Answer:
The probability that the sample proportion will be within 6 percent of the population proportion is 0.9556.
Step-by-step explanation:
The question is:
What is the probability that the sample proportion will be within 6 percent of the population proportion?
Solution:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
The information provided is:
n = 209
p = 0.75
As n = 209 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the Normal distribution.
[tex]\hat p\sim N(\mu_{\hat p}=0.75,\ \sigma_{\hat p}=0.0299)[/tex]
Compute the probability that the sample proportion will be within 6 percent of the population proportion as follows:
[tex]P(p-0.06<\hat p<p+0.06)=P(0.69<\hat p<0.81)[/tex]
[tex]=P(\frac{0.69-0.75}{0.0299}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.81-0.75}{0.0299})\\\\=P(-2.01<Z<2.01)\\\\=P(Z<2.01)-P(Z<-2.01)\\\\=0.97778-0.02222\\\\=0.95556\\\\\approx 0.9556[/tex]
Thus, the probability that the sample proportion will be within 6 percent of the population proportion is 0.9556.
A real estate agent has surveyed houses in twenty nearby zip codes in an attempt to put together a comparison for a new property that she would like to put on the market. The 1057 houses she surveyed have a mean price of $169 comma 400, with a standard deviation of $ 68 comma 438. The mean living area is 2058 sq ft, with a standard deviation of 790 sq ft. Which is more unusual, a house in that market that sells for $300 comma 000 or a house that has 3000 sq ft of living area? Explain. Choose the correct answer below. The house that sells for $300 comma 000 has a z-score of nothing and the house with 3000 sq ft has a z-score of nothing. Thus, a house in that market that ▼ sells for $ 300 comma 000 has 3000 sq ft of living area is more unusual than a house that ▼ sells for $ 300 comma 000 has 3000 sq ft of living area .
Answer:
A a house in that market that sells for $300,000 is unusual.
Step-by-step explanation:
Let the random variable X denote the price of a house and the random variable Y denote the living area of a house.
The number of houses surveyed by the real estate agent is, n = 1057.
Assume that both the random variables, X and Y are approximately normally distributed.
That is,
[tex]X\sim N(\$169400,\ \$68438)\\\\Y\sim N(2058\ \text{sq. ft.},\ 790\ \text{sq. ft.})[/tex]
To compute the probability of a Normal distribution we first need to convert the raw scores to z-scores.
[tex]z=\frac{\text{Raw score}-\mu}{\sigma}[/tex]
A z-score higher than 1.96 and lower than -1.96 are considered unusual. The values having these z-scores are considered as outliers.
(1)
Compute the z-score for X = 300000 as follows:
[tex]z=\frac{X-\mu}{\sigma}\\\\=\frac{300000-169400}{68438}\\\\=2.70[/tex]
(2)
Compute the z-score for Y = 3000 as follows:
[tex]z=\frac{Y-\mu}{\sigma}\\\\=\frac{3000-2058}{790}\\\\=1.19[/tex]
The z-score for a house in that market that sells for $300,000 is more than 1.96.
This implies, that the price $300,000 is unusually high.
The complete statement is:
The house that sells for $300 comma 000 has a z-score of 2.70 and the house with 3000 sq ft has a z-score of 1.19.
a square pyramid has a side length each measuring 8 centimeters
Complete question is;
A square pyramid has side lengths each measuring 8 centimeters. The height of the pyramid is 3 centimeters. What is the lateral area of the pyramid?
Answer:
Lateral area = 80 cm²
Step-by-step explanation:
We are given;
Side length; a = 8 cm
Height of pyramid; h = 3 cm
Now, formula for Lateral area of pyramid = ½ × p × L
Where p is perimeter of base and L is slant length.
Since we know the side length and height of pyramid, we can find the slant height using Pythagoreas theorem.
L² = (½×side length)² + h²
L² = (½×8)² + 3²
L² = 16 + 9
L = √25
L = 5 cm
Now perimeter of square base = 4a = 4 x 8 = 32cm
So,
Lateral area = ½ × p × L = ½ × 32 × 5
Lateral area = 80 cm²
Answer:
80 square centimeters
Step-by-step explanation:
we need to find the hypotenuse or the slant height of the triangle so 3^2+4^2 = the square root of 25 = 5
We got 4 because half of 8 is 4 and we are basically cutting the triangle in half because the height (3) is perpendicular to the side length.
8(5)/2 = 20
20(4) = 80
On the day you were born, Uncle Peyton gave your parents a piece of sports memorabilia valued at
$75. If past trends continue, it should appreciate in value 12% per year. If you sell it on your 18th
birthday, what can you expect the sale price to be?
Answer:
$162
Step-by-step explanation:
12% of $75 is $9 Therefore,
$9 x 18 = 162 ( 18 being the years )
Hope this helps!!!
-Conrad
Calculate the volume of the following shapes with the given information. For the first three questions, give each answer both in terms of and by using to approximate . Make sure to include units.
Sphere with a diameter of 6 inches
Cylinder with a height of 6 inches and a diameter of 6 inches
Cone with a height of 6 inches and a radius of 3 inches
How are these three volumes related?
Answer:
They all have PI π in the formulas
Step-by-step explanation:
The volume of Sphere is, [tex]36\pi inch^3[/tex].
The volume of Cylinder is, [tex]36\pi inch^3[/tex].
The volume of Cone is,[tex]18\pi inch^3[/tex].
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
First to find the volume of Sphere.
Given a diameter of sphere is 6 inches.
So, the radius is 6/2 = 3 inches.
Volume of Sphere is,
[tex]V = \frac{4}{3} \pi r^3\\V = \frac{4}{3} \pi (3^3)\\V = 36\pi inch^3[/tex]
Now, to find volume of Cylinder.
Given: Height = 6 inch, diameter = 6 inch so, radius = 3 inch
Volume of cylinder is,
[tex]V = \pi r^2h\\V = \pi (3^2)6\\V = 36\pi inch^3[/tex]
Now, to find the volume of Cone.
Given: Height = 6 inch, radius = 3 inch
Volume of cone is,
[tex]V = \frac{h}{3} \pi r^2\\V = \frac{6}{3} \pi (3^2)\\ V = 18 \pi inch^3[/tex]
Therefore, the above the volume of Sphere and Cylinder are equal.
And the volume of Cone is half of the volumes of Sphere and Cylinder.
To know more about the Volume, click on the link
https://brainly.com/question/463363
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Which of these is not a possible r-value?
ОА. 1.2
Ов. 0.5
Ос. -0.75
OD. -0.1
Answer:
Step-by-step explanation:
A
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
y = x² - 8x + 17
Step-by-step explanation:
Recall this formula:
y = a(x-h)² + k
Original equation was y = x², which in this form looks like
y = 1(x - 0)² + 0
If the shape of the graph didn't change, that means that a (the compressor/intensifier) stayed the same (a - value) meaning we can write the equation as..
y = (x-h)² + k
Remember, (h, k) is the vertex, which looking from your graph is at (4, 1)
y = (x - 4)² + 1
y = x^2- 8x + 16+1
y = x² - 8x + 17
Noel read 90 minutes each day for 6 days. Tyra read minutes each day for 8 days. What is the difference, in minutes, between the total amount of time Noel read and the total amount of time Tyra read?
A) 30
B) 40
C) 60
D) 80
Help with this please
Answer:
C) 60
Step-by-step explanation:
For computing the difference between the time taken in minutes by Noel and Tyra first we have to compute individually which are as follows
For Noel, the time taken required
[tex]= Time\ required \times number\ of\ days[/tex]
[tex]= 90\ minutes \times 6\ days[/tex]
= 540 minutes
For Tyra, the time taken required
[tex]= Time\ required \times number\ of\ days[/tex]
[tex]= 60\ minutes \times 8\ days[/tex]
= 480 minutes
So the difference is
= 540 minutes - 480 minutes
= 60 minutes
Hence, the third option is correct
artie multiplies a number by 4 and then adds 3. alice first add 3 to the same number and then multiplies it by 4. alice's answer is ___ more than Artie's number.
Answer:
Alice's answer is 15 more than Artie's number.
Step-by-step explanation:
The number initially is x.
Artie's number:
Multiplies by 4, so 4x.
Subtracts 3, so 4x - 3.
Alice's number:
Adds 3, so x + 3.
Multiplies by 4, so 4(x + 3) = 4x + 12
Alice's number is how much more than Artie's?
We subtract Alice's number by Artie's number.
4x + 12 - (4x - 3) = 4x + 12 - 4x + 3 = 15
Alice's answer is 15 more than Artie's number.
What is the area of circle with a diameter of 22 ft? (use 3.14 for pi; show your work in numbers)
The right answer is 379.94 ft^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex]379.94 {in}^{2} [/tex]
Step-by-step explanation:
[tex]d = 2r \\ 22 = 2r \\ \frac{22}{2} = \frac{2r}{2} \\ \\ r = 11ft[/tex]
[tex]area = \pi {r}^{2} \\ = 3.14 \times 11 \times 11 \\ = 379.94 {ft}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is greater 16.5 or 18750
Answer:
18750
Step-by-step explanation:
This is because 18750 is 5 digits and 16.5 is only 2 whole digits
Grouping 12x3 – 9x2 + 4x - 3?
[tex]12x^{3} - {9x}^{2} + 4x - 3 = \\ = 3 {x}^{2} (4x - 3) + 1(4x - 3) = \\ = (4x - 3)( {3x}^{2} + 1)[/tex]
Answer:4x+15
Step-by-step explanation: PEMDAS. First you multiply 12x3 and 9x2 so you get 36-18. Then you subtract 18 from 36 leaving you with 18. Then you combine 18 and -3, leaving you with 4x-15.
Use a net of the square pyramid, if necessary, to find the surface area of the pyramid
Answer:
- When all side faces are the same:
Surface Area = (Area of the Base) + 1/2 × Perimeter × (Slant Length)
- When side faces are different :
Surface Area = (Area of base) + (Lateral Area).
Step-by-step explanation:
A pyramid is formed by connecting a base to a top. There are no curves in a pyramid, the base is a polygon and all other faces are triangles.
There are many types of Pyramids, and they are named after the shape of their base.
We have Triangular Pyramid, Square Pyramid, Pentagonal Pyramid, and so on.
The Surface Area of a Pyramid.
We need to consider the two cases:
- When all side faces are the same:
Surface Area = (Area of the base) + 1/2 × Perimeter × (Slant Length)
- When side faces are different :
Surface Area = (Area of base) + (Lateral Area).
We consider the Area of Base because a pyramid's base varies, as I have explained earlier. It can be a square, a triangle, a pentagon, and so on.
I would just like to say how happy I have been for getting answers from other people - it's been great!
Just one more question of the day!!!!
Can people please tell me what shapes they are mathematically.
Cheers
Jake
Answer:
Image A could be a Cylinder
Image B is a Tetrahedron
Step-by-step explanation:
Hope this helps : )
The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for Pi.
cylinder. height 4 feet. radius 14 feet
a
351.68 cubic feet
b
703.36 cubic feet
c
2,461.76 cubic feet
d
615.44 cubic feet
Select one of these options to each of these 6 question thar apply to
A .Slope formula
B. Given
C. Perpendicular lines intersect to form right angles.
D. Multiply.
E. Definition of right triangle
F. If the product of the slopes of two nonvertical lines is −1
the lines are perpendicular.
Answer:
1) Given
2) Slope Formula
3) Multiply
4) If the product of the slopes of two non vertical lines is -1, then the lines are perpendicular
5) Perpendicular lines intersect to form right angles
6) Definition of right triangle
This Venn diagram shows the pizza topping preferences for 9 students let event A= The student likes pepperoni let event B= the student likes olives
What is P(a or b)
Answer:
B. 5/9
Step-by-step explanation:
There are 5 names listed in the circles representing pepperoni and olives, so of the 9 students, 5 like pepperoni or olives.
P(A or B) = 5/9
Complete the equation of the line whose slope is -2 and y-intercept is (0,-8).
y =
Answer:
y = -2x - 8
Step-by-step explanation:
The slope is the number in front of the x. If it is a whole number then the slope is number/1. Then the slope is rise over runs. Then the y-intercept is the number after the x. Sometimes there isn't y-intercept. In this one the y-intercept is -8.
A community is building a square park with side is that measure 120 m to separate the picnic area from the play area the park is split by a diagonal line what is the approximate length of the diagonal line
Answer:
(120^2+120^2)^0.5 = 169.705m
Step-by-step explanation:
Pythagorean Theorem
What is the value of x in the equation 1.5(x+4)-3=4.5(x-2)
Answer:
x = 4
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
1.5(x + 4) - 3 = 4.5(x - 2)
1.5x + 6 - 3 = 4.5x - 9
1.5x - 4.5x = -9 - 6 + 3
-3x = -12
x = -12/-3
x = 4
Need help with this question
Answer:
[tex]\dfrac{-5x^2+34x-32}{x^2-10x+24}[/tex]
Step-by-step explanation:
Write each fraction using a common denominator, then combine numerators and collect terms. "Simplify" usually means "eliminate parentheses."
[tex]\dfrac{8}{x-4}-\dfrac{4}{x-6}-\dfrac{5x}{x-4}=\dfrac{8(x-6)}{(x-4)(x-6)}-\dfrac{4(x-4)}{(x-4)(x-6)}-\dfrac{5x(x-6)}{(x-4)(x-6}\\\\=\dfrac{8(x-6)-4(x-4)-5x(x-6)}{(x-4)(x-6)}=\dfrac{8x-48-4x+16-5x^2+30x}{(x-4)(x-6)}\\\\=\boxed{\dfrac{-5x^2+34x-32}{x^2-10x+24}}[/tex]
Plz help me with my school work.
Answer:
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
Step-by-step explanation:
There are several useful rules regarding angles:
right angles are 90°the sum of angles in a triangle is 180°angles of a linear pair are supplementary (total 180°)vertical angles are congruentan exterior angle is equal to the sum of the remote interior anglesThis last observation is a consequence of the 2nd and 3rd observations.
__
angle ECD
Using the last observation, ∠ECD = 124° -90° = 34°.
angle HGB
Again, using the last observation, ∠HGB = 110° -90° = 20°.
angle GBH
There are at least a couple of ways to find this one. We assume that lines FB and EC are parallel, so angles HBC and ECD are corresponding, hence congruent. Angle GBC is the supplement of of 110°, so is 70°. Then ...
∠GBH = 70° -34° = 36°
angle FGH
Again, this angle can be found multiple ways. Here, we'll use the sum of angles in triangle FGB.
∠FGB +∠GBF +∠BFG = 180°
(∠FGH +∠HGB) +∠GBF +∠BFG = 180°
∠FGH +20° +36° +87° = 180°
∠FGH = 180° -143° = 37°
__
Least to greatest, the angles are ...
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
A freshman English class at a certain college has 49 women and 20 men. If 5 students are randomly selected, what is the probability that they are all men? Round to five decimal places.
Answer:
0.00138
Step-by-step explanation:
Alejandro plotted the location of a reclining chair and an end table on a coordinate plane. The end table is represented by the circle, and the chair is represented by the square with solid sides. The image of the chair along a translation is represented by the square with dashed sides.
Answer:
Step-by-step explanation:
Please locate the answers to this question in the file attached below, the solution is there.
You can type 36 words per 18 minute. How many words can you type in 2 minutes?
Answer:
4 words in 2 minutes
Step-by-step explanation:
36 / 18 = 2
2 words per minutes
2 x 2 = 4
You can type 4 words in two minutes
Step-by-step explanation:
So if you can type 36 word in 18 minutes then divide 36 by 18 to get 2 words per minute. Now multiply 2 words by 2 minutes to get 4 words per minute, your answer.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
(x -4)^2 +1
Step-by-step explanation:
For some f(x), a translation to the right by "h" and up by "k" transforms it to ...
g(x) = f(x -h) +k
You want your G(x) to be a translation 4 units right and 1 unit up from F(x), so you have ...
G(x) = F(x -4) +1
G(x) = (x -4)^2 +1
What is the determinant of A = [ -2 2 -5 4 -1 -2 1 3 -5]
Answer:
-51
Step-by-step explanation:
[tex]\begin{vmatrix}-2&2&-5\\4&-1&-2\\1&3&-5\end{vmatrix}=\\=\mathsf{-10-4-60-5+40-12}=\\=\mathsf{-91+40}=\\=\mathsf{-51}[/tex]
Answer:
-51
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}-2&2&-5\\4&-1&-2\\1&3&-5\end{array}\right] =1*\left[\begin{array}{ccc}2&-5\\-1&-2\end{array}\right] +(-3)*\left[\begin{array}{ccc}-2&-5\\4&-2\end{array}\right] +(-5)*\left[\begin{array}{ccc}-2&2\\4&-1\end{array}\right] =-9+(-72)+30=-9-72+30=-51[/tex]
A line passes through the point (4,-6) and has the slope of -3/4. Which is the equation of the line? y=-3/4x-3 y=-3/4x-6 y=-3x-3/4 y=-6x-3/4
use photomath it helps alot
5 people are evenly sharing 12 kilograms of apples how many kilograms of apples should each person get
Answer:
2.4 kilograms
Step-by-step explanation:
Given: 5 people are evenly sharing 12 kilograms of apples
To find: quantity of apples that each person should get
Solution:
Use the unitary method to get the required answer.
Under unitary method, if the value of multiple items is given to us, divide the total value by the number of items to obtain the value of one item.
Quantity of apples for 5 people = 12 kilograms
Quantity of apples for 1 person = [tex]\frac{12}{5} =2.4[/tex] kilograms
So, each person should get 2.4 kilograms of apples.
Answer:
12/5 or 2 2/5
Step-by-step explanation:
We need to divide the 12 kilograms of apples by the 5 people sharing them, or 125
12 ÷ 5 = 12/5
12/5 = 5/5 + 5/5 + 2/5
= 1 + 1 + 2/5
= 2 2/5
Each person should get 12/5, or 2 2/5, kilograms of apple
what makes an equation true?
Answer:
Step-by-step explanation:
An equation is true when certain values are able to be substituted for the variable which is most of the time "x", the values that make an equation true is when the answer has a solution.
Use the figure to complete the statements.
The area of the base, B, of the pyramid is cm2.
The volume of the pyramid is cm3.asap
Answer:
The area of the base, B, of the pyramid is 96 cm2
he volume of the pyramid is 320 cm3.
Step-by-step explanation:
Answer:
96 320
Step-by-step explanation: