Answer:
Jordan wins the second race.
Step-by-step explanation:
Jordan and Amari run a 200-meter race, and Jordan wins by 23 meters.
This means that while Jordan ran 200 meters, Amari will have ran 200 - 23 = 177 meters.
Thus, for each meter that Jordan runs, Amari runs 177/200 = 0.885 meters.
Second race:
Jordan starting 23 meters behind the starting line, and thus, he will have to run 200 + 23 = 223 meters.
When Jordan reaches the finish line, having ran 223 meters(200 + 23 behind), Amari will have ran 223*0.885 = 197.335 meters(< 200, so he will not have reached the finish line), and thus, Jordan wins the second race.
Please show ur work too!
(Image is the whole problem)
Answer:
ST = 15
Step-by-step explanation:
Given:
QR = 3x
LM = x + 9
ST = 6x - 3
Required:
ST
Solution:
First, we need to find the value of x by creating an equation.
Based on the trapezoid mid-segment theorem, we have the following equation:
LM = ½(QR + ST)
Substitute
x + 9 = ½(3x + 6x - 3)
x + 9 = ½(9x - 3)
Multiply both sides by 2
2(x + 9) = 9x - 3
2x + 18 = 9x - 3
Collect like terms
2x - 9x = -18 - 3
-7x = -21
Divide both sides by -7
x = -21/-7
x = 3
Find ST:
ST = 6x - 3
Plug in the value of x
ST = 6(3) - 3 = 18 - 3
ST = 15
ang
Name two vertical angles, two supplementary
angles in the diagram below.
Answer:
5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.
How many centimeters are there in 3.35 meters?
A. 115
B. 225
C. 335
D. 445
Answer:
335
Step-by-step explanation:
To convert meters to centimeters, move the decimal point two spaces to the right.
Answer:
335
Step-by-step explanation:
a centimeter is one hundredth of a meter so multiply 3.35x100
The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below.
Robert, 1.11 Juan, 1.66 Susan, –1.9 Joel, 0.00 Jan, –0.65 Linda, 1.46
(a) Which of these students scored above the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(b) Which of these students scored on the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(c) Which of these students scored below the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(d) If the mean score was ? = 156 with standard deviation ? = 24, what was the final exam score for each student? (Round your answers to the nearest whole number.)
a. Janb. Joelc. Juand. Lindae. Robertf. Susan
Answer:
a)
b. Joel
c. Juan
d. Linda
b)
b. Joel
c)
a. Jan
f.Susan
d)
a. Jan: 140
b. Joel: 156
c. Juan: 196
d. Linda: 191
e. Robert: 183
f. Susan: 110
Step-by-step explanation:
Z-score:
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, positive z-scores are above the mean, negative are below the mean and 0 is 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.
Question a:
Robert, Juan and Linda had positive z-scores, so they scored above the mean, and the correct options are c,d,e.
(b) Which of these students scored on the mean?
Joel, which had a z-score of 0, so the correct option is b.
(c) Which of these students scored below the mean?
Jan and Susan had negative z-scores, so them, options a and f.
Question d:
We have that [tex]\mu = 156, \sigma = 24[/tex], so we have to find X for each student.
Jan:
Z = -0.65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.65 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -0.65*24[/tex]
[tex]X = 140[/tex]
b. Joel
Z = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 0*24[/tex]
[tex]X = 156[/tex]
c. Juan
Z = 1.66, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.66 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.66*24[/tex]
[tex]X = 196[/tex]
d. Linda
Z = 1.46. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.46 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.46*24[/tex]
[tex]X = 191[/tex]
e. Robert
Z = 1.11. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.11 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.11*24[/tex]
[tex]X = 183[/tex]
f. Susan
Z = -1.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.9 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -1.9*24[/tex]
[tex]X = 110[/tex]
Using the diagram below, what is the measure of ZE?
Answer:
50
Step-by-step explanation:
Think of line AE as a transversal. with DE and AB cutting across it. If we draw it out, looking at the picture, we can see that angles A and E correspond, meaning that angle A = angle E = 50
Circle the answer choice below that does not equal the following:
- 48/16
1) 48/-16
2) -3
3) 3
4) -(48/16)
Answer:
3
Step-by-step explanation:
-48/16 = 48/16
-48/16 = -3/1 = -3
Please help me figure out which is the correct answer, i have attached the picture for you to look at. Thanks so much!
Answer:
The answer is B ;)
Step-by-step explanation:
4x+5 is greater than or equal to 13
subtract 5 from each side to get 4x is greater than or equal to 8
then divide both sides by 2 to get
x is greater than or equal to 2
This table on a package of dog food tells how much to feed a dog, depending on its weight. Weight of Dog (pounds)153045 Amount of Food (scoops)246 The amount of food in scoops (s) is related to the weight of the dog in pounds (p) by the equation s = kp. What is k?
9514 1404 393
Answer:
k = 2/15
Step-by-step explanation:
We can solve the given equation for k:
k = s/p . . . . . . divide the given equation by p on both sides
Using the first values from the table (15 pounds, 2 scoops), we have ...
k = 2/15
The value of k is 2/15.
Find the area
76 sq meters
60 sq meters
30.5 sq meters
65 sq meters
Answer:
60 square meters
Step-by-step explanation:
Please help!! Will mark brainilest, thank you in advance. :))
Answer:
See image below:) :)
Step-by-step explanation:
Drew hiked two trails Rocky Hill is 7 /8 miles long battle in Brook Trail is 4/5 mile long how much further did Drew hike on Rocky Hill Trail then I'll babbling Brook Trail write an equation
Chris and Jen decide to go apple picking at a local apple orchard. As the number of apples they pick increases the cost of the apples also increases. The function ff relates the varying cost of Chris and Jen's apples, cc , in terms of the varying number of pounds of apples that Chris and Jen pick, nn , where c=f(n)c=f(n) and ff is defined by f(n)=0.4n+6f(n)=0.4n+6.
Evaluate f−1(33) Note( this is F^-1)
Determine the rule for the function f^-1
Any relation that has an inverse is a function
The value of [tex]\mathbf{f^{-1}(33)}[/tex] is [tex]\mathbf{f^{-1}(33) = 67.5}[/tex]The rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]The function is given as:
[tex]\mathbf{f(n) = 0.4n + 6}[/tex]
(a) Evaluate [tex]\mathbf{f^{-1}(33)}[/tex]
First, we calculate the inverse function
We have:
[tex]\mathbf{f(n) = 0.4n + 6}[/tex]
Rewrite as:
[tex]\mathbf{y = 0.4n + 6}[/tex]
Subtract 6 from both sides
[tex]\mathbf{y -6= 0.4n + 6 - 6}[/tex]
[tex]\mathbf{y -6= 0.4n}[/tex]
Divide both sides by 0.4
[tex]\mathbf{\frac{1}{0.4}(y -6)= \frac{0.4n}{0.4}}[/tex]
[tex]\mathbf{\frac{1}{0.4}(y -6)= n}[/tex]
[tex]\mathbf{2.5(y -6)= n}[/tex]
Make n the subject
[tex]\mathbf{n = 2.5(y -6)}[/tex]
Rewrite as:
[tex]\mathbf{n = 2.5(f(n) -6)}[/tex]
So, the inverse function is:
[tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Substitute 33 for n to calculate [tex]\mathbf{f^{-1}(33)}[/tex]
[tex]\mathbf{f^{-1}(33) = 2.5(33 -6)}[/tex]
[tex]\mathbf{f^{-1}(33) = 2.5(27)}[/tex]
[tex]\mathbf{f^{-1}(33) = 67.5}[/tex]
(b) The rule of [tex]\mathbf{f^{-1}(n)}[/tex]
In (a), we have: [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Hence, the rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Read more about functions and inverses at:
https://brainly.com/question/10300045
A farm categorizes its chickens into 3 classes according to the weight: small, medium, andbig. For any chicken in this farm, the distribution of the weight (denoted byW) follows a GaussianPDF with mean 3.8 lb and standard deviation 0.6 lb. The categories follow the following rule
small: W <= 3.5lb
medium: 3.5 <= 4.9lb
Large: W > 4.9lb
Required:
a. What are the probabilities that a chicken is in the classes of small, medium, and large, respectively?
b. Find c such that PW < c = 0.6.
c. Suppose that 5 chickens are selected at random. What is the probability that 3 out of the 5 will be small?
Answer:
A) P ( chicken is small ) = 0.3085, P ( chicken is medium ) = 0.6621
P (chicken is large ) = 0.0294
B) C = 3.9233
C) 0.1404
Step-by-step explanation:
A) Probabilities
i) P ( chicken is small )
P( w ≤ 3.5 ) = Fw ( 3 .5 )
= F ( 3.5 - 3.8 / 0.6 )
= F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]
= 1 - 0.6915 ( from Table )
= 0.3085
ii) P ( chicken is medium )
P ( 3.5 < w < 4.9 )
P ( w < 4.9 ) - P ( w < 3.5 )
= Fw ( 4.9 ) - Fw ( 3.5 )
= F ( 4.9 - 3.8 / 0.6 ) - 0.3085
= 0.9706 - 0.3085 = 0.6621
iii) P (chicken is large )
= P ( w > 4.9 )
= 1 - P ( w < 4.9 )
= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294
B) Find c
Given: P( w < c ) = 0.6
Fw ( c ) = 0.6
F ( c - 3.8 / 0.6 ) = 0.6
c - 3.8 / 0.6 = 0.2055 ( from table )
∴C = 3.9233
C) P ( 3 out of 5 = small )
P ( 3 of 5 = small ) = 0.1404
attached below is a detailed solution
WILL MARK YOU IF YOU CAN HELP ME
Answer:
x= 62
first take linear pair angle with any line then once again with x then you're done
Answer:
x value is 62 degree
because they are vertically opposite angles
A shipping carton is in the shape of a triangular prism. The base area of the triangle is 6 inches squared and the the height of the prism is 15 inches. how many cubic inches of space are in the carton?
51
Step-by-step explanation:
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Find the value of the trigonometric ratio. Simplify the ratio if possible.
(Hint: You may need to use some pythagorean theorem first!)
Answer:
in this tiangle tanA = 8/15
Anyone know the answer to this?
Answer:
is it correct if yes you may follow me for more helps ☺️
Workplace accidents are categorized in three groups: minor, moderate, and severe. The probability that a given accident is minor is 0.5, that it is moderate is 0.4, and that it is severe is 0.1. Two accidents occur independently in one month. Calculate the probability that neither accident is severe and at most one is moderate.
Answer: The probability when neither of the accidents is severe and at most one is moderate is 0.65
Step-by-step explanation:
Given values:
Probability when the accident is minor = 0.5
Probability when the accident is moderate = 0.4
Probability when the accident is severe = 0.1
As two accidents are occurring independently and we need to calculate the probability of an event that neither accident is severe and at most one is moderate.
So, the equation for the probability becomes:
[tex]=\text{P[moderate, minor]}+\text{P[minor, moderate]}+\text{P[minor, minor]}\\\\= (\text{P[moderate]}\times \text{P[minor]}) + (\text{P[minor]}\times \text{P[moderate]}) + (\text{P[minor]}\times \text{P[minor]})[/tex]
Putting values in above equation, we get:
[tex]=[(0.40)\times (0.5)] + [(0.5)\times (0.4)] +[((0.5)\times (0.5)]\\\\= 0.65[/tex]
Hence, the probability when neither of the accidents is severe and at most one is moderate is 0.65
Divide Rs. 1800 among Marmik, Sujata and Kapil in the ratio of 1/3:1/4:1/6
Answer:
Marmik = 800; Sujata = 600; Kapil = 400
Step-by-step explanation:
Given
Let
[tex]M \to Marmik[/tex]
[tex]S \to Sujata[/tex]
[tex]K \to Kapil[/tex]
Given
[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]
[tex]Amount = 1800[/tex]
Required
Divide
We have:
[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]
Multiply the ratio by 12 (to convert them to whole numbers)
[tex]M:S:K = 12 *\frac{1}{3}:12*\frac{1}{4}:12*\frac{1}{6}[/tex]
[tex]M:S:K = 4 : 3 : 2[/tex]
The total ratio is:
[tex]Total = 4 + 3 + 2 = 9[/tex]
So, the amount each collected is:
[tex]Marmik = \frac{M}{Total} * Amount[/tex]
[tex]Marmik = \frac{4}{9} *1800 = 800[/tex]
Using the same formula for others, we have:
[tex]Sujata = \frac{3}{9} *1800 = 600[/tex]
[tex]Kapil = \frac{2}{9} *1800 = 400[/tex]
an arrow is shot vertically upward from a platform 33ft high at a rate of 174 ft/sec. when will the arrow hit the ground?
Answer:
h(t) = -16t2 + 186t + 43
at the ground h = 0
hence; -16t2 + 186t + 43 = 0
solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a
gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)
Step-by-step explanation:
Mr Zuro finds the mean height of all 13 students in his statistics class to be 68.0inches. Danielle walks in late. Danielle is 72.2 inches tall. What is the mean height of the 14 students in the class
Answer:
68.3 inches
Step-by-step explanation:
Let the sum of the original 13 students heights be S, so the average of their heights are S/13.
We are given that average height of the original 13 students heights is 68 inches, so S/13 = 68 -> S = 68*13 = 884 inches.
The average of the heights of all 14 students is the sum of all 14 students (S + Danielle’s height) divided by 14. We are given that Danielle’s height is 72.2 inches, so the mean height of all 14 students is:
(S+72.2)/14 = (884+72.2)/14 = 68.3 inches
I hope this helps! :)
let abc is a right angle triangle at b. if ac=10cm and ab=8cm the what is the lenght of bc is
Answer:
using Pythagoras theorem
bc²=ac²-ab²
bc²=100-64
bc=√36
bc =6
C) 6
I
3)
4)
12x + 12
13x + 5
A) -
C) -10
A) 6
C) 7
B) 8
D) 9
5)
6)
Answer:
x=7
Step-by-step explanation:
Alternate interior angles so they are congruent. So, 13x+5=12x+12. Subtract 12x and get x+5=12. Subtract 5 and you get x=7
Write the equation of a line with a slope of −2 and a y-intercept of 5.
9514 1404 393
Answer:
y = -2x +5
Step-by-step explanation:
The slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . . . . line with slope m and y-intercept b
You want a line with slope -2 and y-intercept 5, so your equation is ...
y = -2x + 5
What are the domain and range of this function?
Answer:
D x is all real numbers
R y ≥ -3
Step-by-step explanation:
The domain is the values that x can take
The domain is all real numbers
The range is the values that y can take
The range is y is greater than or equal to -3
Find the size of angle x.
Answer:
x = 111
Step-by-step explanation:
180- 82 -29 is 69 and 180-69 is x which x is equal to 111
Answer:
111°
Step-by-step explanation:
By exterior angle theorem:
[tex]x = 82 \degree + 29 \degree \\ = 111 \degree[/tex]
A hemispherical tank is filled with water and has a diameter of 22 feet. If water
weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank,
to the nearest pounds
Answer:
173 949 pounds
Step-by-step explanation:
radius of the hemisphere = diameter / 2 = 11 feet
Volume of the hemisphere = (2/3 * radius^3 * pi) = = (2/3 * 11^3 * pi) = 2.787,639881 ft^3
Total weight = volume of the hemisphere * 62.4 = 173,948.728592
I'm Stuck and need help please). The table shows the test scores and the sleep averages of several students. A) Write the least squares regression equation that models the data. Let x = the test score and y = average sleep. B) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. Show Your Work. ( Will Mark Brainliest but no Links or nonsense answers please). Answer A and Answer B.
Answer:
a
you should take values of x and y that are similar or they are close to each other like 8 is close to 8.5
b
u will take the average of all the scores with 8hr sleep
Helppop!!A car and van are driving on a highway. The table shows the amount y (in gallons) of gas in the cars gas tank after driving x miles. The amount of gas in the van’s gas tank after driving x miles is represented by the equation y=- 1/5x + 31. Which vehicle uses less gasoline per mile? How many miles must the vehicles travel for the amount of gas in each tank to be the same?
Answer:
The car uses less gas
They use the same amount of gas after [tex]\frac{640}{7}[/tex] miles
Step-by-step explanation:
Given
The table represents the car mileage
[tex]y = -\frac{1}{5}x + 31[/tex] --- The van
First, calculate the car's slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
From the table, we have:
[tex](x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)[/tex]
So, we have:
[tex]m = \frac{10.5 - 13.5}{180 - 60}[/tex]
[tex]m = \frac{-3}{120}[/tex]
[tex]m = -\frac{1}{40}[/tex]
Calculate the equation using:
[tex]y = -\frac{1}{40}(x - 60)+13.5[/tex]
[tex]y = -\frac{1}{40}x + 1.5+13.5[/tex]
[tex]y = -\frac{1}{40}x + 15[/tex]
[tex]m = -\frac{1}{40}[/tex] implies that for every mile traveled, the car uses 1/40 gallon of gas
Also:
[tex]y = -\frac{1}{5}x + 31[/tex] --- The van
By comparison to: [tex]y = mx + b[/tex]
[tex]m = -\frac{1}{5}[/tex]
This implies that for every mile traveled, the van uses 1/5 gallon of gas.
By comparison:
[tex]1/40 < 1/5[/tex]
This means that the car uses less gas
Solving (b): Distance traveled for them to use the same amount of gas.
We have:
[tex]y = -\frac{1}{5}x + 31[/tex] --- The van
[tex]y = -\frac{1}{40}x + 15[/tex] --- The car
Equate both
[tex]-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15[/tex]
Collect like terms
[tex]\frac{1}{40}x -\frac{1}{5}x =-31 + 15[/tex]
[tex]\frac{1}{40}x -\frac{1}{5}x =-16[/tex]
Take LCM
[tex]\frac{x - 8x}{40} = -16[/tex]
[tex]\frac{- 7x}{40} = -16[/tex]
Solve for -7x
[tex]-7x = -640[/tex]
Solve for x
[tex]x = \frac{640}{7}[/tex]
If f(x) = 5x - 3 and g(x) = 3x - 3, find f(x) - g(x).
A 2x
B. 8x - 6W
C2x-6
D. 8x
Replace f(x) to 5x-3 and g(x) to 3x-3 then subtract f(x) by g(x).
[tex] \large{f(x) - g(x) = (5x - 3) - (3x - 3)}[/tex]
Cancel the brackets, remember that multiplying or expanding the negative symbol will switch the sign. From plus to minus and minus to plus.
[tex] \large{ f(x) - g(x)= 5x - 3 - 3x + 3 }[/tex]
Combine like terms.
[tex] \large{f(x) - g(x) = 2x + 0 \longrightarrow \boxed{2x}}[/tex]
Answer
f(x)-g(x) = 2xAnswer:
5x-3-(3x-3)
5x-3-3x+3
5x-3x
2x