Solution :
Given data :
The mean length of the steel rod = 29 centimeter (cm)
The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)
a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).
Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)
= P(z < -1.42)
= 0.0778
b). Any rods which is shorter than [tex]24.84[/tex] cm or longer than [tex]25.16[/tex] cm that re discarded.
Therefore,
P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)
= 1.052
Ibrahim likes to run a loop around the park near his house that is ⅞ mile long. There is a water fountain ½ way around the loop. Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
Answer:
7/16 mile
Step-by-step explanation:
Distance of the loop = 7/8 mile
Distance of Water fountain = 1/2 of the Distance of the loop
= 1/2 of 7/8
Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
= 1/2 of 7/8
= 1/2 * 7/8
= (1 * 7) / (2 * 8)
= 7/16
Ibrahim ran 7/16 mile to drink water at the water fountain around the loop
Next year, air fares will rise by 3%.
Calculate the new price of a R 1 400 ticket.
9514 1404 393
Answer:
₹1442
Step-by-step explanation:
The new price will be 1+3% = 1.03 times the old price.
₹1400 × 1.03 = ₹1442
Find the surface area of the solid given the net
suppose the team wins ten of it's following remaining 18 games. What is it's winning percentage?
A simple random sample is drawn from a normally distributed population. The value of which of the following will not
known for certain but can be inferred?
o u
o-x
os
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Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level
Answer:
It must be a positive number since it represents a number of hours.
Step-by-step explanation:
Given Pieter's equation :
7h – 5(3h – 8) = –72
Opening up the bracket
7h - 15h + 40 = - 72
7h - 15h = - 72 - 40
-8h = - 112
Divide both sides by -8
-8h / -8 = - 112 / - 8
h = 14
Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.
Answer:
B.It must be a positive number since it represents a numbers of hours.
Step-by-step explanation:
Subtract the second equation from the first.
Answer:
2y = 8
Step-by-step explanation:
4x+3y = 17
- ( 4x+y = 9)
----------------------
Distribute the minus sign
4x+3y = 17
- 4x -y =- 9
----------------------
0x +2y = 8
Answer:
2y = 8
Step-by-step explanation:
4x+3y=17
-4x-y=9
_______
0+2y=8
2y=8
can someone answer this
Answer:sadwer
Step-by-step explanation:
The probability that Sara wins a raffle is given by the expression n/n+3
Write down an expression, in the form of a combined single fraction, for the probability that Sara does not win.
Answer:
3/(n + 3)
Step-by-step explanation:
The given probability that Sara wins a raffle draw, P = n/(n + 3)
Given that the sum of all probabilities is 1, we get
The probability that Sara does not win, Q = 1 - P
Therefore;
Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)
The probability that Sara does not win, Q = 3/(n + 3)
what is the solution to this equation?
3x+x-13+4-6x=12
A. x= -21/2
B. x= 21/2
C. x= 3/2
D. x= -3/2
Answer:
A.
Step-by-step explanation:
3x + x - 13 + 4 - 6x = 12
we try to combine the elements with the same power of x (including the ones without any x) :
3x + x - 6x
-13 + 4
so, we get
-2x - 9 = 12
-2x = 21
x = -21/2
Answer:
A
Step-by-step explanation:
group the like terms
3x+x-6x-13+4=12
-2x=12+9
divide both sides by -2
-2x/-2=21/-2
x= -21/2
hope it helps
what is the square root of 25
the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!
what is the solution to the system of equation below y=2/5x-3 and X=_10
Answer:
read explanation
Step-by-step explanation:
since y=2/5x-3 we substitute x=10 in making it y=2/5*10-3
following PAMDAS we do multiplication first so 2/5*10=4.
so y=4-3 and then we subtract and get y=1. Hope this helps:> if you need more explanation message me. If not give this a heart for helping. Good luck.
The system of equations shown below is graphed on a coordinate grid:
3y + x = 4
2y − x = 6
Which statement is true about the coordinates of the point that is the solution to the system of equations?
A. It is (−2, 2) and lies on both lines.
B. It is (−5, 3) and lies on both lines.
C. It is (−5, 3) and does not lie on either line.
D. It is (−2, 2) and does not lie on either line.
Please help asap!! WILL GIVE BRAINlIEST!! tysssm if u help!!!
Answer:
add 2 equations given
3y+x+2y- x = 10
5y =10
y = 2
find x using the value of y
x = - 2
these values of x and y are can satisfy both equations .so (-2,2) lies on both lines
A rectangular prism has a square base with edges measuring 8 inches each. Its volume is 768 cubic inches. Find the height and the surface area of the prism
Answer:
Height = 12in
Surface area = 320in²
Step-by-step explanation:
Given
Length of the square base = 8in
Volume of the prism = 768 cubic inches
Using the formula;
Volume of the prism = Base area * Height of prism
768 = 8² * H
768 = 64H
H = 768/64
H = 12in
Hence the height of the prism is 12in
Get the surface area
Surface area = 2l² + 2lh
Surface area = 2(8)² + 2 (8)(12)
Surface area = 128 + 192
Surface area = 320in²
Hence the Surface area of the prism is 320in²
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
A 90 ° angle is divided into 2 angles. Find the size of the angles. 5x+10 and 6x-41 Not drawn to scale
Answer:
65 and 25
Step-by-step explanation:
90=(5x+10)+(6x-41)
121=11x
11=x
Going back to the angles:
5(11)+10
=55+10
=65 this is the first angle
6(11)-41
=66-41
25 this is the second angle
if we put a marble in 10 ml of water how can we find its volume
please answer
i will mark brainliest
Answer: See below
Step-by-step explanation:
This relates to the usage of water displacement.
Have the 10 ml of water ready in a measuring flask (or any container that has a scale)Put the marble into the waterObserve how much did the water riseSubtract the current water level by the original 10 mlThe final answer would be the volume.------------------------------------------------------------------------
EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)
Refer to the attachment below to finish the question.
Assuming the water levels are integer,
The original water level is 13.33 mlAfter the rock is put in, the water level is raised to 30 mlThen, we do the fourth step which is subtraction
30 - 13.33 = 16.66 mlHope this helps!! :)
Please let me know if you have any quesitons
Find the solution of this system of equations
4x - 5y = -12
-X + 5y = 18
4x - 5y = -12
-x + 5y = 18
Add the equations together:
4x + -x = 3x
-5y + 5y = 0
-12 + 18 = 6
So now you have:
3x = 6
Divide both sides by 3:
X = 2
Now you have the value of x, replace x with 2 in one of the equations and solve for y:
4(2) -5y = -12
8 -5y = -12
Subtract 8 from both sides:
-5y = -20
Divide both sides by -5:
Y = 4
The solution is x = 2 and y = 4 which is written as (2,4)
Simplify this expression.
Can anyone help pls
Answer:
Step-by-step explanation:
Which of the graphs represent y=-x^2
Answer:
Step-by-step explanation:
Can't see all the graphs, but the graph of [tex]y=-x^2[/tex] is an upside down parabola with the vertex at the origin.
differentiate with product rule
Answer:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]
u = ( x + 1 )
v = ( 2x + 5 )²
[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]
Bob's Shoe Emporium sold 5,787 shoes in March. In April they sold 6,245 shoes. How many more shoes did they sell in April than in March? Explain how you got your answer.
Find the missing segment in the image below
Answer:
If there are two line which is parallel in a triangle the triangle has a ratio
Step-by-step explanation:
So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8
Answer:
Step-by-step explanation:
the graph of a linear function is given below
Answer:
A
Step-by-step explanation:
The zero of the function is where the y-value is zero.
then it's -5
There is a bag with 50 popsicles inside. 5 are red, 15 are orange, 12 are blue, 8 are
yellow and 10 are purple. If you were to
grab one popsicle from the bag, what is
the probability that it is red or not orange?
P(red or not orange)
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
First one gram equals 1000 grams, so a 39 kilogram equals 39000 grams. Then, 1000 pillows times 300 equals a 39 kilogram sofa. Is my answer correct?
Answer:
No
Step-by-step explanation:
Kilogram is the unit of weight. Kilogram is the measure of how much matter or the mass an object has in it. Kilogram is the bigger unit of measurement while gram and milligram are the smaller units to measure the weight of any object.
We know,
1 kilogram = 1000 gram x 1
So, 1000 gram is equal to 1 kilogram
That means, 39,000 gram is equal to 39 kilogram.
In the question it is asked whether 1000 pillows times 300 is equal to 39 kilogram sofa or not.
The answer is not correct, because we do not know the weight of the 1000 pillows.
And also, 1000 x 300 will give you 300,000 and not 39 kilogram or 39,000 grams.
please help with math properties I need 5 and 8 :)
Answer:
Step-by-step explanation:
Statements Reasons
1. m∠A = 6x - 10 1. Given
2. m∠B = 2x 2. Given
3. m∠C = 8x - 2 3. Given
4. m∠A + m∠B + m∠C = 180° 4. Triangle sum theorem
5. (6x - 10) + (2x) + (8x - 2) = 180° 5. Substitution
6. 16x - 12 = 180 6. Algebra
7. 6x = 192 7. Addition property of equality
8. x = 12 8. Division property of equality
