Answer:
For sample size n = 39 ; P(X < 31.6) = 0.9756
For sample size n = 76 ; P(X < 31.6) = 0.9970
Step-by-step explanation:
Given that:
population mean μ = 31
standard deviation σ = 1.9
sample mean [tex]\overline X[/tex] = 31.6
Sample size n Probability
39
76
The probabilities that the sample mean is less than 31.6 for both sample size can be computed as follows:
For sample size n = 39
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]
[tex]P(X < 31.6) = P(Z< 1.972)[/tex]
From standard normal tables
P(X < 31.6) = 0.9756
For sample size n = 76
[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]
[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]
[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]
[tex]P(X < 31.6) = P(Z< 2.75)[/tex]
From standard normal tables
P(X < 31.6) = 0.9970
F(x) = 3x+2 what is f(5)
Answer:
f(5) = 17Step-by-step explanation:
f(x) = 3x + 2
To find f(5) substitute 5 into f(x)
That's
f(5) = 3(5) + 2
= 15 + 2
= 17
Hope this helps you
Answer:
17
Step-by-step explanation:
You just plug 5 into the equation
f(5)= 3(5)+2
=15+2
=17
Hope this helped! :)
A restaurant catered a party for 40 people. A child’s dinner (c) cost $11 and an adult’s dinner (a) cost $20. The total cost of the dinner was $728. How many children and adults were at the party? Use the table to guess and check. 8 children and 32 adults 9 children and 31 adults 10 children and 30 adults 12 children and 28 adults
Answer:
x=8 number of children
y=32 number of adults
Step-by-step explanation:
x be children and y for adults
x+y=40 ⇒ y=40-x
11x+20y=728 solve by substitution of y=40-x
11x+20(40-x)=728
11x+800-20x=728
-9x=728-800
x=72/9 ⇒ x=8 number of children
y=40-x
y=40-8⇒ y=32 number of adults
There are 25 students in Mr. Jones’ art class. Mr. Jones is planning a project where each student needs 0.3 jar of paint. Exactly how much paint does Mr. Jones need for the art project?
Answer:
7.5 jars
Step-by-step explanation:
There are 25 students in the art class.
Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.
The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.
That is:
25 * 0.3 = 7.5 jars of paint
Mr Jones needs 7.5 jars of paint for the art project.
Mark the absolute maximum point of the graph.
is the absolute maximum point (-3,5)?
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
Graph [tex]y=\frac{2}{3} x[/tex] Which of the following statements are true?
Answer:
A,C,D
Step-by-step explanation:
When b=0, there is a proportional relationship.
The slope in y=mx+b is the value next to x.
Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
graph itttt plssssss
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator. Attached is a picture of it graphed.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
which line segment could be a midsegment of ∆abc
Answer:
[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.
Step-by-step explanation:
A midsegment of a triangle must be two things:
1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].
2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].
Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].
Hope this helped!
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
This is Algebra 1 functions and I'm struggling with this one function-
-1•f(-9)+7•g(6)=_____
Answer:
38
Step-by-step explanation:
f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:
-1 * 4 + 7 * 6
= -4 + 42
= 38
find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
Find the value of x in the
following parallelogram:
2x - 10
2x + 50
Answer:
The value of x is 35
Step-by-step explanation:
In order to calculate the value of x in the following parallelogram: 2x - 10
2x + 50, we would have to calculate the following formula:
m<QPS+m<PQR=180°
According to the given data we have the following:
m<QPS=2x - 10
m<PQR=2x + 50
Therefore, 2x - 10+2x + 50=180
4x+40=180
x=140/4
x=35
Part 2: describe the shape of your cross section of a slice of banana at 45° angle to a space draw picture of the sheep. Part 3: describe the shape of a cross sections if you slice banana and half with a cut perpendicular to its base draw a picture of the shape (hint remember to think of a banana a cylinder)
Answer:
Part 2:
The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points
The drawing of the angle cross section of a cylinder representing the banana is attached
Part 3:
When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle
The drawing of the perpendicular cross section of a cylinder representing the banana is
Step-by-step explanation:
Which expression is equivalent to -80
Answer:
what expressions?
Step-by-step explanation:
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
anyone plss heeelp me...i only need answer 6c..
Answer:
6c1; [tex]Area = 81.12m^2[/tex]
6cii: See Explanation
Step-by-step explanation:
Given
[tex]A = 3p^2[/tex]
[tex]0 \leq p \leq 6[/tex]
Where A represents Area and P represents Width
Required
Solve 6c
Please note that because you only need 6c, I'll solve using calculations;
Solving 6ci:
Area of the cage, when width is 5.2m
Substitute 5.2m for p in[tex]A = 3p^2[/tex]
[tex]A = 3 * 5.2m^2[/tex]
[tex]A = 3 * 27.04m^2[/tex]
[tex]A = 81.12m^2[/tex]
Hence, the area of the cage is 81.12m²
Solving 6cii:
Area of the cage, when width is 40m
From the range of value of p: [tex]0 \leq p \leq 6[/tex], 40m is out of range of the values of p
However, if the range is extended; the value of Area is as follows;
Substitute 40m for p
[tex]A = 3 * 40m^2[/tex]
[tex]A = 3 * 1600m^2[/tex]
[tex]A = 4,800m^2[/tex]
which geometric solid is formed by rotating the rectangle about line m?
Answer:
rectangular prism
Step-by-step explanation:
check by rotating the shape in images
Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answer:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
What is the maximum value of the function
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Answer:
10
Step-by-step explanation:
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5
Answer: 3 x minus 3 + 4 = 2 minus x minus 3
3 x + 1 = negative x minus 1
Step-by-step explanation:
A and D. Edge 2020
The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.
The equation is the relationship between variables and represented as[tex]y = ax +b[/tex] is an example of a polynomial equation.
Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
x = -1/2
Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ5
HELPPPP I need help finding x a and b pleaseeee
Answer:
5x-18 this angle is equal to 92
3x+22 this angle is equal to 88
angle a=88
angle b=92
Step-by-step explanation:
set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22
angle b will be equal to the angle 5x-18
Answer:
The value of x is22°, a is 88° and b is 92°.
Hope it helps..
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). F(x) = -4x + 1; g(x) = (x+1)/4 Choices: a. G(x) has to be: (1-x)/4 b. Inverses c. G(x) has to be: 1/(4 - x) d. G(x) has to be: x/4
Answer:
G(x) = (1 - x)/4
is the inverse function required.
Step-by-step explanation:
Given F(x) = -4x + 1
Let y = F(x)
Then y = -4x + 1
=> y - 1 = -4x
4x = 1 - y
x = (1 - y)/4
That is, the inverse is (1 - x)/4
Therefore, G(x) has to be (1 - x)/4
My age if I am half as old as two more than twice Mack's age if Mack is m years old.
Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
need HELP ON THIS A S AP !!!!!
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]
We are given the radius of 8 yards.
Using 3.14 for pi:
[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
a sector with a radius of 12cm has an area of 60pi cm what is the central angle in radians
Answer:
5/6π.
Step-by-step explanation:
The following data were obtained from the question:
Radius (r) = 12 cm
Area (A) = 60π cm²
Centre angle in radian (∅) =...?
Since we are to look for the centre angle in radian, the area of the sector will be given by:
A = ½r²∅
Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:
A = ½r²∅
60π = ½ × 12² × ∅
60π = ½ × 144 × ∅
60π = 72 × ∅
Divide both side by 72
∅ = 60π/72
∅ = 5/6π
Therefore, the centre angle measured in radian is 5/6π.
Check all that apply. If tan theta = 15/8 then:
Answer:
B, C, D
Step-by-step explanation:
if tan theta = 15/8 then the hypotenuse is 17
therefore the correct answers are B, C, D
Use the rationalized expression from the previous question to
calculate the time, in seconds, that the cliff diver is in free fall.
Assume the acceleration due to gravity, a, is -9.8 m/s2, and the
dive distance, d, is -35 m. The negative numbers indicate the
direction is downward. Round the answer to two decimal places.
Answer:
Time taken (t) = 2.67 s (Approx)
Step-by-step explanation:
Find:
Time taken (t)
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity(a) = -9.8 m/s²
Distance (d) = -35 m
Computation:
Using 2nd equation of motion,
d = ut + (1/2)at²
-35 = (0)t + (1/2)(-9.8)t²
-35 = -4.9 (t²)
t² = 7.1428
t = 2.6726
Time taken (t) = 2.67 s (Approx)
In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music, if the total of 55 students got medals and only 6 students got medals in the three categories ,how many students get medals in exactly two of these categories?
Answer:
210
Note: this answer might be incorrect because of the value of music (212). This doesn't make logical sense.
Step-by-step explanation:
Hello,
This question can easily be solved through the use of a venn diagram.
Total number of students = 55
Number of medals in sport = 40 = A
Number of medals in dance = 25 = B
Number of medals in music = 212 = C
Number of students that got award in the three categories = (AnBnC) = 6
n(AuBuC) = 55
n(AnB) + n(BnC) + n(AnC) - 3n(AnBnC) =
n(AnB) + n(AnB) + n(AnC) -3×6 ......equation (i)
n(AuBuC) = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Therefore,
n(AnB) + n(BnC) + n(AnC) = n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC)
n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC) - 18
40 + 25 + 212 + 6 - 55 - 18 = 210
Note: this answer might be incorrect because of the value of C (music)
What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?
Answer:
2
Step-by-step explanation:
Polygons on either side of a common edge need to be colored differently, so 2 colors are needed, as a minimum. Polygons of the same shape do not share an edge, so all can be colored the same color.