Using the probability concept, we have that:
a) It would not be unusual to observe one component fail, since the probability that one component fails is greater than 0.05.
b) It would be unusual to observe two components fail, since the probability that two components fail is less than 0.05.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. If a probability is less than 0.05, the event is considered unusual.
In this problem, the probabilities are given as follows:
0.21 probability that one component fails, hence not unusual.(0.21)² = 0.0441 probability that two components fail, hence unusual.More can be learned about probabilities at https://brainly.com/question/14398287
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Name all the fractions that are between 12/13 and 19/20
whose NUMERATORS are one less than the DENOMINATORS.
The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Fractions that are between 12/13 and 19/20 such that:
The numerator(N) is one less than the denominator(D).
N = D - 1
N = (12, 19)
D = (13, 20)
D = 14, N = 13
D = 15, N = 14
D = 16, N = 15
D = 17, N = 16
D = 18, N = 17
D = 19, N = 18
The fractions that are between 12/13 and 19/20:
N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}
Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
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Use linear equation to calculate intercepts.
x minus one-half y = negative 4
Complete the table with values for a and b.
A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.
a =
b =
The x intercept of the linear equation is -4 and y intercept is 8.
Intercept of the linear equation
The intercept of the linear equation is calculated as follows;
x - y/2 = -4
make y the subject of the formula;
y/2 = x + 4
y = 2x + 8
y intercept is obtained at point, x = 0y = 0 + 8
y = 8
x intercept is obtained at point, y = 00 = 2x + 8
2x = -8
x = -4
Thus, the x intercept of the linear equation is -4 and y intercept is 8.
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Answer:
The x intercept of the linear equation is -4 and y intercept is 8
Step-by-step explanation:
Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answer:
12
Step-by-step explanation:
1.5 is 1 1/2 in decimal form
1.5×8=12
Let f(x)=(3)^x−3. What is f(0) in fraction form?
Answer:
1/27
Step-by-step explanation:
We can substitute x=0 into the function to get:
f(0) = 3^(0-3)f(0) = 3^(-3)f(0) = 1/27a plane intersects a sphere 5 cm away from the center of the sphere. the cross section is a circle whose diameter is 12cm. determine the radius of the sphere
Answer:
7.81 cm
Step-by-step explanation:
diameter = 12, 12/2 = 6
(r+5)(r-5) = 6 * 6
r^2 - 25 = 36
r^2 = 61
r = 7.81
radius = 7.81 cm
Answer:
26
Step-by-step explanation:
An entrance examination for a job consists of 25% English, 50% Mathematics, 5% Typing and 20% Accounting, and the passing mark is 50. If an applicant sat for the examination and scored 48% in English, 35% in Mathematics, 80% in Typing and 50% in Accounting, do you think she will be accepted? Why?
Answer:
No, the total is 43.5 which is below 50.
Step-by-step explanation:
English: 25% × 48 = 12
Mathematics: 50% × 35 = 17.5
Typing: 5% × 80 = 4
Accounting 20% × 50 = 10
12 + 17.5 + 4 + 10 = 43.5
Total: 43.5
Passing: 50
Answer: No. The total is too low.
Another day, another math problem
Answer:
4x+2h+5
Step-by-step explanation:
[tex]\frac{(2(x+h)^{2}+5(x+h)) - (2x^{2} +5x) }{h} \\[/tex]
For now I'm just going to ignore the denominator for simplicity
[tex](2(x^{2}+2xh+h^{2})+5x+5h) - (2x^{2} +5x)\\(2x^{2}+4xh+2h^{2}+5x+5h) - (2x^{2} +5x)\\(4xh+2h^{2}+5h)\\\\\frac{(4xh+2h^{2}+5h)}{h}\\ 4x+2h+5[/tex]
Final step just distributes the division
6. The diagram on the right shows the cross-section of a cylindrical pipe with water lying in the bottom. a) If the maximum depth of the water is 2 cm and the radius of the pipe is 7 cm, find the area shaded. b) What is the volume of water in a length of 30 cm?
Answer:
404 cm³ Anyway... Look down here for my explanation.
Step-by-step explanation:
Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.
We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area 88.8/360*area of circle - ½*7*788.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
Volume of water = cross-sectional area * length
13.5 * 30 cm³
404 cm³
Suppose that land in downtown Savannah is valued at $20 per square foot. What is
the value of a triangular lot with side lengths of 112, 148, and 190 feet?
Answer:
$165554
Step-by-step explanation: I use the Law of Cosines to find one of the angles of the triangle. Then use the formula for the area of the triangle: A = (1/2)absinC.
C= 92.856 degree
Area = (1/2)(112)(148)sin(92.856°) = 8277.7 ft^2
To find the price just need to take 8277.7 time 20 = 165554
So the answer is $165554
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
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What is the answer to this question?
Y=x^2-1 with the input as 5
We can see that, when the input is 5, the output is 24.
How to evaluate an equation?
Here we have the equation:
[tex]y = x^2 - 1[/tex]
Where y is the output and x is the input.
We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:
[tex]y = 5^2 - 1 = 24[/tex]
Then we can see that, when the input is 5, the output is 24.
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paul asked to order snacks for an office meeting of 180 people. she decides to order desert squares which come in boxes of 24. she estimates she will need 3.5 snacks per person. how many boxes should she buy?
Answer:
27 boxses
Step-by-step explanation:
calculations is shown in the picture
Find the zeros of the quadratic polynomial f(x) = 6x²-3, and verify the relationship between the zeros and its coefficients.
Step-by-step explanation:
1) zeros of the given function:
6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔
[tex]\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}[/tex]
2) relationship:
if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ The polynomial
f(x) = 6x² - 3
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}[/tex]
★ Zeroes of the polynomial f(x) = 6x² - 3
[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
We have,
[tex]f(x) = \tt 6 {x}^{2} - 3[/tex]
Which can also be written as
[tex] \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} [/tex]
Using a² - b² = (a - b) (a + b)
[tex] \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )[/tex]
To find the zeroes, solve f(x) = 0
[tex] \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0[/tex]
either [tex] \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0[/tex]
[tex] \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}[/tex]
[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }[/tex]
[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }[/tex]
[tex]\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }[/tex]
[tex]\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }[/tex]
Hence, the zeroes of f(x) = 6x² - 3 are:
[tex] \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}[/tex]
• Verification
Sum of zeroes = [tex] ( \alpha + \beta )[/tex]
[tex] = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)[/tex]
[tex] = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } [/tex]
[tex]= \tt 0[/tex]
and, [tex]\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }[/tex]
[tex] \tt = - \dfrac{0}{6} [/tex]
[tex] \tt = 0[/tex]
[tex] \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]
Also,
Product of zeroes = [tex] \alpha \beta [/tex]
[tex] = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } [/tex]
[tex] = - \dfrac{1}{ 2 } [/tex]
and, [tex]\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }[/tex]
[tex] \tt = \dfrac{ - 3}{6} [/tex]
[tex] \tt = \dfrac{ - 1}{2} [/tex]
[tex] \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]
[tex]\rule{280pt}{2pt}[/tex]
What are m and b in the linear equation 3+4x+6+2x=y
Answer:
m = 6, b= 9
Step-by-step explanation:
Simplifying the equation, we get y = 6x + 9.
Matching this up with y = mx + b, we get m = 6 and b = 9.
f is an even function, g is an even function. a=
Answer:
a=6 it's even
Step-by-step explanation:
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Answer:
A= 4
B= 3
i got it right.
Which number comes next in this series 1/64 1/32 1/16 1/8 1/4 1/2
Answer:
1/1
Step-by-step explanation:
As the question is halfing by 2
So
2 divide 2 equals 1
Answer:
1
Step-by-step explanation:
it's fractions of divided half. next one will be number 1
Chef Fabio does beginning inventory on Thursday night and finds that he has $1456 in food products in the restaurant. Throughout the week he purchases:
$457 produce,
$632 protein,
$356 dry goods, and
$147 dairy.
The following Thursday he does ending inventory and finds that he has $1643 in food. He looks at his sales and finds that he made $5546 over the same 7 day period. What is his food cost as a percentage of sales (food cost percentage)?
Using it's concept, it is found that the percentage of his sales that area food costs is of 29.62%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, he has $1643 out of $5546 in food, hence the percentage is given by:
[tex]P = \frac{1643}{5546} \times 100\% = 29.62%[/tex]
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Translate the phrase; then simplify. Find the sum of −45, −13, and 37.
Answer:
-21
Step-by-step explanation:
37 - 45 - 13 is translated
-8 - 13
-21
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
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Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
If the value of mean is 781.67, then the standard deviation will be 100. Then the correct option is C.
The complete question is given below.
Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130
What is a standard deviation?It is a metric for statistical information dispersion. The degree of spread indicates how much the result varies.
Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan.
The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
The mean of the data will be
Mean = (700 + 735 + 680 + ...... + 820 + 750) / 12
Mean = 781.67
Then the standard deviation will be
SD² = [(700 – 781.67)² + (735 – 781.67)² + ..... + (750 – 781.67)²] / 12
SD² = 10072.2222
SD = 100.36 ≈ 100
Then the correct option is C.
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Solve the following subtraction problem. Remember to borrow as necessary.
9cu yd113cu in
− 4cu ft129cu in
−−−−−−−−−−−−−−−−−−−−−−
The subtraction of the expression will be 238 cubic feet, 551 cubic inches.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in
1 cubic yard = 27 cubic feet
1 cubic feet = 1728 cubic inches
Then the subtraction will be
242 cu ft 1841 cu in
− 4 cu ft 1290 cu in
238 cu ft 551 cu in
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determined about the triangle formed by the ground,
wall, and ladder? Check all that apply.
The triangle is isosceles.
The leg-to-hypotenuse
ratio is 1:√√2.
The leg-to-hypotenuse ratio is 1:√2.
The nonright angles are congruent.
The ladder represents the longest length in the
triangle.
(A,B,D,E)
Answer:
a² b² c² equals mc² and that is the answer
Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
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Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
A- f(x) is decreasing for all x < 6
B- f(x) is increasing for all x > 6
C- f(x) is decreasing for all x < 3
D- f(x) is increasing for all x < 3
Answer:
Step-by-step explanation:
The graph of the given f(x) shows you what you need to know. Nothing cancels. Two answers are going to be true: one for x<3 and one for x>6.
From the graph, you can see that for x>6 the graph is decreasing. That makes B incorrect.
You can also see that for x < 6 The bottom parabola shape is decreasing which makes A true.
Finally at least one of C or D has to be true. As you can see, they both are depending on which shape you look at.
The correct answer is B: f(x) is increasing for all x > 6.
To determine the intervals of increase and decrease for the function f(x), we can analyze the critical points and the behavior of the derivative. The derivative of f(x) is given by:
f'(x) = [(x² - 9x + 18)'(x + 6) - (x + 6)'(x² - 9x + 18)] / (x² - 9x + 18)²
Simplifying the derivative and finding the critical points, we get:
f'(x) = (x² - 3x - 18) / (x² - 9x + 18)²
Setting the numerator equal to zero and solving for x, we find the critical points:
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
x = 6 or x = -3
Analyzing the intervals created by the critical points and using test points, we find that f(x) is increasing for all x > 6. Therefore, the correct answer is B: f(x) is increasing for all x > 6.
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Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 151515 boys and 131313 girls in her class.
What is \text{P(boy})P(boy)start text, P, left parenthesis, b, o, y, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
The probability that a boy is selected is 0.5357 or 53.57%
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
P(boy) is asking for the probability that a boy will be chosen to read a poem out loud. Since there are 15 boys, we can get the probability by dividing this by the total number of students.
This is because out of all the students, there is an equal possibility that each of the 15 boys will be chosen.
P = ( 15 ) / ( 15+13)
P = 15 / 28
P = 0.5357
Therefore the probability that a boy is selected is 0.5357 or 53.57%
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Answer:
53.57%
Step-by-step explanation:
15
16
Matt had 1 pound of dog food in a bag.
He fed his puppy pound of the food.
How much dog food is left in the bag?
Give your answer in simplest form.
pound
WOOF!
Step-by-step explanation:
1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).
like 4/8 or 6/12 or 128/256 or ...
what do we need in the denominator to calculate with 15/16 ?
the same : 16.
and what is half of 16 ? 8.
so, we need the 1/2 based on 16th = 8/16.
so, the dog ate 8/16 (1/2) of the original 15/16.
what was left was
15/16 - 8/16 = 7/16 pound
Perform the operation and
simplify.
x² + 10x + 24
3x² + 3x
÷ (x + 6)
244x3+1474x2+63x/
x+6
what is the %rf for .04?
What is the range of the function represented by the following graph?
*
1 point
Captionless Image
A. all real numbers greater than 4
B. all real numbers less than - 1
C. all real numbers greater than - 6
D. all real numbers less than - 4
Answer:
C the prove is right there on the graph
Answer:
C
Step-by-step explanation:
The graph clearly shows that all the numbers are greater than -6
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f- g)(x).
Step-by-step explanation:
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