Answer:
1,0
8/15,-7/25
Step-by-step explanation:
3x - 5y = 3
5y = 3x-3
y = (3x-3)/5
y= 3x² -4x +1
or, (3x-3)/5 = 3x²-4x +1
or, 3x-3 = 15x²-20x+5
or, 15x² - 23x +8 =0
or, 15x² - (15+8)x +8 =0
or, 15x² - 15x -8x +8 = 0
or, 15x (x - 1) -8(x-1) =0
or, (x-1)(15x-8)=0
Either,
x-1=0
x = 1
when x=1,
y= 0
or,
15x-8=0
x=8/15
when x= 8/15,
y= -7/25
In a pre-election poll, 58% of a large random sample of voters responded as planning to vote for the school enhancement millage. A 95% confidence interval was computed for the proportion of all such voters who plan to vote for the school enhancement millage. Review each of the following statements regarding the meaning of the 95% confidence level. Determine if it is a correct (true) meaning or incorrect (false).
Answer: Hello the statement related to your question is missing attached below is the statement
answer : The statement is false
Step-by-step explanation:
The statement is false
This is because a confidence interval gives a range of values for an unknown parameter.
A 95% confidence interval is calculated and it gives a lower and upper limit in which the 58% of the voters can fall into i.e. The 58% of voters can fall within the upper and lower limit of the 95% confidence interval and not exactly 95% . Hence the statement is false.
Suppose that an appliance is constructed in such a way that it requires that n independent electronic components are all functioning. Assume that the lifespan of each of these, Tj, is an exponential random variable with parameter λj.
a. Let X be the random variable giving the lifespan of the appliance. Find the CDF and PDF for X.
b. Find the expected value of X.
c. Now find the median lifespan of the appliance (that is, the time t at which half of the appliances are likely to have broken and half to be working ).
Answer:
Step-by-step explanation:
[tex]T_j \sim exp ( \lambda j) \ \ \ j = 1 (1) n \\ \\ f_{Tj}(tj) = \lambda j e^{-\lambda j tj } , tj>0 \\ \\ P\Big[ Tj> x\Big] = \int \limits ^{\infty}_{x} \lambda j e^{-\lambda j tj}\ dtj \\ \\ = e^{-\lambda j x}, x > 0 \\ \\ \\ \\ a) F_x (x) \\ \\ = P[X \le x ] \\ \\ = 1 - P[X> x] \\ \\ = 1 - \pi \limits ^{n}_{j =1} \Big\{ P[T_j > x ] \Big \}[/tex]
[tex]\text{This is because the appliance has the capacity to work for more than (x) }[/tex][tex]\text{hours if and only if all the "n" components work more than (x) hours.}[/tex]
[tex]\text{Then:}[/tex]
[tex]= 1 - e \ \pi^{n}_{j=1} \ e^{-\lambda j x} \\ \\ = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}[/tex]
∴
[tex]CDF = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]PDF =\Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]f_x(x) = \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
(b)
[tex]E(x) = \int \limits ^{\infty}_{o }x f_x (x) \ dx \\ \\ = \int \limits ^{\infty}_{o }x \ \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ dx[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j=1} \lambda j} \ \ \int \limits ^{\infty}_{o} \Big [(\sum \limits ^n_{j=1} \lambda j )x \Big] e ^{-\Big ( \sum \limits ^{n}_{j=1} \lambda j \Big)x} \ \ d \Big( x \sum \limits ^n_{j=1} \lambda j \Big)[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt \ \ \ \ \text{\Big[By transformation }t =( \sum \limits ^n_{j=1} \lambda j )x \Big][/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j}[/tex]
(c)
[tex]Let \ \ l_y_{\dfrac{1}{2}} \text{ be the median}[/tex]
∴
[tex]F(l_y_{\dfrac{1}{2}}) = \dfrac{1}{2} \\ \\ 1 - e ^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} = \dfrac{1}{2} \\ \\ \dfrac{1}{2} = e^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big) } {l_y}_{\frac{1}{2}} \\ \\ - In 2 = {-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} \\ \\ \\ \\ \mathbf{ {l_y}_{\frac{1}{2}} = \dfrac{ In \ 2}{\sum \limits ^{n}_{j=1} \lambda j }}[/tex]
The height of a thrown ball is a quadratic function of the time it has been in the air. The graph of the quadratic function is the parabolic path of the ball.The vertex of the graph is (1, 20) and the path of the ball includes the point (0,4). What is an expression that defines this function? Write the quadratic function in vertex form.
Answer:
f(x) = a(x - 1) + 20
Step-by-step explanation:
Vertex form is written in this format: f(x) = a(x - h) + k. The vertex point is written in the form (h,k). To write the vertex in the equation, fill in the digits where they belong.
Hope it helps!
The ball's parabolic route is represented by the quadratic function's graph. The quadratic function is x²-2x+4=0.
Given that,
A thrown ball's height is a quadratic function of the amount of time it has been in the air. The ball's parabolic route is represented by the quadratic function's graph. The ball's route includes the location (1, 20), which is the graph's vertex (0,4).
We have to find what does the expression for this function look like? In vertex form, write the quadratic function.
What is the vertex form of a parabola?Use y= a(x-h)² + k as the vertex form of a parabola.
(The parabola opens upward if "a" is positive and downward if "a" is negative.) Additionally, the vertex of the (h,k) is a parabola.
The vertex of the parabola (h,k) is (1,20)
The a value is 4 and y as 0.
y=a(x-h)²+k
0=4(x-1)²+20
0=4(x²-2x+1)+20
0=4x²-8x-4+20
0=4x²-8x+16
4x²-8x+16=0
x²-2x+4=0
Therefore, the quadratic function is x²-2x+4=0.
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In a lumberjack competition, a contestant is blindfolded and then spun around 9 times. The contestant then immediately tries to hit a single point (the target) in the middle of a horizontal log with an axe (while still blindfolded). The contestant receives
15 points if their swing is within 3cm of the target.
10 points if their swing is between 3cm and 10cm of the target.
5 points if their swing is between 10cm and 20cm of the target
zero points if their swing is further away from the target (and someone may lose a finger!).
Let Y record the position of the hit, so that Y = y > 0 corresponds to missing the target point to the right by y cm and Y = - y < 0 corresponds to missing the target to the left by y cm. Assume that Y is normally distributed with mean mu = 0 and variance 100 cm^2. Find the expected number of points that the contestant wins.
Answer:
9.364 is the expected number of points.
we can approximate this to 10 points if we want a whole number
Step-by-step explanation:
We have these variables:
[0,5,10,15]
P(x= 0) = p(y>20)+p(y<-20) = 2p(y>20)
P(x=5) = p(-20<=y<=10)+p(10<=y<=20) = 2p(10<=y<=20)
P(x=10) = p(-10<=y<=-3)+p(3<=y<=10) = 2p(3<=y<=10)
P(x=15) = p(-3<=y<=3) = 2p(0<=y<=3)
Z = y/10
Therefore
P(x= 0) = 2(y>20)
= 2p(z>2) = 2(1-p<=2)
= 2(1-0.9772)
= 0.0456
P(x= 5)
= 2p(10<=y<=20)
= 2p(1<=z<=2)
= 2(0.9772-0.8413)
= 0.2718
P(x= 10)
= 2p(3<=y<=10)
= 2p(0.3<=z<=1)
= 2(0.8413-0.6179)
= 0.4468
P(x = 15)
= P(0.6179-0.3821)
= 0.2358
To get expected value of Y
0(0.0456)+5(0.2718)+10(0.4468)+15(0.2358)
= 1.359 + 4.468 + 3.537
= 9.364
E[Y] = 9.364
Ali's dog weighs 8 times as much as her cat together the two pets weigh 54 lb how much does Ali's dog weigh
Answer:
48
Step-by-step explanation:
Cat = x
Dog = 8x
x + 8x = 54
9x = 54
x = 6, Dog = 8 * 6 = 48
Can somebody help me plsssss
5,0 is not a solution to the system of linear inequalities.
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Answer:
d≈21.99
Step-by-step explanation:
identify each coefficient for 3m. this question is on my homework what Is the answer?
Answer: 3
Step-by-step explanation: The number in front of your variable is called your coefficient so we say that 3 is the coeficient.
Make sure to understand that a variable
is just a letter that represents any number.
Trisha and Beth are going to play a couple video games. Trisha has her favorite and beth has adifferent favorite. if 2 games are chosen at random out of the total games, what is the chance that both of their favorites are chosen?
Answer:
2/12 or 1/6
Step-by-step explanation:
12 games total
they have 2 games that are there favorite
On a map, the distance of two inches is equal to ten miles. How many
miles does 4 inches represent on the map?
10
20
30
40
Wayne charges the following for repairing washing machines:
£28 call-out charge + £16 for each half-hour he spends on the repair
If a repair costs £76, how long did it take?
180 students in a 10th grade class high school take a survey about which video game consoles they own. 80 students answer that one of the consuls is a PlayStation 90 answer that one of the consules is an Xbox out of these there are 30 who are both systems > continue reading on picture pls help very important
Answer:
Ur answer is in attachment
Step-by-step explanation:
please mark me as brainliest
The probability that a student has both box and a console is 1/6 and the P(B/A) = 0.378
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, the number of students with both video games is 30 thus
The probability that a student has both box and a console is 30/180=1/6
And the conditional probability P(B/A) is = 1/6/0.44
= 0.378
Hence, The probability that a student has both box and a console is 1/6, and the P(B/A) = 0.378
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Plz help quick I will give brainly points
What is the horizontal distance from the origin to the point (8, 1)?
Answer:
Me encanta el pollo, de todos modos, un día que es hoy, por cierto, fui a la tierra de los pollos y caminé en México, ¿sabías que es mi sueño? ¿Olvidé que mi nombre es jemma y me gusta caminar? párrafo así que nos vemos
A manufacturer of cream filled donuts collected data from its automatic filling process. The amount of cream inserted into the donuts is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts. The correct value of t to construct a 90% confidence interval for the true mean amount of cream filling is _______.
Answer:
The appropriate solution is "1.7109". A further explanation is provided below.
Step-by-step explanation:
The given values are:
Sample size,
n = 25
Degree of freedom,
[tex]df=n-1[/tex]
[tex]=25-1[/tex]
[tex]=24[/tex]
At 90% confidence level,
[tex]\alpha=1-90 \ percent[/tex]
[tex]=1-0.9[/tex]
[tex]=0.1[/tex]
and,
[tex]\frac{\alpha}{2}=\frac{0.1}{2}[/tex]
[tex]=0.05[/tex]
Now,
The correct values of t will be:
= [tex]t_{\frac{\alpha}{2}, df }[/tex]
= [tex]t_{0.05,24}[/tex]
= [tex]1.7109[/tex]
Carl has visited 49 of the 50 states.
What percent of the states has he visited?
Need help quick
Answer:
98%
Step-by-step explanation:
Solve for x In the equation.
Answer:
x = 16
Step-by-step explanation:
[tex] \frac{2x - 5}{x + 8} = \frac{22.5}{20} [/tex]
Cross multiply
[tex] (2x - 5)*20 = (x + 8)*22.5 [/tex]
[tex] 40x - 100 = 22.5x + 180 [/tex]
Collect like terms
40x - 22.5x = 100 + 180
17.5x = 280
Divide both sides by 17.5
x = 280/17.5
x = 16
16 is the sum of a number and 2.
What is the equation?
Answer:
14
Step-by-step explanation:
[tex]x + 2 = 16 \\ x = 16 - 2 \\ x = 14[/tex]
Like this ？？？
Answer:
16 = 2 + 14
Step-by-step explanation:
Sum means to add to numbers, so we are finding x + 2 = 16.
x + 2 - 2 = 16 - 2
x = 14
slove for q: q/10 = 4
Answer:
4
Step-by-step explanation:
Answer:
1/10 = 4
Step-by-step explanation:
A shape is made of 9 right triangles of equal size and three identical rectangles. Each rectangle measures 7 mm wide and 3 mm high. What is the total area, in square mm of the shape?
Answer:
21
Step-by-step explanation:
The Total cost to rent 5 chairs and 3 tables is $31 dollars. What is the cost to rent each chair and each table? No links please
Answer:
b
Step-by-step explanation:
A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Step-by-step explanation:
i think that the equations might be y = x - 7
what is 4x-2=3(x-3)
Answer:
x = -7
Step-by-step explanation:
4x - 2 = 3(x - 3)
use the distributive property
4x - 2 = 3x - 9
+9 +9
4x + 7 = 3x
-4x -4x
7 = -1x
x = -7
Hope I helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
Find the largest number which divides 248 and 1032 leaving the remainder 8 in each case.
Answer:
...... .................
HELP PLEASE I NEED HALP
Answer:
16
Step-by-step explanation:
8x2
Mike needs to buy a water tank. The tank must fit inside a storage box that is shaped like a cube with the side lengths of 30 feet. Water tanks are available in cylinders, cones, square pyramids, and spheres. Mike wants to buy the tank that has the largest capacity. What shape tank should Mike buy?
Answer:
sphere
Step-by-step explanation:
sphere has a larger volume
helppppppppppppppppppppp
Answer:
26 square feet
Step-by-step explanation:
I dont know if this is right
ill mark brainlist plss help
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer....
○ 28 cm2Hope it helps!
Mark me brainliest pls....
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Simplify.
Remove all perfect squares from inside the square root.
√56z^7
Answer:
[tex]2[/tex][tex]z^{3}[/tex][tex]\sqrt{14z}[/tex]
Step-by-step explanation:
The simplified form of √56z⁷ is 2z³√(14z⁴ ) in the given question.
To simplify √56z⁷, we can break down the number 56 into its prime factors and remove any perfect square factors from inside the square root.
When simplifying a square root expression, removing perfect square factors from inside the square root helps simplify the expression further. This is because the square root of a perfect square is a whole number.
First, let's factorize 56:
56 = 2 * 2 * 2 * 7
Since 2 is a perfect square, we can remove it from inside the square root:
√56z⁷ = √(2 * 2 * 2 * 7 * z⁷ )
Simplifying further:
√56z⁷ = 2z³√(2 * 7 * z)
Therefore, the simplified form of √56z⁷ is 2z³ √(14z⁴ ).
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please help me with this :)))
Answer:
C, 33 1/3%
Step-by-step explanation:
Because there are only two even number that follow this rule: 2<x≥6, and since there are only 6 possible outcomes, the probabilty is 2/6, which is 1/3. In a percent form, this is 100%*2/3, or 33 1/3%.