Answer:
2.74 microns
Step-by-step explanation:
According to the given situation, the calculation of position, in microns, is shown below:-
Here we will use the standard normal table,
P(Z > z) = 20%
1 - P(Z < z) = 0.2
P(Z < z) = 1 - 0.2
P(Z < 0.84) = 0.8
after solving the above equation we will get
z = 0.84
Now we will use the z-score formula,
[tex]x = z \times \sigma + \mu[/tex]
[tex]x = 0.84 \times 0.35 + 2.45[/tex]
x = 0.294 + 2.45
= 2.744 microns
or
= 2.74 microns
______ income is gross income minus taxes and deductions. fill in the blank
Answer:
Net
Step-by-step explanation:
The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.
A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)
Answer: 82 sq. units .
Step-by-step explanation:
Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.
Then we plot them on graph ( as provided in attachment)
Length = AB [tex]=\sqrt{(9+1)^2+(-1-7)^2}[/tex] units [By distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]]
[tex]=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}[/tex] units
Width = BC = [tex]\sqrt{(-1+5)^2+(7-2)^2}[/tex] units
[tex]=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}[/tex]
Area = length x width
= [tex]2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}[/tex]
Hence, the area of the rectangle is 82 sq. units .
Edward walks at a pace 2 1/4 miles in 2/3 hour. How many miles does Edward walk per hour
Divide distance walked by time:
2 1/4 miles / 2/3 hours = 3 3/8 miles per hour
Tim and Nikko bought new computers. Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer. The total amount that Tim and Nikko spent for their computers was $2,870. How much did Nikko spend for his computer?
A. $1,181.00
B. $1,407.50
C. $1,689.00
D. $1,755.00
Answer:
C. $1,689.00Step-by-step explanation:
Let the amount spent by Tim be x and the amount spent by Nikko be y
If Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer, then amount spent by Tim will be x = 55+2/3 y
Since the total amount that Tim and Nikko spent for their computers was $2,870 then;
x+y = $2,870
Substituting x = 55+2/3y into the equation above, we will have;
55+2y/3 + y = 2,870
(165 + 2y)/3 + y = 2,870
(165 + 2y+3y)/3 = 2,870
cross multiply
165 + 2y+3y = 3*2870
165+5y = 8610
5y = 8610-165
5y = 8445
y = 8445/5
y = 1689
Hence Nikko spent a sum of $1,689.00 on his computer.
Answer this pleaseeeeeeeee
Answer:
.= 157
Step-by-step explanation:
There are three clock summing up to 21
One clock=21/3
One clock= 7
There are three calculator summing up to 30
One calculator= 30/3
One calculator= 10
There are three light bulb summing up to 15
One light bulb =15/3
One light bulb= 5
So the problem expression is
Clock +calculator *3bulb
= Clock +(calculator*3bulb)
= 7+(10*3(5))
= 7 +(10*15)
= 7 + 150
.= 157
A jar contains 100 ounces of lemonade. A spout at the bottom of the jar is opened and the lemonade pours out at a rate of 10 ounces per second. Which graph below represents the amount of lemonade in the jar for the first 15 seconds after the spout was opened?
Answer:
100 ounces(hope it help)
Step-by-step explanation:
because there is only 100 ounces in the jar.
Convert standard to slope-intercept forms. 1. Standard form: 10x − 7y = −8
Answer:
Step-by-step explanation:
-7y = -10x - 8
y = 10/7x + 8/7
(b-(a-a)) ÷ 3; use a = 6, and b = 3
Answer:
The answer is 1Step-by-step explanation:
(b-(a-a)) ÷ 3
a = 6 , b = 3
Substitute the values into the above formula
That's
[tex](3 - (6 - 6)) \div 3[/tex]
Using PEDMAS solve the terms in the bracket first
That's
[tex](3 - 0) \div 3[/tex]
We have
3 ÷ 3
The final answer is 1Hope this helps you
Use the quadratic formula to solve the equation: 0 = x2 + x - 20
Answer:
(x-4)*(x+5) : x =4,-5
Step-by-step explanation:
a= 1
b= 1
c= -20
x1,2 = (-1+-(1 - (4*1*-20))^0.5)/2
x1,2 = (-1+-(1+80)^0.5)/2
x1,2 = (-1+-(81^0.5))/2
x1,2 =(-1+-9)/2
x1 = 8/2 = 4 x2 = -10/2 = -5
I=prt,for p please show step by step for this variable
Answer:
[tex] p = \dfrac{I}{rt} [/tex]
Step-by-step explanation:
I = prt
Switch sides.
prt = I
We are solving for p. We want p alone on the left side. p is being multiplied by r and t, so we divide both sides by r and t.
[tex] \dfrac{prt}{rt} = \dfrac{I}{rt} [/tex]
[tex] p = \dfrac{I}{rt} [/tex]
[tex]f(x) = {x}^{2} + 4x - 5[/tex]
when [tex]x > - 2[/tex]
find[tex] \frac{d {f}^{ - 1} }{dx} at \: x = 16[/tex]
Answer:
[tex] \dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10} [/tex]
Step-by-step explanation:
[tex] f(x) = x^2 + 4x - 5 [/tex]
First we find the inverse function.
[tex] y = x^2 + 4x - 5 [/tex]
[tex] x = y^2 + 4y - 5 [/tex]
[tex] y^2 + 4y - 5 = x [/tex]
[tex] y^2 + 4y = x + 5 [/tex]
[tex] y^2 + 4y + 4 = x + 5 + 4 [/tex]
[tex] (y + 2)^2 = x + 9 [/tex]
[tex] y + 2 = \pm\sqrt{x + 9} [/tex]
[tex] y = -2 \pm\sqrt{x + 9} [/tex]
[tex]f^{-1}(x) = -2 \pm\sqrt{x + 9}[/tex]
[tex]f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}[/tex]
Now we find the derivative of the inverse function.
[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}[/tex]
[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}[/tex]
Now we evaluate the derivative of the inverse function at x = 16.
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }[/tex]
[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}[/tex]
The following list is of 4 measurements.
There are four levels of measurement – nominal, ordinal, and interval/ratio – with nominal being the least precise and informative and interval/ratio variable being most precise and informative.
solve from here by understanding what i have write
Question 1 of 4
A statistics test was taken in Mrs. Everett's class. Some of the students were surveyed for their
scores and here are the results of that survey:
25 30 35 40 40 45 45 50 50 50
55 55 55 60 60 65 65 70 75 80
✓ What is the average score of the student surveyed? a. 55.5
b. 52.5
What is the median of the student's surveyed?
c. 20.0
d. 60.5
How many students were surveyed?
Answer:
1) What is the average score of the student surveyed?
b. 52.5
2) What is the median of the student's surveyed?
52.5
3) How many students were surveyed?
20 students
Step-by-step explanation:
1) What is the average score of the student surveyed?
Average score of the student's been surveyed means we should calculate the mean of the above scores
The formula for Mean = Sum of the number of terms/ Number of terms
Number of terms = 20
Average(Mean score) =
25 + 30 + 35 + 40 + 40 + 45 + 45 + 50 + 50 + 50 + 55 + 55 + 55 + 60 + 60 + 65 + 65 + 70 + 75 + 80/20
= 1050/20
= 52.5
2) What is the median of the student's surveyed?
25, 30, 35, 40, 40, 45, 45, 50, 50, 50, 55, 55, 55, 60, 60, 65, 65, 70, 75, 80
From the above data, we can see that 20 students were surveyed. To find the Median, we find the sum of the 10th value and the 11th value and we divide by 2
Hence,
25, 30, 35, 40, 40, 45, 45, 50, 50,) 50, 55, (55, 55, 60, 60, 65, 65, 70, 75, 80
10th value = 50
11th value = 55
Median = 50 + 55/2
= 105/2
= 52.5
3) How many students were surveyed?
Counting the results of the survey, the number of students that were surveyed = 20 students
como dividir ? ? . . .. . . .. . . .. . .. . . .. .
Answer:
What
Step-by-step explanation:
What Do You Mean Bro
The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown. However, records indicate that the mean time is 11.4 minutes and the standard deviation is 4.5 minutes.
a) To compute the probabilities regarding the sample mean using the normal model, what size sample would be required?
b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time of less than 10 minutes?
1) Choose the required sample size:
i) Sample size need to be greater than 30
ii) The normal model cannot be used if the shape of the distribution is unknown
iii) Any sample size could be used.
iv) Sample size needs to be less than 30
2) The probability is approximately ___________. (round to 4 decimal places as needed)
Answer:
a) Sample size need to be greater than 30
b) The probability is approximately 0.0571
Step-by-step explanation:
a) For a normal distribution, the sample size has to be greater than 30. A sample size greater than 30 makes it to be an approximate normal distribution.
b) Given that:
μ = 11.2 minutes, σ = 4.5 minutes, n = 35
The z score determines how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x < 10 minutes
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.5/\sqrt{35} }= -1.58[/tex]
Therefore from the normal distribution table, P(x < 10) = P(z < -1.58) = 0.0571
The probability is approximately 0.0571
Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively
Answer:
[tex]x_n=7(-3)^{n-1}[/tex]
Step-by-step explanation:
First, write some equations so we can figure out the common ratio and the initial term. The standard explicit formula for a geometric sequence is:
[tex]x_n=ar^{n-1}[/tex]
Where xₙ is the nth term, a is the initial value, and r is the common ratio.
We know that the second and fifth terms are -21 and 567, respectively. Thus:
[tex]a_2=-21\\a_5=567[/tex]
Substitute them into the equations:
[tex]x_2=ar^{(2)-1}\\-21=ar[/tex]
And:
[tex]a^5=ar^{(5)-1}\\567=ar^4[/tex]
To find a and r, divide both sides by a in the first equation:
[tex]r=-\frac{21}{a}[/tex]
And substitute this into the second equation:
[tex]567=a(\frac{-21}{a} )^4[/tex]
Simplify:
[tex]567=a(\frac{(-21)^4}{a^4})[/tex]
The as cancel out. (-21)^4 is 194481:
[tex]\frac{567}{1}=\frac{194481}{a^3}[/tex]
Cross multiply:
[tex]194481=567a^3\\a^3=194481/567=343[/tex]
Take the cube root of both sides:
[tex]a=\sqrt[3]{343} =7[/tex]
Therefore, the initial value is 7.
And the common ratio is (going back to the equation previously):
[tex]r=-21/a\\r=-21/(7)\\r=-3[/tex]
Thus, the common ratio is -3.
Therefore, the equation is:
[tex]x_n=7(-3)^{n-1}[/tex]
need help asap!!will mark brainliest
Answer:
x = -1
Step-by-step explanation:
[tex]Midpoint =(1,2)= (x,y)\\J(3,-3)=(x_1,y_1) \:and\:K(x,7)= (x_2,y_2)\\\\x = \frac{x_1+x_2}{2} \\\\1 = \frac{3+x}{2}\\ \\Cross\:Multiply \\2\times 1 = 3+x\\2 =3+x\\2-3=x\\-1=x\\\\x =-1[/tex]
Please help fast :) I really need the help thanks !!
Step-by-step explanation:
6 x 1/7 is Less than 1 since 6 x 1/7 is equal to 6/7 in decimal form is 0.8571429.
4 x 4/9 is greater than 1 since 4 x 4/9 is equal to 1 7/9 in decimal form is 1.777...
8 x 1/8 is equal to 1 since 8 x 1/8 is equal to 1.
7 x 1/5 is greater than 1 since 7 x 1/5 is equal to 1 2/5 in decimal form is 1.4
3 x 1/2 is greater than 1 since 3 x 12 is equal to 1 1/2 in decimal form is 1.5
1 x 3/4 is is less than 1 since 1 x 3/4 is equal to 3/4 in decimal form is 0.75
Help please urgent !!!!The students of a certain college were asked to choose which of six movie genres was their favorite. The pie chart below shows the distribution of the students’ answers. If there are 18,500 students at the college, how many chose Drama , Other, or Comedy ?
Answer:
12,950
Step-by-step explanation:
drama: 23%
other: 27%
comedy: 20%
23% + 27% + 20% = 70%
70% of 18,500 =
= 0.7 * 18,500
= 12,950
Fatoring Trinomials
x^2+2x=-1
Answer:
[tex]\Huge \boxed{x=-1}[/tex]
Step-by-step explanation:
[tex]x^2+2x=-1[/tex]
Adding 1 to both sides of the equation.
[tex]x^2+2x+1=-1+1[/tex]
[tex]x^2 +2x+1=0[/tex]
Factoring the left side of the equation.
[tex]x^2 +1x+1x+1=0[/tex]
[tex]x(x+1)+1(x+1)=0[/tex]
[tex](x+1)(x+1) = 0[/tex]
[tex](x+1)^2 =0[/tex]
Taking the square root of both sides of the equation.
[tex]\sqrt{(x+1)^2} =\sqrt{0}[/tex]
[tex]x+1=0[/tex]
Subtracting 1 from both sides of the equation.
[tex]x+1-1=0-1[/tex]
[tex]x=-1[/tex]
Answer:
x = -1
Step-by-step explanation:
[tex]x^2+2x = -1\\=0\\=x^2+2x+1 \\= (x+1)(x+1)\\=(x+1)^2\\\\0 = \sqrt{(x+1)^2} \\= x+1\\\\x+1=0\\x=-1[/tex]
Zev read 15% of his 56-page book. Kelly read 12% of her 64-page book. Marneisha read 14% of his 68-page book Aleisha read 10% of her 72-page book. what the grastest
Answer:
Marneisha with 9.52 pages.
Step-by-step explanation:
Zev: 56×0.15 = 8.4
Kelly: 64×0.12 = 7.68
Marneisha: 68×0.14 - 9.52
Aleisha: 72×0.10 = 7.2
In a triangle ABC, AB=AC and ˂A=70°, find the angles,˂B and ˂C
please help !!!!!!!!!!!!!
Answer:
Then angles [tex]\angle B[/tex] and [tex]\angle C[/tex] both measure [tex]55^o[/tex]
Step-by-step explanation:
Notice that if sides AB and AC are equal, then the angles opposed to them (that is angle [tex]\angle C[/tex] and angle [tex]\angle B[/tex] respectively) have to be equal since equal sides oppose equal angles in a triangle.
So you also know that the addition of the three angles in a triangle must equal [tex]180^o[/tex], then:
[tex]\angle A + \angle B+\angle C= 180^o\\70^o+\angle B + \angle B = 180^o\\2\,\angle B = 180^o-70^o\\2 \angle B=110^o\\\angle B=55^o\\\angle C = 55^o[/tex]
Find the horizontal asymptote (Show your work)
Answer:
[tex] y = 0 [/tex]
Step-by-step explanation:
To find the given asymptote of the given function, [tex] f(x) = \frac{x^2 - 2x + 1}{x^3 + x - 7} [/tex], first, compare the degrees of the lead term of the polynomial of the numerator and that of the denominator.
The numerator has a 2nd degree polynomial (x²).
The denominator has a 3rd degree polynomial (x³).
The polynomial of the numerator has a lower degree compared to the denominator, therefore, the horizontal asymptote is y = 0.
The area of a rectangular parking lot is represented by A = 6x^2 − 19x − 7 If x represents 15 m, what are the length and width of the parking lot?
Answer:
The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.
Step-by-step explanation:
The surface formula ([tex]A[/tex]) for the rectangular parking lot is represented by:
[tex]A = w\cdot l[/tex]
Where:
[tex]w[/tex] - Width of the rectangle, measured in meters.
[tex]l[/tex] - Length of the rectangle, measured in meters.
Since, surface formula is a second-order polynomial, in which each binomial is associated with width and length. If [tex]A = 6\cdot x^{2}-19\cdot x -7[/tex], the factorized form is:
[tex]A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)[/tex]
Now, let consider that [tex]w = \left(x-\frac{7}{2}\,m \right)[/tex] and [tex]l = \left(x+\frac{1}{3}\,m \right)[/tex], if [tex]x = 15\,m[/tex], the length and width of the parking lot are, respectively:
[tex]w =\left(15\,m-\frac{7}{2}\,m \right)[/tex]
[tex]w = \frac{23}{2}\,m[/tex]
[tex]l =\left(15\,m+\frac{1}{3}\,m \right)[/tex]
[tex]l = \frac{46}{3}\,m[/tex]
The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.
CAN SOMEONE PLEASE HELP ME WITH THIS?
Look it up then u get the answer
Answer:
hey mate!
kindly see attached picture
hope it helped you:)
4-2(3+2)
2
How do you do this help me
Answer:
-46Step-by-step explanation:
[tex]4 - 2(3 + 2) ^{2} \\ 4 - 2( {5}^{2} ) \\ 4 - 2(25) \\ 4 - 50 = - 46[/tex]
NEED THIS AND HOW U GOT THE ANSWER find the value of X given that M is greater than PQS equals 119°
Answer:
4.7 =x
Step-by-step explanation:
PQS = PQR + RQS
119 = 72+ 10x
Subtract 72 from each side
119 - 72 = 72+10x -72
47 = 10x
Divide by 10
47/10 = 10x/10
4.7 =x
Johnny has 6 apples,12 bananas, and 14 strawberries. Write the ratio of apples:bananas: strawberries in its simplest form.
Please help
Answer:
apples:bananas: strawberries
3 : 6 : 7
Step-by-step explanation:
apples:bananas: strawberries
6 12 14
Divide each by 2
6/2 12/2 14/2
3 6 7
The ratio is
3 : 6 : 7
Answer:
3:6:7
Step-by-step explanation
The answer is 3:6:7 because if you divide the numbers by 2, you will get a answer of 3, 6, and 7, the simplest form of the ratio.
Hope this helped!
~Emilie Greene
Can someone please help me !❤️❤️
If m∠PQR=(12x−2)∘, and mPR=(20x−10)∘, what is m∠PQR?
a. 137.5
b. 70
c. 16
d. 81
Answer:
Step-by-step explanation:
12x - 2 + 20x - 10 = 180
32x - 12 = 180
32x = 192
x = 6
12*6 - 2
72 - 2 = 70
the solution is b