Answer: Choice A.) 88.2 < μ < 93.0
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Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0
Recall the angle sum identity for cosine:
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))
Then rewrite the equation as
sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0
1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0
1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0
sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0
-sin(5x) (sin(4x) + sin(2x)) = 0
sin(5x) (sin(4x) + sin(2x)) = 0
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
Rewrite the equation again as
sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0
sin(5x) sin(2x) (2 cos(2x) + 1) = 0
sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0
sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2
sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ
… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π
… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5
sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ
… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π
… … … … … ==> x = nπ or x = (2n + 1)π/2
cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ
… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ
… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ
(where n is any integer)
Carlos owns a small business. There was a profit of $9 on Saturday and a loss of $6 on Sunday. Find the total profit or loss for the weekend. $15 profit $3 loss $3 profit $15 loss
Answer:
$3 profit
Step-by-step explanation:
Since you got a profit of $9 on Saturday and a loss of $6 on Sunday, you have to subtract 9 and 6, which is 3.
find r and s on the triangle
Answer:
r=24
s=21
Step-by-step explanation:
I use proportion of 2 to 3
I multiply 16 and 3/2 to get r
r=24
I multiply 14 and 3/2 to get s
s=21
Find the missing length. The triangles are similar.
Answer:
Missing length = 12
Step-by-step explanation:
Let x represent the missing length.
Since the triangles are similar, ∆KLM ~ ∆KRS, therefore, the ratio of their corresponding side lengths would be the same. This implies that:
KL/KR = KM/KS
KL = 65
KR = 65 - 52
KR = 13
KM = 60
KS = x
Plug in the values
65/13 = 60/x
Cross multiply
65*x = 60*13
65x = 780
Divide both sides by 65
65x/65 = 780/65
x = 12
I NEED HELP PLEASE!!
sine --> cosecant
csc(x) = 1/sin(x)
cosine --> secant
sec(x) = 1/cos(x)
tangent --> cotangent
cot(x) = 1/tan(x)
Correct Answer: A
Hope this helps!
In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to
Answer:
Step-by-step explanation:
4
How much does college tuition cost? That depends, of course, on where you go to college. Construct a weighted average. Using the data from "College Affordable for Most," estimate midpoints for the cost intervals. Say 46% of tuitions cost about $4,500; 21% cost about $7,500; 7% cost about $12,000; 8% cost about $18,000; 9% cost about $24,000; and 9% cost about $31,000. Compute the weighted average of college tuition charged at all colleges.
Answer:
0.127
Step-by-step explanation:
at a local college, four sections of economics are taught during the day and two sections are taught at night. 85 percent of the day sections are taught by full-time faculty. 30 percent of the evening sections are taught by full-time faculty. if jane has a part-time teacher for her economics course, what is the probability that she is taking a night class
Answer:
Hence The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher) = 0.6999.
Step-by-step explanation:
Probability(full-time teacher/ day ) = 0.85
Probability(part-time teacher/ day ) = 1- 0.85 = 0.15
Probability(full-time teacher/ night) = 0.30
Probability(part-time teacher/ night) = 1 - 0.30 = 0.70
total no of section = 4+2 = 6
P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)
= (4/6)(0.15)+(2/6)(0.70) = 0.33
P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23
According to Bayes theorem :
The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)
= 0.23/0.33
= 0.6999
help with 1 b please. using ln.
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]
Step 2: Rewrite
[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]Step 3: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Would a scatter plot of the data described below be likely to show a positive relationship, negative relationship, or no relationship.
The number of letters in a person's first name and their heigh
There would likely be no relationship between first name and height of a person in a random sample.
Hope this helps :)
Answer: it’s B. I answered it right now and it said it was correct.
Step-by-step explanation:
McDonald’s fry’s are better than jack in the box’s fry’s.
A rectangle has a perimeter equal to 24 if we consider its width x how could we talk about its length y in terms of x what are the possible values of x what aree the possible values of y
2x + 2y must equal 24. 24 - 2x = 2y and 24 - 2y = 2x. Therefore, 12 - y = x. x could be able to add with y to get 12.
example: x = 4, y = 8. (4 + 4 + 8 + 8 = 16 + 8 = 24)
x = 9, y = 3. (9 + 9 + 3 + 3 = 24)
x = 5, y = 7. (5 + 5 + 7 + 7 = 24)
What is the equation
Answer:
y=3x+1
Step-by-step explanation:
Determine slope with two coordinates and use it in the formula
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
Temperatures in northern Canada ranged as high as 37°F one summer. That same year the lowest temperature was −28°F. What was the range of temperatures for the year?
Answer:
65 degrees
Step-by-step explanation:
Find the range of temperatures by finding the difference between the lowest and highest temperatures:
37 - (-28)
37 + 28
= 65
So, the range of temperatures was 65 degrees
z/3 - 4(z-1) = 5(z-2)+1
What is the value of z?
Answer: [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
First, we need to open the brackets on either side of the equation.
[tex]\frac{z}3}[/tex] - 4z+4 = 5z-10+1
After opening the brackets, we need to separate the variables from the constants.
[tex]\frac{z}{3}[/tex] -4z-5z = -10+1-4
Then we need to convert the variable fraction into a normal variable by multiplying the variable fraction and also all other terms in the equation.
3([tex]\frac{z}{3}[/tex]) 3(-4z) 3(-5z) = 3(-10) + 3(1) + 3(-4)
z -12z -15z = -30+3-12
Now, we can simplify the equation !
-26z = -39
z = -39÷-26
= [tex]\frac{3}{2}[/tex]
Use the elimination method to solve this system. − 4 x − 2 y = − 12, 4 x + 8 y = − 24
Answer:
x = 6; y = -6
Step-by-step explanation:
-4x - 2y = -12
4x + 8y = -24
Add the two equations, so x is eliminated:
6y = -36
6y/6 = -36/6
y = -6
Plug in y, to solve for x
-4x - 2y = -12
-4x - 2(-6) = -12
-4x +12 = -12
-4x = -12 -12
-4x = -24
-4x/-4 = -24/-4
x = 6
Answer from Gauthmath
Evaluate the expression for n = –8.
–2n − 6 =
Answer:
10Step-by-step explanation:
-2n - 6 = ?let n be -8-2 (-8) - 6 = ?= 10[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm.
V'(5) = mm3/mm
What does V'(5) mean in this situation?
Answer:
I don't know the answer it is to hard.
3. Find the value of x in this figure
answer:
120°
Step-by-step explanation:
∠OPM=∠ONM=90°
X°＝360°-60°-90°*2＝120°
Hey guys can help me please
Answer:
Can you select multiple answers to this question? then option A, B and C all three applies, if only one the go for option C, since that's the major change happens to the parent function
Helen’s father’s car can travel an average of 18.5 miles on 1 gallon of gasoline. Gas at the local station costs $3.79 per gallon.
a) Helen’s mom took the car to the gas station and hand the cashier a $10 bill. How much gas could she buy? Round your answer to the nearest hundredth of a gallon.
9514 1404 393
Answer:
2.64 gallons
Step-by-step explanation:
Each gallon costs $3.79, so the number of gallons that can be bought with $10 is ...
$10/($3.79/gal) = (10/3.79) gal ≈ 2.6385 gal ≈ 2.64 gallons
How many solutions does the nonlinear system of equations graphed below have?
A. Four
B. Two
C. One
D. Zero
Answer:
Option (A)
Step-by-step explanation:
Solution of two functions represented by the graph are the common points or point of intersection of the graphs.
From the graph attached,
Parabola and ellipse are intersecting each other at four points.
Therefore, solutions of the given non linear functions will be FOUR.
Option (A) will be the correct option.
The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh more than 15.6 ounces
Answer:
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
Step-by-step explanation:
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.
Mean of 15.0 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 15, \sigma = 0.2[/tex]
What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?
This is 1 subtracted by the p-value of Z when X = 15.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.6 - 15}{0.2}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
1 - 0.9987 = 0.0013
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
Name the three digit number. My ones digit is an even number which is three times as much as my tens digit. My tens digit is the same as my hundreds digit. The sum of all my digits is 10. What number am i?
A. 424
B. 028
C. 226
D. 622
Using the applet, explore the results for simulating a group of 30 people and noting whether there is a duplicated birthday (whether at least two people have a matching birthday). Run at least 40 trials. What is the relative frequency of trials that had at least two people with the same birthday
Answer:I just need points
Step-by-step explanation:
Hey
Base conversion. Perform the following conversion
675_10= ?___6
Answer:
3043 (base 6)
Step-by-step explanation:
216 36 6 1
3 0 4 3
216* 3 = 648
6*4 = 24
1*3 = 3
648+24+3 = 675
find the sum of the given infinite geometric series. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW
Answer:
320/3
Step-by-step explanation:
First find the common ratio
20/80 = 1/4
The sum of an infinite geometric series
sum = a1/ (1-r) where a1 is the first term and r is the common ratio
=80/ ( 1-1/4)
= 80/(3/4)
= 80 *4/3
= 320/3
g A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is: Group of answer choices
Answer:
0.236
Step-by-step explanation:
Given :
x1 = 667 ; n1 = 10 s1 = 20
x2 = 679 ; n2 = 14 s2 = 15
Test statistic :
(x1 - x2) / √[Sp² (1/n1 + 1/n2)]
The pooled Variance, Sp² :
Sp² = [(n1 - 1)s1² + (n2 - 1)s2²] / (n1 + n2 - 2)
Sp² = [(9*20²) + (13*15²)] / (10+14-2)
Sp² = 6525 / 22 = 296.59
T = (667 - 679) / √(296.59*(1/10 + 1/14)
T = -12 / 50.844
T = 0.236
Test statistic = 0.236
Joey's strategy for his first marathon (26.2 miles)was to run 2 miles, walk 1 mile, run 2 miles, walk 1 mile, and continue this pattern until he completed the race. Joey's average running pace is 8 minutes per mile, and his average walking pace is 16 minutes per mile. How many minutes will it take Joey to complete the marathon
========================================================
Explanation:
We have this sequence
(2+1)+(2+1)+(2+1)...
Effectively, we're repeating "2+1" over and over.
We can see that
2+1 = 3(2+1)+(2+1) = 3+3 = 6(2+1)+(2+1)+(2+1) = 3+3+3 = 9Each time we add on another copy of (2+1), we're adding on 3
Dividing 26.2 over 3 gets us (26.2)/3 = 8.733 approximately
If we had 8 copies of (2+1) added together, then we would get
8*(2+1) = 8*3 = 24
This is 26.2-24 = 2.2 miles short of his goal.
He'll need to run 2 more miles, plus walk another 0.2 of a mile
----------------------------------------------------
In summary so far, Joey will run 8+1 = 9 sections (two miles each) and walk 8 sections that are 1 mile each. At the very end, he'll walk 0.2 miles to finish the race. Each running and walking section is alternated of course.
Since he runs 9 sections, each 2 miles, that accounts for 9*2 = 18 miles.
His running pace is 8 minutes per mile, so this means he has run for 8*18 = 144 minutes. This is just the running part and not the walking part.
Let A = 144 so we can use it later.
----------------------------------------------------
He walks 8 sections of 1 mile each. His walking pace is 16 minutes per mile. This must mean he spends 8*16 = 128 minutes on this walking portion.
Then for the last 0.2 mile section he walks, we can solve the proportion below
(1 mile)/(16 min) = (0.2 miles)/(x min)
1/16 = 0.2/x
1*x = 16*0.2
x = 3.2
He spends 3.2 minutes walking the remaining 0.2 of a mile at the end.
So his total walking time is 128+3.2 = 131.2 minutes.
Let B = 131.2
-----------------------------------------------------
To wrap things up, we'll add up the results of each of the previous two sections.
A = total running time = 144 min
B = total walking time = 131.2 min
C = total marathon time
C = A+B
C = 144+131.2
C = 275.2 minutes
This converts to 275 min, 12 sec.
This is also equivalent to 4 hrs, 35 min, 12 sec.
Write the number 16,107,320 expanded form.
Answer:
Sixteen million, one hundred and seven thousand, three hundred twenty
Step-by-step explanation:
