Answer:
1. Elanor's standardized score is 1.08.
2. Gerald's standardized score is 3.24.
3. A. Gerald.
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. 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.
1. What is Elanor's standardized score?
Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 561 and standard deviation 110. This means that we have [tex]X = 680, \mu = 561, \sigma = 110[/tex].
The standardized score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{680 - 561}{110}[/tex]
[tex]Z = 1.08[/tex]
Elanor's standardized score is 1.08.
2. What is Gerald's standardized score?
Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 20.2 and standard deviation 2.1. This means that we have [tex]X = 27, \mu = 20.2, \sigma = 2.1[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27 - 20.2}{2.1}[/tex]
[tex]Z = 3.24[/tex]
Gerald's standardized score is 3.24.
3. Assuming that both tests measure the same kind of ability, who has the higher score?
Due to the higher standardized score, Gerald
Solve the equation
z³=27
Answer: z = 3, -1.5 + 1.5[tex]\sqrt{3}[/tex]i, -1.5 - 1.5[tex]\sqrt{3}[/tex]i
Step-by-step explanation:
A cubic equation will have three solutions. This equatoin will give us one real solution. We will also have two complex solutions. These are solutions that involve "imaginary numbers" and will utilize the value i. We will write the equation in standard form and factor it.
z³ - 27 = 0
(z - 3)(z² + 3z + 9) = 0
The first factor gives us z = 3, because 3 - 3 = 0. Now, we will look at when the second factor equals 0. Let us complete the square.
z² + 3z + 9 = 0
(z² + 3z + 2.25) + 9 - 1.5 = 0
(z² + 3z + 2.25) + 6.75 = 0
(z + 1.5)² + 6.75 = 0
Lastly, we can continue solving. We will subtract 7.5 from both sides of the equation and then take the square root of both sides. Then, we will subtract 1.5 from both sides of the equation and simplify the radical. [tex]i=\sqrt{-1}[/tex].
(z + 1.5)² = -6.75
z + 1.5 = ±[tex]\sqrt{6.75}[/tex]i
z = -1.5 ±1.5[tex]\sqrt{3}[/tex]i
Answer:
z = 3, -1.5+1.5√3i, -1.5-1.5√3i
Step-by-step explanation:
You want the solutions to the equation z³ = 27.
CubicA cubic equation has three solutions. This one has one positive real solution and two complex conjugate solutions.
We can rewrite the equation to standard form, then factor the difference of cubes.
z³ -27 = 0
(z -3)(z² +3z +9) = 0
The first factor will be zero when z = 3, so that is one solution.
The second factor will be zero when ...
(z +1.5)² +6.75 = 0 . . . . . . . complete the square
(z +1.5) = ±√(-6.75) = ±√(-27/4) = ±(3/2)√(-3) . . . subtract 6.75; square root
z = -1.5 ±1.5√3i
The three solutions to the equation are ...
z = 3z = -1.5+1.5(√3)iz = -1.5-1.5(√3)i<95141404393>
Which choice is equivalent to the fraction below? Hint: Rationalize the
denominator and simplify.
Answer:
Option D. 4√2
Step-by-step explanation:
8/√2
The above expression can be simplified as follow:
8/√2
Rationalise the denominator i.e multiply the numerator and the demoninator by √2. This is illustrated below:
8/√2 × (√2/√2)
8 × √2 / √2 × √2
8√2 / 2
4√2
Thus, option D gives the correct answer to the question.
Find x. Round your answer to the nearest tenth of a degree.
A
27
18
to
B
С
x = _(blank)
find the volume of the sphere
Helpppp 8 &11/13 as an improper fraction
Answer:
115/13
Step-by-step explanation:
convert mixed number into improper fraction
8×13+11
multiply
104+11/13
add
104+11=115
115/13
Nicholas performs an experiment in which he pulls a marble from a bag. In his experiment, he finds that he is twice as likely to pull a red marble as a blue marble. If Nicholas pulls 10 red marbles, how many blue marbles does he pull?
Answer:
Nicholas pulls 5 blue marbles from the bag.
Step-by-step explanation:
Since Nicholas performs an experiment in which he pulls a marble from a bag, and in his experiment, he finds that he is twice as likely to pull a red marble as a blue marble, to determine, if Nicholas pulls 10 red marbles, how many blue marbles does he pull, the following calculation must be performed:
10/2 = X
5 = X
Therefore, Nicholas pulls 5 blue marbles from the bag.
The sum of two numbers is 32. One number is 10 more than the other. Find the numbers
Answer:
12 and 10
Step-by-step explanation:
Answer:
11 and 21
Step-by-step explanation:
Let the first number equal x. If the first number, the second number is ten more, and can represented as x + 10. Now, the sum is 32, so we can add the two numbers to get 32:
x + x + 10 = 32
2x + 10 = 32
2x = 22
x = 11
If the first number 11, the second number is 10 more, and therefore is 21.
what is the value of x in the triangle?
Answer:
X = 102
Step-by-step explanation:
41 + 37 + x = 180
78 + x = 180
X = 180 - 78 = 102
1. Find the area of each of the composite figures:
a)
6 m
8 m
10 m
Answer:
Could u include a picture of the figures as well?
Step-by-step explanation:
SOMEONE HELP ILL GIVE BRAINLIEST!!
61 POINTES!!!!!! (I will give brainliest)
A landscape architect designs a small splash pad represented by ΔABC. Then she decides to make the splash pad larger as shown by ΔADE. How are the splash pad designs alike? How are they different?
I think it is -4 and positive 2
Jffkdjdjdjdkskkskskskskakskkdkdkskdk
Answer:
the anser is d
Step-by-step explanation:
Answer:
b) 7x² - 12x√14 + 72
Step-by-step explanation:
Let's solve the problem,
→ (x√7 - 3√8)(x√7 - 3√8)
→ (x√7 - 3√8)²
→ 7x² - 12x√14 + 72
Hence, option (b) is correct.
I need help plzzzzz this is really confusing
Answer:
B. x< -3
hope it helps.
stay safe healthy and happy.Explanation:
The blue shaded region describes any x value that is smaller than -3, or that is equal to -3. We can phrase it as "x is less than or equal to -3". Therefore, that's why we go for [tex]x \le -3[/tex]
If you graphed [tex]x < -3[/tex], without the "or equal to" portion, then you would have an open circle at the endpoint. The open circle means we don't include that value as part of the solution set.
Anyone helps??
Mr. Cruz has 60 students. 24 are taking Math, 15 are taking Biology, and 31 are taking neither.
How many students are taking both, Math and Biology.
Answer:
39
Step-by-step explanation:
24+15= 39. 39 students are taking both math and biology.
12 hrs 40 min + 10 hrs 30 min
Answer:
23 hours and 10 minutes
Solve the value of p
Answer:
but where is que
Step-by-step explanation:
i don't see the question
Write the number 4, 207 in expanded form.
A. (41000) + (2 · 100) + (0 · 10) + (7.1)
B. (4.1000) + (2 · 100) + (7.10)
C. (4.1000) + (20 · 100) + (7.10)
D. (4 .100) + (2 · 10) + (1 .7)
Answer:
(4.1000)+ (2.100) + (7.10)
A window in the shape of a rectangle as shown below has a width of 2X +1 and the length of X squared minus 5X -7
Answer;
14x-12
Explanation:
Since we are not asked what to fine, we can find the perimeter of the rectangle
Perimeter = 2(L+W)
Perimeter = 2(2x+1+5x-7)
Perimeter = 2(7x - 6)
Perimeter = 14x - 12
Hence the perimeter of the rectangle is 14x-12
A number is 3 1/3 greater than another. If the sum of the numbers is doubled, the result in 19 1/2. What is the smaller number?
Answer:
77/24
Step-by-step explanation:
give 5 each examples of acute angle
and obtuse angle
Answer:
acute (<90°): 2° 35° 47° 78° 89.5°
obtuse (>90°): 91° 180° 290° 110° 359°
What is the value of x
Hey there! :)
Please keep in mind that SOH-CAH-TOA is a life saver when it comes to trig! Where:
- SOH = Sin: opposite over hypotenuse
- CAH = Cos: adjacent over hypotenuse
- TOA = Tan: opposite over adjacent
The question is asking us to find the value of x given the following located in the image provided.
Because we've been given 51°, we'll use this angle to determine whether we're using Sin, Cos, or Tan.
We must now look at the other given variables in this triangle - specifically where they are located.
While looking at our given angle (51°), we see that x is located on the opposite side of 51° while 8 is located adjacent (also known as next) to 51°.
Because of this, we now know that we'll be using Tan (opposite over adjacent) to find the value of x because our given values are opposite and adjacent to 51°.
We now set up our equation to find the value of x:
tan (51°) = [tex]\frac{x}{8}[/tex] ⇒ we set it up this way because x is opposite of 51° & 8 is adjacent to it.
Now, we must remove all fractions. We can do this by multiplying both sides by 8.
8 × tan (51°) = [tex]\frac{x}{8}[/tex] × 8
Now, we simplify.
8 × tan (51°) = x
Now, we plug this into our calculator. Make sure your calculator is in degrees mode since we are using degrees, not radians.
8 × 1.2348 = x
Simplify.
x = 9.9
Therefore, angle x is 9.9
Hope this helped! :)
(Image attached for visual reference)
Simplify the expression.
4y-y(3 - 7y) + 5+ 2(8- y)
7y2-y +21
-7y2 - y + 21
-8y + 21
-7y+21
Answer:
7y² - y + 21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
4y - y(3 - 7y) + 5 + 2(8 - y)
Step 2: Simplify
[Distributive Property] Distribute parenthesis: 4y - 3y + 7y² + 5 + 16 - 2yCombine like terms (y): 7y² - y + 5 + 16Combine like terms: 7y² - y + 21Suppose that in a large metropolitan area, 85% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will exactly four of the six households have cable tv?
Solution :
Let X denotes the number of the households tha have a cable TV.
Percentage of household that have a cable TV = 85 %
[tex]$X \sim \text{Binomial}(6, 0.85)$[/tex]
Here, we can see that each of the observations is independent and the number of the observations is fixed, n.
The probability of the success P is the same for each of the outcomes.
Therefore,
[tex]P(X=4)= \binom{6}{4}0.85^40.15^2[/tex]
= 0.08324
A shape has 2 pairs of parallel sides and no right angles. Its sides are all the same length. What shape is it?
A. Rhombus
B. Trapezoid
C. Rectangle
D. Square
Answer: The attached figure is a parallelogram with one corner chopped off, making it a pentagon. It still has two pairs of parallel sides & no right angles.
Step-by-step explanation:
Parallelogram is the word that most generally describes such a figure. A square or rectangle, which do, of course have right angles, are special cases of the parallelogram.
I am assuming (perhaps unjustifiably) that when you say “two pairs of parallel sides” you are talking of a figure with no other sides than those four.
There are, of course, many other polygons (hexagons, octagons, decagons, etc) which have two pairs of parallel sides and other sides, any two of which may or may not be parallel.
What is the surface area of the cylinder with height 7 ft and radius 3 ft? Round your answer to the nearest thousandth.
Use the integers that are closest to the number in the middle. √32
Answer:
4√2
Step-by-step explanation:
√32 = √(16 * 2) = 4√2
The point (8, 7) is reflected over the x-axis. What quadrant is the new point located in? A. Quadrant I
B.Quadrant II
C.Quadrant III
D.Quadrant IV
Answer:
.quadrant 4 is the new point locatef
an experienced bricklayer can construct a small wall in 7 hours. An apprentice can complete the job in 42 hours
Answer:
6 hours
Step-by-step explanation:
The trick to this type of problem is using an equal amount of time.
The least common multiple of 7 and 42 is 42
At 7 hours per wall
In 42 hours the bricklayer could build
42/7 = 6 walls
At 42 hours per wall
In 42 hours the apprentice could build
42/1 = 1 walls
Working together in 42 hours they could build 6 + 1 = 7 walls
42hours/7walls = 6hours/ wall
--------------------------
Math only
x = 1 wall/7hours + 1wall/42 hours
use common denominator of 42
x = 6w/42 hr + 1w/42hr
x = 7w/42 hr
reduce
x = 1w / 6hr
I need help asap! Thank you.
Solve for x PLEASE HELP DUE TODAY!!!
Answer:
x = 4
Step-by-step explanation:
By intersecting tangent and secant theorem:
[tex] {(x + 2)}^{2} = x(x + 5) \\ \\ {x}^{2} + 4x + 4 = {x}^{2} + 5x \\ \\ 4x + 4 = 5x \\ \\ 4 = 5x - 4x \\ \\ 4 = x \\ \\ x = 4[/tex]
Answer:
x = 4
Step-by-step explanation:
When a secant and a tangent are drawn to a circle from a point outside the circle, the lengths are related this way:
The square of the length of the tangent equals the product of the length of the secant and the length of the segment of the secant outside the circle.
(x + 2)² = x(x + 5)
x² + 4x + 4 = x² + 5x
x = 4