The answer is x=-2
As you could see, this is a factored function.
The un-factored version is x^2+4x-12
-b/2a=x
-4/2=-2= x of vertex
Yuki and Zana are on a swimming team. They often compete against each other in the 100 meter freestyle race. Yuki's times in this race are normally distributed with a mean of 808080 seconds and a standard deviation of 4.24.24, point, 2 seconds. Zana's times are also normally distributed with a mean of 858585 seconds and a standard deviation of 5.65.65, point, 6 seconds. We can assume that their times are independent.
Suppose we choose a random 100 meter freestyle race and calculate the difference between their times.
Find the probability that Yuki's time is faster than Zana's.
You may round your answer to two decimal places.
Answer:
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
Step-by-step explanation:
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.
Subtraction of normal variables:
When normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Yuki's times in this race are normally distributed with a mean 80 seconds and standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds.
Yuki's is faster than Zana if the subtraction of Yuki by Zana is larger than 0.
The mean is:
[tex]\mu = 80 - 85 = -5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{4.2^2 + 5.6^2} = 7[/tex]
Find the probability that Yuki's time is faster than Zana's.
This is P(X > 0), which is 1 subtracted by the pvalue of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-5)}{7}[/tex]
[tex]Z = 0.71[/tex]
[tex]Z = 0.71[/tex] has a pvalue of 0.7611
1 - 0.7611 = 0.2389
0.2389 = 23.89% probability that Yuki's time is faster than Zana's.
What is the value of x?
Enter your answer in the box.
x =
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x.
Answer:
That did not make sense
Answer:
x = 3
Step-by-step explanation:
Verified correct with test results.
Just had to delete the jibberish to find the actual question for this problem:
The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x. What is the value of x?
Using the product of the means equals the product of the extremes, solve for x, to the nearest tenth. 4:9=x:6
Cross multiply:
4 x 6 = 9x
24 = 9x
Divide both sides by 9
X = 24/9
X = 2.7 ( rounded to the nearest tenth)
HELO WILL GIVE BRANLIEST!
Answer:
Step-by-step explanation:
he surface area of a cube is equal to 6 times the side length squared.
SA=68^2
where SA is the surface area and 8 is the side length.
If the side length of the cube is 4 cm each, then let s=4 cm
So the surface area of the 4-cm-side-length cube is:
SA=6∗(4 cm)^2
=6∗16 cm^2
=96 cm^2
dividing fractions
16 4
__ ÷ __
21 9
to find the answer we are using KCF( keep change flip)
Answer:
36/21 (simplified)
Step-by-step explanation:
To use KCF, multiply by the reciprocal. 16/21 x 9/4
Just flip the denominator with the numerator
Mr. Beck has 5 brown socks, 1 pair of green socks, and 4 pairs of blue socks in his sock drawer. If he randomly chooses one pair from the drawer, what is the probability that he will choose a blue pair of socks?
a. 1/2
b. 1/10
c. 3/5
d. 2/5
Answer:
D. 2/5
Step-by-step explanation:
First, find the total number of sock pairs in his drawer:
5 + 1 + 4
= 10
Since there are 4 pairs of blue socks, the probability that he will choose a blue pair of socks is 4/10.
This can be simplified by dividing each number by 2.
Simplified, the probability is 2/5.
So, the correct answer is D. 2/5
5x^2-4v^2=-99
2x^2+2v^2=90
Please show your work, if you show your work I will mark Brainiest!!!
9514 1404 393
Answer:
(x, v) ∈ {(-3, -6), (-3, 6), (3, -6), (3, 6)}
Step-by-step explanation:
For a quick and easy answer, my "work" is to use a graphing calculator.
(x, v) = (±3, ±6) . . . . in all 4 combinations
__
Add double the second equation to the first.
(5x^2 -4v^2) +2(2x^2 +2v^2) = (-99) +2(90)
9x^2 = 81
x^2 = 9
Substituting this into the second equation gives ...
2(9) +2v^2 = 90
2v^2 = 72
v^2 = 36
So, (x^2, v^2) = (9, 36). Taking square roots, we get ...
(x, v) = (±3, ±6) . . . . in all combinations
Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:
(a) Develop a regression model that could be used to predict the final average in the course based on the first test grade.
(b) Predict the final average of a student who made an 83 on the first test.
(c) Give the values of r and for this model. Interpret the value of in the context of this problem. Student 1 2 3 4 5 6 7 8 9 1st test grade 98 77 88 80 96 61 66 95 69 final average 93 78 84 73 84 64 64 95 76
Answer:
A.) ŷ = 0.73986X + 18.98921
B.) 80
C.) r = 0.9205
Step-by-step explanation:
Given :
1st test grade (X) :
98
77
88
80
96
61
66
95
69
final average (Y) :
93
78
84
73
84
64
64
95
76
Using a linear regression calculator :
The model obtained is :
ŷ = 0.73986X + 18.98921
Student with x = 83
ŷ = 0.73986(83) + 18.98921
ŷ = 80.39759
ŷ = 80 (nearest whole number)
The R value is : 0.9205 which shows that there is a strong linear correlation between the first test grade and the final average a student Obtian in an exam because the r value is very close to 1.
R² = √0.9205 = 0.8473 ; this means about 84.73% of variation in final average can be explained by the regression line.
2) Assinale a alternativa correta: *
1 ponto
Imagem sem legenda
a) 8
b) 12
c) 14
d) 16
Answer:
Step-by-step explanation:
¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.
Use the graph to determine the vertex point of the quadratic function. Is the vertex a
maximum or a minimum?
A) Vertex (2,1), minimum
B) Vertex (1,2), maximum
C) Vertex (2,1), maximum
D) Vertex (1,2), minimum
Answer:
B) Vertex (1,2), maximum
Step-by-step explanation:
First, determine if the graph has a maximum or a minimum value. Since the graph opens downwards, it has a maximum value.
The maximum is the point that has the greatest y value. We can see that the greatest y value is at [tex]y=2[/tex]. Going down two units from that spot, we can see that the x value is at [tex]x=1[/tex]. We can plug those into the vertex form, [tex](x,y)[/tex]. By plugging in we get the point [tex](1,2)[/tex].
I need help please !!!!!!!!
Answer:
B. 7√3
Step-by-step explanation:
30-60-90 triangles have special side proportions that would be very beneficial to memorize because I guarantee you will use it in the future.
Please see the attached image.
The answer is 7*√3=7√3
Please help me, I need the answer in the next 5mins. AND NO LINKS!!!!!!!
Can somebody help me with this quickly whoever answers first gets a thanks
G. From the origin move right 3 units,then up 6 units
H. From the origin move left 2 units,then up 11 units
J. From the origin move right 8 units, then down 10 units
K. From the origin move left 16 units, then down 20 units
L. Plot the first point at the origin then move up 5 units
M. From the origin move left 14 units and plot the next point at the origin
Drag and drop each area on top of the triangle it matches. i already did the 4 that have the answers on them qith the teacher. PLS HELP!!
Answer:
Step-by-step explanation:
in a raffle 200 tickets are sold 78 children and 93 women buy one ticket each men buy the rest of the tickets. work out the probability that a man buys the winning ticket
Answer:
The probability that a man buys the winning ticket is 107/200
Step-by-step explanation:
78 men buy tickets, 93 women buy tickets. If the rest of the tickets are given to men, there are 200-93-78, or 29 tickets left, which go to men. 78 + 29 = 107 men who have tickets.
The probability that a man buys the winning ticket is
number of men with tickets / number of tickets, or
107 / 200.
The negative integers greater than or equal to -12
Answer:
The negative integers are greater than -12
The queen of hearts, queen of diamonds, queen of spades, and queen of clubs are taken out of a deck of cards. They are to be put in 3 places on a table. In how many different ways can they be placed in the 3 spots?
Answer:
Hello There!!
Step-by-step explanation:
The answer is 52.
hope this helps,have a great day!!
~Pinky~
Which triangle side lengths form a right triangle? Choose all that apply.
➪ 5, 6, 7
➪ 6, 8, 14
➪ 8, 15, 17
➪ 10, 12 15
➪ 15, 20, 15
➪ 16, 18, 20
Your answer would be C (8,15,17) and E (15,20,15) or is it 25?
Step-by-step explanation:
:)
sum of -4/5 and -5/12. please answer.
Answer:
[tex]- 1 \frac{13}{60} [/tex]
Step-by-step explanation:
[tex] - \frac{4}{5} + - \frac{5}{12} \\ \frac{ - 48 - 25}{60} \\ \frac{ - 73}{60} \\ = - 1 \frac{13}{60} [/tex]
Hope this helps you.
Can I have the brainliest please?
Determine the simple interest rate for each given principal, time, and simple interest earned.
Principal: $1200
Time: 15 years
Simple Interest: 5720
Answer:
31.8%
Step-by-step explanation:
The formula for simple interest is I = PRT, where I = interest earned/paid, P = principal amount deposited or borrowed, R = rate of interest as a decimal, and T = time in years.
I = PRT
5720 = (1200)(R)(15)
5720 = 18,000R
R = 0.3177777, rounded to 31.8%
Answer:
32%
Step-by-step explanation:
5720/15=381.33 interest per year
principal x interest rate = interest per year
1200 x interest rate =381.33
interest rate = 381.33/1200
interest rate = 32%
HELP!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A D 1 Vertical
Step-by-step explanation:
x always represents 1
Pls help! ASAP! I will mark Brainliest! If you give me a file or guess I will report you!
Answer:
the second and last one
....................
Mrs townsend conducted a study of 145 students. She found that 20% of the students did NOT play video games. How many students did NOT play video games?
Please explain
Answer:
29 students
Step-by-step explanation:
Given that 20% of the 145 student did not play video games, you take the 145 times .20 and should be able to find the number that did NOT play video games.
[tex]0.2(145) = 29[/tex]
What is the value of x in the figure? Enter your answer in the box.
145°
(2x + 15)°
x=
Answer:
Answer: x=65
Step-by-step explanation:
Since they're vertical angles both sides are equal to 145 degrees
So, 145-15= 130 to get rid of the constant
Then, 130/2=65
To check you work add up all of your solutions to get 145
2*65=130 & 130+15=145
Therefore, x=65
Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longboard (L) users and 30 shortboard (S) users. Treat these data as though they were from two independent random samples. Test the hypothesis that the mean days surfed for all longboarders is larger than the mean days surfed for all shortboarders (because longboards can go out in many different surfing conditions). Use a level of significance of 0.05.
Longboard :4,8,9,4,9,7,9,6,6,1 1,1 3, 12, 10, 151316,12,10. 12,18,20.15,10.15,19,21,9,22, 1923 Shortboard: 6,4,4,6,7,7,7,10,4,6,7,5,8,9,4,15,13,9,12,11,12,13,9,11,13,15,9,19,20,11
Determine the hypotheses for this test. Choose the correct answer below. Find the test statistic for this test. Find the p-value for this test. What is the conclusion for this test? Reject H0. The mean days surfed for longboarders is not significantly larger than the mean days surfed for all shortboarders Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders Do not reject H0. The mean days surfed for longboarders is not significantly larger than the mean days surfed for all shortboarders
Answer:
Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders
Step-by-step explanation:
The null hypothesis is that the mean days surfed for all long boarders is larger than the mean days surfed for all short boarders
H0: μL > μs against the claim Ha: μL≤ μs
the alternate hypothesis is the mean days surfed for all long boarders isless or equal to the mean days surfed for all short boarders (because long boards can go out in many different surfing conditions)
The test statistic is
t= x1- x2/ √s1/n1+ s2/n2
1) Calculations
Longboards
Mean
ˉx=∑x/n=4+8+9+4+9+7+9+6+6+11+15+13+16+12+10+12+18+20+15+10+15+19+21+9+22+19+23+13+12+10/30
=377/30
=12.5667
Longboard Variance S2=[∑dx²-(∑dx)²/n]/n-1
=[831-(-13)²/30]/29
=831-5.6333/29
=825.3667/29
=28.4609
Shortboard Mean
ˉx=∑x/n=6+4+6+6+7+7+7+10+4+6+7+5+8+9+4+15+13+9+12+11+12+13+9+11+13+15+9+19+20+11/30
=288/30
=9.6
Shortboard Variance S2=[∑x²-(∑x)²/n]/n-1
=[ 3270-(288)2/30]/29
=3270-2764.8/29
=505.2/29
=17.4207
2) Putting values in the test statistic
t=|x1-x2|/√S²1/n1+S²2/n2
t =|12.5667-9.6|/√28.4609/30+17.4207/30
t =|2.9667|/√0.9487+0.5807
t=|2.9667|/√1.5294
t=|2.9667|/1.2367
t=2.3989
3) Degree of freedom =n1+n2-2=30+30-2=58
4) The critical region is t ≤ t(0.05) (58) =1.6716
5) Since the calculated t= 2.4 does not fall in the critical region t(0.05) (58) ≤ 1.6716 we do not reject H0.
The p-value is 0.008969. The result is significant at p <0 .05.
A factory makes 1554 units in 14 days with the help of 20 workers. If 2 workers go on leave, how many units can be produced, if there are only 10 days?
Find the perimeter of each polygon. Assume that lines which appear to be tangent are tangent.
Answer:
Step-by-step explanation:
The sales tax in Callie's town is
8.5%. Callie bought 3 DVDs for
$24.60 each and 1 book for $15.20
How much did she pay in sales tax?
Answer:
7.57
Step-by-step explanation:
Find the value for x
Answer:
x=4
Step-by-step explanation:
The two angles together are complementary, which means they add up to 90 degrees
solving for x:
9x+4x+38=90
9x+4x=13x
13x+38=90
13x+38-38=90-38
13x=90-38
13x=52
x=4
hope this helps ^D^
Answer:
9x=4x+38
5x=38
x=38/5
Step-by-step explanation:
NO LINKS PLEASE
What are the 3 missing numbers on the 3 blanks?
Answer:
[tex]y=\frac{3}{2} x+0[/tex]
Step-by-step explanation:
points on the line are:-
[tex](0,0) and(2,3)[/tex]
[tex]m=\frac{3-0}{2-0} =\frac{3}{2}[/tex]
[tex]y=mx+b[/tex]
[tex]y=\frac{3}{2} x+b[/tex]
[tex]0=\frac{3}{2}(0)+b[/tex]
[tex]0=b[/tex]
so...
[tex]y=\frac{3}{2} x+0[/tex]
[tex]---------[/tex]
hope it helps...
have a great day!!