We have been given that a of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars. A leather sofa has a price of 2410 dollars. We are asked to find the proportion of sofa prices that are higher than the price of the leather sofa.
First of all, we will find the z-score corresponding to sample score 2410.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{2410-2500}{200}[/tex]
[tex]z=\frac{-90}{200}[/tex]
[tex]z=-0.45[/tex]
Now we need to find area under normal curve that is greater than z-score of [tex]-0.45[/tex] that is [tex]P(z>-0.45)[/tex].
Using formula [tex]P(z>a)=1-P(z<a)[/tex], we will get:
[tex]P(z>-0.45)=1-P(z<-0.45)[/tex]
Now we will find area under curve using normal distribution table.
[tex]P(z>-0.45)=1-0.32636[/tex]
[tex]P(z>-0.45)=0.67364[/tex]
Upon rounding to 4 decimal places, we will get:
[tex]P(z>-0.45)\approx 0.6736[/tex]
Therefore, approximately 0.6736 of sofa prices are higher than the price of the leather sofa.
Answer:
0.6736
Step-by-step explanation:
khan academy
Which expression represents the distance between point (0, a) and point (a, 0) on a coordinate grid?
2a1
Answer:
[tex]\sqrt{2} a[/tex]
Step-by-step explanation:
The distance between point (x1,y1) and (x2,y2) on a coordinate plane is given by expression [tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
In the problem given coordinate points are
(0, a) and (a, 0).
Thus, distance between these points are given by
[tex]distance = \sqrt{(x1-x2)^2+(y1-y2)^2}\\=>distance = \sqrt{(0-a)^2+(a-0)^2}\\=>distance = \sqrt{(a)^2+(a)^2}\\\\=>distance = \sqrt{2a^2}\\=>distance = \sqrt{2} a[/tex]
Thus , expression [tex]\sqrt{2} a[/tex] gives the distance between point (0, a) and point (a, 0) on a coordinate grid.
Answer:
A) √2a^2
Step-by-step explanation:
I just took the quiz on edge
Round 425 to the nearest ten and to nearest hundred
430; 400
420; 500
430; 500
420; 400
Answer:
430;400
Step-by-step explanation:
So tenth is the 2.. 5 makes it go to 3 430
hundred we look to change 4 so we look at tenths 2 is less than 5 so it stays the same 400
A man has a salary of 1200 and saves 18% of it. How much did he save
PLLZZZ QUICKLY!,!!
Answer:
216
Step-by-step explanation:
Savings = amount times percent saved
savings = 1200 * 18%
Change to decimal form
savings = 1200*.18
savings =216
What is the surface area
Answer:
579.29
Step-by-step explanation:
Answer:
1512m2
I think this is the answer please do not report if wrong.
Prove: The quadrilateral formed by joining in order the midpoints of the sides of a rectangle is a parallelogram. Given: ABCD is rectangle K, L, M, N are midpoints Prove: KLMN is a parallelogram Which of the following reasons would complete the proof in line 6? If both pair of opposite sides of a quadrilateral are equal, then it is a parallelogram. If both pair of opposite sides of a quadrilateral are parallel, then it is a parallelogram. If a pair of opposite sides of a quadrilateral are parallel and equal, then it is a parallelogram.
Answer:
If a pair of opposite sides of a quadrilateral are parallel and equal, then it is a parallelogram.
Step-by-step explanation:
By definition, a parallelogram is a quadrilateral with two pairs of parallel sides. These parallel sides are of equal length and the opposite angles of a parallelogram are of equal measure.
Answer:
if a pair of opposite sides of a quadrilateral are parallel and equal, then it is a parallelogram.
Step-by-step explanation:
got it right on oddyssey
Select all of the zeros of the function f(x) = (3x − 4)(x + 2)
4
2
4/3
-4/3
-2
-4
Answer:
Hi Gracie pretty sure the answer is 4/3, -2
Step-by-step explanation:
The zeroes of the function f(x) = (3x − 4)(x + 2) is 4/3, -2 option (3) and option (5) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = (3x - 4)(x +2)
To find the zeroes of the function:
Applying zero product property:
(3x - 4)(x +2) = 0
The above equation represents a quadratic equation,
As we know, Any equation of the form[tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
3x - 4 = 0
3x = 4
x = 4/3
or
x + 2 = 0
x = -2
Thus, the zeroes of the function f(x) = (3x − 4)(x + 2) is 4/3, -2 option (3) and option (5) are correct.
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Hamsters, i tried to times it by 2 but its 10 and the answers are not close, i think ive done something wrong, maybe i times it 3 times? 15? or do i just choose 5?
Answer:
WHAAAAAAAAAAAAAAAAAAAAAAAAAAAAAT
Step-by-step explanation:
HURRY!! will mark brainliest and 15pts!! The volume of the composite figure is BLANK cubic centimeters ???HURRY!!
Answer:
This is how you find the comosite figure
Separate the figure in simpler forms, which can be discovered in a composite figure field. Then merge the fields. Keep in mind that none of the simple figures have overlaps. Example 1: Find the area shown below for the composite form
Step-by-step explanation:
If you still need help, i will give you the answer.
Hope that helps.
Answer:
48
Step-by-step explanation:
The instructions weren’t very clear to me and there was an example :/ please help and thank you!
Answer & Step-by-step explanation:
You are supposed to write the equation you would use to solve for x.
The triangle is a right triangle, classified by it's 90° angle, or right angle. This means that you can use the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
(a) and (b) are the legs and (c) is the hypotenuse. The hypotenuse is always the longest side and opposite the 90° angle. Insert the given values into the formula:
[tex]4^2+7^2=x^2[/tex]
Enter this equation into the boxes, and done.
Answer this maths challenge question to earn 20... points!! :0
Answer:
first x would be 1 second would 4. And the first y would be 3 and the second one would be 4
Step-by-step explanation:
Which expressions are equivalent to 5+(-3)(6x-5)?
Choose all answers that apply:
(Choice A)
18x-20
(Choice B)
3x-3
(Choice C)
None of the above
So the right answer is none of the above
look at the attached picture
hope it will help you
Multiply (x+6)(x+7). What is the product?
Answer:
x^2 +13x+42
Step-by-step explanation:
(x+6)(x+7)
FOIL
first: x*x = x^2
outer: 7x
inner:6x
Last: 6*7 =42
Add them together
x^2+7x+6x +42
Combine terms
x^2 +13x+42
Answer:
X^2 + 13x + 42
Step-by-step explanation:
(X+6)(x+7)
x^2 + 7x + 6x + 42
X^2 + 13x + 42
Andrea built a circular barbecue pit with a circumference
of 9 feet. She wants a rod to go across the pit to use for a
rotisserie. The rod must go from one edge of the pit to
the other, passing through its center. To the nearest foot,
how long must the rod be?
Answer:
if the circumference is 9 is a simple process if of dividing the circumference by pi which turns out to be roughly 2.86
2:21:27 PM what is this in non military time
Answer:9.27 pm
Step-by-step explanation:
Answer:
09:27 PM
Step-by-step explanation:
when using 12-hour clock notation then 21:27 PM would be 09:27 PM
hope this helped!
What is the rectangular equivalence to the parametric equations?
x(θ)=3cosθ+2
y(θ)=2sinθ−1 ,
where 0≤θ<2π .
Answer:
For x(θ) = 3cosθ + 2
y² = [9x²/(x - 2)²] - x²
For x(θ) = 3cosθ + 2
x² = [4y²/(y - 1)²] - y²
Step-by-step explanation:
Given the following equivalence:
x² + y² = r²
r = √(x² + y²)
x = rcosθ
cosθ = x/r
y = rsinθ
sinθ = y/r
Applying these to the given equations,
x(θ) = 3cosθ + 2
x = 3(x/r) + 2
xr = 3x + 2r
(x - 2)r = 3x
r = 3x/(x - 2)
Square both sides
r² = 9x²/(x - 2)²
(x - 2)²r² = 9x²
(x - 2)²(x² + y²) = 9x²
(x² + y²) = 9x²/(x - 2)²
y² = [9x²/(x - 2)²] - x²
y(θ) = 2sinθ - 1
y = 2y/r - 1
yr = 2y - r
(y - 1)r = 2y
r = 2y/(y - 1)
Square both sides
r² = 4y²/(y - 1)²
x² + y² = 4y²/(y - 1)²
x² = [4y²/(y - 1)²] - y²
The quotient of two numbers is 4, and the difference is 3. What are the two numbers
Answer:
The numbers are 4 and 1
Step-by-step explanation:
Let x and y be the numbers
Quotient is division
x/y = 4
x-y =3
Taking the first equation and multiplying each side by y
x = 4y
Replacing into the second equation
4y -y = 3
3y = 3
Divide by 3
3y/3 = 3/3
y=1
Now we can find x
x -y =3
x-1 =3
Add 1 to each side
x= 4
There are 6 cherry ice pops, 10 grape ice pops, and 8 lime ice pops in a box. If one ice pop is randomly taken from the box, what is the probability that the ice pop will be lime?
Answer:
20%
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
6+8+10=24
8/24 which is 1/3
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
A = 78.5 cm²
Step-by-step explanation:
Area of Circle = πr²
A = (3.14)(5)²
A = (3.14)(25)
A = 78.5 cm²
The area formula of a circle is r² x π.
With that being said, we can now substitute in our radius value.
(5)² x π
From there, we can find the square root of the radius.
(25) x π
And then we can multiply by pi to solve.
78.539816..
Finally, we'll round to the nearest tenth to get our answer.
78.5
Therefore, the area of the circle is 78.5 cm.
Hope this helped! :)
can someone help me with this question.
Answer:
52 degrees
Step-by-step explanation:
According to the vertical angle theorem, the opposite should be the same.
Answer:
z = 52
Step-by-step explanation:
Angle z and 52 are vertical angles so they are equal
z = 52
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios.
6 ounces of pistachios cost $7.50
StartFraction 7 dollars and 50 cents Over 6 ounces EndFraction = StartFraction dollar-sign question mark Over 1 ounce EndFraction
Unit price = $0.80 per ounce
(16 ounces) (StartFraction 80 cents Over 1 ounce EndFraction) = 12 dollars and 80 cents
What was his first error?
Answer:
He made a math error
Step-by-step explanation:
6 ounces of pistachios cost $7.50
take 7.50 / 6=1.25 per ounce ( not .80 per ounce)
Then 1.26 * 16 = 20.00 for 16 ounces
Answer: B
Step-by-step explanation: The price per ounce should have been $1.25 per ounce.
I hope this helps! °ω°
What is the image point if (8,4) after a translation left 2 units and down 4 units
Answer:
(6,0) I think
my memory is rusty on this subject sorry if it's wrong.
The image point of (8, 4) is (6, 2).
What is translation?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation may alternatively be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Given:
The point (8, 4).
To find the image point:
The translation rule:
The image point of (8, 4),
= (8 - 2, 4 - 2)
= (6, 2)
Therefore, the image point is (6, 2).
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You jog 2 miles every 15 minutes. How much do you jog per minute? Write your answer as a fraction in simplest form.
Answer:
7 and 1/2 miles per minute. Just divide 2 by 15.
2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. The top angle of the triangle is (2 x + 10) degrees. The bottom right angle of the triangle is 79 degrees. The exterior angle to the bottom left angle is (6 x + 1) degrees. What is the value of x? x = 2.25 x = 11.25 x = 13 x = 22
Answer:
11.25
Step-by-step explanation:
8x+11=180-79
8x+11=101
8x=90
x=11.25
By angle sum property the value of x in the expression (2 x + 10) + (6 x + 1) +79 =180 is 11.25
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles.
The top angle of the triangle is (2 x + 10) degrees. The bottom right angle of the triangle is 79 degrees.
The exterior angle to the bottom left angle is (6 x + 1) degrees.
By angle sum property
(2 x + 10) + (6 x + 1) +79 =180
8x+11 + 79 =180
8x+11=180-79
8x+11 =101
8x = 90
x = 11.25
Learn more about the triangles;
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what is the product of 4r^2-3 and 2r?
Show all work.
Answer:
8[tex]r^{3}[/tex] - 6r
Step-by-step explanation:
2r(4r^2-3)
= 8[tex]r^{3}[/tex] - 6r
A clerk earns $12 an hour. How much does the clerk earn for p hours of work?
Answer:
You can't do this without knowing the number of hours, but you can write an equation. The equation would be 12p. P means the number of hours they worked and 12 stands for how much they earn each hour. Therefore you would multiple both of them together.
The box plot compares the number of events that Mrs. Cai’s and Mr. Roland’s classes won over the last 10 years on the school’s field day.
A number line goes from 0 to 10. Mrs. Cai's class's whiskers range from 0 to 8, and the box ranges from 2 to 4. A line divides the box at 3. Mr. Roland's class's whiskers range from 1 to 8, and the box ranges from 4 to 7. A line divides the box at 5.
Based on the data in the box plots, what is the best evidence to show which class has had greater success on field day over the last 10 years?
Mrs. Cai’s class was more successful because her interquartile range was less spread out.
Mrs. Cai’s class was more successful because she had the greater total spread.
Mr. Roland’s class was more successful because his class always won at least one event.
Mr. Roland’s class was more successful because his class’s lower quartile was the same as Mrs. Cai’s class’s upper quartile.
Answer:
D. Mr. Roland’s class was more successful because his class’s lower quartile was the same as Mrs. Cai’s class’s upper quartile.
Step-by-step explanation:
Mrs. Cai's class's box ranges from 2 to 4, that is, her class’s upper quartile is 4.
Mr. Roland's class's box ranges from 4 to 7, that is, his class’s lower quartile 4.
Answer:
D
Step-by-step explanation:
Mr. Roland’s class was more successful because his class’s lower quartile was the same as Mrs. Cai’s class’s upper quartile.
Find the value of x for which
2. Find the lateral area and surface area of the
prism.
4 cm
5 cm
4 cm
3 cm
Answer:
Lateral = 48 cm squared and Surface area = 60 cm squared
Step-by-step explanation:
Lateral surface area = 4 x 4 + 5x4( Slope) + 4 x 3 (Cross section x2) = 48
Surface area: Lateral + 4x3(base)
The stem-and-leaf plot shows the number of confirmed cases of a virus in 15 countries.
stem leaf
4 1 1 3 3 5
5 0 2 3 4
6 2 3 3 7
7 5
8
9 7
Find the mean, median, rage, and interquartile rage of the data. Round your answer to the nearest tenth, if necessary.
The mean is
The median is
The range is
Answer: the mean is 4 the meadian is 2.5 and 6.5
and the range is 9
Step-by-step explanation: i may not be right since i havent done this kinda work in a long time but im pretty sure this is right. cause i graphed it out and the mean is the middle while the median is like the 2/4 and the range is the highest - the lowest number
Find the upper bound for the following lengths:
a) 60 cm measured to the nearest cm.
b) 96.3 cm measured to the nearest tenth of a cm.
Answer:
60cm=60.5cm
96.3cm=96.35cm
The upper bound lengths are 60.4 cm and 96.34 cm for the given lengths of 60 cm and 96.3 cm.
What are the upper and lower bounds of an approximation?The upper bound for the given value is the numerical value that is rounded for the next value of the given value.
the Lower bound for the given value is the numerical value that is rounded for the previous value or the estimated value of the given value.
Approximation of the given lengths:a) 60 cm - this is rounded off for the values,
Lower bound - 59.5 cm and Upper bound - 60.4 cm
b) 96.3 cm - this is rounded off for the values,
Lower bound - 96.25 cm and Upper bound - 96.34 cm (rounded to the nearest tenth)
So,
The upper bounds for the given lengths are 60.4 cm and 96.34 cm.
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