Answer:
c = 27/40.
Step-by-step explanation:
1/8 + c = 4/5
1/8 - 1/8 + c = 4/5 - 1/8
c = 4/5 - 1/8
c = 32/40 - 5/40
c = 27/40.
Selena and Tracey play on a softball team.Selena has 8 hits out of 20 times at bat, andTracey has 6 hits out of 16 times at bat.Based on their past performance, what is theprobability that both girls will get a hit nexttime at bat?[A] 31 40[B] 48 320[C] 1 [D] 14 36
Answer:
The correct option is option [B].
The probability that both girls Selena and Tracey will a next at bat is [tex]\frac{48}{320}[/tex].
Step-by-step explanation:
Independent events:
If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.
P(A and B) =P(A)× P(B)
Dependent events:
If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.
P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)
Given that,
Selena has 8 hits out of 20 times at bat.
The number of hits by Tracey out of 16 is 6 at bat.
A= Selena hits a softball.
B= Tracey hits a softball.
The probability that the Selena his a softball is
=P(A)
[tex]=\frac{8}{20}[/tex]
The probability that the Tracey his a softball is
=P(B)
[tex]=\frac{6}{16}[/tex]
Both event are independent. Sine the events do not affect the outcomes of other event.
The probability that both girls will a next at bat is
=P(A and B)
=P(A)×P(B)
[tex]=\frac{8}{20}\times \frac{6}{16}[/tex]
[tex]=\frac{48}{320}[/tex]
If a stone is thrown up at 10 m per second from a height of 100 meters above the surface of the moon, its height in meters after t seconds is given by s = 100+10t-0.8t^2 . What is its acceleration?
Answer:
-1.6 m/s
Step-by-step explanation:
According to the equations of motion, the height in meters (s) after t seconds is:
[tex]s(t) = s_0+v_0t+a\frac{t^2}{2}[/tex]
If the initial position is 10 m and the initial velocity is 10 m/s:
[tex]s(t) = 100+10+a\frac{t^2}{2}[/tex]
When comparing it with the given height equation, it is possible to obtain the acceleration as follows:
[tex]100+10+a\frac{t^2}{2} =100+10t-0.8t^2\\\frac{a}{2}=-0.8\\ a=-1.6\ m/s[/tex]
Acceleration is -1.6 m/s.
An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet.What is the volume of the tank?Use 3.14 for pi
Answer:
the anser is c
Step-by-step explanation:
just did the quiz and got 100 percent :)
Correct answer is C)
Step-by-step explanation:sorry this may not be helpful but the other answer is (A)
Angles PTQ and STR are vertical angles and congruent.
Which chords are congruent?
O QP and SR
O QR and PO
PR and RS
PR and PS
Answer: QP and SR on ed
Step-by-step explanation:
The chords in the circle that are congruent are PQ and SR.
CircleCircle is the locus of a point such that its distance from a fixed point known as the center is constant.
Given from the diagram that:
∠PTQ = ∠STR (Vertical opposite angles are congruent)
Hence:
PQ = SR
The chords in the circle that are congruent are PQ and SR.
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Please help me with the Square Root problems, Part 4. Please Show and Check the work.
[tex]13. x + 2 = 4\sqrt{x-2} \\\\14. \sqrt{2x-1} +\sqrt{3x-12} = 0\\\\15. x = 2\sqrt{x-4} + 4\\\\16. x-2= \sqrt{9x-36}[/tex]
Answers and Step-by-step explanations
13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32
Move all the terms to one side: x^2 - 12x + 36 = 0
Factorize: (x - 6)^2 = 0 ⇒ x = 6
14. Move one of the roots to one side: [tex]-\sqrt{2x-1} =\sqrt{3x-12}[/tex]
Square both sides: 2x - 1 = 3x - 12
Solve for x: x = 11
15. Subtract 4 from both sides: x - 4 = [tex]2\sqrt{x-4}[/tex]
Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16
Move all the terms to one side: x^2 - 12x + 32 = 0
Factorize: (x - 4)(x - 8) = 0 ⇒ x = 4 or x = 8
16. Square both sides: x^2 - 4x + 4 = 9x - 36
Move all the terms to one side: x^2 - 13x + 40 = 0
Factorize: (x - 5)(x - 8) = 0 ⇒ x = 5 or x = 8
Hope this helps!
Answer:
13. x = 6
14. No real solutions
15. x = 4, 8
16. x = 5, 8
Step-by-step explanation:
13. Square both sides
(x + 2)² = 4²(x - 2)
x² + 4x + 4 = 16x - 32
x² - 12x + 36 = 0
x² - 6x - 6x + 36 = 0
x(x - 6) - 6(x - 6) = 0
(x - 6)(x - 6) = 0
x = 6
14. sqrt(2x - 1) = -sqrt(3x - 12)
No real solutions because a positive square root can not be equal to a negative square root
15. x - 4 = 2sqrt(x - 4)
(x - 4)² = 4(x - 4)
(x - 4)² - 4(x - 4) = 0
(x - 4)(x - 4 - 4) = 0
(x - 4)(x - 8) = 0
x = 4, 8
16. x - 2 = sqrt(9x - 36)
(x - 2)² = (9x - 36)
x² - 4x + 4 - 9x + 36 = 0
x² - 13x + 40 = 0
x² - 5x - 8x + 40 = 0
x(x - 5) - 8(x - 5) = 0
(x - 8)(x - 5) = 0
x = 5, 8
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?
Consider this data set 1, 2, 5, 7, 9, 11, 12. Match the type of the statistic to the correct value.
upper quartile
lower quartile
TOO 000
minimum
maximum
median
HURRY!!
Answer:
median-7
minimum-1
lower quartile-2
maximum-12
upper quartile-11
Step-by-step explanation:hope this helps
Answer:
The upper quartile is 11.
the lower quartile is 2.
the maximum is 12.
the minimum is 1.
the median is 7.
Step-by-step explanation:
What is the length of PR?
Answer:
[tex]8\sqrt{3}[/tex]
Step-by-step explanation:
2/3 pi radians = 2/3 * 180 = 2 * 60 = 120 degrees
split triangle in half:
30, 60, 90 triangle
1/2 PR= 4 root 3
One person can complete a task 8 hours sooner than another person. Working together, both people can perform the task in 3 hours. How many hours does it take each person to complete the tasking working alone?
Answer:
it takes 1st person 4 hour and second person is 8 hours
Step-by-step explanation:
Let t is the time (t >0)
We have:
1st person working rate per one task: 1/t-8 2nd person working rate per one task: 1/t Working rate per one task from 2 person: 1/3<=> 1/3 = 1/t + 1/t-8
<=> [tex]t^{2} -14t = -24[/tex]
<=> [tex](t-7)^{2} =25[/tex]
<=> t - 7 = 5
<=> t = 12
So it takes 1st person 4 hour and second person is 8 hours
Answer:
Person A complete the task in 1.125 hours
Person B complete the task in 9 hours
Step-by-step explanation:
Person A complete a task 8 hours sooner than person B
Working together they perform the task in 3 hours
Let call "x" hours person A need to do the task alone
Then person B will take 8*x hours to do the job
In 1 hour person A do 1/x part of the task
In 1 hour person B do 1/8*x part of the task
Then A + B in one hour of work will do
1/x + 1/8x = [ 8 + 1 ]/8*x ⇒ 9/8*x
And according to problem statement that time is 1/3 (one third of the time)
Then 3* (9/8*x) = 3
9 = 8*x
x = 9/8
x = 1.125 hours
And person B will take 8*1,125 = 9 hours
What problem led to playgrounds becoming more common in America cities
Answer: there were not a lot of safe places kids could play
Step-by-step explanation:
i got it right.
The problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
What is playgrounds?Playgrounds is a safe place that is specifically set aside for children to play.
Playgrounds can tend to contribute to a child social growth when the child plays among is age group or peer group.
Playgrounds is common in America in order to prevent danger and injury because there were not safe places for children to play.
Therefore the problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
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It is generally believed that nearsightedness affects about 1212% of children in a certain region. A school district tests the vision of 160160 incoming kindergarten children. How many would be expected to be nearsighted? What is the standard deviation for the number of nearsighted children in this group?
Answer:
Step-by-step explanation:
Total number of kindergarten children in that region that were tested is 160
It is generally believed that nearsightedness affects about 12% of children in a certain region. Therefore,
The expected number of kindergarten children expected to be nearsighted is
12/100 × 160 = 19
Probability of success, p = 0.12
Probability of failure, q = 1 - p = 1 - 0.12 = 0.88
Standard deviation = √npq = √(160 × 0.12 × 0.88) = 4.11
The function y = 8.5(1.1)x models the population in thousands of a town where x is the number of years after 2000. What will be the town's population in 2007? Give the answer to two decimal places.
The population of the town in 2007, according to the exponential growth function y = 8.5(1.1)x, would be approximately 16,630 people.
Explanation:The function given is an exponential growth function, where y = 8.5(1.1)x. Here, the variable y represents the population in thousands and x represents the number of years after 2000. To find the town's population in 2007, we replace x with 7 (since 2007 is 7 years after 2000) and calculate y.
Using the formula, y = 8.5 * (1.1)7. When calculated, we find y to be approximately 16.63. This means that, according to the model, the town's population in 2007 would be approximately 16630 (because the model represents the population in thousands).
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Evaluate 6c + e2 when c = 6 and e = 2
[tex]c=6, e=2; so\\6\times6+2\times2=40[/tex]
What is 75k industry into a percent?
Answer:
100%
Step-by-step explanation:
\text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 121212 181818 232323 262626 292929 The five-number summary suggests that about 75\%75%75, percent of lakes in Minnesota have more than what number of house boats? Choose 1 answer:
Answer:
18 Houseboats
Step-by-step explanation:
Given the set of numbers
12 18 23 26 29
Minimum = 12
First Quartile, Q₁ = 18
Median, Q₂ = 23
Third Quartile, Q₃ = 26
Maximum = 29
The first 25% of lakes have less than or equal to 18 houseboats.
Therefore, the 5-Number Summary suggests that about 75% of lakes in Minessotta have more than 18 Houseboats.
Answer:
18
YEET
Step-by-step explanation:
Sam subtracted 5 from the quotient of a number and 3. Write an algebraic expression to represent the operations that Sam preformed
Answer:
(x/3) - 5.
Step-by-step explanation:
Let the number be x.
The quotient of the number and 3 is x/3.
So the expression is:
(x/3) - 5.
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground.
After how many seconds does the object hit the ground?
2
4
8
16
Answer:
C. 8
At 8 seconds the object will hit the ground.
Answer: C. 8
Step-by-step explanation:
just did this
Rico wants to find the distance between the points (-2,-3) and (2,-5) his work is shown.|-3| + |-5| = 3+5 = 8the distance is 8 unitsis Riko correct explain why or why not?
Answer:
Riko is wrong
Step-by-step explanation:
To find the distance of two point, we use the following formula:
A (x1, y1)
B (x1, y2)
AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
In this situation, we have:
A (-2,-3)
B (2,-5)
So the distance is: [tex]\sqrt{(2 - (-2))^{2} + (-5 - (-3))^{2} }[/tex] = [tex]\sqrt{4^{2} + 8^{2} }[/tex] = [tex]\sqrt{80} = 4\sqrt{5}[/tex]
Hope it will find you well.
Sample Response: No, Riko is not correct. The points do not have the same x-coordinates. If you connect the points, they do not form a horizontal or vertical line, so you cannot count spaces or use absolute value to find the distance.
Given a sector of a circle has an area of 40.8 square inches and a radius of 8 inches. What is the measure central angle of the circle round to the nearest degree?
Answer: The measure of the central angle of the circle is 73°
Step-by-step explanation: Please see the attachments below
Answer: 287 degree
Step-by-step explanation:
Area of a sector = θ/360 x pi r^2
Where pi = 22/7
Given that the
area = 40.8 square inches
radius = 8 inches
40.8 = θ/360 × 3.143 × 8 × 8
θ = (360 × 40.8)/201.06
θ = 73 degree
The measure of the central angle of the circle = 360 - θ
= 360 - 73
= 287 degree
If g(x)=x2-2x+11; find g(-2)
Amanda can word process 7 words in 6 seconds. At this rate, how many words can she word process in 3 minutes?
210
350
35
3.5
Answer:
He can process 210 words in 3 minutes
-5-n/9=-8
-3/7=-2/3+x
3x-13=7(x+2)-4(x-7)
1/2x-9=15-5/6x
8(4x-3)=6(-7x-4)
2(a-24)=16-1/3(9a+27)
^^ solve the equations above and explain how you got the answer.
Answer:
ok
1) n=27
2) x=5/21
3) no solution
4) x=18
5) x=0
6) a=11
Step-by-step explanation:
hope this helps you..(:
15 POINTS PLZ HELP
It’s all in pic
Answer:
D
Step-by-step explanation:
it's In the picture
please like and Mark as brainliest
Answer:
Volume of the cylinder = D) 113.04 cubic cm
Step-by-step explanation:
[tex] \boxed{ \bold{formula = \pi \: {r}^{2} \: h }}[/tex]
= 3.14 × 2 × 2 × 9
= 3.14 × 36
= 113.04 cm³
when 5√20 is written in simplest radical form , the result is k√5 what is the value of K
A : 20
B : 10
C : 7
D : 4
Answer:
Step-by-step explanation:
√20 can be rewritten as the product of two radicals: √4√5,
and √4 = 2.
Thus, 5√20 = 5(2)√5 = 10√5. Thus, B: 10 is correct; k = 10.
A 25-foot long board is cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?
Answer:
Longer: 17 ft and Shorter: 8 ft
Step-by-step explanation:
Here is what we know:
a = longer part
b = shorter part
a + b = 25
2b + 1 = a
Let's rearrange the equation
b = 25 - a
Now we can plug this into the other equation.
2(25 - a) + 1 = a
50 - 2a + 1 = a
51 - 2a = a
51 = 3a
a = 17 ft
To find b, plug a into one of the equations.
17 + b = 25
b = 8 ft
I hope this helped! :)
I think of a number multiply by 3,add 4,i get 22
Answer:
6
Step-by-step explanation:
22 - 4 = 18
18 / 3 = 6
Answer:
6
Step-by-step explanation:
22-4=18/3=6
start from what you get that use the inverse to get the the original answer
Two number cubes each have sides that are labeled 1 to 6. Isis rolls the 2 number cubes. What is the probability that the sum of the numbers rolled will equal 4?
Answer:
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Total possible outcome is 36
The sample space for the dice is shown below
[tex]\left[\begin{array}{cccccc}1,1&1,2&1,3&1,4&1, 5&1,6\\2,1&2,2&2,3&2,4&2, 5&2,6\\3,1&3,2&3,3&3,4&3, 5&3,6\\4,1&4,2&4,3&4,4&4, 5&4,6\\5,1&5,2&5,3&5,4&5, 5&5,6\\6,1&6,2&6,3&6,4&6, 5&6,6\end{array}\right][/tex]
From the above sample, the event of sum equals 4 is:
(1, 3)
(2, 2)
(3, 1)
Number of outcome with sum equals 4 is 3
[tex]Probability = \frac{number of possible outcome}{number of total outcome} \\Probability = \frac{3}{36} = \frac{1}{12}[/tex]
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Answer:
0.3333
Step-by-step explanation:
Out of 6x6 = 36 different scenarios that could happen when rolling the 2 cubes, there are 3 cases where the sum of the numbers rolled will equal 4:
(1,3) (3,1) and (2,2)
So the probability for these 3 cases to happen out of 36 is
[tex]\frac{3}{36} = \frac{1}{3}[/tex] or 0.3333
# 15. Tycho wants to prepare a schedule for his exercise over the next few months. Every
week, he wants to exercise on the same days of the week. He does not want to exercise on
two consecutive days. He wants to exercise three days per week. How many schedules can he
choose from?
(A) 6
(B) 7
(C) 9
(D) 10
(E) 35
There are a total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).
To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.
So, the possibilities are:
1. Tycho chooses Monday, Wednesday, and Friday.
The schedule is MW FSu.
2. Tycho chooses Monday, Wednesday, and Saturday.
The schedule is MW SaSu.
3. Tycho chooses Monday, Thursday, and Saturday.
The schedule is MT F SaSu.
4. Tycho chooses Monday, Thursday, and Sunday.
The schedule is MT SaSu.
5. Tycho chooses Tuesday, Thursday, and Saturday.
The schedule is TThSaSu.
6. Tycho chooses Tuesday, Thursday, and Sunday.
The schedule is TTSaSu.
7. Tycho chooses Tuesday, Friday, and Sunday.
The schedule is TFSaSu.
8. Tycho chooses Wednesday, Friday, and Sunday.
The schedule is W F SaSu.
9. Tycho chooses Wednesday, Thursday, and Saturday.
The schedule is W T FSaSu.
Thus, total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
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Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.
a. Explain why the information Mary was given cannot be correct.
b. If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the
coordinates of another point on the line
c. If the given points are correct for the line, what is the slope? Write an equation for the line
Answer:
a. The slope is incorrect
b. y = 3x, ( 0 , 0 )
c) y = 4 - x
Step-by-step explanation:
Given:-
The slope between two points (1, 3) and (6, -2) is 3.
a. Explain why the information Mary was given cannot be correct.
- The slope between two arbitrary points, ( x1 , y1 ) and (x2 , y2) is given by the following relationship:
slope = ( y2 - y1 ) / ( x2 - x1)
- Use the given points (1, 3) and (6, -2) and determine the slope:
slope = ( -2 - 3 ) / ( 6 - 1 )
slope = ( -5 ) / ( 5 )
slope = -1
- Yes, the given slope is incorrect it should be = -1
b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line
- We will assume the point (1,3) lies on line with a slope = 3.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = 3x + c
Using the given correct point to evaluate the y-intercept (c):
3 = 3*1 + c
c = 0
- The equation of line is,
y = 3x
- The origin (0,0) lies on the line y = 3x.
c. If the given points are correct for the line, what is the slope? Write an equation for the line
- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = -x + c
Using the given points to evaluate the y-intercept (c):
3 = -1 + c
c = 4
- The equation of line is,
y = -x + 4
Mary's information is incorrect because the slope of the line passing through the points (1, 3) and (6, -2) is -1, not 3. If the slope is actually 3, the line equation is y = 3x and an additional point on the line is (2, 6). If the given points are correct, the line equation is y = -x + 4.
Explanation:To understand these questions, it's important to know how the slope of a line is defined and how to write the equation of a line.
Given two points (x1, y1) and (x2, y2), the slope of the line is calculated as (y2 - y1) / (x2 - x1). For the points given, (1, 3) and (6, -2), the slope would be (-2 - 3) / (6 - 1) = -5/5 = -1. So, the slope of the line passing through these two points is not 3, which contradicts the information given. Therefore, the information Mary was given cannot be correct.
If the point (1, 3) and the slope 3 are correct, the equation of the line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Substituting these values we get y - 3 = 3(x - 1). This simplifies to y = 3x. A point on this line can be (2, 6).
If the points (1, 3) and (6, -2) are correct, we've already calculated the slope as -1. To find the equation of the line we use the same formula, y - y1 = m(x - x1). Substituting these values we get y - 3 = -1(x - 1), simplifying to y = -x + 4.
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The distribution of room and board expenses per year at a four-year college is normally distribute with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Which of the following mean expenses would be considered unusual?a) 5180b)6180c)6350
Answer:
a) 5180
Step-by-step explanation:
We must calculate with respect to each of the options:
a) 5180
We have that the mean (m) is equal to 5850, the standard deviation (sd) 1125 and the sample size (n) = 20
They ask us for P (x <5180)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (5180 - 5850) / (1125 / (20 ^ 1/2))
z = -2.66
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <-2.66) = 0.0039
Which means that the probability is 0.39%, which is a very low probability, which is not necessary to calculate the other options, we already know that this data is very unusual.
The mean expense of (a) 5180 is considered unusual because its z-score is approximately -2.67, which is beyond the usual ±2 range for a normal distribution.
To determine which of the given mean expenses would be considered unusual, we will use the concept of the Standard Error of the Mean (SEM) and the properties of a normal distribution.
The SEM can be calculated as:
[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]
Where:
[tex]\sigma[/tex] is the population standard deviation, $1125n is the sample size, 20.So,
[tex]SEM = \frac{1125}{\sqrt{20}} = 251.21[/tex]
We then determine the z-scores for the given mean expenses to see how many standard errors away from the population mean they are. The population mean is $5850.
For 5180: [tex]z = \frac{5180 - 5850}{251.21} \approx -2.67[/tex]For 6180: [tex]z = \frac{6180 - 5850}{251.21} \approx 1.31[/tex]For 6350: [tex]z = \frac{6350 - 5850}{251.21} \approx 1.99[/tex]A z-score beyond ±2 is generally considered unusual. Therefore, the mean expense of 5180 would be considered unusual as its z-score is approximately -2.67.