Answer:
Step-by-step explanation:
We can solve each inequality apart and then see the possible solution sets.
Consider the inequality 4x+8 < -16. If we divide by 4 on both sides, we get
x+2 < -4. If we substract 2 on both sides we get x<-6. So the solution set for this inequality is the set of real numbers that are less than -6 (lie to the left of the point -6).
Consider 4x+8>4. If we divide by 4 on both sides we get x+2>1. If we substract 2 on both sides we get x>-1. So the solution set for this inequality is the set of real numbers that are bigger than -1 (lie to the right of the point -1).
So, for us to have 4x+8<-16 or 4x+8>4 we must have that either x <-6 or x>-1. So the solution set for the set of inequalities is the union of both sets, that is
[tex](\-infty, -6) \cup (-1,\infty)[/tex]
Please show step by step working out of stationary points and points of inflection with the y coordinates (and sketch graph) for the equation y=x^4-36x^2
Answer:
See picture attached
Step-by-step explanation:
Consider the expression 8 – 4 / 2. One student says the answer is 2 and another says it is 6. Which student is correct? Explain what went wrong with the student who made a mistake.
Answer:
It is 6. The student who got a two did not use order of operations.
Step-by-step explanation:
PEMDAS
You must do division before subtraction. 4/2 = 2.
8 - 2 = 6
Please help I am doing test ! A woman borrows $4,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Answer:
Monthly Loan Payment
Loan Amount (P) = $6,000
Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]
Number of months (n) = 36 Months [3 Years x 12 months]
Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]
= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]
= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]
= [$6,000 x 0.009815] / 0.308645
= $58.89 / 0.308645
= $190.80
Monthly Loan Amortization Schedule
“Therefore, the total interest paid during the first year will be $465.99”
HOPE this example helps
Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the y-axis.
y=x³,
x=1,
y=0
Each shell has radius [tex]x[/tex] and height [tex]x^3[/tex], so the volume of this solid is
[tex]\displaystyle2\pi\int_0^1x^4\,\mathrm dx=\boxed{\frac{2\pi}5}[/tex]
I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Calculate the probability of the following.
a. 11 heads:
b. 2 or more heads:
c. 7 heads:
d. 9 tails:
e. 8 or less heads:
Answer:
a. 0.0368
b. 0.99992131
c. 0.2039
d. 0.0048
e. 0.6533
Step-by-step explanation:
Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35
Since this is a binomial probability, we use a binomial probability.
a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368
b. Probability of 2 or more heads P(x ≥ 2) is
P(x ≥ 2) = 1 - P(x ≤ 1)
Now P(x ≤ 1) = P(0) + P(1)
= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹
= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹
= 0.000003379 + 0.00007531
= 0.0007869
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - 0.00007869
= 0.99992131
c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039
d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048
e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴
= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴
= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367
= 0.6533
The volume of a cylinder varies jointly with the base (area) and the height. The volume is 40 inches^3 when the base (area) is 6 inches^2 and the height is 20 inches. Find the volume of the cylinder (after finding the variation constant) when the base (area) is 8 inches^2 and the height is 12 inches.
Answer: K = ¹/₃, V = 32in³
Step-by-step explanation:
Volume of s cylinder (V) = πr²h where πr² is the base area.
Now from the question,
V ∞ πr²h
V = kπr²h where k is the constant of proportionality which is also the variation constant.
40 = 6 x 20 x k
40 = 120k and
k = ⁴⁰/₁₂₀
= ¹/₃.
Now to find the volume when base area is 8in² and h is 12,
V = 8 x 12 x ¹/₃
V = 32in³
2. Compare the function ƒ(x) = –x^2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)?
Answer:
g(x)
Step-by-step explanation:
The vertex of g(x) as shwon in the graph is located in the point wich coordinates are (3.5,6.25) approximatively
We need to khow the coordinates of f(x) vertex
Here is a way without derivating:f(x) = -x² + 4x -5
let a be the leading factor, b the factor of x and c the constant:
a= -1b= 4c= -5The coordinates of a vertex are: ([tex]\frac{-b}{2a}[/tex] , f([tex]\frac{-b}{2a}[/tex]) )
-b/2a = -4/ (-1*2) = 4/2 = 2
f(2)= -2²+4*2-4 = -4+4-4 = -4
obviosly f(x) has a minimum wich less than g(x)'s maximum
Answer:
Step-by-step explanation:
g(x) i think
Please answer this correctly without making mistakes my work is due today
Answer:
24.24
Step-by-step explanation:
brainlist plzzzzzzzzzzz
An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 99% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?
Answer: n = 2401
Step-by-step explanation:
Given;
Confidence level = 2% - 99%
n = ? ( which is the sample size is unknown ).
Solution:
Where;
n = [z/E]^2*pq
Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2
Substituting the given data into the formula.
n = [1.96/0.02]^2(1/2)(1/2)
n = 2401
The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401
Find x.................
Answer:
90°
Step-by-step explanation:
Theres a right angke beside x
And Angles on a straight line = 180 so 180-90°= 90°
Answer:
90
Step-by-step explanation:
I looked it up on the internet
If ABC=DEC B=48 and E=C+4
x=?
Answer:44
Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48
So, x+4=48 , x=44 degree
The formula to convert Fahrenheit to Celsius is C=5/9(F-32). Convert 30c to Fahrenheit. Round to the nearest degree
Answer:
86 degrees farenheit
Step-by-step explanation:
First, we plug 30 in for C.
Next, solve for F
Multiplying both sides by 9/5 gives us 54=F-32
Add 32 to both sides 86=F
What is the y-intercept of the function f(x)=4 - 5x?
-5
-4
4
5
Answer:
y-intercept = (0,4)
Step-by-step explanation:
To find the y-intercept, the place at which the value of x is 0, simply plug zero into your function:
f(x) = 4 - 5x
f(0) = 4 - 5(0)
f(0) = 4
Hence, the y-intercept occurs at (0,4).
The y-intercept of f(x) = 4 - 5x is 4.
Using the slope intercept formula the y-intercept can be found below
y = mx + bwhere
m = slope
b = y-intercept
From the equation:
f(x) = 4 - 5x
According to the slope intercept format,
m = slope = -5
y- intercept = 4
Therefore, the y-intercept of f(x) = 4 - 5x is 4.
read more: https://brainly.com/question/4023516?referrer=searchResults
10. Here is a list of 25 scores on a Math midterm exam: 38.5, 41.5, 52, 52.5, 61, 63, 63.5, 68, 69, 69, 78.5, 79, 80, 83, 87, 88.5, 88.5, 91, 91.5, 92, 92.5, 94, 94, 97, 97 Find P36:
Answer:
69
Step-by-step explanation:
Since the values in the data set has been ranked already from smallest to largest, as shown in the question.
Then calculate the index,
To find the 36th percentile using the data set,
Multiply k (36/100) by n (25) to reach an index of 9.
Then since the index is whole number,
To calculate percentile according to the 'greater than' method, count the values in the data set from smallest to largest until you reach the number ranked 9th
Which is 69.
Since the value for the 36th percentile must be greater than the first nine values, the 10th ranked value would be the kth (36th) percentile. In this data set, that value is 69.
Alternatively, using the 'greater than or equal to' method, after getting the 9th rank,
Include the ninth-ranked value, (69) in this data set.
The kth (36th) percentile is then calculated by taking the average of that value in the data set (69) and the next ranked value (69). (59 + 69) / 2 = 69.
Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? choices
Answer: 2⁹5³ = 64,000
Step-by-step explanation:
There are 9 questions with 2 options (true or false) = 2⁹
There are 3 multiple questions with 5 options = 5³
true/false questions AND multiple choice questions
2⁹ x 5³ = 2⁹5³
Facespace is a popular form of social media. Recent reports show that the mean time spent on Facespace is 35 minutes a day with a standard deviation of 6 minutes a day. The data is normally distributed. If 1100 people are on in one sitting, how many of them lie within one standard deviation below the mean and two standard deviations above the mean?
Answer:
897
Step-by-step explanation:
I think it deleted my prior solution because I linked the Wikipedia article for the empirical rule... So to retype this:
We'll be using the empirical, or 68-95-97.5 rule of normal distributions which says that 68% of data in a normal distribution is within 1 standard deviation, 95% is within two, and 97.5% is within three. Graphical representations of the rule can be found online and may be helpful to understand it more easily.
The first part of the problem is relatively straightforward, to get the two pieces within one standard deviation, that's 68% of the total population of 1100. So, 0.68*1100=748.
The second part is a bit trickier, since it is just the part of the second standard deviation out that is above the mean. To get this, we need to think about the difference between one standard deviation out and two, percentage-wise. Since two standard deviations out is 95% of the data, the difference between one and two is 95%-68%, or 27% of the data. However, since we only want the upper half of that, we'll just be using 13.5%. So our second piece is 13.5% of 1100, or 148.5.
Add together our two pieces, 748+148.5=896.5 and round up to 897.
Find the exact perimeter (in inches) and area (in square inches) of the segment shown, given that m∠O = 60° and OA = 24 in.
Answer:
A. Perimeter of segment = 49 in.
B. Area of segment = 52 in².
Step-by-step explanation:
Data obtained from the question include:
Radius (r) = 24 in.
Angle at the centre (θ) = 60°
Perimeter of segment =.?
Area of segment =.?
A. Determination of the perimeter of the segment.
Perimeter of segment = length of arc + length of chord
Length of arc = θ/360 x 2πr
Length of chord = 2r x sine (θ/2)
Pi (π) = 3.14
Length of arc = θ/360 x 2πr
Length of arc = 60/360 x 2 x 3.14 x 24
Lenght of arc = 25.12 in
Length of chord = 2r x sine (θ/2)
Length of chord = 2 x 24 x sine (60/2)
Length of chord = 24 in
Perimeter of segment = length of arc + length of chord
Perimeter of segment = 25.12 + 24
Perimeter of segment = 49.12 ≈ 49 in.
B. Determination of the area of the segment.
Area of segment = Area of sector – Area of triangle.
Area of sector = θ/360 x πr²
Area of triangle = r²/2 sine θ
Area of sector = θ/360 x πr²
Area of sector = 60/360 x 3.14 x 24²
Area of sector = 301.44 in²
Area of triangle = r²/2 sine θ
Area of triangle = 24²/2 x sine 60
Area of triangle = 249.42 in².
Area of segment = Area of sector – Area of triangle.
Area of segment = 301.44 – 249.42
Area of segment = 52.02 ≈ 52 in²
A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer:
(2,0)
Step-by-step explanation:
From the information the first equation is y = 0.5 x - 1 and the the line through (3,1) and (-5,-7) is
y = x - 2 . From those two equations you get
x - 2 = 0.5 x -1 and x = 2 , y = 0. So it is the last point. (2,0)
Answer:
D. (2,0)
Step-by-step explanation:
Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.
University A University B
Sample Size 50 40
Average Purchase $280 $250
Standard Deviation $20 $23
At 95% confidence test to determine if, on the average, students at University A spend more on textbooks then the students at University B.
Answer:
Z > Zα
6.511 > 1.645
Step-by-step explanation:
University A University B
Sample Size 50 40
Average Purchase $280 $250
Standard Deviation $20 $23
We formulate
H0: x1` > x2` null hypothesis that the mean of the University A is greater than the mean of the University B
HA: x1`≤ x2` one tailed test
Test statistic
Z= x1`-x2`/ √s₁²/n₁ +s²₂/n₂
Z= 280-250/√400/50 + 529/40
Z= 30/√8 +13.225
Z= 30 /4.607
Z= 6.511
For one tailed test at α= 0.05 = 1.645
Z > Zα
6.511 > 1.645
Thus we reject null hypothesis.On the average, students at University A spend more on textbooks then the students at University B.
6th grade math, help pleasee:)
Answer:
1/5 cup
Step-by-step explanation:
Sugar: water
1 5
We want 1 cup water, so divide each side by 5
1/5 : 5/5
1/5 : 1
There is 1/5 cup sugar to 1 cup water
SCREENSHOT OF MY QUESTION:
Answer in fraction form = 9/8
Answer in decimal form = 1.125
note: the improper fraction 9/8 converts to the mixed number 1 & 1/8
To get this answer, we divide both sides by 8 to isolate n. The expression 8n really means "8 times n". We divide to undo the multiplication.
Simplify the following algebraic expression.
square root of 39x^7
Answer: x^3 square root 39x
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
c. When redesigning the ejection seat which probability is more relevant?
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb
z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%
b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%
c) The probability from part C is more important
Solve the following system of equations. Express your answer as an ordered pair in the format (a,b). 3x+4y=17 -4x-7y=-18
Answer:
Step-by-step explanation:
3x+4y = 17 _______ equation 1
-4x -7y= -18 _______ equation 2
muliply by 4 in equation 1
12x + 16y = 68 ______ equation 3
multiply by 3 in equation 2
-12x - 21y = -54 ________ equation 4
add equation 3 & 4
- 5y = 14
y = - 14/5
substitute y in equation 1
3x + 4 (-14/5) =17
3x = 17+ (56/5)
3x =( 85 + 56) / 5
3x = 141/5
x = 47/5
hence (a,b) = (47/5, -14/5)
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
[tex]12x + 8y > 2500\\x + y < 280[/tex]
Kindly find the attached image as the graph and solution to this problem.
Learn more on graphically solution for inequality here;
https://brainly.com/question/24372553
#SPJ2
Helppppp............
Answer:
A (15/16)
D (0.45)
E (1/14)
F (0)
Step-by-step explanation:
Allowable values for probabilities (p) are numbers greater than or equal to zero and smaller than or equal to one:
[tex]0\leq p\leq 1[/tex]
Therefore you can select answers:
A (15/16)
D (0.45)
E (1/14)
F (0)
Answer:
0, 1/2, 0.1, 15/16 are the answers
Step-by-step explanation: I don't think negative numbers count as a probability
Find the indicated binomial probability. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. If a student guesses on every question, find the probability of getting exactly 12 correct.
Answer:
0.02906
Step-by-step explanation:
number of questions =30
getting exactly right : 12
30C12 the number of possibilities
probability to get it right (1/4)^12
probability of failure =1-1/4=(3/4)^18 ( 18 = 30 questions -12 right )
P(12)=30C12*(1/4)^12*(3/4)^18=0.02906
hope it helps
You visit a farm and notice that white chickens lay white eggs and colored chickens lay colored eggs, so you decide that only white chickens lay white eggs. What type of reasoning is this?
Answer:
This is called an Inductive reasoning.
Step-by-step explanation:
It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.
Hope it helps.
6th grade math, help me please:)
Answer:
8:3 is the ratio of kids to adults
32 kids, so there are 12 adults
Answer:
32 kids to 4 adults
Step-by-step explanation:
1st row- 8 kids to 3 adults
2nd row- 16 kids to 6 adults
3rd row- 24 kids to 9 adults
4th row- 32 kids to 12 adults
16. Use yesterday’s stock table for the company Icarus to answer the following questions.
52-week Price
High Low
Stock
Symbol
Dividend
Annual Yield Return (%)
P/E ratio
Volume Traded
High Low
Price Price
Closing Price
Net Change
28.38 15
Icarus
ICR
0.41
1.1
24
105300
24 23.5
24
. . . .
a. What was the high price for Icarus stock over the last 52 weeks?16a. _______________
b. If you owned 1000 shares of Icarus stock last year, what is the dollar amount of the b. _________________
dividend you received?
c. What is the annual yield return for dividends alone?c. _________________
d. How many shares of Icarus stock were traded yesterday?d. _________________
e. What was the low price for Icarus stock yesterday?e. _________________
f. What was the price of Icarus stock at the close of the stock exchange yesterday?f. _________________
g. Compute Icarus’s annual earnings per share using the formula below.g. _________________