Answer:
-2/3 -3/5 -1/2 3/8
..................……
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
10)
X + 80
70°
A) 5
C) -10
B) 8
D) 7
Answer:
C: x=-10
Step-by-step explanation:
Alternate interior angles are congruent to each other meaning that x+80=70 making x equal to -10. I hope this helped and this is one of my favorite units so post more these questions :)
Help pls it’s urgent. If your able to solve it than I’d really would appreciate you.
Answer:
Step-by-step explanation:
If the radius of the circle is equal to
[tex]\sqrt{\frac{A}{3} }[/tex] and the area is given as 45, then
[tex]r=\sqrt{\frac{45}{3} }[/tex] which simplifies to
[tex]r=\sqrt{15}[/tex] and to the nearest tenth,
r = 3.9
Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______
a) sec sqr Theta
b) Cot theta
c) cot (pie/2-Theta)
d) csc sqr theta
Answer:
[tex](a)\ \sec^2(\theta) = 82[/tex]
[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]
[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]
[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]
Step-by-step explanation:
Given
[tex]\tan(\theta) = 9[/tex]
Required
Solve (a) to (d)
Using tan formula, we have:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
This gives:
[tex]\frac{Opposite}{Adjacent} = 9[/tex]
Rewrite as:
[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]
Using a unit ratio;
[tex]Opposite = 9; Adjacent = 1[/tex]
Using Pythagoras theorem, we have:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]
[tex]Hypotenuse^2 = 81 + 1[/tex]
[tex]Hypotenuse^2 = 82[/tex]
Take square roots of both sides
[tex]Hypotenuse =\sqrt{82}[/tex]
So, we have:
[tex]Opposite = 9; Adjacent = 1[/tex]
[tex]Hypotenuse =\sqrt{82}[/tex]
Solving (a):
[tex]\sec^2(\theta)[/tex]
This is calculated as:
[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
Where:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]
So:
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]
[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]
[tex]\sec^2(\theta) = 82[/tex]
Solving (b):
[tex]\cot(\theta)[/tex]
This is calculated as:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
Where:
[tex]\tan(\theta) = 9[/tex] ---- given
So:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
[tex]\cot(\theta) = \frac{1}{9}[/tex]
Solving (c):
[tex]\cot(\frac{\pi}{2} - \theta)[/tex]
In trigonometry:
[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]
Hence:
[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]
Solving (d):
[tex]\csc^2(\theta)[/tex]
This is calculated as:
[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]
[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]
Where:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]
So:
[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]
[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]
[tex]\csc^2(\theta) = \frac{82}{81}[/tex]
Calculating area of rectangle.
Your measurements Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2) ________ ________
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Answer:
Your measurements; Area = 216.108 cm²
Another student's measurements; Area = 216.9404 cm²
- Difference in area could be as a result of human error or perhaps that they made use of different measuring tools.
Step-by-step explanation:
For Your measurements;
Length of rectangle = 20.70 cm
Width of rectangle = 10.44 cm
Area of rectangle is given by; A = length × width = 20.7 × 10.44 = 216.108 cm²
For Another student's measurements;
Length of rectangle = 20.74 cm
Width of rectangle = 10.46 cm
Area = 20.74 × 10.46
Area = 216.9404 cm²
The areas they both obtained are not of equal values and this could be as a result of human error or perhaps that they used different measuring tools.
The Sweet Slice Cafe has 6 pastries for sale, including 3 glazed donuts.
What is the probability that a randomly selected pastry will be a glazed donut?
Write your answer as a fraction or whole number.
Answer:
50% or 3/6 (1/2).
Step-by-step explanation:
Choose the solution set represented by the following graph.
{x | x R, x ≤ -2}
{x | x R, x > -2}
{x | x R, x < -2}
{x | x R, x ≥ -2}
Answer:
{x|x rx>-2}
Step-by-step explanation:
hope helpful answer
Can you help me with this question? 15 points and brainliest if right!
Answer:
3/4
Step-by-step explanation:
because it is a linear function it means it has the same slope in every point
so you have to take 2 points and find the slope
I take points (0,1) and (4,4)
m = (y2-y1) / (x2-x1)
note that it does not matter which points you chose to be second or first
m = (4-1) / (4-0) = 3/4
you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up
Question 5 of 20 :
Select the best answer for the question.
5. Determine the diameter of a circle with circumference units.
O A. Tt2 units
O B. 1 unit
O C. T units
O D. 2 units
Mark for review (Will be highlighted the review page)
<< Previous Question
Next Question >>
Answer:
B. 1 unit
Step-by-step explanation:
the circumference of a circle is
Cc = 2×pi×r
r = radius = diameter / 2
now we need to find the diameter (= 2×r) of a circle with the circumference of pi.
=>
pi = 2×pi×r
1 = 2×r = diameter
so, the diameter is 1 unit.
6.) Ms. Speer is scuba diving. She descends 5 feet below sea level. She descends the same distance 4 more times. What is Ms. Speer's final elevation? *
Answer:
-25 feet
Step-by-step explanation:
First she descends 5 feet below sea level
She then descends the SAME DISTANCE ( so 5 feet ) 4 MORE TIMES
So feet descended = 4 * 5 + 5
4 * 5 = 20
20 + 5 = 25
Her final elevation will be -25 feet
( it's important that we add a negative sign because she is descending meaning going down )
What is the result when 16x + 9 is subtracted from 4x + 6
Answer:
(4x+9)-(16x+9) = 4x+9-16x-9
= -12x
Can y’all help me on question 11?!
Answer:
The correct answer is choice C.
Step-by-step explanation:
To find the area of the arrow, we must add together the areas of the rectangle and the triangle that make up the arrow. The rectangle has a length of 10 inches and a width of 4 inches, and the triangle has a base of 8 inches and a height of 2 inches. Using this information, we can plug numbers into the following formula:
Area of arrow = area of rectangle + area of triangle
Area of arrow = (10*4)+(1/2*8*2)
Area of arrow = 40 inches squared + 8 inches squared
Area of arrow = 48 inches squared
Therefore, the correct answer is option C, 48 square units (in this case, inches).
Hope this helps!
Can y’all help me a question 4?!
============================================================
Explanation:
Ignore the portions that are 12 and 13 units long.
The base of triangle ABC is 8 units long. The height is 5 units. The base and height are always perpendicular.
The area is base*height/2 = 8*5/2 = 40/2 = 20 square units
---------
Side note:
You could find the area of triangle ABD, where D is at the 90 degree angle location, and then subtract off the area of triangle ACD. This is a slightly longer approach compared to the first section above.
The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can this be accomplished if there are 25 members on the board of directors
Answer:
2400 ways
Step-by-step explanation:
Combination has to do with the idea of selection. Here we need to select a president, a secretary, and a treasurer.
This means to select three out of twenty five persons.
From;
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Thus we have;
25C3 = 25!/(25 - 3)! 3!
=
1.6× 10^25/1.1×10^21 × 6
= 2400 ways
What is the domain of the function graphed below?
Answer:
x < 7
Step-by-step explanation:
the domain of a function defines the valid x values for the function.
as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.
the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.
so, x < 7 is the right one.
Answer: A
Step-by-step explanation:
Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for asparagus, B for bacon, P for pepperoni, I for Italian, and V for vinaigrette. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: mushrooms, asparagus. Also, you will add one of following meats: bacon, pepperoni. Lastly, you will decide on one of the following dressings: Italian, vinaigrette.
Answer:
MBI, MBV, ABV, ABI, MPI, MPV, APV, API
The correlation coefficient for practicing violin and getting better grades in a group of people is 0.8. Analyze the following statement:
Playing violin causes students to get better grades.
Is this a reasonable conclusion?
Answer:
D No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades
In 2006 the number of tickets sold was 210.
The ratio Number of adult tickets: Number of student tickets was 23:19.
How
many
adult tickets were sold?
Answer:
115
Step-by-step explanation:
There were 115 adult tickets were sold.
What is ratio?A ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six.
Given that, the number of tickets sold was 210. The ratio Number of adult tickets: Number of student tickets was 23:19.
Let the number of tickets sold for adults be 23x and for students be 19x
Therefore, 23x+19x = 210
42x = 210
x = 210/42
x = 5
So, Number of adult tickets = 5x23 = 115
Hence, There were 115 adult tickets were sold.
For more references on ratios, click;
https://brainly.com/question/13419413
#SPJ2
1:prove that the tangent at the point (1,-2) to the circle x²+y²=5 also touches the circle x²+y²-8x+6y+20=0 .Also find the point of contact.
2:find the length of tangent to the circle
3x²+3y²-7x-6y=12 drawn from (6,-7)
Circle 1 has center at (0, 0)
The tangent passes through the center and point (1, -2).
Equation of tangent at (1, -2):
x*1 + y*(-2) = 5x - 2y = 5x = 2y + 5If the same line is tangent to circle 2 then they have one common point.
Solve the system:
x = 2y + 5x² + y² - 8x + 6y + 20 = 0Substitute x:
(2y + 5)² + y² - 8(2y + 5) + 6y + 20 = 04y² + 20y + 25 - 16y - 40 + 6y + 20 = 05y² + 10y + 5 = 0y² + 2y + 1 = 0(y + 1)² = 0y + 1 = 0y = -1 ⇒ x = 2(-1) + 5 = -2 + 5 = 3We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.
#2Given circle:
3x² + 3y² - 7x - 6y = 12 and external point (6, -7).Rewrite the equation of the circle as:
3x² + 3y² - 7x - 6y = 12x² + y² - 7/3x - 2y = 4x² - 2*7/6x + 49/36 + y² - 2y + 1 = 4 + 49/36 + 1(x - 7/6)² + (y - 1)² = 229/36The center is (7/6, 1) the radius is √229/36
The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:
t² = d² - r²t² = (6 - 7/6)² + (-7 - 1)² - 229/36t² = 36 - 14 + 49/36 + 64 - 229/36t² = 86 - 180/36t² = 81t = 9Find the difference,
(20m+ 3) - (7m - 5)
A. 27m - 2
B. 13m +8
C. 27m +8
D. 13m - 2
SUBMU
Answer:
B 13m+8
Step-by-step explanation:
(20m+3) - (7m-5)
20m+3-7m+5
13m+8
3
3
X
14. Aşağıdaki cümlelerin hangisinde ikilemenin
oluşum yolu diğerlerinden farklıdır?
L
A) Çamurda bata çıka ilerlemeye çalıştık.
er-
B) Denizde irili ufaklı taşlar vardı.
C) Maaşımla iyi kötü geçinip gidiyoruz.
D) Eski püskü eşyaları kenara ayırdı.
es
?
Answer:
hygu
Step-by-step explanation:
yg9k
What is the y intercept of the function f (x) = -2/9x + 1/3 ?? Please help ! :0 :)
y intercept of the function f (x) = -2/9x + 1/3
is
[tex] \frac{1}{3} [/tex]
OPTION C
Only answer if you're very good at Math.
Given f(x) = x + 1 and g(x) = x^2, what is
( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) (x) = ( x + 1)^2
C: ( g o f) (x) = x^2 + x + 1
D: ( g o f) (x) = x^2 ( x + 1)
Answer:
The answer is B: ( g o f) (x) = ( x + 1)^2
Explanation:
⟹ (g ∘ f) (x) = g [f (x)]
Replace x in g(x) = x^2 with x+1
= ( x + 1 ) ^2
5.) $28,000 invested at a rate of 4% compounded annually
a.) Write a compound interest function to model the situation.
Answer:
ok so we know the amount we know the interest amount but we do know know the period of time so the equation would look like this
28000(0.4)T=I
T=Time
I=interest
Erika wondered if there is a relationship between the amount of sugar (in grams) and the number of calories in movie theater candy.
She gathered the data from a sample of 12 types of candy and constructed the scatter plot shown below.
Find the approximate slope and y-intercept (0,b) of an estimated line of best fit.
Answer:
the slope is 8/7 and the y-intercept is 300
Step-by-step explanation:
The y-intercept is 300 because that is where the estimated line of bets fit (the red line) crosses the y-intercept.
Question in pic, please help
Answer:
The first one
(I can't see it too properly but if the dot on -10 has a hole in it then this is the answer)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y=-16x^2+239x+127
Answer:
7.47 seconds
Step-by-step explanation:
From the quadratic equation the x coordinate of the vertex is
x = -b/(2a)
---------------------------
y = -16x² + 239x + 127
x = -239/ ( 2 * (-16) )
x = -239 / (-32)
x = 7.46875
Rounded
x = 7.47
Let f(x)= 6x^2+7x-4. Find:
a) f(3)
b) f(m)
c) f(x+1)
SHOW WORK PLEASE.
Answer: b) f(m)
Step-by-step explanation:
A car manufacturing company produces blue and black cars only. If 54% of 85658 total
production is blue cars, how many black cars are there?
Answer:
About 39,402.
Step-by-step explanation:
You need to find the 46% of black cars.
i need help with this!
9514 1404 393
Answer:
64.6
Step-by-step explanation:
One standard deviation is 4.3. Then +2 standard deviations is ...
(+2)(4.3) = +8.6
This amount added to the mean gives ...
56 +8.6 = 64.6 . . . . +2σ from the mean
