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Related Questions
A box contains 13 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective.
b. none are defective.
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Answer:
A. 1/1287
B. 56/1287
Step-by-step explanation:
Probability of getting all are defective transistors is 5/12.
Given that, a box contains 13 transistors, 5 of which are defective.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
a) Probability of getting all are defective
Number of favorable outcomes = 5
Total number of outcomes = 12
Probability of getting all are defective = 5/12
b) Probability of getting none are defective
Number of favorable outcomes = 7
Total number of outcomes = 12
Probability of getting none are defective = 7/12
Therefore, probability of getting all are defective transistors is 5/12.
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a small bunch of flowers costs $5 and a large bunch costs $20. what fraction of the cost of the large bunch is the small bunch
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Hope it's helpful.....
the dimensions of a porch are 16 feet long by 12 feet wide use the scale 1 inch=4 feet what is the width and length in inches
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Since the scale is 1 in = 4 ft, we divide both the length and width by 4 to get the new length and width with the scale factor applied.
16 / 4 = 4
12 / 4 = 3
So, the
length = 4
width = 3
Hope this helps!
Find the value of x. The diagram is not to scale.
A. x=70
B. None of these
C. x=20
D. x=16
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We then have two equal sides:
RS = ST
Thus,
Angle R = Angle T
Then, we have the following equation:
5x = 180- (5x-20)
From here, we clear the value of x:
5x = -5x + 180 + 20
10x = 200
x = 200/10
x = 20
Answer:
the value of x is:
C. x = 20
Find the equation of the line that has these features: slope, m=-6/5 passes through the point (-5,10)
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the equation of the line is
y-y1=m(x-x1)
then
m=-6/5 passes through the point (-5,10)
y-10=(-6/5)*(x+5)-------> y-10=(-6x/5)-6------------> y=(-6x/5)+4---------> y=-1.2x+4
see the attached figure
the answer is
y=-1.2x+4
Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? Enter your answer in the box
https://static.k12.com/nextgen_media/assets/8120449-SUM_CR_GMT_SemB_06_UC_DP100_864_003.jpg
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2. As you can see, m∠B=(2x-1)° and m∠D=(3x-59)° are opposite angles, then:
m∠B+m∠D=180°
3. When you substitute the values of m∠B and m∠D into m∠B+m∠D=180°, you obtain:
m∠B+m∠D=180°
(2x-1)+(3x-59)=180°
4. You must clear the "x", as below:
(2x-1)+(3x-59)=180°
5x-60=180
x=48°
5. Now, you can find the value of m∠A, m∠B and m∠D:
m∠A=2x+4
m∠A=2(48)+4
m∠A=100°
m∠B=2x-1
m∠B=2(48)-1
m∠B=95°
m∠D=3x-59
m∠D=3(48)-59
m∠D=85°
6. Therefore, the value of m∠C is:
m∠A+m∠B+m∠C+m∠D=360°
m∠C=360-m∠A-m∠B-m∠D
m∠C=360°-100°-95°-85°
m∠C=80°
What is the measure of angle C?
The answer is: 80°
Read the line of poetry:
And the dish ran away with the spoon.
This line is an example of what term?
A.
alliteration
B.
personification
C.
onomatopoeia
D.
imagery
Please help I AM SO SCARED IF I FAIL THIS...
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Two sides of a triangle are equal in length, and the third side is 5 inches. If the perimeter is 17 inches, how long are the two equal sides?
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Perimeter of a triangle can be found by adding up all three sides of the triangle. That means if you know the length of one side, subtracting that length from the perimeter gives you the length of the other two sides added up. So:
[tex]P = s1 + s2 + s3 [/tex]
[tex]17 = 5 + s2 + s3 [/tex]
[tex]12 = s2 + s3[/tex]
Since you know the two mystery sides are the same length, just divide 12 by 2. 12/2 = 6in. That means each one of the two equal sides is 6in long.
ABCD and JKLM are similar rectangles. What is the perimeter of JKLM?
21 m
22 m
24 m
28 m
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So multiply AD by 3/2 to find the length of JM . The length would be 3*3/2=9/2
Next find the perimeter of JKML. It would be 2(9/2+6)=21
Answer:
Step-by-step explanation:
21
The enrollment in college a may be modeled by y = 0.051x + 0.470, and the enrollment in college b may be modeled by y = –0.041x + 1.850, where x is the number of years since 1990 and y is the enrollment in thousands. when will the two colleges have the same enrollment and what is that enrollment?
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The second equation represents the enrollments of college B
if you let two equation equal to each other, you can understand them as the enrollments of college A and college B at "x" year.
0.051x + 0.470 = -0.041x + 1.850
0.051x + 0.041x = 1.850 - 0.470
0.092x = 1.38
x = 1.38/0.092 = 15 years from 1990, 1990 + 15 = 2005
both equations represents the enrollments, but for specific the year of 2005, they have the same enrollments. You can either plug 2005 in the first or second equation, the answer will come out the same.
y = 0.051(2005) + 0.470 = 102.745 thousands of enrollments. It's awkward to say it this way, you can multiply 102.745 by 1000.
==> 102.725 * 1000 = 102725 enrollements
===================================================================
The year of 2005 college A and college B both have the same enrollments of 102725.
In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.
What is Two Variable linear Equation?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Here, given relation between enrollment year and total number of enrollment
y = 0.051x + 0.470 ..............(i)
y = -0.041x + 1.850 ................(ii)
On comapring eq. (i) and eq. (ii), we get
0.051x + 0.470 = -0.041x + 1.850
0.051x + 0.041x = 1.850 - 0.470
0.092x = 1.380
x = 1.380 / 0.092
x = 15
put the value of x in equation (i), we get
y = 1235
Thus, In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.
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The enrollment in college A may be modeled by y = 0.046x + 0.570, and the enrollment in college B may be modeled by y = –0.036x + 2.702, where x is the number of years since 1990 and y is the enrollment in thousands. When will the two colleges have the same enrollment and what is that enrollment?
In 1974, both colleges had an enrollment of 1,766 students.
In 2016, both colleges will have an enrollment of 1,766 students.
In 2012, both colleges will have an enrollment of 1,122 students.
In 1992, both colleges had an enrollment of 1,600 students.
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Since both ys are equal, you can equate the right side of each equation to each other.
0.046 x + 0.570 = - 0.036x + 2.702 There are a number of ways to go on. The easiest is to dig out your calculator. Add 0.036x to both sides.
0.046x + 0.036x + 0.570 = 2.702
0.082x + 0.570 = 2.702 Now subtract 0.570 from both sides.
0.082x = 2.702 - 0.570
0.082x = 2.132 Divide by 0.084
x = 2.132 / 0.082
x = 26 which means you add 26 onto 1990. The year this took place was 2016
x = 2016 (That's the year there was equality in enrollment). The second one is the only year that gives 2016 as an answer. So you don't have to find y. But we'll do it anyway.
Now you have to solve for y
y = 0.046x +0.57 put 26 in for x
y = 0.046 * 26 + 0.570
y = 1.196 + 0.570
y = 1.766 enrollment numbers were equal, but this is in thousands.
y = 1766 enrollment in actual numbers of students.
Second choice <<<<<===== answer.
Answer:
In 2016, both colleges will have an enrollment of 1,766 students.
Step-by-step explanation:
gradpoint
When changes in one variable are usually accompanied by changes in the same direction in another variable?
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If r = 1, s = 2, and t = 3, what value do you expect y will have?
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There are 18 students enrolled in Mr. Baker's class. Today 3 of them are absent. What is the ratio of the number of students present in class today to the total number enrolled?
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Answer:
5/6
Step-by-step explanation:18 total -3 absent = 15
15 divided by 3
18 divided by 3=
5/6
The ratio for the given two numbers is 5 : 6.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The total number of students are given as 18.
And, the number of students absent is 3.
Then, the number of present students is given as 18 - 3 = 15.
Now, the ratio as per the given case can be obtained as follows,
Number of students present ÷ Number of enrolled students
⇒ 15 ÷ 18
⇒ 15/18
⇒ 5 : 6
Hence, the required ratio for the two numbers is 5 : 6.
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Zach has 53 flowers to plant. he wants to plant them in groups of 10s and 1s. zach can plant 10 flowers in each flower box. He can plant 1 flower in each pot. Zach only wants to plant a group of ten flowers in each box. Is there any way that zach could plant all 53 flowers using boxes only? Explain your answer.
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Solution:
we are given that
Zach has 53 flowers to plant.
He wants to plant them in groups of 10s and 1s.
zach can plant 10 flowers in each flower box.
Zach only wants to plant a group of ten flowers in each box.
We have been asked to find Is there any way that zach could plant all 53 flowers using boxes only?
since zach can plant 10 flowers in each flower box. so in 5 boxes he can plant
50 flowers.
Now we have 3 left. These 3 can be planted in pot.
But he wants to use boxes only with 10 flowers in each box.
So its not possible to plant all 53 flowers using boxes only.
The angle a vector makes with the x-axis of a coordinate system must be what size in order to make one or more of its components negative? A) Less the 30 degrees B) between 30 and 60 degrees C) between 61 and 90 degrees D) greater then 90 degrees
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_____
An angle greater than 90 degrees will put it in the second quadrant, where the x-component is negative.
Answer:
Greater than 90 degrees.
Step-by-step explanation:
Let a vector R make angle [tex]\theta[/tex] with the x-axis. Then, the component along the x-axis would be
[tex]R cos\theta[/tex]
Component along y-axis would be
[tex]R sin\theta[/tex]
For [tex]0<\theta<90[/tex] both the components will be positive and lie in the first quadrant. If angle of vector is more than 90 degrees, one of the components would be negative. For example, angle between 90 to 180 degrees, x-component would be negative while between 180-270 degrees, both the components would be negative.
The table below shows the total cost for purchasing a certain number of equally-priced concert tickets. Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),
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Answer:
c = 55t
Step-by-step explanation:
Since there are no handling fees and the price of tickets is constant, we know the cost will be proportional to the number of tickets purchased. The generic form of an equation expressing a proportional relationship between cost (c) and number of tickets (t) is ...
c = kt
where k is the constant of proportionality (the cost per ticket). We can find k by using any of the data points given in the table. Using the first point, we have ...
110 = k·2
110/2 = k = 55 . . . . . divide by 2
Then using this value for k, the desired equation can be written ...
c = 55t
bob started mowing at 9:55 am .It took him 25 minutes to mow the front yard and 45 minutes to mow back yard.at what did bob finish mowing?
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The final answer should be: 11:05 am.
is this correct....help me with the 2 questions
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Which of the following graphs matches the circle defined by this equation ? (X+2)^2+(y-4)^2=9
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Radius :3
This equation represents the circle having a radius of 3 units and a center situated at (-2, 4). Hence, graph D is correct.
Use the concept of a circle defined as:
A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.
A circle is also known as the location of points that are evenly spaced apart from the center.
The radius of a circle is measured from the center to the edge.
The given equation of a circle is:
(X+2)²+(y-4)²= 9
Since we know that,
The general equation of the circle is,
(x-a)²+(y-b)²= r²
Where (a, b) is the center of the circle
r is the radius of the circle.
Now compare with the given equation we have,
(a, b) = (-2, 4)
And radius r² = 9
Then r = 3
Then this circle has a radius of 3 units and a center situated at (-2, 4).
Hence,
Graph D is correct.
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The complete question is:
Which of the following graphs matches the circle defined by this equation? (x-a)²+(y-b)²= r²
I Need help please cmon
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[tex]\bf \cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}\implies \cfrac{3+3+3}{4}\implies \cfrac{9}{4}\implies 2\frac{1}{4}[/tex]
Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take rich and Michelle to meet?
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Answer:
2 7/27 hours, about 2 hours 15 minutes, 33 seconds
Step-by-step explanation:
You want to know how long it takes for Rich and Michelle to meet if they start 305 miles apart and are driving toward each other. Rich is driving 70 mph, and Michelle is driving 65 mph.
Closing speedThe speed at which they are moving toward each other is ...
70 mph + 65 mph = 135 mph
Meeting timeThat means they will reduce their separation distance to zero after ...
time = distance / speed
time = (305 mi)/(135 mi/h) = 2 7/27 h
It will take 2 7/27 hours, about 2.26 hours, for Rich and Michelle to meet.
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A random variable x that assumes the values x1, x2, . . . , xk is called a discrete uniform random variable if its probability mass function is f(x) = 1 k for all of x1, x2, . . . , xk and 0 otherwise. find the mean and variance of x.
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[tex]\mathbb E[X]=\displaystyle\sum_x x\,f_X(x)[/tex]
where [tex]f_X(x)=\mathbb P(X=x)[/tex] is the PMF of [tex]X[/tex]. We have
[tex]f_X(x)=\begin{cases}\dfrac1k&\text{for }x\in\{x_1,\ldots,x_k\}\\\\0&\text{otherwise}\end{cases}[/tex]
So the expectation (mean) of the given uniformly distributed [tex]X[/tex] is
[tex]\mathbb E[X]=\displaystyle\sum_x x\,f_X(x)=\sum_{i=1}^k x_i\,f_X(x_i)=\frac1k\sum_{i=1}^k x_i[/tex]
Without any more specific information, this is all we can say about the mean.
The variance of [tex]X[/tex] is defined by
[tex]\mathbb V[X]=\mathbb E[(X-\mathbb E[X])^2]=\mathbb E[X^2]-\mathbb E[X]^2[/tex]
In computing the second moment [tex](\mathbb E[X^2])[/tex] we run into the same issue as before - we can't find a "complete" result - but we do get
[tex]\mathbb E[X^2]=\displaystyle\sum_x x^2\,f_X(x)=\frac1k\sum_{i=1}^k{x_i}^2[/tex]
and so
[tex]\mathbb V[X]=\displaystyle\frac1k\sum_{i=1}^k{x_i}^2-\left(\frac1k\sum_{i=1}^kx_i\right)^2[/tex]
We can expand [tex]\mathbb E[X]^2[/tex] a bit. Denoting the set [tex]K=\{1,2,\ldots,k\}[/tex], we can write
[tex]\displaystyle\left(\frac1k\sum_{i=1}^kx_i\right)^2=\frac1{k^2}\left(\sum_{i=1}^k{x_i}^2+\sum_{i,j\in K,\,i\neq j}x_ix_j\right)[/tex]
and so
[tex]\mathbb V[X]=\displaystyle\left(\frac1k-\frac1{k^2}\right)\sum_{i=1}^k{x_i}^2-\frac1{k^2}\sum_{i,j\in K,\,i\neq j}x_ix_j[/tex]
[tex]\mathbb V[X]=\displaystyle\frac{k-1}{k^2}\sum_{i=1}^k{x_i}^2-\frac1{k^2}\sum_{i,j\in K,\,i\neq j}x_ix_j[/tex]
but again, that's as much as we can say without any more specific information.
A discrete uniform random variable has values which are equally likely to occur. The mean can be calculated by summing all the values of the variable and dividing by the number of values, represented as μ = Σx/k. The variance, a measure of dispersion, can be calculated using the formula σ² = Σ(x − μ)²/k.
Explanation:In the context of a discrete uniform random variable, the mean (μ) and variance (σ²) can be calculated using specific formulas. This is related to the nature of a discrete uniform distribution, where x assumes the values x1, x2, ..., xk, and the probability of each outcome is equally likely.
Firstly, to find the mean
you simply need to add up all the values of x and divide by the number of values (k). This could be represented as μ = Σx/k.
Secondly, the variance can be calculated using the formula σ² = Σ(x − μ)²/k. In this equation, x represents the values of the random variable, μ is the mean (which we calculated earlier), and k represents the total number of values.
The concept here is essentially determining the central tendency (mean) and dispersion (variance) of a discrete uniform random variable. This is a fundamental topic in the field of probability and statistics.
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Which expression is an equivalent expression of 12x + 10 + 4y? 2(6x + 2y + 6) 3(4x + y + 10) 2(6x + 4y + 8) 2(6x + 5 + 2y)
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2(6x + 5 + 2y).
This is because
2(6x + 5 + 2y) =
2 * 6x + 2 * 5 + 2 * 2y =
12x + 10 + 4y
Multiply it out
=2(6x + 5 + 2y)
distribute 2 to every term in parentheses
=(2*6x) + (2*5) + (2*2y)
=12x + 10 + 4y
ANSWER: Last choice 2(6x + 5 + 2y)
Hope this helps! :)
PLZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPP!
Using similarity solve for x. Show all work.
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see the attached figure with letters
applying the Pythagorean theorem
in the triangle ABE
BE²=x²-9²------------> equation 1
in the triangle ABD
BD²=(16+9)²-x²--------> BD²=25²-x²-----------> equation 2
in the triangle BED
BD²=(BE)²+16²--------------> equation 3
I substitute 1 and 2 in 3
25²-x²=x²-9²+16²------> 25²+9²-16²=2x²-------> 2x²=450--------> x²=225
x=√225--------> x=15 cm
the answer is x=15 cm
Express the confidence interval (0.070, 0.126) in the form of
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Solution 1
Let's find E
2E=(0.126-0.070)
E=(0.126-0.070)/2
E=0.056/2
E=0.028
Solution 2
Let's find U
u=(0.126+0.070)/2
u=0.196/2
u=0.098
Then:
CI=(u-E < p < u+E)
Replace the number according to the formula
CI=(0.098-0.028 < p < 0.098+0.028)
A particle moves along the x-axis in such a way that its velocity at any time t > 0 is given by v(t)=3t^2-4t-4. the particl's position x(t) has a value of 1 when t=1
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Why is partitioning a directed line segment with a ratio of 1:2 not the same as finding half the length of the directed line segment
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With the ratio 1:2, you would have 1 cookie while your friend has 2 cookies. This is no longer a fair split. Things are not 50/50 anymore. You have 1/3 of the cookies while your friend has 2/3 of the cookies. Your friend would have twice as much.
So that applies to the segment lengths as well. The line segment would be split up into two parts A and B. Part A is the smaller segment that is half as long as part B. Or put another way, part B is twice as long as part A
Answer:
Sample response: A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.
Step-by-step explanation:
someone help me on this question please
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peanuts : raisins : chocolate chips = 4 : 6 : 2
tells you that peanuts make up
4/(4+6+2) = 1/3
of the total quantity of the mix.
The quantity of peanuts required is (1/3)*(48 ounces) = 16 ounces (or 1 pound).
_____
In the 48 ounces of mix, 1 part = 4 ounces.
2, 3, 6, 8, . . . is an example of an infinite alternating series. True False
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Explanation: An alternating series is on in which the alternate terms are negative & positive.
Example, 1/2 − 1/4 + 1/8 − 1/16 + ⋯ is an alternating series.
but here, in the given series - all numbers are positive . Hence, it is not an infinite alternating series.
Answer:
false
Step-by-step explanation:
took the test