Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 67 and standard deviation 10 when given to third graders. Sixth graders have mean score 86 and standard deviation 9 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)
(a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.) a = b = (b)
Do the same for the sixth-grade scores.
a =
b =
(c) David is a third-grade student who scores 79 on the test. Find David's transformed score.
Nancy is a sixth-grade student who scores 79. What is her transformed score?
Who scores higher within his or her grade? Nancy or David
Answer:
a.) a = -34 and b = 2
b.) a = -91.11 b = 2.22
c.) David scored 124, nancy scored 84.27
David scored higher
Step-by-step explanation:
for those in the 3rd grade
mean u = 67
s = 10
we used the z formula
[tex]z=\frac{x-u}{s}[/tex]
[tex]z=\frac{x-67}{10}[/tex]
we have the new score
u = 100
s = 20
we use this formula [tex]z*s+u[/tex]
[tex][\frac{x-67}{10} ]20\\[/tex] + 100
multiply through by 20
[tex][\frac{20x-1340}{10} ] +100[/tex]
dividing the bracket by 10
= [tex]2x-134+100[/tex]
= [tex]2x-34[/tex]
from this solution above,
a = -34 and b = 2
b.)
we solve for those in the 6th grade
u = 86
s = 9
[tex]\frac{x-86}{9}[/tex]
for new score,
y = 100
s = 20
[tex][\frac{x-86}{9} ]20+100[/tex]
[tex]2.22x-191.11+100\\= 2.22x - 91.11[/tex]
from this solution
a = -91.11
b = 2.22
c.) if David scored 79
[tex]= 2(x)-34[/tex]
= 2(79) - 34
= 158 - 34
= 124
if nancy scored 79
= 2.22(79) - 91.11
= 175.38 - 91.11
= 84.27
from these scores we can see that David scored higher in his grade
find the value of x. round to the nearest tenth. 9,4, x
Answer:
Not sure what you mean here, is this a table? If so, you need to provide the y value or a screenshot!
Answer:
24.6° (nearest tenth) .
Dan's car depreciates at a rate of 7% per year.
By what percentage has Dan's car depreciated after 6 years?
Give your answer to the nearest percent.
Answer:
20%
Step-by-step explanation:
Given that
The car is depreciated at a rate of 7% per year
We need to find out the percentage when the car is depreciated after 6 years
So,
Since the car is depreciated by 7% so we can say it can be 0.93 times in a year
Now after 6 years, it would make
= 0.93^3
= 0.80
So, the percentage is
= 1 - 0.80
= 0.20
= 20%
1. A drama club earned $662.50 from a production where 85 adult tickets were sold and 65
student tickets were sold. An adult ticket costs $2.50 more than a student ticket. Which
system of equations can be used to find a, the cost of an adult ticket, and s, the cost of a
student ticket?
Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44
Step-by-step explanation:
Let the cost of adult ticket be 'x' and cost of student ticket be 'y'
From the question, the equations formed are:
[tex]662.5=85x+65y[/tex] .....(1)
[tex]x=2.5y[/tex] ......(2)
Putting value of 'y' from equation 2 to equation 1:
[tex]662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44[/tex]
Now, solving for 'x', we get:
[tex]x=2.5(2.44)=\$ 6.1[/tex]
Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44
which term in the quotient of this expression contains an error?
Answer:
The + 78 :- it should be + 60.
Step-by-step explanation:
Long division:-
x - 3 )4x^4 - 6x^3 + 0x^2 + 6x + 3 ( 4x^3 + 6x^2 + 18x + 60 <--- Quotient.
4x^4 - 12x^3
6x^3 + 0x^2
6x^2 - 18x^2
18x^2 + 6x
18x^2 - 54x
60x + 3
60x - 180
183
identify the angle type, then find the value of x
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Answer:
acute anglex = 25Step-by-step explanation:
The angle shown is 75°. It is less than 90°, so is an acute angle. (The diagram is misleading in that respect.)
__
The two marked angles are vertical angles, so have the same measure.
3x° = 75°
x = 25 . . . . . . . . divide both sides by 3°
please help quick!!!
Which drink has more sugar per fluid ounce? 50 POINTS
A research team conducted a study showing that approximately 30% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 30 businessmen, all of whom wear ties, what are the following probabilities?
a. at least one tie is too tight
b. more than two ties are too tight
c. no tie is too tight
d. at least 18 ties are not too tight
Answer:
a) 0.9998
b) 0.9979
c) 0.7
d) 0.9155
Step-by-step explanation:
P( people who wear their ties tightly ) = 0.3
P( people who do not wear their ties tightly ) = 1 - 0.3 = 0.7
sample size ( n ) = 30
Given that the events are independent and there are only two outcomes we will apply Binomial distribution
a) P( at least one tie is too tight )
P ( x ≥ 1 ) = 1 - P ( x < 1 ) = 1 - P ( x = 0 )
= 1 - 0.00002 = 0.9998 ( excel function: 1 - BINOMDIST(0,30,0.3,0) )
b) P( more than two ties are too tight )
P ( x > 2 ) = 1 - P ( x ≤ 2 ) = 1 - BINOMDIST(2, 30, 0.3, 1 )
= 1 - 0.002113178
= 0.9979
c) P ( no tie is tight )
P ( x = 0 ) = 0.7
d) P( at least 18 ties are not too tight ) i.e. ( P = 0.7 )
P ( x ≥ 18 ) = 1 - P( x ≤ 17 )
= 1 - BINOMDIST ( 17, 30, 0.7, 1 )
= 1 - 0.08447006
= 0.9155
libreng puntoss
yeeah
PA BRAINLIEST
I need help with #4. Please help. I have to show all work so please explain
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Answer:
5
Step-by-step explanation:
Use the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -0)²+(3 -0)²) = √(4² +3²) = √(16 +9) = √25
d = 5
The distance between the two points is 5 units.
_____
Additional comment
The most commonly seen Pythagorean triples are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) and their multiples.
In problem 4, once you see that the differences of the coordinates are 3 and 4, you can consult your memory of the (3, 4, 5) Pythagorean triple to recognize the hypotenuse length of a triangle with sides 3 and 4 is 5.
Similarly, in problem 5, you recognize the coordinate differences as 5 and 12, so you know from the (5, 12, 13) Pythagorean triple that the distance will be 13.
help me please geometry!!
Find the missing side length.
Set up a ratio:
16/12 = 28/?
Cross multiply:
16? = 12 x 28
16? = 336
Divide both sides by 16:
? = 336/16
? = 21
Given: x - 6 ≤ 1. Choose the solution set.
Answer:
x<7
Step-by-step explanation:
See image below:)
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200. Construct a 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200.
Answer:
The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200.
This means that [tex]n = 150, \pi = \frac{60}{150} = 0.4[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.3216[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.4784[/tex]
The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).
Suppose that the logons to a computer network follow a Poisson process with an average of 3 logons per minute. (a) What is the mean time between logons (in minutes)
Answer:
The mean time between logons is of 0.3333 minutes.
Step-by-step explanation:
Poisson process with an average of 3 logons per minute.
This means that the time between logons follows an exponential distribution, which mean is given by:
[tex]E(X) = \frac{1}{\lambda}[/tex]
For this question, we have that [tex]\lambda = 3[/tex], and thus:
[tex]E(X) = \frac{1}{\lambda} = \frac{1}{3} = 0.3333[/tex]
The mean time between logons is of 0.3333 minutes.
Which is the graph of an even monomial function?
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
Which of the following are mutually exclusive events?
A. An athlete being 5 feet tall and 6 feet tall
B. A student belonging to the chess club and the math club
C. A person having brown eyes and brown hair
D. A teacher teaching English composition and English literature
Answer: A
Step-by-step explanation: Ape x
you and your friend start biking to opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. a) how far apart are you and your friend after 15 minutes? b) after 20 minutes you take a 5- minutes rest, but your friend does not. How far apart are you and your friend after 40 minutes? Explain your reasoning.
Answer:
To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.
15 mins x 60 seconds = 900 seconds.
Step-by-step explanation:
In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.
112.5 x 108 = 12150 feet
12150 feet/5280 feet is approximately 2.3 miles.
For your friend you take 900/6 = 150 groups of 6 seconds.
150 x 63 = 9540 feet
9540 feet/5280 feet = 1.79 miles
1.79 miles + 2.3 miles = 2.09 miles
You and your friend are about 2.09 miles apart after 15 minutes.
B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more
3.07 + 2.3 = 5.37 miles after 40 minutes (you).
Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes
0.6 x 5 (5 x 5 = 25 minutes)= 3 miles
1.79 + 3 miles= 4.79 miles (friend)
4.79 + 5.37 = 10.16 miles
You and your friend are about 10.16 miles apart after 40 minutes.
What is the density of this object? (A sphere)
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Answer:
about 0.299 kg/m³
Step-by-step explanation:
Density is the ratio of mass to volume.
ρ = M/V
ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³
I’ll mark brainliest
Answer:
[tex]\text{A. }y=1.30x+1.50[/tex]
Step-by-step explanation:
The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.
Solve the following system of equations with the substitution method.
{x+y=25
y=4x
(x,y)=( , )
Answer:
(5,20)
Step-by-step explanation:
x+y=25
If you substitute y=4x,
x+4x=25
Now add like terms
5x=25
Divide 5
x=5
Put it back into the equation
5+y=25
Subtract 5
y=20
Answer: (5,20)
I’ll mark you as brainliest
Step-by-step explanation:
1) -5n+10n
= 5n
2) -x-9+2x-10
= 2x-x-9-10
= x-19
3) -5(x-10)-x
= -5x+50-x
= -6x+50
4) 9-5(1-7x)
= 9-5+35x
= 35x+4
5) y^2-x
= 3^2-2
= 9-2
= 7
Do the remain questions by yourself, you can do it!
Find the distance between A(-3, 2) and B(5, -1).
Help me asap!!pleaseeee
Answer:
a
Step-by-step explanation:
yes
Are the triangles congruent? Why or why not?
Answer:
ffffffssssssssssssssssscv
Step-by-step explanation:
For any exponential function of the form f(x) = a · b^x where b≠0, what is the y-intercept of the graph of f(x)?
(0,a)
(1,0)
(a,0)
(0,1)
Answer:
1) (0,a)
Step-by-step explanation:
f(0) = a. b^0 = a. 1 = a
=> (0,a)
As shown in the diagram below, AABC - A DEF, AB=14, BC=4, DE=7, and EF = X
D
14
B
4
С
E
X
F
What is the length of EF?
А
28
B
14
2
4
Answer:
EF=4
Step-by-step explanation:
vì diện tích bằng nhau và bằng 28 áp dụng công thức tính diện tích
Find the surface area of the
prism.
Answer:
Area of front and back = 2 * 2 * 5 = 20 cm^2
Area of sides = 2 * 3 * 4 = 24 cm^2
Area of top and bottom = 2 * 4 * 5 = 40 cm^2
TOTAL area = 84 cm^2
Step-by-step explanation:
The ratio of winners to losers was 7 to 5. If the total number of winners and losers was 1260, how many more winners were there than losers?
Answer:
210
Step-by-step explanation:
7:5
First add the ratios
7+5=12
Put each ratio over the denominator 12 then multiply each by the total
7/12×1260= 735
5/12 × 1260 = 525
To find how many more winners than losers
735-525= 210
will mark brainliest
Answer:
(x, y) = (-2,-5)
Step-by-step explanation:
Multiply the first equation by 3,and multiply the second equation by 1.
3(3x+y=−11)
1(4x−3y=7)
Becomes:
9x+3y=−33
4x−3y=7
Add these equations to eliminate y:
13x=−26
Then solve13x=−26for x:
13x=−26
13x
13
=
−26
13
(Divide both sides by 13)
x=−2
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x+y=−11
Substitute−2forxin3x+y=−11:
(3)(−2)+y=−11
y−6=−11(Simplify both sides of the equation)
y−6+6=−11+6(Add 6 to both sides)
y=−5
Answer:
x=−2 and y=−5