Step-by-step explanation:
A square prism is a three-dimensional cuboid where the base and top are equal squares and the remaining 4 faces are rectangles.
to get the surface area of the package (that square prism) the size of the content inside is irrelevant and only there to confuse us.
the package has a base area of 16 in².
that means it also has a top (or cover) area of the same size : 16 in².
as top and bottom are squares, that means their areas are the square of their side lengths.
therefore, the side length of such a square is
s = sqrt(16) = 4 in
now we know also the dimensions of the 4 rectangles that are the side areas (faces) : 4 in × 4.25 in
the area of such a rectangle is
4 × 4.25 = 17 in²
so, the total surface area is (top and bottom + 4 side areas)
2×16 + 4×17 = 32 + 68 = 100 in²
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as
they sneeze. Complete parts (a) through (c)
(a) What is the probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing?
Using the binomial distribution, the probability is
(Round to four decimal places as needed.)
(b) What is the probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing?
Using the binomial distribution, the probability is 1
(Round to four decimal places as needed.)
(c) Would you be surprised if, after observing 12 individuals, fewer than half covered their mouth when sneezing? Why?
No, I would not be surprising, because using the binomial distribution, the probability is . which is v0.05
(Round to four decimal places as needed.)
Using the binomial distribution, it is found that:
a) There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
b) There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
c) The probability is higher than 5%, so it would not be unusual.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
Sample of 12, thus [tex]n = 12[/tex]0.267 probability that a person covers their mouth, thus [tex]p = 0.27[/tex].Item a:
This probability is P(X = 7), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{12,7}.(0.267)^{7}.(0.733)^{5} = 0.0162[/tex]
There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
Item b:
The probability is P(X < 4), which is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.267)^{0}.(0.733)^{12} = 0.0241[/tex]
[tex]P(X = 1) = C_{12,1}.(0.267)^{1}.(0.733)^{11} = 0.1052[/tex]
[tex]P(X = 2) = C_{12,2}.(0.267)^{2}.(0.733)^{10} = 0.2107[/tex]
[tex]P(X = 3) = C_{12,3}.(0.267)^{3}.(0.733)^{9} = 0.2558[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0241 + 0.1052 + 0.2107 + 0.2558 = 0.5958[/tex]
There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
Item c:
This probability is:
[tex]P(X < 6) = P(X < 4) + P(X = 5) = 0.5958 + P(X = 5)[/tex]
Negative probabilities do no exist, thus, this probability is guaranteed to be above 0.05, which means that it would not be unusual if fewer than half covered their mouth when sneezing.
A similar problem is given at https://brainly.com/question/24923631
142% as a fraction or mixed number
Please answer! No links!!!
Picture is included
Answer:
10x+276
Step-by-step explanation:
multiply length times width to get the area
12(5/6x +23)
simplify
10x +276
i hope your test is going well <3
If c = 5, what is the value of 9 + c?
Answer:
The value of 9 + c= 14 because 9 + 5=14
Kevin's earnings vary directly with the number of hours he works. Suppose that he worked 7 hours yesterday and earned $112. How much will he earn today if he works 10 hours?
Answer:
$160 in 10 hours
Step-by-step explanation:
We know that Kevin earns $112 for working 7 hours. To find the answer for 10 hours, we need to find the unit rate.
Divide 112÷7= $16 for every 1 hour he works.
Now, we can use the unit rate to find the amount earned for 10 hours.
16×10= $160
In the figure shown, r || s. If the measure of ∠ 2 = 146°, what is the measure of ∠ 7
Answer:
34°
Step-by-step explanation:
1. First, let's find the measure of ∠1 because since r || s, that means ∠1 = ∠7 because they're both alternate exterior angles. Alternate exterior angles are congruent.
2. (Solving for ∠1)
[tex]146 + x = 180[/tex] [tex]146 + x - 146 = 180 - 146[/tex] [tex]x = 34[/tex]3. Now, since we know ∠1 = ∠7, ∠7 = 34°.
Describe the type of transformation from figure A to figure B.
nahhhh man ain't answering that lololollozz
2x - 6y = 6
6x - 4y = 2
Answer:
x = - 3/7
y = - 8/7
Step-by-step explanation:
(2x - 6y = 6)/2 =
x - 3y = 3
x = 3y + 3
Substitution:
6 (3y +3) - 4y = 2
18y + 18 - 4y = 2
14y = -18+2
y = -16/14
y = - 8/7
Substitution:
x = 3(-8/7)+3
x = -24/7 + 3
x = -3/7
9514 1404 393
Answer:
(x, y) = (-3/7, -1 1/7)
Step-by-step explanation:
We can divide each equation by 2 and subtract the constant to put them in general form.
x -3y -3 = 0
3x -2y -1 = 0
This form facilitates use of the "cross multiplication method" of solution. That method tells us ...
1/d1 = x/d2 = y/d3
where the differences d1, d2, d3 are the differences of cross-products:
d1 = 1(-2) -(3(-3)) = 7
d2 = -3(-1) -(-2(-3)) = -3
d3 = -3(3) -(-1(1)) = -8
Then the solutions are ...
x = d2/d1 = -3/7
y = d3/d1 = -8/7
(x, y) = (-3/7, -8/7)
_____
Additional comment
When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)
a, b, c, ad, e, g, dThe pattern in the cross-differences is relatively easy to see:
d1 = ae -dbd2 = bg -ecd3 = cd -gaThe expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.
the sum of the outer angles is half the sum of inner angles. how many sides does it have?
.............................
plzz help me .....
Answer:
The sum of the outer angles of polygon is twice the sum of the inner angles. (i) How many sides does it have? (ii) What if the sum of outer angles
Evaluate t-7 for t =20
Find the slope intercept form of an equation of the line perpendicular to the graph y = 2/3x - 5/3 and passing through the point (0, 6).
The perpendicular slope is:
State the y value of the y-intercept of the perpendicular line:
The equation of the perpendicular line is:
Answer:
Perpendicular slope: -3/2
Y-value of the y-intercept: 6
Linear equation of the perpendicular line: y = -3/2x + 6
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, which means that multiplying the slopes of both lines will result in -1.
Given the linear equation, y = 2/3x - 5/3, and the point, (0, 6):
Let m1 = slope of line 1
m2 = slope of the other line
Since the slope of y = 2/3x - 5/3 is 2/3, then the other line must have a slope of -3/2 because:
m1 × m2 = -1
[tex](\frac{2}{3}) (-\frac{3}{2}) = -1[/tex]
Therefore, the slope of the other line (m2) = -3/2.
The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The given point has coordinates (0, 6), which means that it is the y-intercept. Its y-coordinate, (b) = 6.
Therefore, given the slope m = -3/2, and the y-value of the y-intercept, b = 6, then the equation of the perpendicular line is: y = -3/2x + 6.
Please mark my answers as the Brainliest if you find my explanations helpful :)
9y''-12y'+4y=0 y1=e^2x/3 by Reduction Order
Answer:
[tex]9 \frac{ {d}^{2}y }{ {dx}^{2} } - 12 \frac{dy}{dx} + 4y = 0) \div 9 \\ \frac{ {d}^{2}y }{ {dx}^{2} } - \frac{4}{3} \frac{dy}{dx} + \frac{4}{9} y = 0 \\ y_{1}(x) = {e}^{ \frac{2}{3} x} \\ p(x) = - \frac{4}{3} \\ y_{2}(x) = y_{1}(x) \int \frac{ {e}^{ - \int \: p(x)dx} }{ {(y_{1}(x))}^{2} } dx \\ = {e}^{ \frac{2}{3} x} \int \frac{ {e}^{ \int \: \frac{4}{3} dx} }{ { ({e}^{ \frac{2}{3} x})}^{2} } dx \\= {e}^{ \frac{2}{3} x} \int \frac{ {e}^{ \frac{4}{3} x} }{ { {e}^{ \frac{4}{3} x}}} dx \\ = {e}^{ \frac{2}{3} x} \int dx \\ \boxed{y_{2}(x) =x{e}^{ \frac{2}{3} x}}[/tex]
Use the graph to determine the y intercept
Answers:
y intercept: 9zeros: -3, -1, 1, 3===============================================
Explanation:
The y intercept is where the curve crosses the y axis. The curve appears to do so just below y = 10, so y = 9 seems like a good estimate. I'm basing this off of the answer choices given. The y intercept always occurs when x = 0.
The zeros, aka roots or x intercepts, are where the curve crosses or touches the x axis. This occurs in four locations: x = -3, x = -1, x = 1 and x = 3. The x intercepts always occur when y = 0.
y = 1/2x^2 – 2x + 1
Does anyone know how to turn this into vertex form?
Answer:
i do just simplyfy it that the easeasttttttt way am always. here to help i will be your persenol assitent
Step-by-step explanation:
likeeee eomg simplify to it yea i will always helpppppp youuu i likeee helppppppppppppppinggg
the length of 6 identical iron rods is 48 unit what will be the total length of 9 such rods
The total length of 9 rods will be 72 units.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The length of 6 identical iron rods is 48 unit.
Now,
Since, the length of 6 identical iron rods is 48 unit.
Hence, the length of 9 identical iron rods = 9 × 48 / 6
= 9 × 8
= 72 units
Thus, The total length of 9 rods will be 72 units.
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3. Let : (0,1] → R be defined by 0 ifr> Let e > 0. Prove that there exists a partition, P. of (0,1) with S(f,P) -s(f,p)<€
Step-by-step explanation:
defined by 0 ifr> Let e > 0. Prove that there exists a partition, P. of (0,1) with ... - did not match any documents.
Suggestions:
is there anyone or does anyone know where i can get help for my statistics exam tomorrow, i didnt study at all and im doomed now?
Answer:
Quizziz (Another educational site) or asking questions about the Exam/Quiz on Brainly.
Step-by-step explanation:
Suppose you write 10 consecutive natural numbers on a board. When one of the numbers is erased, the sum of the remaining numbers is 2015. What number was erased?
*NOTE: If any troll/false responses are added, I won't hesitate to report.*
If (x-3) ²=16, find the positive value of x.
7
Step-by-step explanation:
(x - 3)² = 16
x² - 6x + 9 = 16
x² - 6x + 9 - 16 = 0
x² - 6x - 7 = 0
(x - 7)(x + 1)
x = 7 \/ x = -1
so positive value of x = 7
30 inches to 1 feet simplify
Answer:
30 inches into feet
12 inches = 1 feet
12in = 1ft
24in = 2ft
30 - 24 = 6
The answer is 2 ft and 1/2
or 2 ft and 6 inches
***hope this helps
Step-by-step explanation:
find the mean of, -21,-24,-37,-52,-56
Answer:
-38
Step-by-step explanation:
(-21 + -24 + -37 + -52 + - 56)/5 = -38
absolute value of 3(x-2)=12
What is 3.125 as a
Fraction!
At the Roseville Middle School Spring Festival, Ellen is running the egg-dying station. She needs 5 tablespoons of vinegar for every 2 color tablets she uses. Ellen plans to use 16 color tablets.
How many tablespoons of vinegar will Ellen need?
Answer:
40 table spoons
Step-by-step explanation:
We need to divide 16 by 2 because it says for every 2 color tablets she need 5 table spoons of vinegar
16/2 = 8
8 x 5 = 4
-7.532 devided by (-2.69)
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 20 pounds each. There are 135 boxes in all. If the truck is carrying a total of 4450 pounds in boxes, how many of each type of box is it carrying?
Answer:
45 - big boxes, 200 - small boxes
Step-by-step explanation:
45 x 10 = 450
200 x 20 = 4000
Total = 4,450
Hope it's correct
Please help me on my homework
6 is a whole number so the answer is 6
The sales tax rate for the state of Washington was 9.4%. what is the state sales tax on a $3900 car in Washington? What is the final cost of the car, including tax?
Answer:
3900 x.094 = 366.60
366.6+3900=4266.60
Solve and check the equation.[tex]\frac{x}{10}=\frac{5x}{7} -43[/tex]
Answer:
x = 70
Step-by-step explanation:
Step 1: Simplify both sides of the equations.
[tex]\frac{x}{10} = \frac{5x}{7}-43[/tex] [tex]\frac{1}{10}x=\frac{5}{7}x-43[/tex]Step 2: Subtract 5/7x from both sides.
[tex]\frac{1}{10}x- \frac{5}{7}x = \frac{5}{7}x - 43 - \frac{5}{7}x[/tex] [tex]\frac{-43}{70}x = -43[/tex]Step 3: Multiply both sides by 70/(-43).
[tex]\frac{-43}{70}x * \frac{70}{-43} = -43*\frac{70}{-43}[/tex] [tex]x = 70[/tex]Step 4: Check if solution is correct.
[tex]\frac{(70)}{10}=\frac{5(70)}{7} -43[/tex] [tex]7 = \frac{350}{7} - 43[/tex] [tex]7 = 50 - 43[/tex] [tex]7 = 7[/tex]Therefore, x = 70.
Question 8 (1 point)
A company laid off 80% of its work force. The number of employees after the layoff is 400. How many employees were
there before the layoff?
15,000
Oь
O
Od
2000
3600
2200
Next Page
Once you click Next Page you will not be able to change your answer
Step-by-step explanation:
The number of employees before the layoff = 2000
What is percentage?"It is a number can be expressed as a fraction of 100."
For given question,
Let 'n' be the the number of employees before layoff.
A company laid off 80% of its work force.
The number of employees after the layoff is 400.
The number of employees after the layoff would be,
⇒ n - (80 percent of n) = 400
[tex]\Rightarrow n-(n\times \frac{80}{100} )=400\\\\\Rightarrow n[1-0.8]=400\\\\\Rightarrow n\times 0.2=400\\\\\Rightarrow n=2000[/tex]
Therefore, the number of employees before the layoff = 2000
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