The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins. About how many balls are in bins 1 through 17? 500 680 950 975
Answers
Answer:
Step-by-step explanation:
The total number of bin is 21
the mean of 21 bins is
\(=\frac{21}{2} \\\\=10.5\\\\\approx11\)
The standard deviation is 3 bins.
We calculate , by using z formula
\(P(x<7)=P(z<\frac{x-\mu}{\sigma} \\\\=P(z<\frac{7-11}{3} )\\\\=P(z<-1.33)\\\\=0.0918 (z \ \ table)\\\\\therefore P(x<7)=0.0918\)
Since after 1000 balls is drop, we will mutiply with 1000
0.0918 x 1000
= 91.8
≅ 92
Therefore, we have 92 balls
Related Questions
Use the substitution u = 9x2 + 8 to find the following indefinite integral Check your answer by differentiation '18x sin (9x2 + 8) 18x sin (9x2 + 8) dx=
Answers
The value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
Explain about the indefinite integral?A function that accepts the antiderivative of that other function is said to take an endless integral. Visually, it is shown as an integral indicator, a function, and finally a dx. It is simpler to represent taking the antiderivative using the indefinite integral.The given integral is;
y = ∫18x sin (9x² + 8) dx
Put u = 9x² + 8
Then, on differentiation
18x dx = du
substitute the values:
y = ∫ sin (u) du.
y = -cos u
Put u = 9x² + 8
y = -cos (9x² + 8) + c
c is the constant of integration.
Thus, the value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
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Please look at the pic and help!!
Answers
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
Expand this equation
Answers
Answer:
Step-by-step explanation:
First multiply 9x3
=\(27xy^4x^3y\)
give the terms that dont have a exponent a 1
=\(27x^1y^4x^3y^1\)
Multiply terms with the same base
\(27x^{1+3} y^4x^3y^1\)
Multiply terms of same base
\(27x^{1+3}y^{4+1}\)
Just add all the exponents
\(27x^{4}y^{5}\)
7. Jose's mother is trying to decide whether or not she should buy a 12 ounce package of coffee on
sale for $7.50 or the same coffee for $9.00 per pound. Which is the better buy?
(10 Points)
Enter your answer
8. In question 7 what is the price per ounce for the $9.00 coffee?
(10 Points)
Enter your answer
Pls help :/
Answers
Answer:
7. She should choose the $9 coffe because its cheaper per ounce.
9. 57 cents
Step-by-step explanation:
$7.50/12 ounces = 63 cents
$9/16 ounces = 57 cents
m.
x-intercept =
1/2
and y-intercept = 3
Write an equation for the line in point-slope form and in slope-intercept form
Answers
Answer:
slope intercept form: y= -6x+3
point slope form: y-0= -6(x -1/2)
Step-by-step explanation:
point slope form: y - y1 = m(x - x1)
substitute the values y-0=-6(x-1/2)
slope intercept form:
find the slope using two given points
m = (y2 - y1) / (x2 - x1)
= (3 - 0) / (0 - 1/2)
= 3 / (-1/2)
= -6
substitute into equation
y= -6x+3
determine what type of model bets fits the given situation: A $500 raise in salary each year
Answers
The type of model that best fits the situation of a $500 raise in salary each year is a linear model.
In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.
In the given case, the dependent variable is the salary and the independent variable is the year.
You may build a table to show that for increments of 1 year the increments of the salary is $500:
Year Salary Change in year Change in salary
2010 A - -
2011 A + 500 2011 - 2010 = 1 A + 500 - 500 = 500
2012 A + 1,000 2012 - 2011 = 1 A + 1,000 - (A + 500) = 500
So, you can see that every year the salary increases the same amount ($500).
In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).
In this case, m = $500 and b is the starting salary: y = 500x + b.
Determine whether the distribution is a discrete probability distribution. x 0 100 200 300 400 Upper P (x )0 0 0 0 1 Is the distribution a discrete probability distribution? A. Yes comma because the sum of the probabilities is equal to 1. B. Yes comma because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 comma inclusive. C. No comma because the sum of the probabilties is not equal to 1. D. No comma because each probability is not between 0 and 1 comma inclusive.
Answers
Complete Question
Determine whether the distribution is a discrete probability distribution.
xP(x)
0 0.100
1 0.200
2 0.300
3 0.400
Is the distribution a discrete probability distribution?
A. Yes , because the sum of the probabilities is equal to 1.
B. Yes , because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 comma inclusive.
C. No , because the sum of the probabilties is not equal to 1.
D. No , because each probability is not between 0 and 1 comma inclusive.
Answer:
The correct option is B
Step-by-step explanation:
From the question the probabilites are
\(p_1 = 0.100\)
\(p_2 = 0.200\)
\(p_3 = 0.300\)
\(p_4 = 0.400\)
The sum of the probability is
\(\sum p(x) = 0.100 + 0.200+ 0.300+ 0.400 = 1\)
A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answers
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
70+20=90
90+20=110
110+20=130
help me pls mathhh mhm
Answers
Answer:
f = -15
Step-by-step explanation:
3(f/3) equals f
3(-5) equals -15
The final equation becomes: f = -15
A wooden board in the shape of a rectangle prism measures 0.3 m by 2.1 m by 0.1 m and has a mass of 0.17 kilogram. What is the density of the board?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
To find the density of the wooden board, we need to divide the mass of the board by its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given:
Length (l) = 0.3 m
Width (w) = 2.1 m
Height (h) = 0.1 m
Mass (m) = 0.17 kg
Volume (V) = l × w × h
V = 0.3 m × 2.1 m × 0.1 m
V = 0.063 m³
Density (ρ) = mass / volume
ρ = 0.17 kg / 0.063 m³
ρ ≈ 2.7 kg/m³
The density of the wooden board is approximately 2.7 kg/m³.
You and your family go camping.
Your campsite is square. The area
of your campsite is 900 square
feet. What is the perimeter of the
campsite?
Answers
Answer:
The campsite would be 65 m by 65 m. 65 x 65 = 4,225. Another way to put it (and the way to figure it out) is that the square root of 4,225 is 65.
Step-by-step explanation:
a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
Answers
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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A circle has a radius of 30 cm and a central angle that measures 312 degrees. Find the length of the arc defined by this central angle
Answers
The length of the arc defined by the central angle of 312 degrees is 26π cm.
The formula for the arc length of a circle is given by:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
Substituting the given values, we get:
L = (312/360) × 2π(30)
L = (26/30) × π × 30
L = 26π cm
Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.
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easy question????????????/
Answers
Answer:
The answer to this is...........
Step-by-step explanation:
unknown
or 95
Answer:
95
Step-by-step explanation:
PHOTO ATTACHED CAN SOMEONE PLZ FR HELP LIKE NOT LIKE A LINK OR A ANSWER FOR THE POINTS I NEED SOME HELP!!!!!!!! thank you :)
Answers
Answer:
80a²b³c
Step-by-step explanation:
As with numbers, the LCM is the product of the highest-powered factors.
16ab³ = 2⁴×a×b³
5a²b² = 5×a²×b²
20ac = 2²×5×a×c
The highest power of the factor 2 is 2⁴.
The highest power of the factor 5 is 5.
The highest power of the factor a is a².
The highest power of the factor b is b³.
The highest power of the factor c is c.
The LCM is 2⁴×5×a²×b³×c = 80a²b³c
The table shows the number of magazines printed by a machine after each minute of printing.
Time (t, in minutes) :1, 2,3,4,5
Magazines Printed :70 ,140 ,210 ,280 ,350
Which expression gives the number of magazines printed after 1 minutes?
A. 21t
B. 70t
c. t + 70
D. 2t + 70
Answers
kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail. imagine an angle with its vertex at the center of the circular ski trail that subtends kelsey's path.
a) How many radians has the angle swept out since kelsey started skiing?
b) How many km has kelsey skied since she started skiing?
Answers
a) The angle swept out since kelsey started skiing: 1.1498 radians
b) The distance Kelsey skied: 3.334 km
In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.
Consider the following figure for reference.
We need to find the angle θ and the distance kelsey skied (i.e., the arc length)
Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km
a. the tangent of angle θ would be,
tan(θ) = y/x
tan(θ) = 2.647/1.185
tan(θ) = 2.2337
θ = arctan(2.2337)
θ = 65.88°
θ = 1.1498 radians
b. The length of the arc is:
s = rθ
s = 2.9 * 1.1498
s = 3.334 km
Therefore, a) the angle swept out : 1.1498 radians
b) the distance Kelsey skied: 3.334 km
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The rule T1-4 ORO, 180°(x, y) is applied to rectangle KLMN.
2.
3
Answers
What is the question asking?
Answer:
3
Step-by-step explanation:
EDGE 2021
reduce to the lowest terms 400/5000
Answers
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answers
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
find the volume of the rectangular prism WILL MARK BRAINLEST
Answers
Step-by-step explanation:
volume= l×w×h
1.1/3×1/2×2/3
=1/9
2. 3/4×1/8×13/16
=39/512
3. 1/12×7/8×1/4
=7/384
4. 3/2×1/7×7/8
=3/16
5. 1/5×9/10×2/3
=3/25
6.6/7×7/8×1/2
=3/8
Volume = w * h * l
1) V = 1/9 ft^3
Height (h) = 1/2 ft
Length (l) = 2/3 ft
Width (w) = 1/3 ft
Therefore,
= w * h * l
= 1/3 * 1/2 * 2/3
= 1/6 * 2/3
= 2/18
=> 1/9
Volume = 1/9 ft^3
2) V = 39/512 in^3
Height (h) = 13/16 in
Length (l) = 3/4 in
Width (w) = 1/8 in
Therefore,
= w * h * l
= 1/8 * 13/16 * 3/4
= 13/128 * 3/4
=> 39/512
Volume = 39/512 in^3
3) V = 7/384 cm^3
Height (h) = 1/12 cm
Length (l) = 7/8 cm
Width (w) = 1/4 cm
Therefore,
= w * h * l
= 1/4 * 1/12 * 7/8
= 1/48 * 7/8
=> 7/384
Volume = 7/384 cm^3
4) V = 1/12 cm^3
Height (h) = 2/3 cm
Length (l) = 7/8 cm
Width (w) = 1/7 cm
Therefore,
= w * h * l
= 1/7 * 2/3 * 7/8
= 2/21 * 7/8
= 14/168
= 1/12
Volume = 1/12 cm^3
5) V = 3/25 m^3
Height (h) = 1/5 m
Length (l) = 2/3 m
Width (w) = 9/10 m
Therefore,
= w * h * l
= 9/10 * 1/5 * 2/3
= 9/50 * 2/3
= 18/150
= 6/50
=> 3/25
Volume = 3/25 m^3
6) V = 3/8 yd^3
Height (h) = 1/2 yd
Length (l) = 6/7 yd
Width (w) = 7/8 yd
Therefore,
= w * h * l
= 7/8 * 1/2 * 6/7
= 7/16 * 6/7
= 42/112
=> 3/8
Volume = 3/8 yd^3
2 divide by 3/7 help!!!!!!!!!!!
Answers
2 on division by 3/7 yields 14/3.
For the division of two fractions, we need to multiply the first fraction with the reciprocal of the second. Reciprocal of a fraction means interchanging the numerator and denominator ie, the reciprocal of a is 1/a, the reciprocal of p/q = q/p, and so on.
For example, if a/b and c/d are the fractions the a/b ÷ c/d = a/b x d/c =ad/bc.
Implementing the same method to solve this question,
We have 2/1 = 2 as the first and 3/7 as the second fraction. Thus,
2 ÷3/7 =2 x 7/3 = 14/3. So 14/3 is the answer.
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the area of a certain desert is nine times the area of another desert. if the sum of their areas is 30,000,000 sq miles. find the area of each.
Answers
A scale drawing of a rectangular park is 8 inches wide
and 11 inches long.
The actual park is 330 yards long. What is its area?
Use paper to help you with your thinking.
79200 square yards
240 square yards
88 square yards
2640 square yards
Answers
The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.
What is area of rectangle?Area of rectangle=Length * width.
Given:
scale length of rectangular park = 11 inch =
scale width of rectangular park = 8 inch
scale length / actual length of park = scale width/ actual width of park
11/330= 8/ actual width of park
1/30 = 8/ actual width of park
actual width of park = 240
So,
Area = length* width
=330*240
= 79200 square yards
Hence, the area of the actual parking is 79200 square yards.
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A blueprint used a scale of 1.5 cm = 2 m to
represent a grain silo. If the height of the silo in
the drawing was 33 cm, how tall is the actual grain
silo?
Answers
Answer: The Silo is 44 meters tall
Step-by-step explanation:
To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)
3. Which of the following is the solution to lx + 12| = 3x.
A. x = 3
C. x = 6
b. x = -6
d. x = - 3
Answers
You first subtract 1x from both sides and you are left with 12 = 2x. Then, you divide 2 in both sides and get 6.
Hope this helped!
PLEASE HELP!!!!Choose the equation below that is equivalent to 4(x - 7) - 2(x + 1) = -10
2(x - 7) + (x + 1) = -5
2(x - 7) - (x + 1) = 5
-2(x - 7) + (x + 1) = -5
-2(x - 7) + (x + 1) = 5
Answers
Answer:
\(-2(x-7)+(x+1)=5\)
Step-by-step explanation:
We can divide both sides by -2 to obtain
\(-2(x-7)+(x+1)=5\)
The Duncan family went out for dinner. They ordered 2 meals at $7.25 each and 1
meal at $5.50. They also had 3 drinks at $1.80 each and one dessert at $4.85.
a) Write an expression to evaluate the total amount spent.
b) Evaluate the expression to find the total amount spent before tip.
Answers
Answer:
look below
Step-by-step explanation:
(7.25 * 2) + 5.50 + (3 * 1.80) + 4.85
Lets combine
(7.25 * 2) + (3 * 1.8) + 10.35
7.25 * 2 is 14.50
3 * 1.8 is 5.4
14.50 + 5.4 + 10.35
is $30.25 before tip
(Tip should be 6.05 minimum, 20% of 30.25 is 6.05)
The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?
Answers
Answer:
No
Step-by-step explanation:
Because .5 = 7.2
So 1 = 14.4