Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let X represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]
[tex]=P(Z<-3.4)\\=0.00034[/tex]
*Use the z-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Ben is tiling the floor in his bathroom the area he is tiling is 4m times 2m each tiles measures 400mm times 400mm he has 45 tiles is that enough
Answer:
No, it's not enough
Step-by-step explanation:
Given
Tilling Dimension = 4m by 2m
Tile Dimension = 400mm by 400mm
Required
Determine the 45 tiles is enough
First;
The area of the tiling has to be calculated
[tex]Area = Length * Breadth[/tex]
[tex]Area = 4m * 2m[/tex]
[tex]Area = 8m^2[/tex]
Next, determine the area of the tile
[tex]Area = Length * Breadth[/tex]
[tex]Area = 400mm * 400mm[/tex]
Convert measurements to metres
[tex]Area = 0.4m* 04m[/tex]
[tex]Area = 0.16\ m^2[/tex]
Next, multiply the above area result by the number of files
[tex]Total = 0.16m^2 * 45[/tex]
[tex]Total = 7.2m^2[/tex]
Compare 7.2 to 8
Hence, we conclude that the 45 tiles of 400mm by 400 mm dimension is not enough to floor his bathroom
I need help ? which linear function is represented by the graph?
=================================================
Explanation:
The diagonal line passes through 1 on the vertical y axis. So the y intercept is b = 1. This means the location of the y intercept is (0,1).
Start at (0,1) and move down 1 and to the right 2 to arrive at (2,0). This is another point on the diagonal line. The motion of "down 1 and right 2" is effectively the slope
slope = rise/run = -1/2
rise = -1, run = 2
The rise being negative means we have gone downhill as we move to the right.
With m = -1/2 as the slope and b = 1 as the y intercept, we go from y = mx+b to y = (-1/2)x+1
The last thing to do is replace y with f(x) to get f(x) = (-1/2)x+1 as the final answer.
Answer:
it's b
Step-by-step explanation:
b
Translate and solve: 82 less than a is at least -82
Answer:
a≥0
Step-by-step explanation:
a-82≥-82
a≥-82+82
a≥0
Janine and Thor are both running for class president. Janine goes down a hallway in the school and puts a sticker on every fourth locker. Thor goes down the same hallway, putting one of his stickers on every fifth locker. If there are 130 lockers in the hallway, how many have both students' stickers?
Answer:
6 lockers have both students' stickers
Step-by-step explanation:
There are 130 lockers in the hallway
Janine goes down a hallway in the school and puts a sticker on every fourth locker.
Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.
Thor goes down the same hallway, putting one of his stickers on every fifth locker
Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.
Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120
Therefore,
6 lockers have both students' stickers
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
one car at a time
Step-by-step explanation:
For each car in the shorter train* (A) ...
train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeatWhen there are no more train A cars in front of train B, both trains can continue on their journey.
We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.
_____
* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.
Let f(x) = 12/4x+2 Find f(-1). (1 point)
Answer:
-1
Step-by-step explanation:
let,x=-1
f(x)= 12/4x + 2
f(-1)= 12/4x(-1) + 2
=12/(-4) +2
= -3+2
= -1
A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?
Answer:
9
Step-by-step explanation:
What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.
We can now use a proportion to find the value of w.
[tex]\frac{4}{3} = \frac{12}{x}[/tex]
Cross multiply:
[tex]12\cdot36 = 36\\\\36\div4=9[/tex]
Hope this helped!
Answer: 9
Step-by-step explanation:
he sum of two nonnegative numbers is 300. What is the maximum value of the product of these two numbers?
Answer:
[tex]\boxed{22,500}[/tex]
Step-by-step explanation:
Hey there!
Well, half of 300 is 150, and 150•150 = 22500
So 150 and 150 are it's highest numbers.
Hope this helps :)
A football is kicked with a speed of 18.0 m/s at an angle of 36.9° to the horizontal.
7. What are the respective vertical and horizontal components of the initial velocity of the football?
A) 10.8 m/s, 14.4 m/s
B) 12.9 m/s, 7.61 m/s
C) 7.61 m/s, 12.9 m/s
D) 14.4 m/s, 10.8 m/s
E) 9 m/s, 9 m/s
Answer:
A
Step-by-step explanation:
horizontal component=18cos 36.9°≈14.39 m/s≈14.4 m/s
Vertical component=18 sin 36.9°≈10.81 m/s≈10.8 m/s
4. Explain how the graphs of the functions are similar and how they are different
2x+3y=1470
And
2x+3y=1593
Answer:
they are parallel lines so have the same slope. Difference would be the where they intersect the x and y axis
Step-by-step explanation:
Slope criteria for Parallel and Perpendicular Lines: Mastery Test
Type the correct answer in each box. If necessary, use / for the fraction bar(s).
>
Given: A B || CD
If the coordinates of point A are (8.0) and the coordinates of point Bare (3.7), the y-intercept of AB is
. If the coordinates of
point Dare (5,5). the equation of line CD is y=
X +
Reset
Next
Answer:Each of the points and the y-intercept of their perpendicular bisectors
Step-by-step explanation:
Where AB and CD are parallel lines:
the y-intercept of line AB is -56/5
the equation of line CD is: y = 7/5x - 2
What is the Slope of Parallel Lines?If two lines are parallel, they will have the same slope (m) value in their equation, y = mx + b (slope-intercept form).
Find the slope of AB:
Slope of AB (m) = change in y / change in x = (7 - 0)/(3 - 8) = 7/5
To find the y-intercept (b) of AB, substitute (x, y) = (8, 0) and m = 7/5 into y = mx + b
0 = 7/5(8) + b
0 - 56/5 = b
b = -56/5 (y-intercept of AB)
AB is parallel to CD, so, CD will have the same slope of 7/5.
To find the equation of CD, substitute m = 7/5 and (a, b) = (5, 5) into y - b = m(x - a)
y - 5 = 7/5(x - 5)
y - 5 = 7/5x - 7
y = 7/5x - 7 + 5
y = 7/5x - 2 (equation of line CD)
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,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Answer:
c
Step-by-step explanation:
use the distributive property to expand the expression:
-2(9 + 32n)
-2*9 + (-2*32n)
-18 - 64n
[tex] \frac{3 \cot30 }{2 \cosec30} [/tex]
Correct to two decimal places . Please help .
9514 1404 393
Answer:
0.02
Step-by-step explanation:
We assume your angle is in degrees:
3cot(30°)/230 = 3√3/230 ≈ 0.02259
≈ 0.02 . . . . . rounded to 2 decimal places
__
This is a straightforward calculator problem. You may have to use one or another of the identities ...
cot(30°) = 1/tan(30°) = tan(90° -30°) = tan(60°)
ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information
Answer: B. Always
Explanation:
Two points always create a line. The correct answer is option B.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the two points always create a line. The correct answer is option B.
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A trader bought a bag for one hundred and twenty five.he later sold it at a profit of Thirty percent what was his selling price
Answer:
I can’t really explain this bc i did it mentally, but i got 162.5
A circle has a radius of 7 inches. What is the area of the circle?
A. 21.98 in^2
B. 43.96 in^2
C. 153.86 in^2
D. 615.44 in^2
Please include ALL work! <3
Answer:
C. 153.86 in^2[tex]area = \pi {r}^{2} \\ r = 7 \\ a = \frac{22}{7} \times {7}^{2} [/tex]
[tex]a = \frac{22}{7} \times 49 \\ a = 22 \times 7 = 154 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ a \: = 3.14 \times {7}^{2} \\ a \: = 3.14 \times 49 = 153.86 {cm}^{2} [/tex]
Answer:
C. 153.86 in^2
Step-by-step explanation:
The area of a circle can be found using the following formula.
[tex]a=\pi r^2[/tex]
where r is the radius.
We know the radius is 7 inches. Therefore, we can substitute 7 in for r.
[tex]r= 7 in[/tex]
[tex]a=\pi (7 in)^2[/tex]
Evaluate the exponent.
(7 in)^2= 7 in * 7 in= 49 in^2
[tex]a= \pi * 49 in^2[/tex]
Let's use 3.14 for pi.
[tex]a= 3.14 * 49 in^2[/tex]
Multiply 3.14 and 49
3.14 * 49=153.86
[tex]a= 153.86 in^2[/tex]
The area of the circle is 153.86 square inches. Therefore, C is the correct answer.
In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 6, 6, 7, 10, 14.
Answer
The mean is 8.6
The median is 7
And the mode is 6
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
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Tom bought 750 shares of a company’s stock for $11.06/share. He pays a broker a commission of $12 to buy and sell stock. After one year, Tom sold all his shares, when they were worth $10.24/share. How much did it cost Tom to buy the stock? Show your work. What was Tom’s net gain or loss? Show your work. What was Tom’s annual rate of return? Show your work.
Answer:
Answer:
-7.692%
Step-by-step explanation:
a.)Buying: total cost
Total cost= commission + (price per share* # of shares ) ;
Total cost= 12 + (11.06*750)= 12+8295 = $8,307
b.)Net gain or loss;
First, find cash received from sale of stock and deduct commission;
Cash from sale =10.24 * 750= 7,680
deduct commission= 7680-12= $7,668
Gain or loss= sale-cost = 7668-8307 = -$639, meaning there is a loss.
c.) Annual rate of return= (net gain or loss/amount paid)*100%
return= -639/(8307)*100 = -7.692%
Step-by-step explanation:
The distance a bike travels varies directly as the amount of time the bike has been ridden. Angela is riding her bike. If she travels a distance of 60 miles in 2 hours, how far has Angela traveled in 7 hours?
Answer:
420 miles
Step-by-step explanation:
60 ×7=420
thank
Answer:210 miles
Step-by-step explanation:because there is 7 hours so you need to multiply up to six hours so 60 x 3 = 180 or 6 hours + 1 hour = 30 miles so 180+30= 210
How do i do this equation
-3(-2y-4)-5y-2=
Answer:
combined like terms and then follow the order of operations.
Step-by-step explanation:
find the derivative of f(x)=3x^2✓x
Answer:
[tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]
Step-by-step explanation:
The power rule applies.
d(x^n)/dx = nx^(n-1)
__
[tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]
A=(1)/(2)h(b_(1)+b_(2)) solve for h
Answer:
[tex]A = \frac{1}{2}h(b_1+b_2)\\2A = h(b_1+b_2)\\h = \frac{2A}{b_1+b_2}[/tex]
PLEASE HELP SOON! A 2011 study by the National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using a cell phones or texting. The data showed that 11% of drivers at any time are using cell phones. Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per per year. Given.
A - Let dc= event that a randomly selected driver is using a cell phone. what is P(DC)? B - Let ta = event that a randomly selected driver has a traffic accident. what is P(ta) C - how can you determine if cell phone use while driving and traffic accidents are related? D - Give that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation.
Answer:
(A) 0.11
(B) 0.0526
(C) Related
(D) 0.28
Step-by-step explanation:
The data provided is:
DC = event that a randomly selected driver is using a cell phone
TA = event that a randomly selected driver has a traffic accident
(A)
From the provided data:
P (DC) = 0.11
(B)
From the provided data:
P (TA) = 0.0526
(C)
To determine whether the events DC and TA are dependent, we need to show that:
[tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
The value of P (DC ∩ TA) is,
[tex]P(DC\cap TA)=P(DC|TA)\time P(TA)[/tex]
[tex]=0.28\times 0.0526\\=0.014728[/tex]
Now compute the value of P (DC) × P (TA) as follows:
[tex]P (DC) \times P (TA)=0.11\times 0.0526=0.005786[/tex]
So, [tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
Thus, cell phone use while driving and traffic accidents are related.
(D)
The probability that the driver was distracted by a cell phone given that the driver has an accident is:
P (DC | TA) = 0.28
2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
Answer:
16/45x-11/12
Step-by-step explanation:
Multiply across
2/15x-30/40-1/6+2/9x=
Get common denominators of like terms
6/45x+10/45x-9/12-2/12=
Combine like terms
16/45x-11/12
The simplified expression is: (16/45)x - (11/12)
To simplify the given expression, we'll follow the steps:
Step 1: Distribute the fractions through the parentheses.
Step 2: Simplify the expression by combining like terms.
Let's proceed with the simplification:
Step 1: Distribute the fractions through the parentheses:
2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)
Step 2: Simplify the expression:
To distribute 2/5 through (1/3x - 15/8):
2/5 * 1/3x = 2/15x
2/5 * (-15/8) = -15/20 = -3/4
So, the first part becomes: 2/15x - 3/4
To distribute -1/3 through (1/2 - 2/3x):
-1/3 * 1/2 = -1/6
-1/3 * (-2/3x) = 2/9x
So, the second part becomes: -1/6 + 2/9x
Now, the entire expression becomes:
2/15x - 3/4 - 1/6 + 2/9x
Step 3: Combine like terms:
To combine the terms with "x":
2/15x + 2/9x = (2/15 + 2/9)x
Now, find the common denominator for (2/15) and (2/9), which is 45:
(2/15 + 2/9) = (6/45 + 10/45) = 16/45
So, the combined x term becomes:
(16/45)x
Now, combine the constant terms:
-3/4 - 1/6 = (-18/24 - 4/24) = -22/24
To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):
-22 ÷ 2 = -11
24 ÷ 2 = 12
So, the combined constant term becomes:
(-11/12)
Putting it all together, the simplified expression is:
(16/45)x - (11/12)
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Complete question is:
Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
the angle theta is in the second quadrant and cos theta = -2/√29 determine possible coordinates for point P on the terminal arm of theta a. (2,5) b. (-2,√29) c. (-5,2) d. (-2,5)
[tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex] and $\theta$ lies in $2^{\text{th}}$ quadrant.
where, $x-$ coordinate is negative, and $y-$ coordinate is positive
so it can't a.
now, cosine means, side adjacent over the hypotenuse, in Cartesian plane, that will be $x-$ coordinate over the distance from origin.
Assume the triangle , with base $2$ units and hypotenuse $\sqrt{29}$ and it's in second quadrant. (so [tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex])
now, the leftmost point on $x-$ axis is , obviously $(-2,0)$
and by Pythagoras theorem, we can find the perpendicular side, that will be $y^2=(\sqrt{29})^2-(2)^2\implies y=5$
so the coordinates of the upper vertex is $(-2,5)$, each point lying on this "ray" should have equal ratio of respective coordinates. i.e. $\frac25=\left|\frac xy\right| $
and it should lie on second quadrant, so $x<0 \, y>0$
Option d satisfies this.
Show why (2×3×7)^4 = 2^4 × 3^4 × 7^4 show work
[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]
(2×3×7)⁴=(2×3)⁴×7⁴(2×3×7)⁴=(2×3×7)⁴RHS=LHSplease mark this answer as brainlist
20 POINTS PLEASE HELP
Answer:
2x^3+5x^2+2x
Step-by-step explanation:
x+2 x and 2x+1
The volume of a rectangular prism is solved by multiplying the height, width, and base. So to solve for the volume, it is (x^2+2x)*(2x+1) [just multiplies x+2 and x] 2x^3+5x^2+2x
Step-by-step explanation:
[tex]thank \: you[/tex]
In Omarion's bag of M&Ms, 1/3 were red, 1/4 were yellow, 1/6 were blue, and 1/4 were orange. He picks out a candy without looking. What color candy is he least likely to choose?
Answer:
RED
Step-by-step explanation:
First of all, we will make all candies common, so we will expand the denominators.1/3
1/4
1/6
1/4
all equal at 12So there is a total of 12 candiesthen the new version of the candies is4/12
3/12
2/12
3/12
the most red sugar#achievements