A point is chosen randomly on KN. Identify the probability that the point is on KL or MN. The figure shows segment K N with two points L and M on it in order from left to right. The length of segment K L is 3 units. The length of segment L M is 7 units. The length of segment M N is 8 units.
A point is chosen randomly on KN. The probability that the point is on KL or MN would be 11/18.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
The length of segment K L is 3 units.
The length of segment L M is 7 units.
The length of segment M N is 8 units.
The length of the segment KL + MN
KL + MN = 11
The total length of the segment KN
KL +LM + MN
3 + 7 + 8 = 18
SO, The probability that the point is on KL or MN = 11/18
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A pair of equations is shown below: y = 3x - 5 y = 6x - 8
Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)
Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answer:
See below
Step-by-step explanation:
y = 3x -5 <===== multiply this equation by -2 to get
-2y = -6x+10 now add it to the other equation(this will ELIMINATE x)
y = 6x-8
-y = +2
y = -2 then sub this in to oneof the quations to find x = 1
the two points will intersect at x,y = 1,-2 (because this satisfies both of the equations)
PART A
We start with: y = 3x - 5 y = 6x - 8
Elimination:
If we have two equations that = y, then we can make them equal each other:y = y3x - 5 = 6x - 8We then collect the x term together:3x - 6x = -8 + 5-3x = -3We can divide both sides by -3:x = 1Substitution
We can make one equation turn from a y= to an x=I decided to go with y = 3x - 5 (but it doesn't matter)We basically want to get it into x=y = 3x - 5y + 5 = 3x3x = y + 5 (I'm just flipping the equation to get x on the left for easiness)We then divide both sides by 3:x = [tex]\frac{y + 5}{3}[/tex]Don't forget we've also got y = 6x - 8So we just put x in!y = 6 × [tex]\frac{y + 5}{3}[/tex] - 8y = [tex]\frac{6}{3}[/tex] × (y + 5) - 8y = 2 × (y + 5) - 8y = 2y + 10 - 8y = 2y + 2Rearrange to get y on one side:-y = 2Times both sides by -1:y = -2We can now go back to...x = [tex]\frac{y + 5}{3}[/tex]By putting y = -2 in:x = [tex]\frac{-2 + 5}{3}[/tex]x = [tex]\frac{3}{3}[/tex] = 1PART B
We can find where they intersect/overlap by using elimination/substiutionWe've already covered both, and we get x = 1This means we've already go the x-coordinate of our point where the lines meet(x, y) = (1, ?)We just put our value of x into either equation (since x = 1 is where they meet)I'll go with y = 6x - 8y = 6 × 1 - 8y = 6 - 8 = -2We end up with (1, -2)!!!P.S.:
I've attached a screenshot of the graphs, notice how they meet at (1, -2)
Find the product of the following by writing one of numbers as the sum or difference of two numbers -
785*105
1006*95
3096*91
Answer:
Step-by-step explanation:
Use distributive property: a*(b+c) =a*b +a*c
1) 785 * 105 = 785 * (100 + 5)
= 785*100 + 785*5
= 78500 + 3925
= 82425
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2) 1006 * 95 = (1000 + 6) *95
= 1000*95 + 6*95
= 95000 + 570
= 95570
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3) 3096*91 = 3096 * (100 - 9)
= 3096*100 - 3096*9
= 309600 - 27864
= 281736
A cylinder and its dimensions are shown in the diagram. Which equation can be used to find V, the volume of the cylinder in cubic centimeter? I think A. is the answer :)
Answer: it’s simply a
Step-by-step explanation: X =bsquare
Choose the solution to this inequality.
72≥b+95
A. b≥25
B. b≤1710
C. b≤−23
D. b<227
Answer:
C
Step-by-step explanation:
72≥b+95
Group like them
72-95 ≤ b
the sign changes due to the negative
-23 ≥ b
What is the circumference of a circle with a radius of 8?
Use 3.14 for pi.
Also, can someone tell me what the pattern is, here? I need to know, I can never understand.
Answer:
Step-by-step explanation:
C≈50.27
r Radius
Solution
C=2πr=2·π·8≈50.26548
Which choice is equivalent to the expression below?
√-125
A. 5i√5
B. -5i
C. 5i√-5
D. 5i
E. √125
Answer:
5i√5
Step-by-step explanation:
Remark
125 factors
It is factored into 5*5*5
The rule for √5*5*5 is that two can be taken outside the square root sign. I is placed in front of the root sign like 5√ and the other 5 is thrown away.
The remaining 5 is left under the root sign
As usual
√-1 is i is taken outside the root sign
Solution
5i √5 is what you get.
x(x+1)(x+2)=0
solve for x
Answer:
-2; -1; 0.
Step-by-step explanation:
x(x+1)(x+2)=0;
[tex]\left[\begin{array}{ccc}x=0\\x+1=0\\x+2=0\end{array} \ = > \ \left[\begin{array}{ccc}x=0\\x=-1\\x=-2\end{array}.[/tex]
The measure of one acute angle in this right triangle is 28°.
What is the measure of the other acute angle?
A. 22°
B. 28°
C. 32°
D. 62°
Answer:
[D] 62°
Step-by-step explanation:
A right triangle = 90 degree angle
A triangle = 180 degrees
Therefore,
90 + 28 = 118
180 - 118 = 62
Hence, the measure of the other acute angle is 62
Thus, the answer is [D] 62 degree
Kavinsky
Answer:
D. 62
Step-by-step explanation:
Find the sum of the first 150 positive even integers.
Answer:
Sum of first 150 positive even integers is 22650Step-by-step explanation:
We know that first 150 postive even Integers are 2,4,6,8,10... 300.
Here,
First term (a) = 2 Comman difference (d) = 4 - 2 = 2 Total terms (n) = 150Last term (aₙ) = 300[tex]\\[/tex]
Substituting values in the formula:
[tex] \\ :\implies \sf \: \: S_{n} = \dfrac{n}{2} (a + a_{n}) \\ \\[/tex]
[tex] :\implies \sf \: \: S_{n} = \dfrac{150}{2} (2 + 300) \\ \\ [/tex]
[tex] :\implies \sf \: \: S_{n} = 75(302) \\ \\ [/tex]
[tex] :\implies \: \:{ \underline{ \boxed{ \pmb{ \pink { \rm{S_{n} = 22650 }}}}}} \\ \\[/tex]
Sum of first 150 positive even integers is 22650Answer:
The number series 2, 4, 6 , 8. . . . , 150.The first term (a) = 1The common difference (d) = 4 – 2 = 2Total number of terms (n) = 150last term (an) = 300Formula for finding sum of nth terms =
n/2 × (a + an)
putting the known values ,
Sum = 150/2 × ( 2+300)
Sum = 75 × 302
Sum of first 150 positive even integers = 22650
Find the sticker price and the dealer's cost for the Bobcat SX with a base price of $13,568.00. Options include air conditioning for $765.00, turbo for $643.00, towing package for $236.00, and custom wheels for $422.00. Destination charges total $365.00. The dealer pays 90% of the base price and 65% of the options.
Least to greatest questions 7 and 8
Answer:
7.
4.7 * 10^14 , 9.99 * 10^14 , 2.9 * 10^15 , 4.5 * 10^15
8.
9.99 * 10^-8 , 4.8 * 10^-8 , 9.99 * 10^-4 , 6.5 * 10^-4
i need some urgent help
the thing is to factor the expressions trinomial way
if you want extra points you could help me with my past 2 questions they are 50 each someone gave me a wrong answer so i would really appreciate some help with that too but that's optional
#1
15x²+4x-415x²+10x-6x-45x(3x+2)-2(3x+2)(5x-2)(3x+2)#2
16a²-50a+362(8a²-25a+18)2(8a-9)(a-2)#3
63n²+126n+483(21n²+42n+16)Not more factorable
Evaluate tan (x + pi/2) for x = pi/2
Answer:
0
Step-by-step explanation:
tan(x + [tex]\frac{\pi }{2}[/tex] ) ← substitute x = [tex]\frac{\pi }{2}[/tex]
tan([tex]\frac{\pi }{2}[/tex] + [tex]\frac{\pi }{2}[/tex] )
= tanπ
= 0
find the average rate of change of f(x) = 3x - 7 over the interval 1 ≤ x ≤ 5
Answer:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
Step-by-step explanation:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
Please help. I cant figure it out
Sally rents a life jacket for a one-time fee of 5$. She rents a canoe for $15 per hour. Which expression represents the total cost, in dollars, to rent the life jacket and the canoe for h hours?
A. 5+15h
B. 10h
C. 15+5h
D. 20h
Answer:
A. 5+15h
Step-by-step explanation:
please answer the question pls
SAT scores are used by colleges and universities to evaluate undergraduate applicants. The test
scores are normally distributed. A random sample of 65 student scores has a mean of 1489 and
standard deviation of 306.
Find the 95% confidence interval for the population mean based on this sample and round to
two decimal places.
Using the t-distribution, it is found that the 95% confidence interval for the population mean is (1413.18, 1564.82).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 65 - 1 = 64 df, is t = 1.9977.
The parameters of the interval are given as follows:
[tex]\overline{x} = 1489, s = 306, n = 65[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 1489 - 1.9977\frac{306}{\sqrt{65}} = 1413.18[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 1489 + 1.9977\frac{306}{\sqrt{65}} = 1564.82[/tex]
The 95% confidence interval for the population mean is (1413.18, 1564.82).
More can be learned about the t-distribution at https://brainly.com/question/16162795
y-3x=0
2y+5x=11
solve
with elimination and substitution method
Answer:
x=1, y=3
Step-by-step explanation:
using sublimation method
y-3x=0 ....eqn(1)
2y+5x=11....eqn(2)
from eqn 1
y-3x=0
y=3x
substitute y=3x into eqn 2
2y+5x=11
2(3x)+5x=11
6x+5x=11
11x=11 (divide both sides by the coefficient of x)
x=1
since x=1 , substitute x=1 into eqn 1 to get y
y-3x=0
y-3(1)=0
y-3=0
y=3
Using elimination method
y-3x=0....eqn (1)
2y+5x=11....eqn (2)
multiply eqn 1 through by 2 and eqn 2 through by 1 to eliminate y
2y-6x=0.... eqn 3
2y+5x=11.... eqn 4
subtract eqn 4 from from eqn 3
-11x=-11 (divide both sides by the coefficient of x)
x=1
substitute x=1 into eqn 2 to get y
2y+5x=11
2y+ 5(1) =11
2y+5=11
2y=11-5
2y= 6 (divide both sides by the coefficient of y)
y=3
{96/[36/3-(18 x 2 - 30)]} / (31-16+1)
Answer:
-1/2
Step-by-step explanation:
pemdas rules
1. 18 x 2 - 30 = 6
2. 3-6= -3
3. 36/-3 = -12
4. 96/-12 = -8
5. (31-16+1) = 16
6. -8/16 = -1/2
how many solutions does the equation 5 + -5 + -12 equals 14 - 2 have?
0, 1, 2, many
Hey there!
5 + -5 + -12 = 14 - 2
ASSUMING….
5 - 5 - 12 = 14 - 2
0 - 12 = 14 - 2
-12 = 12
-12 ≠ 12
Thus, your answer should be:
FALSE or simply 0 solutions
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.
In a random sample of 300 people from the 66-69 age group who did not complete high school, 165 were not prepared financially for retirement. What is the p-value for your hypothesis test (to 4 decimals)? If your answer is zero, enter "0".
Using the z-distribution, as we are working with a proportion, it is found that the p-value of the test is of 0.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of 71%, that is:
[tex]H_0: p = 0.71[/tex]
At the alternative hypothesis, it is tested if the proportion has decreased, that is:
[tex]H_1: p < 0.71[/tex].
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, we have that the parameters are:
[tex]n = 300, \overline{p} = \frac{165}{300} = 0.55[/tex]
Hence, the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.71}{\sqrt{\frac{0.71(0.29)}{300}}}[/tex]
z = -6.11
What is the p-value of the test?Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -6.11, it is found that the p-value is of 0.
More can be learned about the z-distribution at https://brainly.com/question/26454209
A straight waterslide is 175 feet above ground and is 200 feet long. What is the angle of depression to the bottom of the slide?
Step-by-step explanation:
see this this will help you
Multiply This Equation & Simplify:
Question Is In The Photo...
Answer:
= 12 x^8
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below?
(3n+13) + (6+7n)
A. 9n + 20
B. 16n + 13
C. 10n + 19
D. 22n + 7
Answer: C) 10n +19
Step-by-step explanation:
Let's simplify the provided expression (3n+13) + (6+7n)
Since this is just addition we can just remove the parenthesis and use the commutative property to make adding easier
3n+13+6+7n
3n+7n+13+6
10n+19
Round the number. Write the result as the product of a single digit and a power of 10. 0.0000001801
Answer:
2x10 to the -7 power
Step-by-step explanation:
hope this helps!
Given the functions:
f (x) = -6x - 19
g(x) = -11x + 9
h (x) = 17x +4
Find f (3)
Answer:
f(3) = -37
Step-by-step explanation:
f (x) = -6x - 19
Let x = 3
f (3) = -6*3 - 19
= -18-19
= -37
Find the area of the circle shown.
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
radius is 1.5 cm
Answer:
7.1 cm^2
Step-by-step explanation:
Area = pie * radius^2
Area = pie * 1.5^2
= 7.0685
Answer: 7.1 cm ^2
Step-by-step explanation:
Please help me ASAP!! Calling all experts, will give brainliest too!
The height of a candle decreases from 10 centimeters to 6 3/4 centimeters after burning for 1/2 hour
The true statement is as follows:
The product 13 / 4 × 2 can be used to find the unit rate in cm per hour.
After one hour, the height of the candle will have decreased by 6 1 / 2 cm.
What is rate?Rate is the ratio between two related quantities in different units.
The height of the candle decreases from 10 cm to 6 3 / 4 cm after burning for 1 / 2 hours.
6 3 / 4 cm = 27 / 4 cm
10 - 27 / 4 = 40 - 27 / 4 = 13 / 4 cm
Therefore, 13 / 4 cm of candles were lost in 1 / 2 hours.
Rate = 13 / 4 × 2 = 26 / 4 = 13 / 2 cm per hour
Therefore, the product 13 / 4 × 2 can be used to find the unit rate in cm per hour.
13 / 4 + 13 / 4 = 13 + 13/ 4 = 26 / 4 = 13 / 2 = 6 1 / 2 cm.
Therefore, after one hour, the height of the candle will have decreased by 6 1 / 2 cm.
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