Answer:
0.00658 = 6.58 * 10^-3
Step-by-step explanation:
The standard form is a way of writing numbers easily in powers of 10.
To write a number in standard form, we have to move the decimal point to the front of the first non zero number.
Depending on the position of the decimal point to the first non zero number, movement can be towards the right or towards the left. When we move towards the right, our power of 10 will be negative, when we move in the left direction, our power of 10 will be positive
In this question, we shall be moving towards the right. Thus, our power of 10 is negative. We shall be moving towards the right 3 three times
Thus our power would be 10^-3
Thus our standard form will be 6.58 * 10^-3
Kindly note that another pointer is, if the value of our number to be written in standard form is less than zero, then the standard form will come in negative powers of 10. If the value of the number is greater or equal to 1 at least, then then the standard form will be in positive powers of 10
Answer:
81.86%
Step-by-step explanation:
We are given that the mean GPA of students in a course at UC Davis is 3.2 with a standard deviation of 0.3.
Assuming that the data follows normal distribution.
Let X = GPA of students in a course at UC Davis
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean GPA = 3.2
= standard deviation = 0.3
Now, the probability that the students in the course have a GPA between 2.9 and 3.8 is given by = P(2.9 < X < 3.8)
P(2.9 < X < 3.8) = P(X < 3.8) - P(X 2.9)
P(X < 3.8) = P( < ) = P(Z < 2) = 0.97725
P(X 2.9) = P( ) = P(Z -1) = 1 - P(Z < 1)
= 1 - 0.84134 = 0.15866
The above probability is calculated by looking at the value of x = 2 and x = 1 in the z table which has an area of 0.97725 and 0.84134 respectively.
Therefore, P(2.9 < X < 3.8) = 0.97725 - 0.15866 = 0.8186
Hence, 81.86% of students in the course have a GPA between 2.9 and 3.8.
2x+7x=747
9x=747
x=83
83(2) = 166
83(7) = 581
Answer:
39.5 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.
Tan = Opposite/Adjacent
This lets us write two equations in two unknowns:
tan(67°) = AD/CD . . . . . . . . . . angle at guy point
tan(39°) = AD/(CD+32) . . . . . .angle 32' farther
__
Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.
CD = AD/tan(67°)
tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation
tan(39°)(AD/tan(67°) +32) = AD
32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term
32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient
AD ≈ 39.486 . . . . feet
The tower is about 39.5 feet high.
