Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
A standardized exam's scores are normally distributed. In a recent year, the mean test score was and the standard deviation was . The test scores of four students selected at random are , , , and . Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are nothing. (Use a comma to separate answers as needed.) B. None of the values are unusual.
Answer:
The z-score for 1880 is 1.34.
The z-score for 1190 is -0.88.
The z-score for 2130 is 2.15.
The z-score for 1350 is -0.37.
And the z-score of 2130 is considered to be unusual.
Step-by-step explanation:
The complete question is: A standardized exam's scores are normally distributed. In recent years, the mean test score was 1464 and the standard deviation was 310. The test scores of four students selected at random are 1880, 1190, 2130, and 1350. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1880 is nothing. (Round to two decimal places as needed.) The z-score for 1190 is nothing. (Round to two decimal places as needed.) The z-score for 2130 is nothing. (Round to two decimal places as needed.) The z-score for 1350 is nothing. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are nothing. (Use a comma to separate answers as needed.) B. None of the values are unusual.
We are given that the mean test score was 1464 and the standard deviation was 310.
Let X = standardized exam's scores
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean test score = 1464
[tex]\sigma[/tex] = standard deviation = 310
S, X ~ Normal([tex]\mu=1464, \sigma^{2} = 310^{2}[/tex])
Now, the test scores of four students selected at random are 1880, 1190, 2130, and 1350.
So, the z-score of 1880 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1880-1464}{310}[/tex] = 1.34
The z-score of 1190 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1190-1464}{310}[/tex] = -0.88
The z-score of 2130 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{2130-1464}{310}[/tex] = 2.15
The z-score of 1350 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1350-1464}{310}[/tex] = -0.37
Now, the values whose z-score is less than -1.96 or higher than 1.96 are considered to be unusual.
According to our z-scores, only the z-score of 2130 is considered to be unusual as all other z-scores lie within the range of -1.96 and 1.96.
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
Reduce the following fraction to lowest terms: 8/14
Answer:
4/7
Step-by-step explanation:
divide both by two for its simplest form
Answer:4/7
Step-by-step explanation
Divide both the numerator and denominator by 2
The result for the numerator is 8/2=4
that of the denominator is 14/2=7
Therefore the resultant answer is 4/7
A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
__
Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
A rectangle has an area of 81 square centimeters. Which of the following would be the rectangle's length and width? (Area = equals length×times width)
Answer:
length: 9cm
width: 9cm
Step-by-step explanation:
9×9=81
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
Find the rectangular coordinates of the point with the given polar coordinates.
Answer:
[tex]( - \sqrt{3} \: an d \: 1)[/tex]
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
What does "C" represent and how do you evaluate this?
[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]
Find the area of the shaded regions:
area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$
so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$
$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$
abd there are 2 such arcs, so double the area.
[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]
Given:-Radius of the circle = 10 inchesAngle of each sector = 72°Number of sectors = 2To FinD:-Find the area of the shaded regions....?How to solve?For solving this question, Let's know how to find the area of a sector in a circle?
[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]
Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.
Solution:-We have,
No. of sectors = 2Angle of sector = 72°By using formula,
⇛ Area of shaded region = 2 × Area of each sector
⇛ Area of shaded region = 2 × Θ/360° × πr²
⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²
⇛ Area of shaded region = 2/5 × 100 × 22/7
⇛ Area of shaded region = 40 × 22/7
⇛ Area of shaded region = 880/7 inch. sq.
⇛ Area of shaded region = 125.71 inch. sq.
☄ Your Required answer is 125.71 inch. sq(approx.)
━━━━━━━━━━━━━━━━━━━━
Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)
Answer:
-7.
Step-by-step explanation:
g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7
= 4 - 12 - 7
= -8 - 7
= -15
f(x) = x + 8
f(-15) = (-15) + 8
= 8 - 15
= -7
Hope this helps!
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ2
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.
So, to answer the first question, [tex]6^2[/tex] is a perfect square.
(a,b,c) is a Pythagorean triple means the following
[tex]a^2+b^2=c^2[/tex]
Here, it means that
[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]
Thank you.
Answer:
Its B
Step-by-step explanation:
In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
[tex]\huge\boxed{y = 8}[/tex]
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.Which of the following is an arithmetic sequence? A.-2, 4, -6, 8, ... B.2, 4, 8, 16, ... C.-8, -6, -4, -2, ...
Answer:
C. -8, -6, -4, -2, ...
Step-by-step explanation:
An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.
A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.
B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.
C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.
Hope this helps!
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
Solve the following equation using the square root property.
9x2 + 10 = 5
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
How many times does 1/4 go into 3/8
Answer:
3/2
Step-by-step explanation:
3/8 ÷ 1/4
Copy dot flip
3/8 * 4/1
12/8
Divide top and bottom by 4
3/2
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?
Answer:
We conclude that no more than 10% of its microwaves need repair during the first five years of use.
Step-by-step explanation:
We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.
In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.
Let p = population proportion of microwaves who need repair during the first five years of use.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that no more than 10% of its microwaves need repair during the first five years of use}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of microwaves who need repair during the first 5 years of use = 12%
n = sample of microwaves = 50
So, the test statistics = [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]
= 0.471
The value of z-test statistics is 0.471.
Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.
What is the volume of a cube with a side length of
of a unit?
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24
Answer:
D question,somewhat confusing, itsit's like simultaneous equation,but values are different
Answer:
x = 4 + 2y/3
Step-by-step explanation:
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
