Answer:
B. Approximately 0.3159
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon.
This means that [tex]\mu = 1, \sigma = 0.1[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{0.1}{\sqrt{9}}[/tex]
If the sample mean is less than 0.97 gallons, the department will fine the dairy. Based on this information, what is the probability that the dairy will get fined even when its filling process is working correctly?
This is the pvalue of Z when X = 0.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.97 - 1}{\frac{0.1}{\sqrt{9}}}[/tex]
[tex]Z = -0.9[/tex]
[tex]Z = -0.9[/tex] has a pvalue of 0.1841.
The correct answer is given by option B.
Answer:
Option C
Step-by-step explanation:
Given
Probability of Mean value less than 0.97
= Mean value -1/(0.1/sqrt (9))
Substituting the given values, we get -
Probability of Mean value less than 0.97
= 0.97 -1/(0.1/sqrt (9))
= 0.97-1/(0.1/3)
= 0.1841
Hence, option C is correct
If you were the number keep 660 times how many times will you likely roll a two or five
Answer:
220
Step-by-step explanation:
a dice has 6 sides
660 divided by 6 = 110
you asked for 2 numbers so
110 times 2 = 220
Find the length of y
Answer:
From SOHCAHTOA
Cos17=73/y
y=73/cos17
y=76.34cm
Option B
Which statement about 214° is correct?
O A. tan 214° < 0
O B. sin 214° < 0
O C. cos 214° > 0
Answer:
B.
Step-by-step explanation:
214 degree terminates in the 3rd quadrant.
Sine and cosines are both negative there.
This means that sin(214)<0 and cos(214)<0.
If sine and cosine are both negative and since tangent is the quotient of them, then tangent is positive, or tan(214)>0.
Alberto ran at a speed of 3 m/hr. After he ran 6 miles, Omar ran in the same direction with a speed of 4.6 m/hr.
How many hours will it take Omar to catch up to Alberto.
Answer:
1.3 Hours (1 Hour and 18 Minutes)
Step-by-step explanation:
It took Alberto 2 hours because he ran 3 miles an hour and the total distance he ran was 6 miles.
Now, you have to divide 6 (Alberto's distance) by 4.6 (Omar's rate) and you get 1.3043.
Round the answer to get 1.3
Answer: jjijmjn
Step-by-step explanation:
Consider the following functions. (See attachment)
Find the area of the region.
Answer:
Area: [tex]\displaystyle \frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationGraphing FunctionsExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Area - Integrals
Area under a curveArea between 2 curvesIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify functions
[tex]\displaystyle f(x) = \sqrt[3]{x - 9}[/tex]
[tex]\displaystyle g(x) = x - 9[/tex]
Step 2: Identify Info
Graph the functions - See Attachment
[1st Integral] Bounds: [8, 9], g(x) top function/f(x) bottom function
[2nd Integral] Bounds: [9, 10], f(x) top function/g(x) bottom function
Step 3: Find Area Pt. 1
Set up integrals [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^9_8 {[(x - 9) - \sqrt[3]{x - 9}]} \, dx + \int\limits^{10}_9 {[\sqrt[3]{x - 9} - (x - 9)]} \, dx[/tex]Rewrite integrals [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^9_8 {(x - 9)} \, dx - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \int\limits^{10}_9 {(x - 9)} \, dx[/tex]Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = (x^2 - 9x) \bigg| \limits^9_8 - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - (x^2 - 9x) \bigg| \limits^9_8[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = \frac{-1}{2} - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \frac{1}{2}[/tex]Subtract: [tex]\displaystyle A = -\int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - 1[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle A = -\int\limits^9_8 {(x - 9)^{\frac{1}{3}}} \, dx + \int\limits^{10}_9 {(x - 9)^{\frac{1}{3}}} \, dx - 1[/tex]Step 4: Identify Variables
Identify variables for u-substitution.
u = x - 9
du = dx
Step 5: Find Area Pt. 2
[Integrals] U-Substitution: [tex]\displaystyle A = -\int\limits^0_{-1} {u^{\frac{1}{3}}} \, du + \int\limits^1_0 {u^{\frac{1}{3}}} \, du - 1[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = -(\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^0_{-1} + (\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^1_0 - 1[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = -(\frac{-3}{4}) + \frac{3}{4} - 1[/tex]Simplify: [tex]\displaystyle A = \frac{1}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integrals - Area between 2 curves
Book: College Calculus 10e
Work out the size or angle X
Answer:
180-132
Step-by-step explanation:
the entire angle should sum to 180
Answer:
48 °
Step-by-step explanation:
132° + x° = 180° (Linear pair)
∴ x° = 180° - 132°
∴ x° = 48°
Hope this helps :) !!!
Find all zeros. Choose all answers that apply.
f(x) = -x3 + 4x² + 5x
O A. X = -5
B. X = -1
O C. x = 0
O D. x = 1
A bucket holds 243.5 oz of water. The bucket loses 0.5 oz of water per second. In how many seconds will the bucket be 40% full?
which two integers does √5 go between?
Answer:
The two integers are 2 and 3
Step-by-step explanation:
√5
=2.2
Fill in the blank. Using the number line below, the plotted number is when rounded to the nearest ten.
The ages of eight different students in a college math class were used to make the box plot shown above. Which of the following numbers below is the median of the ages?
A. 21.5
B. 20.5
C. 22.5
D. 24.5
Use the change of base formula and a calculator to approximate each logarithm. Round to
three decimal places.
log14 (16)
Answer:
[tex]1.051[/tex]
Step-by-step explanation:
The change of base formula is given by [tex]\log_a b=\frac{\log b}{\log a}[/tex]
Substituting given values, we have:
[tex]\log_{14} 16=\frac{\log 16}{\log 14}\approx \boxed{1.051}[/tex]
1250
€ 125oo
Q8 A taxi company charges £5 standing charge and £1.50 per mile for a journey.
A man travels in a taxi for 12.2 miles.
What is the cost of his journey?
Show your working
Answer:
£23.30
Step-by-step explanation:
First, find the cost from traveling 12.2 miles. Since the cost is £1.50 per mile, multiply 12.2 by 1.5:
12.2(1.5)
= 18.3
Add the standing charge to this:
18.3 + 5
= 23.3
So, the cost of his journey is £23.30
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2475 . What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?
Answer:
1st: 105/h
2nd: 95/h
Step-by-step explanation:
10A+15B=2475 (1)
A+B=200 |*10 => 10A+10B=2000 (2)
From (1) - (2), we have 5B=475, so B=95
then A+95=200 so A is 105
2+2=?
i dont remember this, its too complex for me someone help asap
ahem ahem
2+2=69
it's 4 thanks for the points
You went to the barber to get your hair cut. The haircut cost $30. You tipped the barber 20%. How much money did you give the barber for a tip? What is the total amount you paid all together?
Answer:
Tip $6
Total Amount $36
Step-by-step explanation:
20% of $30 is 6
$30 + $6 = 36
Which of the following statistics measures the variability of a distribution?
A) Mean
B) Median
C) Mode
D) Range
Answer:
B
Step-by-step explanation:
B is the answer .
Answer:
[tex]\huge{\textbf{\textsf{{\color{skyblue}{An}}{\blue{sw}}{\red{er}}{\color{red}{:}}}}}[/tex]
[tex]{\boxed{\boxed{\tt { D. \ Range}}}} \ [/tex]
Step-by-step explanation:
The mean, median and mode are central tendency measures. Statisticians use range to describe the amount of variability or spread in a set of data.
⋆┈┈｡ﾟ❃ུ۪❀ུ۪❁ུ۪❃ུ۪❀ུ۪ﾟ｡┈┈⋆
"HOT PIZZA" is offering 20% discount on all its pizza
Ali bought a pizza for £5.60 what was the original price
Answer:
Original price was £7.00
Step-by-step explanation:
20% discount means that ali is paying 80% of the full price
.8p = 5.60
Divide both siides by .8
p = 7
Original price was £7.00
2sqroot97x
Which value of x makes the expression above equivalent to 20 sqroot97? pls provide a step by step explanation (:
Answer:
A
Step-by-step explanation:
The base of a rectangular prism has a base of 15 square cm. The height of the prism is 5 cm. What is the volume of the rectangular prism?
Step-by-step explanation:
eyeyeyeyeyyeyeyeyeeyeyeueueuryryru
Need help on this one plz
Answer:
3 15/18
Step-by-step explanation:
well, 4 5/18 can't take away 8/18 with the fraction itself. so, you take 5 from 8 and get -3. then, take one whole number away and subtract the 18 from 3 (this was the negative 3) and you have the answer. so to conclude it 5 cant take away 8 so its like carrying. you take one whole number that is 18/18 and you subtract the 18 from 3.
make the mathematical expression and simplify.3 times the difference of 17 and 7 is divided by 5
= 3(17-7)/5
=3(10)/5
=30/5
=6
Find the area of the circle.
Use 3.14 for pi
d = 10 cm
A = [?] cm2
A=Pi r2
Step-by-step explanation:
the only thing youre missing is
radius = diameter / 2
Answer:
78.54 cm squared
Step-by-step explanation:
A=πr^2
Since they only give the diameter, divide the diameter by 2
π*25 = 78.54
Have a good day :)
Use the Figure to find the measure of the angle. Explain your Reasoning.
Plz Help
Step-by-step explanation:
look at the picture i have sent
Help me!!!!!!!!!!!!!!!
Answer:
look at the picture i have sent
Answer:
BHM = 64°
x = 16°
Step-by-step explanation:
BHL is 90° and MLH is 26°. This means to find BHM, we have to subtract 26 from 90.
90 - 26 = 64°
BHM = 64°
BHM is also equal to 4x.
So, to find x, divide 64 by 4. (64 = 4x --> 64 ÷ 4 = x)
64 ÷ 4 = 16
x = 16°
Anwer this questions plz
Answer:
2
Step-by-step explanation:
brainliest blz
Answer:I believe the answer is 3 Hope this helps ^w^
Step-by-step explanation:
20/5 is 4 so 4 dollars per tank top and 35/5 is 7 so 7-4=3
A line goes through the points (0, -2) and (5, 18). What is the slope of the line?
Answer:
[tex]\displaystyle m = 4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (0, -2)
Point (5, 18)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{18--2}{5-0}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{20}{5}[/tex][Fraction] Divide: [tex]\displaystyle m = 4[/tex]Please help! I will give Brainliest!
Answer:
p(not L) = 7/8, 0.875, 87.5%
Step-by-step explanation:
8 letters in total
7 are not L
p(not L) = 7/8, 0.875, 87.5%
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answer:A..the diagonal bisect perpendicular one other.Since bisectors divide the diagonals equally in two parts.
.
Answer:
D
Step-by-step explanation:
I'm not smart :)
Can someone do 11-12?