If 3 is added to the absolute value of the product of a number and –9, the result is 4.
1 answer:
Answer:
± (1 ÷ 9)
Step-by-step explanation:
Data provided in the question
Since 3 is added to the absolute value and -9
The result is 4
Now this information should be transformed in a mathematical equation
Let us assume be x so the product of the number and -9 be -9x
Fo rthe absolute value we use the mode. Thus the required expression is:
3 + |-9x|
Given that the result is 4
So, it would be
3 + |-9x| = 4
Now Solving the above equation which is given below:
|-9x| = 4-3
|-9x| = 1
here we will remove the mode by introducing ± sign which is shown below:
-9x = ± 1
-9x = 1 or -9x = -1
x = -1/9
or
x =
Therefore, the value of x is ± (1 ÷ 9).
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Answer:
Step-by-step explanation:
Hello!
For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.
In this example the variable is:
X: height of a college student. (cm)
There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.
The option you have is to apply the Central Limit Theorem.
The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.
As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.
The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:
X[bar]~~N(μ;σ2/n)
Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:
98% CI
1 - α: 0.98
⇒α: 0.02
α/2: 0.01
X[bar] ±
174.5 ±
[172.22; 176.78]
With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].
I hope it helps!
Given:
The expression is:
To find:
The exponential notation for the given expression.
Solution:
We know that
...(i)
We have,
Using (i), the given expression can be written as:
Therefore, the exponential notation of the given expression is .
Since she runs 6 miles each day and there 7 days per week, you will have to multiply 6
times 7.
But since you have to use distributive properties, multiply like this (6)(7)
6 is equal to
Now turn 7 into a fraction, so its
Now multipy (6)(
)
Multiply the numerators, so its 7 * 13 which gives you 91 and multiply the denominators so its 1 * 2 which gives you 2.
Put that back into a fraction as
Divde it to change it to a mixed number and the answer is 45