The coordinate of K on the line segment JL is (4,5).
What is section formula?When a point divides a line segment externally or internally in some ratio, we use section formula to find the coordinates of that point.
Internal section formula[tex]P(x, y) = (\frac{mx_{2} +nx_{1} }{m+n} ,\frac{my_{2}+ny_{1} }{m+n})[/tex]
Where,
(x, y) are the coordinates of point P.
[tex](x_{1},y_{1} )[/tex] are the coordinates of point A.
[tex](x_{2},y_{2})[/tex] are the coordinates of point B.
m and n are the ratio values in which P divides the line segment AB internally.
According to the given question.
Coordinates of points J and L are (4, 2) and (4, 6) respectively.
K divides the line segment JL in the ration 3:1.
Therefore, the coordinates of K by section formula is given by
[tex]K(x, y) = (\frac{3(4)+1(4)}{3+1} , \frac{3(6)+1(2)}{3+1} )[/tex]
⇒ [tex]K(x, y) = (\frac{12+4}{4} , \frac{18 + 2}{4} )[/tex]
⇒ [tex]K(x, y) = (\frac{16}{4} ,\frac{20}{4})[/tex]
⇒[tex]K(x, y) = ( 4, 5)[/tex]
Hence, the coordinate of K on the line segment JL is (4,5).
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Suppose that past records indicate that the probability that a new car will need a warranty repair in the first 90 days of use is 0.04. If a random sample of 400 new cars is selected. what is the probability that the proportion of new cars needing a warranty repair in the first 90 days will be: a. between 0.05 and 0.06? i.e. P(0.05 SpS 0.06) = (round your answer to 4 decimal places). b. above 0.07? i.e. P(p > 0.07) = (round your answer to 5 decimal places) c. below 0.03?ie. P(p < 0.03) = (round your answer to 4 decimal places)
Answer:
a) P(0.05 < p < 0.06) = 0.1332
b) P(p > 0.07) = 0.0011.
c) P(p < 0.03) = 0.1539
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose that past records indicate that the probability that a new car will need a warranty repair in the first 90 days of use is 0.04.
This means that [tex]p = 0.04[/tex]
Sample of 400.
This means that [tex]n = 400, s = \sqrt{\frac{0.04*0.96}{400}} = 0.0098[/tex]
a. between 0.05 and 0.06?
This is the p-value of Z when X = 0.05 subtracted by the p-value of Z when X = 0.05. So
X = 0.06
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.04}{0.0098}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
X = 0.05
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.04}{0.0098}[/tex]
[tex]Z = 1.02[/tex]
[tex]Z = 1.02[/tex] has a p-value of 0.8461.
0.9793 - 0.8461 = 0.1332
So
P(0.05 < p < 0.06) = 0.1332
b. above 0.07?
This is 1 subtracted by the p-value of Z when X = 0.07. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.07 - 0.04}{0.0098}[/tex]
[tex]Z = 3.06[/tex]
[tex]Z = 3.06[/tex] has a p-value of 0.9989.
1 - 0.9989 = 0.0011. So
P(p > 0.07) = 0.0011.
c. below 0.03?
This is the p-value of Z when X = 0.03. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.03 - 0.04}{0.0098}[/tex]
[tex]Z = -1.02[/tex]
[tex]Z = -1.02[/tex] has a p-value of 0.1539. So
P(p < 0.03) = 0.1539
i need help pls it’s timedd!!!!
Answer:
5.
Step-by-step explanation:
If you were to rotate the triangle, you can apply Pythagoras Theorem.
Therefore,
a^2 = 12^2 - 13^2 (Note: a^2 = a squared)
a^2 = 144 - 169
a^2 = -25.
a = 5.
Not sure why its negative though im pretty sure its the right answer.
in BCD triangle :
DC^2 = BC^2 + BD^2
13^2 = 12^2 + BD^2
169 = 144 + BD^2
BD^2 = 169 - 144
BD^2 = 25
BD = 5
_______________________
In the other hand we have :
BD^2 = AB × BC
5^2 = AB × 12
AB = 25/12
________________________
Also we have :
AD^2 = AB × AC
AD^2 = 25/12 × ( 25/12 + 12 )
AD^2 = 25/12 × ( 25/12 + 144/12 )
AD^2 = 25/12 × 169/12
AD^2 = 25 × 169 / 12 × 12
AD^2 = 5 × 5 × 13 × 13 / 12 × 12
AD = 5 × 13 / 12
AD = 65 / 12
AD = 5.42
Thus the correct answer is option C
What is the slope of the line?
Pls help
Answer: 3
Step-by-step explanation:
Pick 2 coordinates that are on the line, for example, (-2,0) and (-1,3)
Slope = Rise/Run = (3-0)/(-1-(-2)) = 3
What is the equation line of A?
What is the equation line of B?
Answer:
see below
Step-by-step explanation:
Line A is a horizontal line
It is of the form y = constant
y = 4
Line B is a vertical line
It is of the form x = constant
x = 8
Multiply (5xy-4)(5xy+4)
[tex]{25x {}^{2} y}^{2} - 16[/tex]
2
3
4
9
10
-1
NS
-6
-7
-8
-9
Which three statements correctly describe key features of the function graphed here?
did u add the attachment of the the statements? cuz i dont see it.
find the GCF of 36 and 54
Answer:
Step-by-step explanation:
The greatest common factor of 36 and 54 is 18. 18×2=36 and 18×3=54.
Need help ASAP
What is the total distance the monkey has traveled when she completes her 10th swing?
Answer:
89.263 m I couldn't remember the easist way of doing this type of summation problem. I used brute force. a spread sheet would have been quicker
Step-by-step explanation: 6 17 22 16
Event Formula Calculation Running Summation
1 20 20 20
2 20(4/5) 16 36
3 20(4/5)(4/5) 12.8 48.8
4 20(4/5)(4/5)(4/5) 10.24 59.04
5 20(4/5)^4 8.192 67.232
6 20(4/5)^5 6.554 73.786
7 20(4/5)^6 5.453 79.028
8 20(4/5)^7 4.194 82.223
9 20(4/5)^8 3.355 86.578
10 20(4/5)^9 2.684 89.263
add the results from each swing
I got 89.263 meters
Jayden drives 22.5 miles in 30 minutes. If he drove one hour in total at the same rate, how far did he go? Before you try that problem, answer the question below. How many minutes did Jayden drive in total?
how far did he go in minutes?
Answer:
45 miles in 1 hour
Step-by-step explanation:
1 hour is 60 minutes
22.5 miles / 30 minutes * 2/2 = 45 miles / 60 minutes = 45 miles in 1 hour
Answer:
He drove 22.5 miles in 60 min. He drove 45 miles in 1 hour
Step-by-step explanation:
22.5 miles in 30 min
1 hour= 60 min
30+30=60
22.5+22.5=45 miles
Over what interval is the parabola below decreasing?
3<. x. <∞
−∞ <. x. <3
−1<. x. <∞
−∞ < x < −1
Answer:
B. -oo < x < 3
Step-by-step explanation:
since the vertex (3, -1), so, x should be less than 3
-oo < x < 3
Pedro and his friend Cody played basketball in the backyard. Cody made 5 Baskets . Pedro made 15 baskets. How many times more baskets did pedro make than cody?
Answer: 10
Step-by-step explanation: 15 - 5 = 10
10
17 A sequence starts at 300 and 40 is subtracted each timee.
300
260
2200
1800...
The sequence continues in the same way,
What is the first number in the sequence which is less than zerol?
[11]
9514 1404 393
Answer:
-20
Step-by-step explanation:
300/40 = 7.5, so the 8th term will be the last positive term. It will be 300 -7×40 = 20. The 9th term will be 20 -40 = -20.
__
The sequence starts ...
300, 260, 220, 180, 140, 100, 60, 20, -20, ...
NEED HELP ASAP
So for this problem I got 10.8 by multiplying 0.60 x 18. However it stated that my answer is incorrect. How do I go about this problem because I am not sure what else to do?
We are looking for the total amount of the solution. We only know part of it, that there are 18 milliliters of the alcohol. We also know that the alcohol makes up only 60% of the solution.
To find the whole, we can set up a proportion using the information given.
60 / 100 <--- This is our percentage, which we were given.
18 / x <--- This is the part (alcohol - 60%) over the whole, which we don't know and which also corresponds to the 100.
Therefore, our proportion is as such:
60 / 100 = 18 / x
To solve, cross-multiply.
100 * 18 = 60 * x
1800 = 60x
x = 30 total milliliters of the solution
Hope this helps!
upandover has a great solution. Here's a slightly different approach.
x = total amount of solution (consisting of water and alcohol mixed)
0.60x = 60% of x = amount of pure alcohol
0.60x = 18 since we have 18 mL of pure alcohol
Divide both sides by 0.60 to isolate x
0.60x = 18
x = 18/0.60
x = 30
Answer: 30 mL of total solution (alcohol + water).
What is the value of 6 / x + 2x squared when x = 3
Answer:
8
Step-by-step explanation:
The equation will become 6/3+2(3)
-->6/3=2
-->Because of Order of Operation we will multiply the 2 and 3 before adding so 2(3) = 6
--> 6+2=8
Answer:
x=6
Step-by-step explanation:
when its squared you multiply by 2
if a binomial trial has a success of .3, how many successes would you expect out of 500 trails
Answer:
gfs
Step-by-step explanation:
the picture
says it
all
Answer:
B. L BAT = L CAT
Step-by-step explanation:
__________
Multiply: 3x⎯⎯⎯⎯√·6y⎯⎯⎯⎯√
.
Answer:
l
Step-by-step explanation:
The probability of rolling a 1 on a 6-sided biased dice is 0.85
The biased dice is rolled twice.
Complete the probability tree diagram.
Answer:
Step-by-step explanation:
If the odds of rolling a 1 is .85 the odds of rolling not a one is
1-.85= .15
The Complete probability tree diagram is
First roll have (0.85, 0.15).
Second Roll have (0.85, 0.85, 0.15, 0.15).
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The probability of rolling a 1 on a 6-sided biased dice is 0.85.
Now, the probability not rolling 1
= 1- 0.85
= 0.15
So, First roll have (0.85, 0.15).
and, the Second Roll have (0.85, 0.85, 0.15, 0.15).
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Can someone answer with steps and explanation? Thanks.
Answer:
[tex]x=-16\text{ or } x=7[/tex]
Step-by-step explanation:
Since ΔABC is mapped onto ΔDEF, we can write that:
[tex]\Delta ABC\cong \Delta DE F[/tex]
By CPCTC:
[tex]\angle A\cong \angle D[/tex]
And since ΔABC is isosceles with Vertex C:
[tex]\angle A \cong \angle B[/tex]
We are given that:
[tex]m\angle D=34[/tex]
Hence:
[tex]m\angle A=34=m\angle B[/tex]
We are also given that:
[tex]m\angle C=x^2+9x[/tex]
The interior angles of a triangle must sum to 180°. Thus:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](34)+(34)+(x^2+9x)=180[/tex]
Simplify:
[tex]68+x^2+9x=180[/tex]
Isolate the equation:
[tex]x^2+9x-112=0[/tex]
Factor:
[tex](x+16)(x-7)=0[/tex]
Zero Product Property:
[tex]x+16=0\text{ or } x-7=0[/tex]
Solve for each case:
[tex]x=-16\text{ or } x=7[/tex]
Testing the solutions, we can see that both yields C = 112°.
Hence, our solutions are:
[tex]x=-16\text{ or } x=7[/tex]
Decide if the following probability is classical, empirical, or subjective.
You guess that there is a 30% chance that you will be assigned homework in your English class on Tuesday
Answer:
Subjective.
Step-by-step explanation:
Classical probability:
A classical probability is a probability based on a formal reasoning, for example, probability of getting heads/tails on a coin toss.
Empirical probability:
An empirical probability is the same as experimental probability, that is, suppose 7 out of 10 people you meet are Buffalo Bills fans, so the next person has a 7/10 = 0.7 = 70% probability of being a Buffalo Bills fan.
Subjective probability:
Probability of somthing happening based on "intuition", that is, based on the person's own experience. In this exercise, we have an example of subjective probability.
First factor out the greatest common factor from each term. Then factor the remaining polynomial.
4x2+4x-80
Can you please help?
Select the correct answer.
Which number has a repeating decimal form?
b.11/25
c.3/20
d.2/6
Answer:
d.2/6 has a repeating decimal form
Answer:
[D. 2/6]
Step-by-step explanation:
For edmentum users (Please check your answers before placing the answer to avoid low grades and misconfusion.)
Question 7(Multiple Choice Worth 1 points)
(02.08 LC)
To follow appropriate safety procedures, what should soccer players wear?
Goggles
Helmets
Mouth pieces
Shin guards
Answer:
The answer is Mouth pieces
The piece of safety equipment that should be worn when painting a ceiling is safety goggles. The correct option is c.
What are safety goggles?Safety goggles are worn on the eyes. They are worn to get safety from sun, wind, and dust. If we work in a factory or some mechanical work, then goggles are must save eyes.
Here, we have,
When working with the ceiling, it has a chance to damage your eyes with the plaster and paint, so wearing safety goggles is necessary.
Thus, the correct option is c. safety goggles, in regard to being worn when painting a ceiling.
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Complete question:
Which of these pieces of safety equipment should be worn when painting a ceiling
a knee guards
b helmet
c safety goggles
d mouth guard
You are riding your bike and notice the square sign above. You mentally draw a
straight line from point A to C. Describe the angle relationship between /_DCA and
/_BCA.
===========================================================
Explanation:
When using the SSS congruence rule, we can prove that triangle DCA is congruent to triangle BCA.
Since the triangles are congruent, the corresponding pieces angle DCA and angle BCA are equal in measure (if they weren't, then the triangles wouldn't be congruent).
Recall that any square has four right angles, ie all angles are 90 degrees each. Angle DCB is cut in half to get 90/2 = 45.
The angles DCA and DCB are 45 degrees each.
Factor completely 3x2 + 9x − 3.
3(x2 + 3)
3(x2 + 3x − 1)
3x(x2 + 3x − 1)
Prime
HELP PLEASE QUICKKKKKK
Answer:
3
lkfbnrld/kgnvr/slkbvluydcfgiufhvgukrghoudgb
Presto Corp. had total variable costs of $180,000, total fixed costs of $110,000, and total revenues of $300,000. Compute the required sales in dollars to break even.
Answer:
$230,000
Step-by-step explanation:
Contribution margin = Sales - Variable costs
=($250,000 - $137,500)
= $112,500
Contribution margin ratio = Contribution margin ÷ Sales
= ($112,500 ÷ $250,000)
= 0.45
Basically
Break-even sales = Fixed expenses ÷ Contribution margin ratio
=($103,500 ÷ 0.45)
= $230,000
The required sales in dollars to break even is $275,000.
Given that, total variable costs of $180,000, total fixed costs of $110,000, and total revenues of $300,000.
What is a total revenue?Total revenue is the total amount of money a company brings in from selling its goods and services. It determines how well a company is bringing in money from its core operations based on demand and price.
The contribution margin ratio = Contribution margin/Sales revenue
= (300,000 - 180,000 = 120,000)/300,000
= 40%
Break-even point in dollars = Fixed cost/Contribution margin ratio
= 110,000/0.40
= $275,000
Therefore, the required sales in dollars to break even is $275,000.
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What is the slope of the line?
2x+ 4y = 6x- y
Answer:
4/5
Step-by-step explanation:
→ Rearrange to get into y = mx + c
5y = 4x + c
→ Divide everything by 5
y = 4/5x + c
If p and q are the roots of 2x²+ 6x = 12 + 4x, and p < q, find q − p
Step-by-step explanation:
The given equation can be further simplified into
[tex]2x^{2}+2x-12=0[/tex]
The roots of a quadratic equation is given by
[tex]x = \dfrac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
where a = 2, b = 2 and c = -12. Putting these into the roots equation, we get
[tex]x = \dfrac{ - 2 \: \pm \: \sqrt{4 \: - \: 4(2)( - 12)} }{2(2)} = \dfrac{ - 2 \: \pm \: 10}{4}[/tex]
This gives us two possible roots:
x = 2, x = -3
Since the condition is that p < q, we see that p = -3 and q = 2. Therefore,
[tex]q - p = 2 - ( - 3) = 5[/tex]
State the domain of the graphed function, using interval notation. The domain is ______
Answer:
[-10,-2) U (-2,2) U [2, 5) U (5, infinity)
Step-by-step explanation:
p/s: I don't have the infinity symbol on my keyboard but you know what it is. Hope this help