Answer:
The z-score for the trainee is of 2.
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.
The mean of the test scores is 72 with a standard deviation of 5.
This means that [tex]\mu = 72, \sigma = 5[/tex]
Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 72}{5}[/tex]
[tex]Z = 2[/tex]
The z-score for the trainee is of 2.
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,000 square feet can be installed for $50,000, whereas the installation of an 800 square foot swimming pool costs $35,000. Select the correct graph that models the given relationship.
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain
The graph of a line goes through the points (-4,3) and (6,8). What is the equation of the line in slope-intercept form?
Enter the correct answer in the box by replacing m and b with the appropriate values.
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CSC seccot log log. In
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2
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y = mx + b
I
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73°F Mostly cloudy
327 PM
7/3/2001
Answer:
[tex]y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Hi there!
Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that lie on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug the given points (-4,3) and (6,8) into the equation
[tex]m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}[/tex]
Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in one of the given points and solve for b
[tex]8=\frac{1}{2}(6)+b\\8=3+b[/tex]
Subtract 3 from both sides to isolate b
[tex]8-3=3+b-3\\5=b[/tex]
Therefore, the y-intercept is 5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x+5[/tex]
I hope this helps!
one story with author and summary please
Answer:
The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.
In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.
When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.
. a) In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.
i)50
Steps
30+20=50
ii)7
Steps
75-(30+20)-18
=75-(50)-18
=7
iii)20
Steps
From the available data from the question
iv)30
Steps
From the available data from the questionl
v)From the attcged image file
Cuanto es 91972×898972819
Answer:
82,680,328,109,068
Step-by-step explanation:
Use the on-line Big Number calculator
Find the domain and range of the relation
Answer:
The domain is "all real numbers" and the range is x more than -3
what is the domain of f(x)
Answer:
Values of x
Step-by-step explanation:
The domain of a function is the set of all possible inputs for the function while the co-domain is the set of all possible outputs of the function.
In other words, domain is the set of x-values that you can put into any given equation while co-domain is the sex of f(x)-values that you get from substituting the values of x.
Hope it's clear
Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $430 in interest, assuming she does not withdraw any of the money?
Answer:
The correct answer is - 7.166 years
Step-by-step explanation:
Given:
principle amount: 3000
rate of interest: 2%
time?
Interent to get: 430
Formula:
I = P*t*r/100
here p = principle
I = interest
r = rate of intrest and t = time
Solution putting value and deriving Time as formula:
(3000*2*t)/100 = 430
t = 43000/3000*2
= 7.166 years.
if A={1,2,3,4,5},B={4,5,6,7} and C={2,3,4}find (A-B)-C
Answer:
(A - B) - C = { 1 , 4 , 6 , 7 }
Step-by-step explanation:
A = { 1 , 2 , 3 , 4 , 5 }
B = { 4 , 5 , 6 , 7 }
A - B = { 1 , 2, 3 ,6 , 7 }
C = { 2 , 3 , 4 }
(A - B) - C = { 1 , 4 , 6 , 7 }
Working to
(simplify y
Lisa, an experienced shipping clerk, can fill a certain order in 7 hours, Bill, a new clerk, needs 9 hours to do the
same job. Working together, how long will it take them to fill the order?
it might take 19 hours i might be wrong
Step-by-step explanation:
Which action is not a step in using paperfolding to find the midpoint of a line segment?
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answer:
[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]
Substitute for x in equation (a) :
[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]
Substitute for y in equation (b) :
[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]
2x+4y =8
x=3y-6 ——> x–3y=–6
x–3y = – 6 ] ×(–2) ——> –2x +6y=12
2x+4y=8
–2x+6y =12
__o_o____
0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2
2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0
(x,y) —> (0,2)
Acellus
First, find the surface area of the yellow prism.
3 cm 3 cm
: ?
4 cm
3 cm
front: [?]
back: [ ]
right: [ ]
left: [ ]
3cm
3cm
4cm
top:[]
5 cm
TOTAL: [ ]
Note: The bottom will not be
included because this is whern
5 cm
Answer:
57 cm²
Step-by-step explanation:
Surface area of the yellow prism = front + back + right + left + top
✔️Area of the front = L * W
L = 4 cm
W = 3 cm
Area of the front = 4*3 = 12 cm²
✔️Area of the back = L * W
L = 4 cm
W = 3 cm
Area of the back = 4*3 = 12 cm²
✔️Area of the right face = L * W
L = 4 cm
W = 3 cm
Area of the right face = 4*3 = 12 cm²
✔️Area of the left face = L * W
L = 4 cm
W = 3 cm
Area of the left face = 4*3 = 12 cm²
✔️Area of the top = L * W
L = 3 cm
W = 3 cm
Area of the top = 3*3 = 9 cm²
✅Total = 12 + 12 + 12 + 12 + 9 = 57 cm²
Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 6.7 Mbps0.2
0.5
1.1
2.7 0.35.60.51.12.55.00.30.51.22.78.20.30.51.22.79.60.30.51.63.210.60.30.61.63.413.00.30.62.13.614.10.40.72.13.815.10.40.82.34.015.20.4l.O2.44.030.4
Answer:
The answer is "58th %".
Step-by-step explanation:
2.4 Mbps in the sort data set is the 30th data point. Therefore 29 numbers out of 50 are less than 2.4 Mbps.
[tex]=\frac{29}{50} = 0.58 =58\%\\\\[/tex]
The X-th percent is just the same as x% below the percent and thus 2,4 Mpbs corresponds to a 58th percent.
You are dealt one card from a 52-card deck.
a) Find the odds in favor of getting a red king.
b) Find the odds against getting a red king.
Answer:
(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.
(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.
The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
You are dealt one card from a 52-card deck.
Total events = 52
The odds in favor of getting a red king will be
Favorable events = 2
Then the probability will be
P = 2/52
P = 1/26
The odds against getting a red king will be
q = 1 – P
q = 1 – 1/26
q = 25/26
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
Determine how much simple interest you would earn on the following investment:
$13,400 invested at a 6/2 % interest rate for 4 years.
Answer:
How do you mean 6/2%? Clarify it for assistance
Answer:
Simple interest = $ 3,484.00
Step-by-step explanation:
I= P×R×T ÷ 100
The rate is 6 1/2 and I will use the decimal form 6.5,to change that to a whole number we simply move the decimal point one place behind.
Since we moved the decimal point in the numerator we need to do the same for the denominator.Therefore 100 becomes 1000.
13400 × 65 × 4 = $ 3,484.00
1000
There are three uncertain (random) variables in this problem. Choose the variables that should represent uncertainty in this model.
a. Yield
b. Initial Research and Development Cost
c. Pre-Orders Picked up
d. What type of fruit to grow
e. Pre-Orders Placed
f. Salvage Price
Answer:
a. Yield
c. Pre-Order picked up
e. Pre-Orders placed.
Step-by-step explanation:
Uncertain random variables are those over which the farmer has no control. These variables are uncontrollable and there can be no prediction for it. The farmer has no control over the yield produced. He can choose what type of fruits to grow and input method but he has no control over output generated.
A family has 5 children. Compute the probabilities of the following events:
All five are born on Friday.
Each one is born on a different day of the week.
Answer:
1/16,807 chance that they all will be born on Friday
Probably 5/7, but don't take my word for it.
Step-by-step explanation:
There are 7 days of the week.
There is a 1/7 chance for one kid to be born on a certain day of the week.
We can attach an exponent of 5 since the 1/7 is a constant, and I'm not going to bother typing the same thing over and over again.
(1/7)^5 = 1/16,807.
The probability of all of them being born on Friday or anyday is 1/16,807.
The probability of each person being born on a different day of the week is probabily going to be 5/7, but it could be different, because you need to factor in the requirement that they are not born on the same day.
I can guarantee that the first question is probably correct, but not the second.
A riverboat travels 52 km downstream in 2 hours. It travels 66 km upstream in 3 hours. Find the speed of the boat and the speed of the stream
The speed of the boat is
and the speed of the stream is
Answer:
The speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Step-by-step explanation:
Given that a riverboat travels 52 km downstream in 2 hours, and it travels 66 km upstream in 3 hours, the following calculations must be performed to find the speed of the boat and the speed of the stream:
Downstream = 52/2 = 26
Upstream = 66/3 = 22
Stream = 4/2 = 2
Therefore, the speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
What transformation to the linear parent function, f(x) = x, gives the function
g(x) = x + 7?
A. Shift 7 units left.
B. Shift 7 units right.
C. Vertically stretch by a factor of 7
D. Shift 7 units down
Answer:
I think A
Step-by-step explanation:
a, b, c are prime numbers and 5≤a
Answer:
a=5
Step-by-step explanation:
Samantha acored 15 points in her laat
basketball game. She made 3 free throwa
that are worth 1 point each. The rest of
her pointa came on 2 point field goala,
Write an equation that can be used to find
the number of 2 point field goals that
Samantha made
(uae p as your variable)
Help fasttt
Answer:
15=2p+3
Step-by-step explanation:
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Select one:
a. 420
4
20
b. 320
3
20
c. 520
5
20
d. 120
1
20
Answer:
4 / 20 = 1/5
Step-by-step explanation:
Given that:
Ticket numbering is from 1 - 20
Hence, total possible number of tickets : (1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
Total possible outcomes = 20
Required outcome = multiples of 5 ; the multiples of 5 from the entire ticket numbers are : 5, 10, 15, 20
Required outcome = 4
P(multiple of 5) = Required outcome / Total possible outcomes
P(multiple of 5) = 4 / 20 = 1 / 5
A coin is tossed times and comes up heads times. Use the Empirical Method to approximate the probability that the coin comes up heads. Round your answer to four decimal places as necessary.
Answer:
[tex]P(head) = 0.5600[/tex]
Step-by-step explanation:
Given
[tex]n = 500[/tex] -- number of toss
[tex]head = 280[/tex] --- outcomes of head
See comment
Required
Empirical probability of head
This is calculated as:
[tex]P(head) = \frac{n(head)}{n}[/tex]
[tex]P(head) = \frac{280}{500}[/tex]
[tex]P(head) = 0.5600[/tex]
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
9514 1404 393
Answer:
(x -3) +(x -1) +(x +1) +(x +3) = -72-21, -19, -17, -15Step-by-step explanation:
Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...
(x -3) +(x -1) +(x +1) +(x +3) = -72
4x = -72
x = -18
The four integers are -21, -19, -17, -15.
_____
Additional comment
You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers.
As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.
is -3 linear pls help
Answer:
Yes it is. Graph will go down as it moves from left to right.
Step-by-step explanation:
can anyone help me with this an explain
Answer:
si a forse that can t negativo AND f so ITS 0;3
The figure below shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4. What set of transformations is performed on triangle ABC to form triangle A′B′C′? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
Option D. The set of transformation that is performed on this triangle (ABCD)' is A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
How to solve for the transformationThe answer choices have been shown to have all solutions to be rotated around their origin.
To shift the triangle, It has to be done through the connection the points ABC ' to the origin in such a way that the line is extended as we can seen in the diagram.
Read more on reflection here:
https://brainly.com/question/1908648
#SPJ1
Solve the exponential equation: 6^-2x = 6^2 ^- 3x
A) 3
B) 2
C)4
D)-2
Answer:
the answer is x = 2 or B, hope this helps
Step-by-step explanation:
NFL Pre-Season Teams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts. Do teams that do well in the pre-season tend to also do well in the regular season? We are interested in whether there is a positive linear association between the number of wins in the pre-season and the number of wins in the regular season for teams in the NFL.
Required:
a. What are the null and alternative hypotheses for this test?
b. The correlation between these two variables for the 32 NFL teams over the 10 year period from 2005 to 2014 was 0.067. Use this sample (with n=320) to calculate the appropriate test statistic and determine the p-value for the test.
c. State the conclusion in context, using a 5% significance level.
Answer:
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic = 1.197
Pvalue = 0.2335
There is no correlation between the two variables
Step-by-step explanation:
The null and alternative hypothesis :
H0 : No correlation exist,
H1 : Correlation exist
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic, T = r / √(1 - r²) / (n - 2)
T = 0.067 / √(1 - 0.067²) / (320 - 2)
T = 0.067 / √(0.995511 / 318)
T = 0.067 / 0.0559512
T = 1.197
The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335
α = 5% = 0.05
The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.