a) [tex]X<67.1[/tex]
b) 0.1539
c) 0.1539
d) 0.6922
Step-by-step explanation:
a)
In this problem, the score on the exam is normally distributed with the following parameters:
[tex]\mu=78.1[/tex] (mean)
[tex]\sigma = 10.8[/tex] (standard deviation)
We call X the name of the variable (the score obtained in the exam).
Therefore, the event "a student obtains a score less than 67.1) means that the variable X has a value less than 67.1. Mathematically, this means that we are asking for:
[tex]X<67.1[/tex]
And the probability for this to occur can be written as:
[tex]p(X<67.1)[/tex]
b)
To find the probability of X to be less than 67.1, we have to calculate the area under the standardized normal distribution (so, with mean 0 and standard deviation 1) between [tex]z=-\infty[/tex] and [tex]z=Z[/tex], where Z is the z-score corresponding to X = 67.1 on the s tandardized normal distribution.
The z-score corresponding to 67.1 is:
[tex]Z=\frac{67.1-\mu}{\sigma}=\frac{67.1-78.1}{10.8}=-1.02[/tex]
Therefore, the probability that X < 67.1 is equal to the probability that z < -1.02 on the standardized normal distribution:
[tex]p(X<67.1)=p(z<-1.02)[/tex]
And by looking at the z-score tables, we find that this probability is:
[tex]p(z<-1.02)=0.1539[/tex]
And so,
[tex]p(X<67.1)=0.1539[/tex]
c)
Here we want to find the probability that a randomly chosen score is greater than 89.1, so
[tex]p(X>89.1)[/tex]
First of all, we have to calculate the z-score corresponding to this value of X, which is:
[tex]Z=\frac{89.1-\mu}{\sigma}=\frac{89.1-78.1}{10.8}=1.02[/tex]
Then we notice that the z-score tables give only the area on the left of the values on the left of the mean (0), so we have to use the following symmetry property:
[tex]p(z>1.02) =p(z<-1.02)[/tex]
Because the normal distribution is symmetric.
But from part b) we know that
[tex]p(z<-1.02)=0.1539[/tex]
Therefore:
[tex]p(X>89.1)=p(z>1.02)=0.1539[/tex]
d)
Here we want to find the probability that the randomly chosen score is between 67.1 and 89.1, which can be written as
[tex]p(67.1<X<89.1)[/tex]
Or also as
[tex]p(67.1<X<89.1)=1-p(X<67.1)-p(X>89.1)[/tex]
Since the overall probability under the whole distribution must be 1.
From part b) and c) we know that:
[tex]p(X<67.1)=0.1539[/tex]
[tex]p(X>89.1)=0.1539[/tex]
Therefore, here we find immediately than:
[tex]p(67.1<X<89.1)=1-0.1539-0.1539=0.6922[/tex]
How do the temperature compare? Fro
Answer:
Step-by-step explanation:
-43.6F/-37.4F/-17/37.3/51.9/52
Find the slope of the line that passes through the two points given
SW. *
(4,3) & (3,-2)
Answer:
5
Step-by-step explanation:
The slope between (4,3) (3,-2) can be found using the following formula
m = (y2-y1)/(x2-x1)
=(-2-3)/(3-4)
= (-5)/(-1)
=5
Can’t put it Into a question because it is a graph kinda urgent
Answer:
Step-by-step explana
a= 1
b= 1/16 or .0625
c= 1/256 or .00390625
What is the complete factorization of the polynomial below?
x3 + 9x2 + 26x + 24
Answer:
(x+2)(x+3)(x+4)
Step-by-step explanation:
For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.
Answer:
y = x² + 2x + 1
Step-by-step explanation:
Same y value at x = -2 & x = 0
So line of symmetry is at:
x = (-2+0)/2
x = -1
Vertex: (-1,0)
y = a(x - -1)² + 0
y = a(x + 1)²
At x = 1, y = 4
4 = a(1 + 1)²
4 = 4a
a = 1
y = (x + 1)²
y = x² + 2x + 1
The general form of the equation of the quadratic function is x² + 2x + 1
The formula expressing the equation of the quadratic function will be expressed as:
y = a(x -h)² + k
From the table shown, we can see that the y-values are the same at where x = -2 and 0
Get the line of symmetry:
[tex]x =\frac{-2+0}{2}\\x=\frac{-2}{2} \\x=-1[/tex]
We can see that when x = -1, y = 0. Hence the vertex will be at (-1, 0)
h = -1
k = 0
Substitute into the formula y = a(x -h)² + k
y = a(x -(-1))² + 0
y = a(x+1)²
From the table at where x = 1, y = 4. On substituting to get "a" we have:
4 = a(1+1)²
4 = 4a
a = 1
Get the required quadratic function by substituting the parameters into the general formula as shown:
y = a(x -h)² + k
y = 1(x +1)² + 0
y = (x+1)²
y = (x+1) (x+1)
y = x² + x +x + 1
y = x² + 2x + 1
Hence the general form of the equation of the quadratic function is x² + 2x + 1
Learn more here: https://brainly.com/question/16842393
A 270° angle is three-fourths of a complete rotation.
Please select the best answer from the choices provided
T
F
The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 65% pure fruit juice?
Answer:
64 70% and 16 45%
Step-by-step explanation:
it's 4 70% and 1 45% to make 5 pints of 65% so 64 70% and 16 45%
Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how much will he have in the account after 42 years?
Answer:
$51,282
Step-by-step explanation:
100*1.75%=1.75*504 months (42 years)=882
100*504 months (42 years)=50,400
50,400+882=$51,282
Hope this is correct, and helps you out :)
He will have $74,356.50 in his account.
what is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Initial investment (PV)= $100
Number of periods (n)=42 years
Interest rate (i)= 1.75%
So, FV= P(1+r/100)^(nt) -1)) / (r/n)
FV= 100(1+0.0175/100)^(12*42) -1)) / (0.0175/12)
FV= $74,356.50
Learn more about this concept here:
https://brainly.com/question/23064365
#SPJ2
write g(x)=4x^2+88 in vertex form
Answer:
y
=
4
(
x
+
11
)
2
−
484
Step-by-step explanation:
solve for x: X + 3 = 15
Answer:
x=12
Step-by-step explanation:
x+3=15
move constant to the right
x=15-3
subtract 15 to 3
x=12
Answer:
X =12
Step-by-step explanation:
X+3 =15
subtract 3 from each side
X+3-3 =15-3
X = 12
HELP!
Use the spinner to find the theoretical probability of the event.
The theoretical probability of spinning blue is ___.
Answer:
2/8 or 1/4
Step-by-step explanation:
2/8 or 1/4 because the spots on the spinner are blue out of 8 is 2/8 or 1/4
Answer:
2/6
Step-by-step explanation:
This should have been simple because you don't include the blue parts
Find the reference angle for 517°
a.23°
c.113°
b.157°
d.67°
the anwser is 23 dregrees
Answer asap please :/
Answer:
the first answer is correct
Step-by-step explanation:
Answer:
The correct function is
A. y = -0.5x+100
A bus with kids and a truck with their bags started moving from the school to the camp at the same time. The speed of the bus was 60 mph. The speed of the truck was 45 mph. It took kids 3 hours to reach the camp. How long did they have to wait for their bags?
The kids have to wait for 1 hour to get their bags.
Step-by-step explanation:
Given that,
A bus with kids and a truck with their bags started moving from the school to the camp at the same time.
The speed of the bus was 60 mph.It took kids 3 hours to reach the camp.To find the distance traveled by the bus :
⇒ Distance = Speed × Time
⇒ 60 × 3
⇒ 180 m
∴ The distance is 180 m.
To find the time taken by the truck to reach the camp :
The speed of the truck was 45 mph.We found the distance as 180 m.Time taken = distance / speed.
⇒ 180 / 45
⇒ 4 hours.
∴ The time taken by the truck to reach the camp is 4 hours.
To find how long the kids have to wait for their bags :
The time taken by the truck to reach the camp - the time it took for the kids to arrive.
⇒ 4 hours - 3 hours
⇒ 1 hour.
∴ The kids have to wait for 1 hour to get their bags.
The bus traveled 180 miles to the camp in 3 hours at 60 mph, while the truck took 4 hours at 45 mph to cover the same distance. Hence, the kids had to wait 1 hour for their bags to arrive.
Travel Time and Waiting Time
To determine how long the kids had to wait for their bags, we need to calculate the time it took for the truck to reach the camp.
The bus travels at a speed of 60 mph and it took the kids 3 hours to reach the camp. The distance to the camp can be calculated using the formula:
Distance = Speed × TimeTherefore, the distance is 60 mph × 3 hours = 180 miles.Next, we calculate the time it took for the truck, traveling at 45 mph, to cover the same distance:
Time = Distance / SpeedThus, the truck's travel time is 180 miles / 45 mph = 4 hours.Since the kids took 3 hours to reach the camp and the truck took 4 hours, the kids had to wait for:4 hours - 3 hours = 1 hour.Therefore, the kids had to wait for 1 hour for their bags to arrive.
last Saturday two of the houses were having a party each family invited 9 guests to their house how many guests were in total
Answer:
18
Step-by-step explanation:
because there where two houses each invited 9 guests and 9 + 9 = 18
A steel hex nut has two regular hexagonal faces and a hole with a diameter of 0.4 cm through the middle. Its mass is 3.03 grams.
Answer:
V=0.45
V=0.06
V=0.39
V=7.77
Which statement could describe the graph?
A. After driving for 3 hours, Will stopped for lunch.
B.Will was stuck in traffic during the second and third hour of his trip so he was travelling slowly.
C.Will’s destination was 160 miles from where he started.
D.Will travelled at the fastest speed in the very beginning of his trip.
Answer:
C
Step-by-step explanation:
none of the others are graphically correct
Answer:
C, "Will's destination was 160 miles from where he started."
Step-by-step explanation:
The first and second choices are absurd. It doesn't give any reason or evidence that he stopped during that time. The time does not line up either. D, does not make sense because he only traveled 40 miles in 2 hours. But from hour 3 to 5 he traveled 120 miles.
Solve: n^2/2 -2 = 5n/6
Answer:
n = -4/3 or n = 3
Step-by-step explanation:
Multiply by 6 to eliminate fractions, then put into standard form.
3n^2 -5n -12 = 0
3n^2 -9n +4n -12 = 0 . . . . . separate -5n into two terms to facilitate factoring
3n(n -3) +4(n -3) = 0 . . . . . factor pairs of terms
(3n +4)(n -3) = 0 . . . . . . . . . factor out the common factor
n = -4/3 or 3 . . . . . . . values that make the factors be zero
Which are the solutions of the quadratic equation?
Plzzz ASAP
Answer:
hello i dont even know how to do this
Step-by-step explanation:
A sphere has a radius of 6 meters. A second sphere has a radius of 3 meters. What is the difference of the volumes of the spheres? The volume of the larger sphere is π cubic meters greater than the volume of the smaller sphere.
Answer:
Step-by-step explanation:
volume of sphere = (4/3)πr³
Difference= [(4/3)*π*6³]-[(4/3)*π*3³]
[tex]=\pi*[(\frac{4}{3}*6*6*6) - (\frac{4}{3}*3*3*3)]\\\\=\pi*[(4*2*6*6)-(4*3*3)]\\\\=\pi *[288-36]\\\\=252\pi[/tex]
The cruising speed of the bullet train will be at least 170 miles per hour. Use s to represent the train's cruising speed (in miles per hour). Write an inequality to represent the situation
Answer:
s ≥ 170
Step-by-step explanation:
The problem raises the following statement: "The cruising speed of the bullet train will be at least 170 miles per hour"
Which means that the train has a speed of 170 miles for now or higher, knowing this we can pose the inequality.
Knowing that "s" is the train's cruising speed (in miles per hour), we have to:
s ≥ 170
This would be the inequality that the statement represents.
The inequality representing the bullet train's cruising speed being at least 170 miles per hour is s ≥ 170.
The situation described involves finding an inequality for the train's cruising speed. To represent the train's cruising speed in miles per hour, we use the variable s.
Given that the cruising speed of the bullet train will be at least 170 miles per hour, we need an inequality that expresses this condition.
The inequality is:
s ≥ 170
This means that the cruising speed s can be 170 miles per hour or higher.
Find the distance between point K and point H.
A) 2
B) 5
C) 7
D) 9
Answer:
Option C
7
Step-by-step explanation:
The coordinate point of K is (-2,5) and H(-2,-2)
[tex]KH =\sqrt{ {(x2 - x1)}^{2}+{(y2 - y1)}^{2} } [/tex]
[tex] = \sqrt{ {( - 2 - 5)}^{2} + {( - 2 + 2)}^{2} } [/tex]
[tex] = \sqrt{ {( - 7)}^{2} + {(0)}^{2} } [/tex]
[tex] = \sqrt{49} = 7[/tex]
What is its length?
Enter the correct answer.
The perimeter of a rectangle is twice the
sum of its length and its width. The
perimeter is 34 meters and its length is 2
meters more than twice its width
What is the length?
Step-by-step explanation:
The answer is 15
Solve the following system of equations
-5x+2y=6
10x-2y=-16
X=
Y=
Answer:
5x = - 10
5. 5
x = 2
y = -10
its easyyy
Find the volume of the sphere. Use 3.14 for π. Round to the nearest tenth.
Answer: The answer is 904.32
PLEASE PLEASE PLEASE HELP ME !
Someone please help meee!!
Answer:x=9
Step-by-step explanation:
Add the numbers and the x's
39x+369= 6 angles
Formula 6-2=4×180=720
39x+369=720
-369. -369
39x =351
Divide by 39
X=9
A regular convex polygon has 14 sides. What is the sum of the measures of the interior angles?
Answer:
he measure of each interior angle of a regular polygon with 14 sides is about 154.3.
Step-by-step explanation:
I’m circle R with m angle QRS=82 and QR=16 units find the of arc length of QS. Round to the nearest hundredth
The length of arc QS in circle R is approximately 22.9 units. This is determined by using the formula for arc length in a circle, which is the radius times the angle (in radians). The angle was first converted from degrees to radians.
Explanation:To find the length of arc QS in circle R, we need to use the formula for the arc length. The arc length of a circle is given by the formula Length = radius * angle (in radians). The angle is provided as 82 degrees, and the radius QR is given as 16 units.
First, we need to convert the angle from degrees to radians. We use the formula: radians = degrees * (π / 180). Hence, 82 degrees is approximately 1.43117 radians.
Now, let's substitute our values into the formula. Length = 16 units * 1.43117 radians.
Hence, the arc length of QS is approximately 22.9 units when rounded to the nearest hundredth.
Learn more about Arc Length here:https://brainly.com/question/32035879
#SPJ12
Josie found a small bird bath at a garage sale. The bird bath has a circular opening with a radius of 10 cm, as shown in the diagram below. Using 3.14 for pi, Josie calculates that the water in the small bird bath has 314 cm2 of surface area. Josie lives in a wooded area with lots of birds, so she plans to use the bird bath she found as a scale model to build a much larger bird bath. If she doubles the dimensions of the scale model, how many square centimeters of surface area will the larger bird bath have for bathing?
Answer: 1256cm
Step-by-step explanation:
Final answer:
When Josie doubles the radius of the bird bath to build a larger one, the new surface area will be 1256 cm², as surface area quadruples when doubling the radius of a circle.
Explanation:
Josie calculated that the surface area of her small bird bath with a radius of 10 cm is 314 cm^2. If she doubles the dimensions for a larger bird bath, the new radius will be 20 cm. To find the surface area of the larger bird bath, we use the formula for the area of a circle, A = πr².
Plugging in the new radius:
A = 3.14 × (20 cm)^2
A = 3.14 × 400 cm^2
A = 1256 cm2
This means the surface area for the larger bird bath Josie plans to build will have 1256 cm^2 for bird bathing. This calculation demonstrates how the surface area of a circle quadruples when the radius is doubled, which is consistent with the principle that surface area scales with the square of the dimension changes.