an airport is 12 °C. The temperature decreases by 5.4 °C for every increase of 1 kilometer above the g
olga_2 [115]

Decrease in the temperature: 5.4×5=27°C

Final temperature: 12-27=-15°C

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3 years ago
Lin took 75 boxes of carrots and 80 boxes of potatoes to the market. She sold 68 boxes of carrots and 71 boxes of potatoes. How
Lady bird [3.3K]

Answer:

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Step-by-step explanation:

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3 years ago
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Help plz will mark brainliest........................
fredd [130]
It would be HL=I !!!!!!!!!!!!!!!!!!!! 
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