Answer:
k=8
Step-by-step explanation:
Since y and x are in direct proportions, the equation is
y= kx, where k is a constant.
when y= 33.6, x=4.2,
33.6= k(4.2)
k= 33.6 ÷4.2
k=8
Answer:
k=8
Step-by-step explanation:
suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?
Step-by-step explanation:
Total catalysts = 10
Probability of 2 lower acidic catalysts = 2/10 = 1/5
For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer: 0.81
Step-by-step explanation:
[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]
A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 400 and the product is a maximum.
Answer:
100 and 200Step-by-step explanation:
Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;
a+2b = 400 ....
From the equation above, a = 400 - 2b ... 2
If the product of the numbers is a maximum then;
ab = (400-2b)b
let f(b) be the product of the function.
f(b) = (400-2b)b
f(b) = 400b-2b²
For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0
f'(b)= 400-4b = 0
400-4b = 0
400 = 4b
b = 400/4
b = 100
Substituting b= 100 into the equation a = 400 - 2b to get a;
a = 400 - 2(100)
a = 400 - 200
a = 200
The two positive integers are 100 and 200.
A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points
Answer: Option B, 16/81
Step-by-step explanation:
So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.
We know that every integer number can be "decomposed" into a product of prime numbers.
Then a number N, that is divisible by 3, can be written as:
N = 3*k
Where k is another integer.
Here we will have a product of 4 numbers, each of them are in between 1 and 6.
Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2
Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.
Then we must have a 1, 2, 4 or 5.
The probability of 4 outcomes out of 6, is:
P = 4/6.
But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:
P = (4/6)^4 = (2/3)^4 = 16/81
Answer:
16
Step-by-step explanation:
(4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000 (c) x 3 100 − 1000x 2 (d) x log x (2) (2 points) U
Answer:
(a) O(x²)
(b) O(x²)
(c) O(x²)
(d) Not O(x²)
Step-by-step explanation:
If a function is O(x²), then the highest power of x in the function ia greater or equal to 2.
(a) 100x + 1000
This is O(x), not O(x²)
(b) 100x² + 1000
This is O(x²)
(c) x³.100 − 1000x²
This is O(x²)
(d) x log x²
This is not O(x²)
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.
Answer:
See answer and graph below
Step-by-step explanation:
∬Ry2x2+y2dA
=∫Ry.2x.2+y.2dA
=A(2y+4Ryx)+c
=∫Ry.2x.2+y.2dA
Integral of a constant ∫pdx=px
=(2x+2.2Ryx)A
=A(2y+4Ryx)
=A(2y+4Ryx)+c
The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2
The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]
The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between
the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].
Let consider x = rcosθ and y = rsinθ because x² + y² = r²;
Now, the double integral can be written in polar coordinates as:
[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]
[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]
[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]
Thus, the integral becomes:
[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]
since 2sin² = 1 - cos2θ∴
[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]
[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]
Learn more about double integral here:
https://brainly.com/question/19756166
Find the sum of the first 12 terms of the sequence 512, 256, 128, …
Answer: 1023.75 (a)
Step-by-step explanation:
The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.
a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.
Now to calculate the sum, we consider two formula here and select the one that is most appropriate,
(1) a( rⁿ - 1 )/r - 1, when r is greater than 1
(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.
In this question, formula 2 shall be appropriate because r is less than 1.
so,
S₁₂ = 512( 1 - 0.5¹² )/1 - 0.5
512( 1 - 2.44 ₓ 10⁻⁴ )/0.5
= 512( 0,9998 )/0.5
= 511.875/0.5
= 1023.75
The answer is a
A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use α = 0.10. Are the owners having their transmissions serviced at 30,000 miles?
Answer:
No, the owners are not having their transmissions serviced at 30,000 miles.
Step-by-step explanation:
We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.
The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.
Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles {means that the owners are having their transmissions serviced at 30,000 miles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles {means that the owners are having their transmissions serviced at different than 30,000 miles}
The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles
[tex]\sigma[/tex] = population standard deviation = 1684 miles
n = sample of customers = 40
So, the test statistics = [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]
= 1.71
The value of z-statistics is 1.71.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)
= 1 - 0.9564 = 0.0436
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.
Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.
PLEASE HELP- MATH
simplify the fraction
5bc/10b^2
[tex]\dfrac{5bc}{10b^2}=\dfrac{\not 5\cdot \not b\cdot c}{2\cdot \not 5\cdot \not b\cdot b}=\dfrac{c}{2b}[/tex]
Answer:
c / ( 2b)
Step-by-step explanation:
5bc/10b^2
Lets look at the numbers first
5/10 = 1/2
Then the variable b
b / b^2 = 1/b
Then the variable c
c/1 = c
Putting them back together
1/2 * 1/b * c/1
c/ 2b
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option (B)
Step-by-step explanation:
The given expression is,
[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]
We can rewrite this expression as,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]
Solving it further,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]
[tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]
[tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]
[tex]=x\sqrt{2}[/tex]
Therefore, quotient will be x√2.
Option (B) will be the correct option.
Draw the function
[tex]y = \tan(x) [/tex]
on the interval [-pi, pi]
Answer:
The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.
Your’re in charge of evening entertainment for an important client group You use the company credit card to take their four representatives out to dinner. Two people order the steak entree for 32.50 Two people order the grilled tuna for 28.90 and you order the lasagna for 24.95 When the bill comes you tip 20% what is the amount of tip you leave
Answer:
total amount paid = 32.5 + 28.9 + 24.95 = 86.35
20% of the total amount paid = 0.2 * 86.35 = 17.27
you tip 17.25$
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n
Answer:
The answer is option AStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6
Substitute the values into the above formula
A(n) = 38 + (n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
a
Step-by-step explanation:
you're welcome!
The histogram shows that nine students had grades of 80 or higher.
The histogram shows there were 22 students in the class.
The histogram shows there were 25 students in the class.
The histogram is symmetrical.
The histogram has a peak.
The histogram shows the data is evenly distributed.
The histogram shows a gap in the data
Answer:
bde
Step-by-step explanation:
Answer:
B: The histogram shows there were 22 students in the class.
D: The histogram is symmetrical.
E:The histogram has a peak.
F: The histogram shows the data is evenly distributed.
Step-by-step explanation:
edg 2020
PLEASE HELP ME WITH THIS QUESTION
Answer:
y-k
x-h
Step-by-step explanation:
Given E &D, F would be at (x, k).
That means E to F would be y-k.
And F to D would be x-h.
I assume you don’t need to find E to D, since that’s just r. (You could use the Distance Formula or Pythagoreans theorem to come up with and equation, but it wouldn‘t be one of those listed.)
someone please help me
Answer:
3 mL
Step-by-step explanation:
The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33t How fast does the tree grow? ANSWER centimeters per year.
Answer:
The tree grows 33cm per year
Step-by-step explanation:
Here in this question, we are interested in knowing how fast the growth of the tree is.
This is easily obtainable from the equation for the height of the tree.
Mathematically, the equation is given as;
H = 210 + 33t
Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.
So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree
Use a double angle identity to rewrite the formula r(Θ)=[tex]1/16v^2sin(theta)cos(theta)[/tex]
Answer:
1/32v²sin2θ
Step-by-step explanation:
Given the expression r(theta) = 1/16v²sinθcosθ
According to double angle of trigonometry identity;
Sin2θ = sin(θ+θ)
Sin2θ = sinθcosθ + cosθsinθ
Sin2θ = 2sinθcosθ
sinθcosθ = sin2θ/2 ... **
Substituting equation ** into the question
1/16v²sinθcosθ = 1/16v²(sin2θ/2)
1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)
1/16v²sinθcosθ = 1/32v²sin2θ
Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ
Jill works at a cell phone store. Jill earns $175 every week plus $45 for every phone p that she sells. if Jill makes $445 at the end of the week how many phones did she sell?
━━━━━━━☆☆━━━━━━━
▹ Answer
6 phones
▹ Step-by-Step Explanation
$445 - $175 = $270
$270 ÷ $45 = 6
6 phones
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is 45x62 Please help.
Answer:
45
62x
______
90
2700+
_________
2790
Step-by-step explanation:
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
What are the Links of two sides of a special right triangle with a 306090° and a Hypotenuse of 10
Answer:
Step-by-step explanation:
60°=2×30°
one angle is double the angle of the same right angled triangle.
so hypotenuse is double the smallest side.
Hypotenuse=10
smallest side=10/2=5
third side =√(10²-5²)=5√(2²-1)=5√3
Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?" transitive reflexive symmetric
Answer: Transitive property.
Step-by-step explanation:
First, for the equality we have:
Reflexive:
For all real numbers x, x = x.
Symmetric:
For all real numbers x, y
if x= y, then y = x.
Transitive:
For reals x, y and z.
if x = y, and y = z, then x = z.
Now, let's talk about inequalities.
first, the reflexive property will say that:
x > x.
This has no sense, so this property does not work for inequalities.
Now, the reflexive.
If x > y, then y > x.
Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.
Not, the transitive property.
if x > y, and y > z, then x > z.
This is true.
x is bigger than y, and y is bigger than z, then x should also be bigger than z.
x > y > z.
And this also works for the inverse case:
x < y and y < z, then x < z.
So the correct option is transitive property.
What is the median of these figure skating ratings?
6.0 6.0 7.0 7.0 7.0 8.0 9.0
Answer:
The median would be 7.0.
Step-by-step explanation:
The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
What is the area of polygon EFGH?
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
a family spent $93 at a carnival.
*they spent $18 on tickets and $30 on food. they spent the rest of the money on games.
which equation can be used to to find "g", the amount of money used on games.
Answer: 93-(18+30)=g
93-48=g
45=g
Step-by-step explanation: yup
The answer is 93-18-30-g=0 or 18+30+g=93
