Answer:
d. normal if the population is normally distributed
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Sample size less than 30, so only will be normal if the population is normally distribution, and thus the correct answer is given by option d.
If f(x) is a linear function, what is the value of n?
х
_4
f(x)
---25
-10
-1
n
20
2
оооо
9
Step-by-step explanation:
You can simply plot these points on a graph and see where the line goes. It go
The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph?
Answer:
Table B
Step-by-step explanation:
correct on edge :)
Convert 1.5% to decimal and a fraction. Show and explain your method.
Answer:
0.015
Step-by-step explanation:
1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015
What are the values of x for which the denominator is equal to zero for y=(x+3)/(x^2+4x)
9514 1404 393
Answer:
-4, 0
Step-by-step explanation:
The denominator is x^2+4x. This is zero when ...
x^2 +4x = 0
x(x +4) = 0
The zero product rule tells you the product is zero when the factors are zero.
x = 0
x +4 = 0 ⇒ x = -4
The denominator is zero for x=0 and x=-4.
In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m?
[Show Workings}
I will give brainlist to the person with the right
If the slope of the line y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.
The general formula for calculating an equation of a line is expressed as:
[tex]y = mx + b[/tex] where:
m is the slope of the line
Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:
[tex]mx=1x\\[/tex]
Divide through by x
[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]
Hence the slope of the line y = x - 1 is 1.
According to the question, since we are told that the slope of the line
y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
Learn more about the slope of a line here: https://brainly.com/question/16949303
Answer:
Step-by-step explanation:
Exercise 2.2.3: The cardinality of a power set. (a) What is the cardinality of P({1, 2, 3, 4, 5, 6})
Answer:
Cardinality of the power set of the given set = [tex]2^6=64[/tex]
Step-by-step explanation:
Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.
Example set:
{1,2,3}
All the possible subsets of this set:
{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}
The power set of the above set is written as:
P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })
Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.
Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]
where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.
Hence in the given case, we have n = 6.
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
help please i don't know how to do this
A ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 24t + 7. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Answer:
Step-by-step explanation:
Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.
If the position function is
[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is
v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:
0 = -32t + 24 and
-24 = -32t so
t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:
s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so
s(.75) = 16 feet
Can the range of a function be written like this {6,7,8,10} instead of like this [tex]6\leq x\leq 10[/tex]?
Answer:
No unless x is being used to define only elements of an integer set.
Step-by-step explanation:
No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....
Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.
{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.
it is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails and the probability for a flase positive is 5%. What is the probability that an email is detected as spam
Answer:
0.52 = 52% probability that an email is detected as spam.
Step-by-step explanation:
Probability that an email is detected as spam:
99% of 50%(are spam).
5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).
What is the probability that an email is detected as spam?
[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]
0.52 = 52% probability that an email is detected as spam.
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
Blank DVD's are sold in packages of 50 for $17.95 if your company will need 2700 blank divide these next year how much money must your budget for blank dvd's
Answer:
Step-by-step explanation:
50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.
What is the value of x in the triangle?
Answer:b
Step-by-step explanation:
Ive done this
(3k + 5)(2k2 – 5k – 3)
in a school there are 650 girls. It is 26% of the whole students, how many boys are there in the school?
Answer:
Step-by-step explanation:
Frt7v6c87buhinjomp,l.;
A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)
Answer:
1100 ft³
Step-by-step explanation:
Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.
V = πr²h
r = d/2 = 20 ft/2 = 10 ft
h = (1 ft + 6 ft)/2 = 3.5 ft
V = π(10 ft)²(3.5 ft)
V = 1100 ft³
4. The average salary for public school teachers for a specific year was reported to be $39,385. A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975. Is there sufficient evidence at the a _ 0.05 level to conclude that the mean salary differs from $39,385
Answer:
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
Step-by-step explanation:
The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385
At the null hypothesis, we test if the mean is of $39,385, that is:
[tex]H_0: \mu = 39385[/tex]
At the alternative hypothesis, we test if the mean differs from this, that is:
[tex]H_1: \mu \neq 39385[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
39385 is tested at the null hypothesis:
This means that [tex]\mu = 39385[/tex]
A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.
This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]
[tex]z = 2.72[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.
Looking at the z-table, Z = -2.72 has a p-value of 0.0033
2*0.0033 = 0.0066
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
If BC = 8.3, CD - 6,7, and AD = 11.6, find AB to the nearest tenth.
Answer:
ab=14.4
Step-by-step explanation:
This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6. Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6. Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4
Find the equation of the lines in problem 1 (0,0) slope =2.
Answer:
y = 2x
Step-by-step explanation:
Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,
[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]
Deon bought a desk on sale for $105.60. This price is 67% less than the original price. What was the original price?
Answer:
.33x = 105.60
$371
Step-by-step explanation:
Answer:
63.44
Step-by-step explanation:
its 63.44697 but you round so its 63.44
Find the volume of the box. The box shows the length is 6 feet, the width is 5 feet, and the height is 3 feet. The volume of the box is blank cubic feet. The solution is
Answer:
[tex]90[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the volume of a rectangular prism is [tex]V=lwh[/tex]
Let's substitute the number for the length, width, and height now.
[tex]V=(6)(5)(3)[/tex]
[tex]V=(30)(3)[/tex]
[tex]V=90[/tex]
--------------------
Hope this is helpful.
What is the amount f rainfall that Miami receives, round to the nearest half or whole? 55 9/10"
Answer:
56"
Step-by-step explanation:
Pls answer
Subtract -37 from -53
Answer:
-37 subtract -53
-53 subtract -37 = -16
Step-by-step explanation:
Answer:
The answer is 16
Step-by-step explanation:
-37-(-53) = -37 + 53
You can flip it to 53 - 37 which equals 16.
Hope this helps! :)
*Heads up you can also search this up* ^^
(URGENT!!) Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
2nd Graph
Step-by-step explanation:
Bases off the graphs, you gave me, I assume your the equation is
[tex]f(x) = - 4(2) {}^{x} [/tex]
The parent equation of this function is
[tex]f(x) = b {}^{x} [/tex]
Let say x=0
Using the rules of exponets, the y value must be 1 so a critical point is
(0,1)
The function is multiplied by -4.
This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be
(0,-4).
The base 2 the function will get compressed by 1/2.
The best graph that represents this is the second graph
Estimate 19.625-6.77 by first rounding each number to the nearest tenth.
Answer:
13
Step-by-step explanation:
1. Round 19.625 up to 20.
2. Round 6.77 up to 7.
3. Calculate the equation. Ans is 13.
SOLVE PLS!! ILL MARK BRAINILEST!!
Answer:
73.3333....
Step-by-step explanation:
please mark me brainliest
Answer:
a: t=13.6 cm
b: h=12.9 mm
Step-by-step explanation:
Hi there!
Let's start with a
in a, we are given a right triangle (notice the right angle), the length of the hypotenuse (the side OPPOSITE from the right angle) as 18 cm, one acute angle given as 41° and the length of one of the legs (the legs are the sides that make up the right angle) as t
We're asked to use the primary trigonometric ratios
Those ratios are:
Sine, which is opposite/hypotenuse
Cosine, which is adjacent/hypotenuse
Tangent, which is opposite/adjacent
We will be basing the ratio off of the 41° angle, so let's find out which sides will be which in reference to that angle
The opposite side will be the other leg, the unmarked side
The adjacent side will be t
The hypotenuse will be the side marked as 18 cm
So let's use cos(41) in this case
cos(41)=t/18
Plug cos(41) into your calculator, and remember to have the calculator in degree mode
cos(41)≈0.8 (rounded to the nearest tenth)
0.8=t/18
multiply both sides by 18
13.6 cm=t
It's already rounded to the nearest tenth :)
b.
We are given a right triangle, and the lengths of the legs as h and 9 mm, as well as one acute angle as 35°
We'll be basing our ratio off of the 35 degree angle, so let's find which sides will be which in reference to that angle
The opposite side will be the leg marked as 9 mm
The adjacent side will be the leg marked as h
The hypotenuse will be the unmarked side
Since we are given the lengths of the opposite and the adjacent, let's use tan(35)
tan(35)=9/h
Plug tan(35) into your calculator, and remember to have it in degree mode
tan(35)≈0.7
0.7=9/h
multiply both sides by h
0.7h=9
divide both sides by 0.7
h=12.9 mm (rounded to the nearest tenth)
Hope this helps!
