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3 years ago

Find the value of a and b when x=12

Mathematics

2 answers:

BigorU [14]3 years ago

8 0

Step-by-step explanation:

$a = \frac{ 5{x}^{2} }{2} = 360 \\ b = \frac{2 {x}^{2}( x - 5) }{10x}$

a =

$\frac{5( {12}^{2} )}{2} = 360 = a \\ \frac{5(144)}{2} = 360 = a \\ 5(72) = 360 = a \\ a = 360$

b =

$b = \frac{2 {x}^{2} (x - 5)}{10x} \\ b = \frac{x(x - 5)}{5 } \\ b = \frac{ {x}^{2} - 5x}{5} \\ b = \frac{ {12}^{2} - 5(12) }{5} \\ b = \frac{144 - 60}{5} \\ b = \frac{84}{5} \\ b = 16.8$

garri49 [273]3 years ago

5 0

A= 360
B= 2(12)²(7)/120= 2016/120=16.8

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Add 5/9+7/9 . Simplify the answer and write a mixed number

Step2247 [10]

Hello there!

First you had to solving by the fractions parts.

$\frac{5}{9}+\frac{7}{9}=\frac{12}{9}$

Then you reducing by the fraction parts of 12/9.

$\frac{12}{9}=\frac{4}{3}$

And finally, you simplify by the fraction parts of 4/3.

$\frac{4}{3}=1 \frac{1}{3}$

Solution by Formulas

Applying the fractions formula for addiction.

$\frac{(5*9)+(7*9)}{9*9}$

$\frac{45+63}{81}$

$=\frac{108}{81}$

Simplifying 108/81 and the answer is

$=1 \frac{1}{3}$

Hope this helps!

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4 years ago

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Lester divided his grapes evenly among himself and four friends write an expression to represent the number of grapes each perso

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To represent the number of grapes each person received using an algebraic expression, you will think of what is happening mathematically and use a variable to represent any unknown value.

x/5 would be the expression where x stands for the number of grapes Lester starts with.

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3 years ago

The graph shows two polygons ABCD and A′B′C′D′.

stellarik [79]

Answer:

Translate ABCD down 1, then reflect it over the y-axis

and

Reflect ABCD over the y-axis, then translate down 1

Step-by-step explanation:

First of all, the two steps are the same, just in a different order

Second, if you look at the instructions you can see what would happen to the quadrilateral. Reflecting over the y-axis would make the shape flip horizontally (left to right), as shown in the image. This means the points on the left move to the right, and the points on the right move to the left. Top and bottom points stay the same. And the "translation" just means to slide. In both the answers, it says "translate 1 unit down", which just means "move 1 unit down", which is exactly what happens in the image

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3 years ago

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2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of

IgorC [24]

Answer:

a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., $\mu$ = 35 and $\sigma$ = 6. We know that the probability density function for a normal distribution with a mean of $\mu$ and a standard deviation of $\sigma$ is given by

$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]$

in this case we have

$f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]$

Let $X$ be the random variable that represents a row score, we find the values we are seeking in the following way

a) we are looking for a number $x_{0}$ such that

$P(X\leq x_{0})$ = $\int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65$ , this number is $x_{0}$ =37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number $x_{1}$ such that

$P(X\leq x_{1})$ = $\int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9$ , this number is $x_{1}$ =42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

$P(28\leq X\leq 38)$ = $\int\limits^{38}_{28} {f(x)} \, dx = 0.57$

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

$P(41\leq X\leq 44)$ = $\int\limits^{44}_{41} {f(x)} \, dx = 0.09$

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

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4 years ago

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swat32

Answer:

0.006 is the probability that the record will be broken in next year.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 62 seconds

Standard Deviation, σ = 0.8 seconds

We are given that the distribution of face time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

The record will be broken if the time is less than 60 seconds.

P(time is less than 60 seconds)

P(x < 60)

$P( x < 60) = P( z < \displaystyle\frac{60 - 62}{0.8}) = P(z < -2.5)$

Calculation the value from standard normal z table, we have,

$P(x < 60) =0.006 = 0.6\%$

Thus, 0.006 is the probability that the record will be broken in next year.

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3 years ago