Answer:
0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
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.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The manager of a donut store believes that 35% of the customers are first-time customers.
This means that [tex]p = 0.35[/tex]
Sample of 150 customers
This means that [tex]n = 150[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.35[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.35*0.65}{150}} = 0.0389[/tex]
What is the probability that the sample proportion will be between 0.2 and 0.4?
p-value of Z when X = 0.4 subtracted by the p-value of Z when X = 0.2.
X = 0.4
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.4 - 0.35}{0.0389}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997
X = 0.2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.35}{0.0389}[/tex]
[tex]Z = -3.85[/tex]
[tex]Z = -3.85[/tex] has a p-value of 0.0001
0.8997 - 0.0001 = 0.8996
0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4
Math algebra 2 show you’re work plz
9514 1404 393
Answer:
(t, u, w) = (1, -2, -2)
Step-by-step explanation:
A graphing calculator makes short work of this, giving the solution as ...
(t, u, w) = (1, -2, -2)
__
There are many ways to solve this "by hand." Here's one of them.
Add the first and third equations. Their sum is ...
-3t +4w = -11 . . . . . [eq4]
Add this to twice the second equation. That sum is ...
(-3t +4w) +2(-4t -2w) = (-11) +2(0)
-11t = -11
t = 1
Substituting this into the second equation gives ...
-4(1) -2w = 0
w +2 = 0 . . . . divide by -2
w = -2 . . . . add -2
Substituting for t in the third equation lets us find u.
2(1) -2u = 6
-1 +u = -3 . . . . . divide by -2
u = -2 . . . . add 1
The solution is (t, u, w) = (1, -2, -2).
Tell whether ΔABC and ΔDCB can be proven congruent.
A. Yes, ΔABC and ΔDCB can be proven congruent by SSS.
B. Yes, ΔABC and ΔDCB can be proven congruent by HL.
C. No, ΔABC and ΔDCB aren’t congruent because they share a side.
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Answer:
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Select the correct answer.
Which chart best represents the following information about student results from a class assignment?
Answer
a) chart
Step-by-step explanation:
a) chart best represents the following information about student results from a class assignment
Graph: y = (x + 3)2 – 4
Which values are solutions of the quadratic equation
0 = (x + 3)2 – 4? Check all that apply.
y
X
-4
WIEC
6
0 -5
-4
.
0 -3
-1
-6
-4
-2
2
4
6
02
3
-2 -4
0,5
-6
Answer:
0.534375
45328
36763
-6
-78
The values of x and y that satisfy the graphs are:
(-1, 0), and (-5, 0).
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We can start by simplifying the quadratic equation:
y = (x + 3)² – 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
Now, we can use various methods to find values of x and y that satisfy this equation. Here are five possible values:
If we substitute x = -1, we get:
y = (-1)² + 6(-1) + 5
y = 0
So, one solution is (-1, 0).
If we substitute x = 0, we get:
y = 0² + 6(0) + 5
y = 5
So, another solution is (0, 5).
If we substitute x = -5, we get:
y = (-5)² + 6(-5) + 5
y = 0
So, another solution is (-5, 0).
To find rational solutions, we can factor in the quadratic expression:
y = x² + 6x + 5
y = (x + 1)(x + 5)
So, the solutions are x = -1 and x = -5. Substituting these values into the equation, we get:
For x = -1, y = (-1)² + 6(-1) + 5 = 0
For x = -5, y = (-5)² + 6(-5) + 5 = 0
So, the solutions are (-1, 0) and (-5, 0).
To learn more about the quadratic equation;
https://brainly.com/question/17177510
#SPJ7
Determine the nature of the roots: 4x2 + 13x + 6 = 0
a. no real solutions
b. cannot be determined
C. a unique real solution
two distinct real solutions d. two distinct real solutions
Answer:
D. is the correct option
Discriminant is greater than zero, so the roots are unequal and real.
Step-by-step explanation:
We use discriminant to find the nature of the roots
discriminant formula is, b^2 - 4ac
13^2 (-4) × 4 × 6 = 169-96
73 >0
if discriminant greater than 0 that means the roots are real and unequal.
In point estimation a. data from the sample is used to estimate the population parameter. b. the mean of the population equals the mean of the sample.
Answer:
a. data from the sample is used to estimate the population parameter.
Step-by-step explanation:
Given
Point estimation
Required
The true statement
Point estimation literally means taking data from the sample to estimate the corresponding population parameter
For instance:
Sample mean estimates population mean
Sample standard deviation estimates population standard deviation
Sample variance estimates population variance
Hence;
(a) is correct
Complete the information for that object by making estimates using appropriate units of measurement of the dimensions and by getting the actual measurements using an appropriate measuring instrument.
Answer:
hlo how are u?whats ur day is going
f it take 20 minutes to boil 6 crates of eggs, how much time will it take to boil 18 crates of eggs
a hour,.....................
Which of the following shows the graph of y=-(2)^3 – 1?
Answer:
The first graph
Step-by-step explanation:
Given
[tex]y = -(2)^x - 1[/tex]
Required
The graph
Set the exponent part to get the minimum/maximum of the graph
So, we have:
[tex]y = 0 - 1[/tex]
[tex]y = - 1[/tex]
The above implies that the curve passes through the y-axis at [tex]y = - 1[/tex].
By comparing the two graphs, we can conclude that the first represents [tex]y = -(2)^x - 1[/tex] because it passes through [tex]y = - 1[/tex]
The square root of the variance is called the: standard deviation beta covariance coefficient of variation
Answer:
standard deviation
Step-by-step explanation:
fill in the missing blinks
36x^2=y^2
Does the equation define y as a function of x ?
Answer:
ya the equation divides y as a function of x
calculate and find the area of the figure below 10m 8m 8m 2m 2m 2m 2m 2m
Answer:
can you be more specific?
Step-by-step explanation:
The measure of angle theta is 7x/6. The measure of its reference angle is _ °, and sin theta is _
Answer:
30° and -1/2. This is pretty easy to do on a piece of paper but I recommend googling "unit circle" and clicking images, it tells you everything you need to know.
Step-by-step explanation:
The coordinate plane below represents a city. Points A through F are schools in the city.
graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.
Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend
What is the mean?
7.9.10.12.15.16
Answer:
11.5
Step-by-step explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Answer:
11.5
Step-by-step explanation:
Add all them all together.
7+9+10+12+15+16=69
Divide by the amount of numbers there are
69/6=11.5
11.5
If h(x) is the parent function, which equation describes the function song shifted 3 units left and 5 units down?
Answer:
h(x + 3) - 5Step-by-step explanation:
Given function h(x).
Shift left:
h(x) → h(x + 3)Shift down:
h(x + 3) → h(x + 3) - 5Given function is,
→ h(x)
As we shift left,
→ h(x) = h(x + 3)
As we shift down,
→ h(x + 3) = h(x+3)-5
Then the equation is,
→ h(x+3)-5
It is correct answer.
What is the equation of the line that is perpendicular to
the given line and has an x-inter cept of 6?
O y = x + 8
O y = x + 6
O y = fx-8
O y=x-6
Answer:
the last one, y=x-6
Step-by-step explanation:
it is the only answer with an x-intercept of 6. you did not provide the line, but I'm assuming it is y=-x.
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 140 in. and the height is 186 in.
Answer:
The volume is increasing at a rate of 27093 cubic inches per second.
Step-by-step explanation:
Volume of a cone:
THe volume of a cone, with radius r and height h, is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
In this question:
We have to differentiate implictly is function of t, so the three variables, V, r and h, are differenciated. So
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s.
This means that [tex]\frac{dr}{dt} = 1.4, \frac{dh}{dt} = -2.4[/tex]
Radius is 140 in. and the height is 186 in.
This means that [tex]r = 140, h = 186[/tex]
At what rate is the volume of the cone changing?
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{\pi (140)^2}{3}(-2.4) + \frac{2\pi 140*186}{3}1.4[/tex]
[tex]\frac{dV}{dt} = -0.8\pi(140)^2 + 62*2\pi*1.4*140[/tex]
[tex]\frac{dV}{dt} = 27093[/tex]
Positive, so increasing.
The volume is increasing at a rate of 27093 cubic inches per second.
Raju and Johari baked 143 muffins altogether. Andrew and Johari baked 211 muffins altogether. (b) If Andrew baked 113 muffins, how many muffins did Raju, Johari and Andrew bake altogether?
Answer:
467 muffins
Step-by-step explanation:
143 + 211 + 113 = 467
Adriana’s z-score on a given measure is -2.5, where the population mean is 5 and the standard deviation is 1.5. What is Adriana’s raw score?
Answer:
Kendriya z-score keva product
im honestly stuck in this question
The correct answer is the fourth one, as it pinpoints both dots perfectly
I’ll give brainliest
Answer:
A
Step-by-step explanation:
From f(x) to k(x), the graphed parabola is stretched and wider.
Answer: Choice B) Vertically compressed by a factor of 8.
Explanation:
Consider a point like (8,64) which is on f(x).
If we plug in x = 8 into k(x), then we would get k(8) = 8. The old output y = 64 is now y = 8. This is an example of a vertical compression of 8. It's 8 times smaller in the vertical direction compared to what it used to be. This is because the k(x) outputs are 1/8 those of the f(x) outputs.
Effectively we have k(x) = (1/8)*f(x).
Another example would be x = 16 leading to y = 256 on f(x). For k(x), we have x = 16 lead to y = 32
Refer to the graph below.
Find the probability that when a couple has children, at least one of them is a . (Assume that boys and girls are equally likely.)
Answer:
[tex]P(At\ least\ one\ girl) = 0.875[/tex]
Step-by-step explanation:
Given
[tex]n = 3[/tex]
[tex]B \to boys[/tex]
[tex]G \to girls[/tex]
[tex]P(G) = P(B) = 0.5[/tex] --- equal probability
See comment for complete question
Required:
[tex]P(At\ least\ one\ girl)[/tex]
To do this, we make use of complement rule:
[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]
The event that there is no girl out of the 3 children is: B B B
And the probability is:
[tex]P(No\ Girl) = P(B) * P(B) * P(B)[/tex]
[tex]P(No\ Girl) = 0.5*0.5*0.5[/tex]
[tex]P(No\ Girl) = 0.125[/tex]
So:
[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]
[tex]P(At\ least\ one\ girl) = 1 - 0.125[/tex]
[tex]P(At\ least\ one\ girl) = 0.875[/tex]
Write down 4 pairs of integers a and b such that a divided by b is -5
A 8 year old boy has 6 different toys and wants to put them all in a straight line.
In how many ways can this be done?
I would appreciate step by step, as I have no clue on how to solve. Thanks!
============================================================
Explanation:
The number 8 from "8 year old boy" can be completely ignored. In my opinion, this is an (un)intentional distraction on your teacher's part.
There are 6 toys to arrange. The order is important.
For the first slot, there are 6 choices. Then the second slot has 5 choices (we cannot have a toy occupy more than one slot at a time).The third slot has 4 choices, and so on.We have this countdown: 6,5,4,3,2,1
Those values multiply out to 6*5*4*3*2*1 = 720
There are 720 ways to arrange the 6 different toys. Order matters.
---------------------
An alternative approach is to use the nPr permutation formula with n = 6 and r = 6. We use a permutation because order matters.
The nPr formula is
[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\[/tex]
where the exclamation marks indicate factorial. For example, 6! = 6*5*4*3*2*1 = 720.
Assume the random variable X is normally distributed, with mean = 54 and standard deviation o = 8. Find the 15th percentile.
Answer:
45.712
Step-by-step explanation:
We need to find the Zscore of the area of 15 percent of the distribution ; using a Z table or calculator ;
Zscore of 15% of the distribution is : - 1.036
Using the Zscore formula :
Zscore = (x - mean) / standard deviation
Where, x = score
-1.036 = (x - 54) / 8
Cross multiply
-1.036 * 8 = x - 54
-1.288 = x - 54
x = - 8.288 + 54
x = 45.712
An employment agency specializing in temporary construction help pays heavy equipment operators $123 per day and general laborers $89 per day. If thirty-one people were hired and the payroll was $3507, how many heavy equipment
operators were employed? How many laborers?
The number of heavy equipment operators hired was
The number of general laborers hired was
Answer:
The number of operators is 22 and the number of laborers is 9
Step-by-step explanation:
This is a 2 line equation system
I'll call the laborers "L" and the equipment operators "E"
The first line of the system is pretty much telling me that the number of laborers plus the number of operators is 31:
L + E = 31
Now we need to calculate the money:
Since we know that laborers are paid $89 per day we're gonna multiply them by that. Same thing with the operator, but the value is now $123
89L + 123E = 3507
Our two line system is like this:
L + E = 31
89L + 123E = 3507
We need either L or E to be the same in both of the equations so that when I subtract one from another I can find the value of one of the variables
I'll choose L cause it's the lower number, so I'll multiply the upper equation:
L+E=31 === *89 ====> 89L + 89E = 2.759
Now we have these equations:
89L + 89E = 2.759
89L + 123E = 3507
Now I'm gonna subtract the lower equation from the upper one:
89L - 89L + 123E - 89E = 3507 - 2759
Since L is now zero it disappears, and by making the other calculations we have:
34E = 748
E = 22
Since E = 22, we can use the value in our first equation:
E+L=31 ===> 22+L=31 ===> L=9
Got it! The number of operators is 22 and the number of laborers is 9.
If you wanna double check this you can calculate the amount of money they're paid, which should add up to $3507:
22 operators * $123 = $2706
9 laborers * $89 = $801
2706+801 = $3507
We're good
If this helped you at all, would it be too much asking for brainliest?
I would really appreciate it
Have a great one
the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards
Answer:
The original dimensions of the park are:
(23/2) yards by 7 yards.
Step-by-step explanation:
Suppose that you have a given dimension X
if you want to reduce that dimension by a scale factor k, such that:
0 < k < 1
The reduced dimension is just:
X' = k*X
Now let's solve the problem:
We know that the dimensions on the blueprint are:
(23/147)yd by (3/14)yd
And the original dimensions are:
A yd by B yd
We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147
Then we just have that:
(2/147)*A = 23/147
(2/147)*B = 3/14
Now we just can solve these two equations for A and B
A = (23/147)*(147/2) = 23/2
B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7
Then the original dimensions of the park are:
(23/2) yards by 7 yards.
Is f(x)=4x^2 linear,quadratic,or exponential
Answer:
Step-by-step explanation:
it is a quadratic function.
