The equation of the hyperbola is
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 3650 = 0[/tex]
What is a hyperbola?
In mathematics, a hyperbola is a conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the centre. It is a type of smooth curve lying in a plane and has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The standard form of writing an equation of the hyperbola is,
[tex]\frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
Where (h, k) is the centre; a is the distance from the centre to vertices; b is the distance from co-vertices to the centre.
Given,
Foci of the hyperbola are (13, -1); (-13, -1)
Co-vertices are (0,11); (0,-13)
As we know that the centre of the hyperbola is the midpoint of the foci, then it will be (h,k) = (0,-1)
Distance from centre to foci is, c = 13 [2c = 26; c = 26 / 2 = 13]
Distance from co vertices to foci is, b = 12 [ 2b = 24; c = 24 / 2 = 12]
let us assume a is the distance from the centre to the vertices.
we know that,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
then,
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]a = \sqrt{ {13}^{2} - {12}^{2} } [/tex]
[tex]a = \sqrt{169 - 144} [/tex]
[tex]a = \sqrt{25} [/tex]
[tex]a = 5[/tex]
Now, the equation of the hyperbola is,
[tex] \frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[tex] \frac{ {(x - 0)}^{2} }{ {5}^{2} } - \frac{ {(y + 1})^{2} }{ {12}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 2y + 1 }{144} = 1[/tex]
[tex] \frac{144 {x}^{2} - 25 {y}^{2} - 50y - 50 }{25 \times 144} = 1[/tex]
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 50 = 25 \times 144[/tex]
Hence the required equation is,
[tex]144 {x}^{2} - 25 {y}^{2} - 3650 = 0[/tex]
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If f(x) = -x^2 + 3, Find f(-3)
x^2 means x to the power of 2
Answer:
-6
Step-by-step explanation:
-(-3)²+3
-9 + 3
-6
how many different 12-bit strings begin with 0101, end with 1100 or have 0110 as the four middle bits?
There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.
We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.
So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.
So, we can write here,
Total possible different positions for 1100 and 0110 is,
= 2 x 2
= 4
Because, the two combination can appear simultaneously or they can appear one by one.
So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.
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A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference. If \blue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measures 40^\circ40 ∘ 40, degrees, what does \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measure?
Answer:
122°
The measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.
∠ABC = 2×∠ADC = 2×61°
∠ABC = 122°
Step-by-step explanation:
what is the relative humidity of the parcel at sea level on the leeward side? (fill in only the letter: a, b, c, or d, all caps) a) 25%, b) 33%, c) 100%, or d) 58%
The relative humidity of the parcel at sea level on the leeward side is 58% that is option D
The amount of water vapour in an air-water mixture relative to the maximum amount is known as relative humidity (RH). RH is a comparison between the humidity of a specific water-air mixture and the saturation humidity ratio at a particular temperature (dry-bulb)
By deducting the temperature on the wet-bulb thermometer from the temperature on the dry-bulb thermometer and utilizing a relative humidity chart, one may determine the relative humidity.
The relative humidity of the parcel at sea level on the leeward side is 58%
Option d is the correct answer
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the equation of a circle is x^2+y^2=42.25
Find the radius of the circle.
Answer:
radius = 6.5
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 42.25 ← is the equation of a circle centred at the origin
with r² = 42.25 ( take square root of both sides )
r = [tex]\sqrt{42.25}[/tex] = 6.5
three factories produce light bulbs to supply the market. factory a produces 20%, 50% of the tools are produced in factory b and 30% in factory c. 2% of the bulbs produced in factory a, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory c are defective. a bulb is selected at random in the market and found to be defective. what is the probability that this bulb was produced by factory b?
0.27 = 0.0027% probability that this bulb was produced by factory B.
Given,
In the question:
Three factories produce light bulbs to supply the market. Factory a produces 20%, 50% of the tools are produced in factory B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory C are defective.
We use the conditional probability formula to solve this question. It is
P(A|B) = P(A∩B) / P(A)
In which,
P(B|A) is the probability of event B happening, given that A happened.
P(A∩B) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Bulb is defective.
Event B: Produced by factory A.
Probability of a bulb being defective.
2% of 20%(factory A)
1% of 50%(factory B)
3% of 30%(factory C). So
P(A) = 0.02 x 0.2 + 0.01 x 0.5 + 0.03 x 0.3
P(A) = 0.018
Defective and from factory B:
1% of 50%. So
P(A∩B) = 0.01 x 0.5 = 0.005
What is the probability that this bulb was produced by factory B?
P(A|B) = P(A∩B) / P(A)
P(A|B) = 0.005/ 0.018
P(A|B) = 0.27
Hence, 0.27 = 0.0027% probability that this bulb was produced by factory B.
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Each bag of cereal should contain 350 grams. a box was selected at ramdon and weighed 342 grams. what is the percent error?
The percentage error in selecting the random box is 2.285 %
Let the total amount of bag of cereal be = 350 grams
The box selected at random had a weight of = 342 grams
We know the formula of percentage error.
The percentage error is calculated by the formula
Percentage Error =
( ( Original Value - Observed Value ) / Original Value ) x 100
Plug the values in above formula:
Percentage Error = ( ( 350 - 342 ) / 350 ) x 100
= ( 8 / 350 ) x 100
= 0.02285 x 100
= 2.285 %
Hence , The percentage error in selecting the random box is 2.285 %
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the average hourly wage in the u.s. in october 2018 was $22.90. considering low unemployment and continued growth of the economy in 2019 it was expected that the hourly wage in october 2019 would increase. the p-value associated with the hypothesis test is .001. the correct conclusion is
The correct conclusion for "it was expected that the hourly wage in October 2019 would increase, and the p-value associated with the hypothesis test is .001" is "the average wage is not increased."
What is hypothesis?A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. A strong hypothesis outlines the predicted link between the dependent and independent variables and is succinct and straightforward. It is best to be as specific and testable as possible when describing this relationship.
The answer to the statement "it was predicted that the hourly wage in October 2019 would grow, and the p-value associated with the hypothesis test is.001" should be "the average wage is not raised."
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consider the following binomial experiment: a study in a certain community showed that 5% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia? a) 520.00 b) 22.23 c) 50.99 d) 9880.00 e) 49400.00 f) none of the above.
The number of those who have insomnia has a standard deviation of 22.23.
Given,
People suffer from insomnia = 5%
Total number of people in the community = 10,400
We have to find the standard deviation of the number of people who suffer from insomnia;
Here,
p = 0.05
q = 0.95
n = 10,400
Then,
np = 10400 x 0.05 = 202
Now,
npq = 202 x 0.95 = 494
Standard deviation = √npq = √494 = 22.23
That is,
The standard deviation of the number of people who suffer from insomnia is 22.23
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how many four-digit numbers greater than 2999 can be formed such that the product of the middle two digits exceeds 5?
The 3360 possible four-digit numbers are greater than 2999.
What is the combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
We know it has to be a four-digit number,
The first digit has to be between 3 and 9 (inclusive) so there are 7 options.
The unit digit can be any number so there are 10 options.
The answer will be 7 * (# of possible middle digit combos) * 10.
There are 7*48*10 = 3360 possible four-digit numbers.
Hence, the 3360 possible four-digit numbers are greater than 2999.
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suppose that a coin is tossed three times and the side showing face up on each toss is noted. suppose also that on each toss heads and tails are equally likely. let hht indicate the outcome heads on the first two tosses and tails on the third, tht the outcome tails on the first and third tosses and heads on the second, and so forth. (a) use set-roster notation to describe the elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses. (b) Write each of the following events as a set, in set-roster notation, and find its probability. (i) The event that exactly one toss results in a head. set probability (ii) The event that at least two tosses result in a head. set probability (ii) The event that no head is obtained. set probability
a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.
Given that
a) A coin is tossed three times and the side showing face up on each toss is noted.
The total number of possible outcome are 2³ = 8
The sample space is given by
SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT}
b) Write each of the following events as a set, in set-roster notation, and find its probability.
(i)The event that exactly one toss results in a head.
In this case we need to include only those outcomes where we have exactly on head,
E(1 head) = {THT, TTH, HTT}
So there are 3 such outcomes, the probability is
P(1 head) = no. of desired outcomes/total number of outcomes
P(1 head) = 3/8
P(1 head) = 0.375
(ii) The event that at least two tosses result in a head
In this case we need to include only those outcomes where we have at least two heads which means two or greater than two,
E(at least 2 heads) = {HHH, THH, HTH, HHT}
So there are 4 such outcomes, the probability is
P(at least 2 heads) = 4/8
P(at least 2 heads) = 0.5
(iii) The event that no head is obtained.
In this case we need to include only those outcomes where we have no heads at all.
E(no heads) = {TTT}
So there is only 1 such outcome, the probability is
P(no heads) = 1/8
P(no heads) = 0.125
Hence the answer is a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.2-cm and a standard deviation of 2.3-cm. For shipment, 25 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm.
P(M < 124.5-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
P(M 169.3 cm 168.3 cm) = 0.7724
Given that,
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.
We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5-cm) =
We know that,
Mean =μ= 125.2
Standard deviation=σ=2.3
n=25
P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]
=P(z<-1.522)
Using the z-table,
=0.0603
Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
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Which of the following graphs could represent a quartic function?
On the assumption that each curve has only real roots, the quartic function is the graph C.
What graph does represent a quartic equation?
In this question we have four choices of graphs of polynomials, that is algebraic expressions of the form:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m - 1, m}
Where m is the grade of the polynomial.
The factor form of the polynomial is described below:
p(x) = a · Π (x - rₙ), for n = {0, 1, 2, 3, ..., m - 1, m}
If we consider that each choice has real roots, then the grade of the polynomial coincides with the number of times that the curve pass through the x-axis. Then, the graph C represent a quartic function, that is, a polynomial with grade 4 with the special feature that is a function of the form f(x) = a · x² · (x - r₁) · (x - r₂).
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do you know how to do this my niece is struggling?
a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
Ship travels 33miles in 3 hours.
What is distance?
Distance is the actual distance that a body travels. Additionally known as path length. For instance, the path length for an item going from point O to point P will be distance OP = 360 m. It is a scalar quantity, the distance. It lacks direction and just possesses magnitude.
Ship travels in one hour = 11miles
Therefore, Ship travels in 3 hours = 11×3
= 33miles
Hence, Ship travels 33 miles in 3 hours.
*SHIP OFF COURSE IS NOT GIVEN IN THE QUESTION.
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An electric cooter company charge 1 to rent a cooter plu an additional 0. 15 per minute the cooter i rented. Which expreion repreent the cot, in dollar, for renting a cooter for m minute
Since the scooter is rented for $1 and the firm charges $0.15 per minute, the necessary expression is 1+0.15m.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
rent of scooter=$1
rent of scooter per minute=$0.15
The expression,
=1+0.15m
The required expression is 1+0.15m as rent of scooter is $1 and per minute rent charged by company is $0.15.
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41. which is not a type of comparison for which you would anticipate a two-sample test? a) before treatment versus after treatment. b) old method versus new method. c) sample mean versus desired mean. d) experimental group versus control group.
The sample mean versus desired mean is not a type of comparison one would anticipate for a two-sample test to be performed. Therefore, the option C holds true.
A sample test can be referred to or considered as the test that includes the conducting of an activity to determine the nearest possible outcome of a much larger set of observations. The purpose of conducting such a test is testing that two population means are the same in a set of observations. If the means are same, it means that the test is successful.
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Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data:
Week #Students
6 Weeks ago 83
5 Weeks ago 110
4 Weeks ago 95
3 Weeks ago 80
2 Weeks ago 65
Last Year 50
What is this week's forecast using the naive approach? Assume that a decreasing trend in student appointments exists.
Other than the original data point 6 weeks ago, there is a clear trend over the last 5 weeks with continuously decreasing demand, so this week's forecast is last week's demand plus the difference between last week's demand and the demand two weeks ago. 50 + (50 - 65) = 35
Professor Very Busy needs to allocate time next week to include time for office hours then TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
Smooth the pattern as well as the arrangement to get the outlook this year.
S(Week 5) = TAF(Week 5) + alpha*(Actual(Week 5) - TAF(Week 5))
= 75 + 0.5(65 - 75) = 70
S(Week 6) = TAF(Week 6) + alpha*(Actual(Week 6) - TAF(Week 6))
= 65 + 0.5(50 - 65) = 57.5
T(Week 6) = T(Week 5) + beta*(TAF(Week 6) - TAF(Week 5) - T(Week5))
= -5 + 0.1(65 - 75 - (-5)) = -5 + (-0.5) = -5.5
Therefore, TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
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The population of city A is 23.5% of city B and the population of city B is 51% of city C. If city C has 9.89 million people, which of the following is the closest approximation of city A's population in millions?
0.95 million
1.2 million
1.25 million
1.3 million
1.42 million
The required closest approximation of city A's population is 1.185 million.
What is percent?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, on the off chance that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:We have, city A is 23.5% of city B
A/B = 235/1000 = 47/200 = (B)47/200-----------(1)
and, city B is 51% of city C.
B/C = 51/100
B = (51/100)×9.89 = 5.0439 million
As C = 9.89 million
Put the value of c in equation (1)
A = (5.0439)47/200 = 1.185 million
Thus, required population of city A is 1.185 million.
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-7/8 is greater than or equal to m - 13/8
Answer:
Step-by-step explanation:
greater than
Answer: Greater than
3x+12=-5x+28 necesito ayuda para mi examen please
Answer:
x = 2
Step-by-step explanation:
3x + 12 = -5x + 28
3x + 12+ 5x = -5x + 28 + 5x
8x + 12 = 28
8x + 12 - 12 = 28 - 12
8x = 16
8x/8 = 16/8
x = 2
Complete the following (use the straight-line method): Auto: $40,000 Residual: $4,000 Estimated life: 5 years Year Cost Depreciation Accumulated Book Expense Depreciation Value
After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
Given,
Cost of auto =$40,000
Residual value =$4000
Estimated lifetime =5 years
Straight-line Method:-
Depreciation cost can be calculated by formula,
[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]
It is constant for every year.
Accumulated depreciation can be calculated by formula,
[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]
Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between cost of asset at that year and depreciation cost.
Using the above formulas all the values for each year is caculated and formed into a table.
Year BookValue DepreciationCost Accumulation Book Value
Start End
1 $40,000 $7,200.00 $7,200 $32,800
2 $32,800 $7,200.00 $14,400 $25,600
3 $25,600 $7,200.00 $21,600 $18,400
4 $18,400 $7,200.00 $28,800 $11,200
5 $11,200 $7,200.00 $36,000 $4,000
Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
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Here is an equation.
y = 3x + 5
a) When x = 10, what is the value of y?
b) When x = -10, what is the value of y?
Answer:
a) y = 35b) y = -25Step-by-step explanation:
Given equation,
→ y = 3x + 5
The value of y when x is 10,
→ y = 3x + 5
→ y = 3(10) + 5
→ y = 30 + 5
→ [ y = 35 ]
The value of y when x is -10,
→ y = 3x + 5
→ y = 3(-10) + 5
→ y = (-30) + 5
→ [ y = -25 ]
So, these are the values of y.
Michael is 333 times as old as brandon. 181818 years ago, michael was 999 times as old as brandon. How old is brandon now?.
Bradon is 24 years old and Micheal is 72 years old.
Michael is 3 times as old as brandon. 18 years ago, michael was 9 times as old as brandon
Let m represent Michael
Let b represent Brandon
Then,
m = 3b <-----------"Michael is 3 times as old as Brandon."
m - 18 = 9(b - 18) <-----------"18 years ago, Michael was 9 times as old as Brandon."
3b - 18 = 9b - 162
-18 = 6b - 162
144 = 6b
b = 24 <-------This is Brandon's age.
3b = m
3(24) = 72 <------This is Michael's age.
Therefore, Michael is 3 times as old as Brandon. Also, 18 years ago, Brandon would have been 6 and Michael would have been 54
Now, Bradon is 24 years old and Micheal is 72 years old.
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the fracture strength of tempered glass averages 13.5 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) what is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 13.8? (round your answer to four decimal places.)
The probability that the average fracture strength of 100 randomly selected pieces will be equal to 33.19%.
In order to find the probability first we find the Z score. The Z score related the standard deviation and the mean of any data as
Z = X - μ/σ where Z is the Z score, X is the random variable, μ is the mean and σ is the standard deviation.
The standard deviation of the randomly selected 100 variables will be given as
s = σ/√n where n = 100 and σ = 2
s = 2/√100
s = 0.2
Now, the Z score for this data will be
Z = X - μ/s where X = 13.8, and μ = 13.5 and the value of s = 0.2
Z = 13.8 - 13.5/0.2
Z = 1.5
Now, for Z = 1.5 the p value will be 0.66807
The probability will be P = 1 - 0.66807 = 0.33193 that is 33.19%
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the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm.use excel to find which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth.
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
X= (Z * σ) + μ
X = (-0.52 * 2)
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
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PLEASE HELP
The variable y varies jointly with x and w when y = -42, x = 2, and w = -3.
1.) Find the constant of variation.
k =
2.) Find w when y = 3 and x = 1/14
w =
Answer:
1). The constant of variation is 7
2). w = 6 for the given values of x and y
Step-by-step explanation:
"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w. We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.
We are given one data point: y=-42 where x is 2 and w is -3. Let's put those values into our trrial expression:
y=Kxw
-42=K(2)(-3)
-42 = -6K
K = 7
The expression becames y = 7xwThe constant of variation is 7.
The value of w for y=3 and x=(1/14) would be:
y=7xw
3 = 7*(1/14)*w
3 = (1/2)*w
w = 6Answer:
1) k = 7
2) w = 6
Step-by-step explanation:
Joint variation equation
If y varies jointly with x and w:
[tex]\boxed{y \propto xw \implies y=kxw}[/tex]
for some constant k.
Given:
y = -42x = 2w = -3Substitute the given values into the joint variation equation and solve for k:
[tex]\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}[/tex]
Therefore, the equation is:
[tex]\boxed{y=7xw}[/tex]
To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:
[tex]\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}[/tex]
Which on blue, light blue yellow or red?
Step-by-step explanation:
of course there is an explanation. and a correct answer (not just a wild guess).
f(x) = 2x
g(x) = 2x² - 1
f(g(x)) means that x is first processed by g, and then the result of that is processed by f.
in other words, the whole functional expression of g becomes the input argument for f.
therefore,
f(g(x) = 2(2x² - 1) = 4x² - 2
so, the correct answer is light blue.
the daily scrum is an event that happens every day. what would be three concerns if the frequency were to be lowered to every two or three days
Three problems would arise if the frequency of scrum was lowered to every two or three days.
(A) There may be missed opportunities to examine and amend the sprint backlog.
(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.
(C) Too much time is spent updating the scrum board prior to meetings.
What is a scrum?
Scrum is a project management framework that was initially focused on software development, while it has now been applied to other areas such as research, sales, marketing, and cutting-edge technology.
It is intended for groups with ten or fewer members who divide their work into tasks that can be finished in sprints, which are time-boxed iterations that can be done in as little as one month and most frequently two weeks.
If the frequency was reduced to every two or three days, there would be three issues.
(A) The chances to review and modify the Sprint Backlog may be missed.
(B) The Sprint plan becomes imprecise; obstacles are raised and removed more slowly.
(C) Too much time is spent before meetings updating the scrum board.
Therefore, three problems would arise if the frequency was lowered to every two or three days.
(A) There may be missed opportunities to examine and amend the sprint backlog.
(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.
(C) Too much time is spent updating the scrum board prior to meetings.
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3
The smallest square achieving this length : 38² = 1444.
Square:
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. The complete length of a square's boundary is its perimeter. As a result, the length of each side can be added to determine the square's perimeter. Since a square has four sides, its perimeter may be calculated by adding all four of its sides. The space a square takes up is its area.
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