We have been given that a normal distribution has a mean of 186.4 and a standard deviation of 48.9. We are asked to find the range of value that represents the upper 2.5% of the data.
We know that upper 2.5% of data would be 97.5% of data.
We will use z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Now we will use normal distribution table to find z-score corresponding to 97.5% area or 0.975.
We can see from the normal distribution table that z-score corresponding to area 0.975 is [tex]1.96[/tex].
[tex]1.96=\frac{x-186.4}{48.9}[/tex]
Let us solve for x.
[tex]1.96\cdot 48.9=\frac{x-186.4}{48.9}\cdot 48.9[/tex]
[tex]95.844=x-186.4[/tex]
[tex]95.844+186.4=x-186.4+186.4[/tex]
[tex]282.244=x[/tex]
Therefore, the range [tex]x>282.244[/tex] represents the upper 2.5% of the data.
Can someone please help me with this?
Answer:
a
Step-by-step explanation:
for x<2, the slope is negative and y-intercept is 3.5
for x>=2, slope is positive and y-intercept is 4
only a satisfies the condition
the coordinates of triangle DEF is D: (-2,3) E: ( -3,0) F: (1, -2)
Triangle DEF is reflected across the x-axis. Which vertex stays the same.
A line is parallel to y = -2x + 1 and
intersects the point (4,1). What is the
equation of this parallel line?
Answer:
For this case since we want a parallel line to -2x+1 we need the same slope so then m = -2 and we have:
[tex] y =-2 x+b[/tex]
Now we can find the intercept b with the condition given x= 4 , y=1 and we got:
[tex] 1 = -2*4 +b[/tex]
And solving for b we got:
[tex] b = 1+8 = 9[/tex]
And our equation would be:
[tex] y = -2x +9[/tex]
Step-by-step explanation:
For this case we need to find an equation for a line who is parallel to y = -2x + 1 and intersects the point (4,1)
The general equation for a line is given by:
[tex] y = mx +b[/tex]
For this case since we want a parallel line to -2x+1 we need the same slope so then m = -2 and we have:
[tex] y =-2 x+b[/tex]
Now we can find the intercept b with the condition given x= 4 , y=1 and we got:
[tex] 1 = -2*4 +b[/tex]
And solving for b we got:
[tex] b = 1+8 = 9[/tex]
And our equation would be:
[tex] y = -2x +9[/tex]
What are the x-intercepts of the function f(x) = –2x2 – 3x + 20? (–4, 0) and five-halves five-halves and (4, 0) (–5, 0) and (2, 0) (–2, 0) and (5, 0)
Answer:
(-4, 0) and (5/2, 0)
Step-by-step explanation:
f(x) = –2x2 – 3x + 20
factor using the diamond method
-2*20 = -40
so -8 * 5 = -40 and -8 + 5 = -3 so...
f(x) = -2x^2 - 8x + 5x + 20
f(x) = -2x (x + 4) + 5 *(x + 4)
f(x) = (-2x + 5)*(x + 4)
x-intercepts are x = 5/2 and x =-4
(-4, 0) and (5/2, 0)
Answer:
(-4, 0) and (5/2, 0)
Step-by-step explanation:
i need help.....
due friday
Simply find the volume of each figure using their corresponding formulas and compare them! :D
CYLINDER: πr2h
CONE: πr2h ÷ 3
CYLINDER WORK:
Your radius is 2, which was a simple find! It wants it squared, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 3, let's plug it in!
π×4×3 (I would suggest putting this in your calculator)
=37.7
CONE WORK:
Your radius is 2 again, which was a simple find because its half your diameter, or 4! It wants it squared again, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 9, let's plug it in! The only difference is you have to divide your whole answer by three since it's different for a cone.
π×4× 9 ÷ 3 (I would suggest putting this in your calculator)
=37.7
Well, what a coincidence, they are the same! This proves that it does not depend on the height, it will only depend on the proportions of your shape, since the cylinder could have had a much larger scale of numbers, which would make it bigger not based on it's shape, but it's overall size.
mary ran 1 3/5 miles on monday and ran 7 1/5 miles on tuesday. how many times her monday’s distance was her tuesdays distance?
Answer:
4.5
Step-by-step explanation:
7 1/5 = 7.2 and 1 3/5= 1.6
so, 7.2/1.6= 4.5
A flagpole is at a (3x + 24)degrees° angle from the ground. Find the value of x.
The value of x is 22. The angle the flagpole makes with the ground, represented as 3x+24∘, is supplementary to the angle the flagpole makes with the vertical line, which is 90 degrees. By setting up the equation 3x+24° + 90° =180°. and solving for x, we find =22. Thus, the flagpole makes a 3(22) + 24° + 90° =180° angle with the ground.
Certainly, let's break it down step by step:
Given: The angle the flagpole makes with the ground is [tex]\(3x + 24^\circ\).[/tex]
1. **Define the problem**: Let [tex]\( \theta \)[/tex] represent the angle the flagpole makes with the ground.
2. **Write the given information**:
[tex]\[ \theta = 3x + 24^\circ \][/tex]
3. **Understand the geometric situation**: The angle formed by the flagpole with the ground is supplementary to the angle formed by the flagpole with the vertical line
4. **Write the equation based on the supplementary angles relationship**:
[tex]\[ \theta + 90^\circ = 180^\circ \][/tex]
5. **Substitute the given value of [tex]\( \theta \)[/tex]**:
[tex]\[ (3x + 24^\circ) + 90^\circ = 180^\circ \][/tex]
6. **Simplify the equation**:
[tex]\[ 3x + 24^\circ + 90^\circ = 180^\circ \][/tex]
7. **Combine like terms**:
[tex]\[ 3x + 114^\circ = 180^\circ \][/tex]
8. **Isolate \(x\)**:
[tex]\[ 3x = 180^\circ - 114^\circ \][/tex]
[tex]\[ 3x = 66^\circ \][/tex]
[tex]\[ x = \frac{66^\circ}{3} \][/tex]
[tex]\[ x = 22 \][/tex]
[tex]So, \( x = 22 \).[/tex]
PLEASE HELP I need an explanation if you can’t do it it’s fine I’ll take what I can get thanks!
Answer: A. 169.65 mi^3
Step-by-step explanation:
The volume of a cylinder is formula is v= π *r^2 *h where r is radius and h is the height being multiplied pie.
V= 3.14 * 3^2 * 6
v= 3.14 * 9 * 6
v =169.6460 to the nearest hundredth is 169.65
Which function increases by 1/3 every time the X increases by 1?
Answer: The correct answer is y = 1/3 x +1
Step-by-step explanation:
A used car dealer sells SUVs and cars. Of all the vehicles, 90% are cars. Of all the vehicles 40% are red cars. What is the probability that a car chosen at random is red? Round your answer to the nearest tenth of a percent.
Answer:
44.4%
Step-by-step explanation:
To calculate this, we proceed as follows.
we use the probability equation below;
P(A|B) = P(A and B) / P(B)
Applying the above to the scenario at hand;
P(red | car) = P(red and car) / P(car)
P(red and car) = 40% or simply 40/100 = 0.4
P(car) = 90% = 90/100 = 0.9
P(red | car) = 0.4/0.9
P(red | car) = 0.4444 which is = 44.44% ; to the nearest tenth of a percent = 44.4%
To find the probability of a randomly chosen car being red, you divide the percentage of red cars by the percentage of all cars. The calculation results in 44.4%, which is the probability that a car is red.
Explanation:To find the probability that a car chosen at random is red, we use the information provided: 90% of all vehicles are cars, and 40% of all vehicles are red cars. To determine the probability of a randomly selected car being red, we must calculate the percentage of red cars within the group of all cars.
This is done by dividing the percentage of red cars by the percentage of all cars, which gives us the probability that a car, given it's a car, is red.
The calculation is (40% / 90%) × 100, which simplifies to 44.4%. Rounded to the nearest tenth of a percent, the probability is 44.4%.
The sum of three consecutive numbers is 72. What is the smallest of
these numbers?
x + (x + 1) + (x + 2) = 72
x+ (x + 2) + (x + 4) = 72
3x = 72
x + y + z =72
Answer:
The smallest number is 23
Step-by-step explanation:
Let x be the first number
x+1 is the next consecutive number
x+2 is the next consecutive number
The sum is
x+ x+1 + x+2 = 72
Combine like terms
3x+3 = 72
subtract 3 from each side
3x+3-3 = 72-3
3x = 69
Divide each side by 3
3x/3 = 69/3
x = 23
x+1 = 24
x+2 =25
The numbers are
23,24,25
What is the volume of the cylinder below?
O A. 45 pi units
OB. 72 pi units
O C. 90 pi units
O D. 36 pi units
Answer D.36 pi unit 3
Answer:
36
Step-by-step explanation:
appeex
!HELP 13,14 and 15 WILL MARK BRAINLIEST
Answer:
sin A = 40/41
tan A = 40/9
cos A = 9/41
Step-by-step explanation:
sin theta = opp/ hyp
tan theta = opp/ adj
cos theta = adj/ hyp
We want to find the measures for angle A
sin A = 40/41
tan A = 40/9
cos A = 9/41
Answer:
SinA = opposite/hypotenuse
SinA = 40/41
SinA = 0.976
(0.9756097561)
TanA = opposite/adjacent
TanA = 40/9
TanA = 4.444
(4.44444444)
CosA = adjacent/hypotenuse
CosA = 9/41
CosA = 0.220
(0.2195121951)
Please help with this
Answer:
26 square feet (no floor)38 square feet (with floor)Step-by-step explanation:
The triangular end of the tent has a base of 3 ft and a height of 2 ft. Its area can be found using the formula for the area of a triangle:
A = (1/2)bh
A = (1/2)(3 ft)(2 ft) = 3 ft^2
__
The rectangular side of the tent has a length of 4 ft and a width of 2.5 ft. Its area can be found using the formula for the area of a rectangle:
A = lw
A = (4 ft)(2.5 ft) = 10 ft^2
___
If we assume the tentmaker makes the two sides not shown exactly the same as these, then the total above-ground material will be ...
2(3 ft^2 +10 ft^2) = 26 ft^2
If there is on-ground material (a floor), that rectangle adds (3 ft)(4 ft) = 12 ft^2 to the total.
The area of the tent above-ground is 26 square feet. With a floor, it is 38 square feet.
The perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensions
Answer:
Length = 13
Width = 9
Step-by-step explanation:
The equation to find the perimeter is 2l+2w=44. The second equation is 2w-5=l since the length is 5 less than double the width.
2l+2w=44,2w-5=l (write equations)
use the equation for length, the second equation, and subtitute it into the first equation's l. Since all l is the same and 2w-5 is equal to l, we can use that equation for the l in 2l+2w=p
2(2w-5)+2w=44 (subtitute)
4w-10+2w=44
6w-10=44 (simplify)
6w=54 (add 10 to both sides)
w=9
use the width to find the length by plugging it into any original equation
2w-5=l
2(9)-5=l
18-5=l
13=l
Answer:
The length is 13.
The width is 9.
Step-by-step explanation:
length = x
width = w
1) x = 2w - 5
2) 44 = 2x + 2w
3) 44 = 2(2w - 5) + 2w
4) 44 = 4w - 10 + 2w
5) 44 = 6w - 10
6) 54 = 6w
7) w = 9
8) x = 2(9) - 5
9) x = 18 - 5
10) x = 13
Which expression represents the greatest common factor (GCF) of 16 and 40? A. 2 x 2 B. 2 x 2 x 3 C. 2 x 2 x 5 D. 2 x 2 x 2
someone plz help me
Answer:
D. 2 x 2 x 2
Step-by-step explanation:
16 is: 2 x 2 x 2 x 2
40 is: 2 x 2 x 2 x 5
16 and 40 have in common are: 2 x 2 x 2
Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $4 comma 500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Multiply the amount he sold by the percent of commission:
4500 x 0.13 = 585
he made $585 last week.
There are 52 weeks in a year, multiply the amount of commission by 52:
585 x 52 = 30,420
he made $30,420 in 2011.
Alexander made $585 in commission last week. In 2011, he made $30,420 in commission.
Explanation:To calculate Alexander's commission, we can multiply the value of the stocks he sold by the commission rate.
$4,500 imes 0.13 = $585
Therefore, Alexander made $585 in commission last week.
To calculate how much he made in commission in 2011, we need to know the number of weeks in 2011. Assuming there are 52 weeks in a year, we can multiply Alexander's weekly commission by the number of weeks in 2011:
$585 imes 52 = $30,420
What are the intercepts of the function?
The x-intercepts are
The y-intercept is
Answer:
x intercepts: x=-1 and x=-11
y intercepts: y = 11
Step-by-step explanation:
x+1=0
x=-1
x+11=0
x=-11
f(0)=11
Answer:
x intercept is -1,0 and -11,0 and y intercept is 0,11
Step-by-step explanation:
PLEASE HELP ME! I ONLY HAVE 2 HOURS!!!
What is the sample space for choosing 1 jelly bean at random from a jar containing 5 red, 7 blue, and 2 green jelly beans?
A. {5, 7, 2}
B. {red, blue, green}
C. {5 red, 7 blue, 2 green}
D. {red, blue, orange}
Answer:
B. red, blue, green
Using the sample space concept, it is found that for this situation, it is given by:
B. {red, blue, green}
------------------------
In a probability experiment, the sample space is the set that contains all possible outcomes.For example, if you are going to have a child, it will either be a boy or a girl, thus, the sample space is: {boy, girl}In this question, one jelly bean will be chosen, which will either be red, blue or green. Thus, the possible outcomes are red, blue or green, which means that the sample space is: {red, blue, green}, given by option B.A similar problem is given at https://brainly.com/question/15006554
What is the value of x
Answer:
x=123
Step-by-step explanation:
x is across from the angle that measures 123 degrees. Therefore, they are vertical angles, and are congruent.
x=123
Additionally, 57 and x are on a straight line. This means they are supplementary and add to 180 degrees
57*x=180
Subtract 57 from both sides to get x by itself.
x=123
Please help me idk this
Answer:
65 square inches.
Step-by-step explanation:
To solve for this irregular figure, you must break it into separate rectangles.
Firstly, we can solve for the area of the top rectangle by:
6×4= 24 sq in.
For the next rectangle, we can do:
4×8= 32 sq in.
Finally, the remaining square can be solved by:
3×3= 9 sq in.
To get the ENTIRE area, you will need to add these areas up which gets you:
24+ 32+ 9= 65 sq in.
Kevin uses each of the digits 5, 7, 4 and 9, once and once only, to make
four-digit numbers.
c)
What is the largest number that he can make?
9754
What is the smallest even number that he can make?
Answer: smallest 5794
Step-by-step explanation:
Answer:
5794
Step-by-step explanation:
5794 is the answer because...
Step one If we want to find the smallest even number we have to find out what the smallest number is first. So A trick I have learned is when you have the biggest number the smallest number is just the biggest number backwards. so if it was 9754 the smallest number is 4579.Step two since this is an odd number we have to make the last number of the smallest number even. To do so we have to take the smallest even number which is 4 and out it at the end. We also have to keep the number at it's smallest.Step 3 is to rewrite the Answer. Now we have four at the end our new number is 5794Hope this helped :)A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show
The cost of each ticket is $4.
How to find the price of each ticket?Here we know that the family buys 6 tickets, and they also pay $3 for a parking fee.
The total amount that they spend is $27.
If we remove what the paid for the parking fee, we only will have the cost of the 6 tickets, then we have:
$27 - $3 = $24
Now, we divide this by the number of tickets bought:
$24/6 = $4
Each ticket costs $4.
If you want to learn more about quotients, you can read:
https://brainly.com/question/7068223
Can someone help me with this one
Answer:
A
Step-by-step explanation:
Equate the congruent sides of the side, that is
2x + 2 = x + 6 ( subtract x from both sides )
x + 2 = 6 ( subtract 2 from both sides )
x = 4
and
y - 5 = x + 5 = 4 + 5 = 9 ( add 5 to both sides )
y = 14
Thus
top pair = x + 5 = 4 + 5 = 9 and lower pair = x + 6 = 4 + 6 = 10
The line of best fit for the scatterplot below passes through which pair of points?
A. P and Q
B. P and T
C. R and Q
D. S and Q
Answer:
C. R and Q
Step-by-step explanation:
If you draw the line of best fit, it passes through the cluster of points along the graph. The two points that are included in the mass are R and Q. The other ones are outliers, and would not be represented on the line of best fit.
I hope this helps!
Answer:
R and Q
Step-by-step explanation:
e.dgenuity
how many minutes is 504 hours
Answer:
30,240 minutes
Step-by-step explanation:
Hope this helps :)
30240 minutes for 504 hours
-7 2/3 +(5 1/2) + 8 3/4 =
Answer:
6 7/12
Step-by-step explanation:
-7 2/3 +(5 1/2) + 8 3/4
Get a common denominator of 12
-7 2/3 * 4/4 +(5 1/2 +6/6) + 8 3/4*3/3
-7 8/12 + 5 6/12 + 8 9/12
Subtract the first two terms first
They have opposite signs so subtract and take the sign of the larger
-7 8/12 + 5 6/12 = -2 2/12
-2 2/12 + 8 9/12
They have opposite signs so subtract and take the sign of the larger
-2 2/12 + 8 9/12 = 6 7/12
What’s the solution to #4?
Answer:
95/pie
Step-by-step explanation:
2 × radius = diameter
2 × pie × radius = circumference
2 × pie × radius = 95cm
radius = 95/2 × pie
Diameter = [95/2 × pie] × 2
Diameter = 190/2 × pie
Diameter = 95/pie
(It wasn't stated in the question but if pie = 22/7, the diameter is 95 × 7/22 = 30.23 (approximately)
Find the median of each set of data.
12, 8, 6, 4, 10, 1
6,3, 5, 11,2, 9,5, 0
30, 16, 49, 25
answer this question (x −2)(x + 5) = 18
Answer:
x=-7 x=4
Step-by-step explanation:
(x −2)(x + 5) = 18
Foil
x^2 +5x-2x-10 = 18
Combine like terms
x^2 +3x -10 =18
Subtract 18 from each side
x^2 +3x -28 = 0
Factor
What two numbers multiply to -28 and add to 3: 7 and -4
(x+7) (x-4) =0
Using the zero product property
x+7=0 x-4 =0
x=-7 x=4