The weight of the component is of length of 12 feet, a width of 13. 5 feet, and a height of 15 feet, and weighs on average 0. 47 pounds per cubic foot is 1142 lbs.
To find the weight of the contents in the container, we need to first find the volume of the container.
The formula for the volume of a right rectangular prism is length x width x height.
So, the volume of the container is:
12 ft x 13.5 ft x 15 ft = 2430 cubic feet
Next, we need to multiply the volume by the weight per cubic foot:
2430 cubic feet x 0.47 lbs/cubic foot = 1141.1 lbs
Rounding to the nearest pound, the weight of the contents in the container is approximately 1142 lbs.
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What is the value of B? Bº 58° 61°
Answer:
61 degrees
Step-by-step explanation:
Triangle interior measures add up to 180 degrees.
61 + 58 + x = 180
119 + x = 180
x = 61
hope this helps :) !!!
On a coordinate plane, a line segment has endpoints P(6,2) and Q(3. 8). 9. Point M lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3. What are the coordinates of point M?
The coordinates of point M come out to be 4.8, 4.4
This case is solved by using the section formula which states that
The coordinate of point P that divides the line segment AB in the ratio of m:n where the coordinate of A is [tex]x_1,y_1[/tex] and the B is [tex]x_2,y_2[/tex] is described as
[tex]\frac{mx_2+nx_1}{m+n}[/tex],[tex]\frac{my_2+ny_1}{m+n}[/tex]
The line to be divided = PQ
Coordinates of P = (6,2)
Coordinates of Q = (3,8)
Ratio = 2:3
Thus, the coordinates of M = [tex]\frac{2*3+3*6}{2+3}[/tex],[tex]\frac{8*2+2*3}{2+3}[/tex]
= 24/5 , 22/5
= 4.8, 4.4
Point M with coordinates (4.8,4.4) lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3
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Help again with math (I'm on 37/64 and I'm about to cry)
Answer:
1,215,000 cubic centimeters
Step-by-step explanation:
1. Find the volume of the cylinder
v = π r (squared) x h
v = 3.14 x 50 (squared) x 100
v = 3.14 x 2,500 x 100
v = 3.14 x 250,00
v = 785,000 cubic centimeters
2. Find the volume of the rectangular prism
v = l x w x h
v = 100 x 200 x 100
v = 2,000,000 cubic centimeters
3. Subtract
2,000,000 - 785,000 = 1,215,000 cubic centimeters
A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be green?
The probability that both marbles drawn will be green is 16.4%.
The probability of drawing a green marble on the first draw is 8/19.
Since there are no replacements, the probability of drawing another green marble on the second draw is 7/18 (since there are now only 18 marbles left in the bag, including 7 green marbles).
Therefore, the probability of drawing two green marbles in a row is:
(8/19) × (7/18)
= 56/342
To convert this to a percentage, we can divide 56 by 342 and multiply by 100:
(56/342) × 100 = 16.37%
Therefore, the probability that both marbles drawn will be green is 16.4%.
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researchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adults diagnosed with acute sinusitis to one of two groups: treatment or control. study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. the placebo consisted of symptomatic treatments such as acetaminophen, nasal decongestants, etc. at the end of the 10-day period, patients were asked if they experienced improvement in symptoms. the distribution of responses is summarized below.3 self-reported improvement in symptoms yes no total treatment 66 19 85 group control 65 16 81 total 131 35 166 (a) what percent of patients in the treatment group experienced improvement in symptoms? (b) what percent experienced improvement in symptoms in the control group? (c) in which group did a higher percentage of patients experience improvement in symptoms? (d) your findings so far might suggest a real difference in effectiveness of antibiotic and placebo treatments for improving symptoms of sinusitis. however, this is not the only possible conclusion that can be drawn based on your findings so far. what is one other possible explanation for the observed difference between the percentages of patients in the antibiotic and placebo treatment groups that experience improvement in symptoms of sinusitis?
77.6% of patients in the antibiotic treatment group experienced improvement in symptoms, while 80.2% of patients in the placebo group experienced improvement. The control group had a slightly higher percentage of improvement. The placebo effect could have contributed to the difference in improvement rates.
The percent of patients in the treatment group who experienced improvement in symptoms is 77.6% ((66/85) x 100). The percent of patients in the control group who experienced improvement in symptoms is 80.2% ((65/81) x 100).
The control group had a higher percentage of patients experience improvement in symptoms (80.2%) compared to the treatment group (77.6%).
One possible explanation for the observed difference between the percentages of patients in the antibiotic and placebo treatment groups that experience improvement in symptoms of sinusitis is that the placebo effect may have played a role.
The placebo effect is a phenomenon in which patients who receive a treatment that is not expected to have a therapeutic effect experience an improvement in their symptoms due to their belief in the treatment.
Therefore, the symptomatic treatments provided in the placebo group may have led to an improvement in symptoms, even though they did not receive an antibiotic.
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Let R(x). C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, tomi the production and sale of x items. I R(%) = 6x and C(X) = 0.001x^2 + 1 8x + 40.
find each of the following
a) P(x)
b) R(200). C(200), and P(200)
c) R'(. C't and P'(x)
d) R' (200). C'(200), and P' (200)
a) P(x) = R(x) - C(x) = 6x - (0.001x^2 + 18x + 40) = -0.001x^2 - 12x - 40
b) R(200) = 6(200) = 1200
C(200) = 0.001(200)^2 + 18(200) + 40 = 4000
P(200) = R(200) - C(200) = 1200 - 4000 = -2800
c) R'(x) = 6
C'(x) = 0.002x + 18
P'(x) = R'(x) - C'(x) = 6 - (0.002x + 18) = -0.002x - 12
d) R'(200) = 6
C'(200) = 0.002(200) + 18 = 18.4
P'(200) = -0.002(200) - 12 = -12.4
Here are the answers to each part:
a) P(x) is the profit function, which is calculated as the difference between the revenue function and the cost function: P(x) = R(x) - C(x). In this case, P(x) = 6x - (0.001x^2 + 18x + 40).
b) To find R(200), C(200), and P(200), plug x = 200 into each function:
R(200) = 6(200) = 1200
C(200) = 0.001(200^2) + 18(200) + 40 = 7600
P(200) = 1200 - 7600 = -6400
c) To find R'(x), C'(x), and P'(x), we need to find the derivative of each function with respect to x:
R'(x) = d(6x)/dx = 6
C'(x) = d(0.001x^2 + 18x + 40)/dx = 0.002x + 18
P'(x) = R'(x) - C'(x) = 6 - (0.002x + 18)
d) To find R'(200), C'(200), and P'(200), plug x = 200 into each derivative function:
R'(200) = 6
C'(200) = 0.002(200) + 18 = 18.4
P'(200) = 6 - 18.4 = -12.4
I hope this helps! Let me know if you have any further questions.
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Select the correct answer.
given a prism with a right triangle base and the dimensions h = x + 1, b = x, l = x + 7, and what is a correct expression for the volume of the prism?
The correct expression for the volume of the prism is:
V = (1/2)(x)(x + 7)(x + 1)
This expression is derived from the formula for the volume of a prism, which is V = Bh, where B is the area of the base and h is the height of the prism. For a right triangle base, the area is equal to half the product of the base and height, or (1/2)(b)(l). Substituting the given values, we get:
B = (1/2)(x)(x + 7)
h = x + 1
Multiplying B and h together and simplifying, we get:
V = (1/2)(x)(x + 7)(x + 1)
Therefore, this is the correct expression for the volume of the given prism.
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The greenery landscaping company puts in an order for 2 pine trees and 5 hydrangea bushes for a neighborhood project. the order costs $150. they put in a second order for 3 pine trees and 4 hydrangea bushes that cost $144.50.
2(2.5) + 5(23) = 150
3(2.5) + 4(23) = 144.5
Both equations are satisfied, so our solution is correct.
The greenery landscaping company orders how many trees and bushes for the neighborhood?To solve the problem, let's first assign some variables. Let x be the cost of one pine tree and y be the cost of one hydrangea bush. We can then use these variables to set up a system of equations:
2x + 5y = 150 (equation 1)
3x + 4y = 144.5 (equation 2)
We can solve this system of equations using various methods. Here, we will use the substitution method.
From equation 1, we can solve for x in terms of y:
2x = 150 - 5y
x = (150 - 5y)/2
We can then substitute this expression for x into equation 2:
3((150 - 5y)/2) + 4y = 144.5
Multiplying both sides by 2 to eliminate the fraction:
3(150 - 5y) + 8y = 289
Expanding and simplifying:
450 - 15y + 8y = 289
-7y = -161
y = 23
We can now substitute this value for y into either equation 1 or 2 to solve for x:
2x + 5(23) = 150
2x = 5
x = 2.5
Therefore, one pine tree costs $2.50 and one hydrangea bush costs $23.
To check our work, we can substitute these values into both equations:
2(2.5) + 5(23) = 150
3(2.5) + 4(23) = 144.5
Both equations are satisfied, so our solution is correct.
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Ailani draws a map of her local town. she places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. the center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0. 5 miles. if the positive x-axis represents east and the positive y-axis represents north, which equation represents the lake? (x 19)2 (y – 3)2 = 0. 5 (x – 19)2 (y 3)2 = 0. 5 (x 19)2 (y – 3)2 = 0. 25 (x – 19)2 (y 3)2 = 0. 25.
The equation is (x^2 + y^2 - 38x + 6y = -369).
The center of the lake is 19 miles east and 3 miles south of the town hall, which means the coordinates of the center are (19,-3). The radius of the lake is 0.5 miles.
Using the standard equation of a circle, we have:
(x - h)^2 + (y - k)^2 = r^2
where (h,k) is the center of the circle and r is the radius.
Substituting the given values, we get: (x - 19)^2 + (y + 3)^2 = 0.5^2
Expanding the left side, we get: x^2 - 38x + 361 + y^2 + 6y + 9 = 0.25
Simplifying and rearranging terms, we get:
x^2 + y^2 - 38x + 6y + 369.25 = 0.25
Subtracting 369 from both sides, we get:
x^2 + y^2 - 38x + 6y = -369
Therefore, the equation that represents the lake on the map is:
(x - 19)^2 + (y + 3)^2 = 0.5^2, which can be simplified to (x^2 + y^2 - 38x + 6y = -369).
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O is the center of the regular hexagon below. Find its area. Round to the nearest tenth if necessary
The area of the regular hexagon is 509.2 square units (to the nearest tenth).
The formula for the area of a regular polygon is:
[tex]\boxed{\text{Area}=\frac{\text{r}^2\text{n sin}\huge \text(\frac{360^\circ}{\text{n}}\huge \text) }{y} }[/tex]
where:
r is the radius (the distance from the center to a vertex).n is the number of sides.From inspection of the given regular polygon:
r = 14 unitsn = 6Substitute the values into the formula and solve for area:
[tex]\text{Area}=\dfrac{14^2\times6\times\text{sin}\huge \text(\frac{360^\circ}{6}\huge \text) }{2}[/tex]
[tex]=\dfrac{196\times6\times\text{sin} (60^\circ)}{2}[/tex]
[tex]=\dfrac{1176\times\frac{\sqrt{3} }{2} }{2}[/tex]
[tex]=\dfrac{588\sqrt{3} }{2}[/tex]
[tex]=294\sqrt{3}[/tex]
[tex]=509.2 \ \text{square units (nearest tenth)}[/tex]
Therefore, the area of the regular hexagon is 509.2 square units (to the nearest tenth).
Find the inverse for each relation: 4 points each
1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}
2. {(4,2),(5,1),(6,0),(7,‐1)}
Find an equation for the inverse for each of the following relations.
3. Y=-8x+3
4. Y=2/3x-5
5. Y=1/2x+10
6. Y=(x-3)^2
Verify that f and g are inverse functions.
7. F(x)=5x+2;g(x)=(x-2)/5
8. F(x)=1/2x-7;g(x)=2x+14
The inverse for each relation:
1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)} - {(-2, 1), (3, 2), (-3, 3), (2, 4)}
2. {(4,2),(5,1),(6,0),(7,‐1)} - {(2, 4), (1, 5), (0, 6), (-1, 7)}
3. Inverse equation: y=(-1/8)x+3/8
4. Inverse equation: y=3/2x+15/2
5. Inverse equation: y=2x-20
6. Inverse equation: y=[tex]x^{(1/2)}+3[/tex]
7. Since fog(x) = gof(x) = x, f and g are inverse functions.
8. Since fog(x) = gof(x) = x, f and g are inverse functions.
1. To find the inverse of the relation, we need to swap the positions of x and y for each point and then solve for y.
{(1, -2), (2, 3), (3, -3), (4, 2)}
Inverse: {(-2, 1), (3, 2), (-3, 3), (2, 4)}
2. Again, we swap x and y and solve for y.
{(4, 2), (5, 1), (6, 0), (7, -1)}
Inverse: {(2, 4), (1, 5), (0, 6), (-1, 7)}
3. To find the inverse equation for y=-8x+3, we swap x and y and solve for y.
x=-8y+3
x-3=-8y
y=(x-3)/-8
Inverse equation: y=(-1/8)x+3/8
4. To find the inverse equation for y=2/3x-5, we swap x and y and solve for y.
x=2/3y-5
x+5=2/3y
y=3/2(x+5)
Inverse equation: y=3/2x+15/2
5. To find the inverse equation for y=1/2x+10, we swap x and y and solve for y.
x=1/2y+10
x-10=1/2y
y=2(x-10)
Inverse equation: y=2x-20
6. To find the inverse equation for y=(x-3)², we swap x and y and solve for y.
x=(y-3)²
[tex]x^{(1/2)}=y-3[/tex]
[tex]y=x^{(1/2)}+3[/tex]
Inverse equation: [tex]y=x^{(1/2)}+3[/tex]
7. To verify that f(x)=5x+2 and g(x)=(x-2)/5 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.
fog(x) = f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x
gof(x) = g(f(x)) = g(5x+2) = ((5x+2)-2)/5 = x/5
Since fog(x) = gof(x) = x, f and g are inverse functions.
8. To verify that f(x)=1/2x-7 and g(x)=2x+14 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.
fog(x) = f(g(x)) = f(2x+14) = 1/2(2x+14) - 7 = x
gof(x) = g(f(x)) = g(1/2x-7) = 2(1/2x-7) + 14 = x
Since fog(x) = gof(x) = x, f and g are inverse functions.
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Shop
Hunter assumed he would only get 64
problems correct on his test, but he
actually got 78 correct. What was his
percent error?
Hint: Percent error =
Prediction - Actual
Actual
x 100
Round to the nearest percent.
[? ]%
Enter
Hunter assumed he would only get 64 problems correct on his test, but he actually got 78 correct, So his percent error is 18%.
To calculate Hunter's percent error, we'll use the given formula:
Percent error = ((Prediction - Actual) / Actual) x 100
Prediction = 64 (the number of problems Hunter assumed he would get correct)
Actual = 78 (the number of problems he actually got correct)
Now, plug in the values:
Percent error = ((64 - 78) / 78) x 100
Percent error = (-14 / 78) x 100
Percent error ≈ -17.95%
Since percent error is typically expressed as a positive value, we can round to the nearest percent and report it as:
Percent error ≈ 18%
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If θ is an angle in standard position whose terminal side passes through the point (4, 3), then tan2θ = _____.
3/2
24/7
7/24
21/32
To find the value of tan(θ), we first need to calculate the values of sine and cosine for the given point (4, 3) terminal side. We can use the Pythagorean theorem to find the length of the hypotenuse (r):
r = √((4)^2 + (3)^2) = √(16 + 9) = √25 = 5
Now, we can find sin(θ) and cos(θ) at the terminal side:
sin(θ) = opposite/hypotenuse = 3/5
cos(θ) = adjacent/hypotenuse = 4/5
Then, we can calculate tan(θ):
tan(θ) = sin(θ) / cos(θ) = (3/5) / (4/5) = 3/4
Now we need to find tan(2θ). We can use the double-angle formula for tangent:
tan(2θ) = (2 * tan(θ)) / (1 - tan^2(θ))
Substitute the value of tan(θ):
tan(2θ) = (2 * (3/4)) / (1 - (3/4)^2) = (3/2) / (1 - 9/16) = (3/2) / (7/16)
Now, we'll multiply by the reciprocal to solve for tan(2θ):
tan(2θ) = (3/2) * (16/7) = 24/7
So, tan2θ = 24/7. Your answer is: 24/7
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Please hurry I need it ASAP
Identify the random variable in each distribution, and classify it as
discrete or continuous. Explain your reasoning.
1) The number of hits for the players of a baseball team.
2) The distances traveled by the tee shots in a golf
The random variable in the first situation is the number of hits for the players of a baseball team and in the second situation is the distance traveled by the tee shots in a golf game.
1) The random variable in this distribution is the number of hits for the players of a baseball team. This is a discrete random variable because hits are counted as whole numbers and cannot take on non-integer values.
2) The random variable in this distribution is the distance traveled by the tee shots in a golf game. This is a continuous random variable because the distances traveled can take on any value within a certain range, including non-integer values. The exact distance traveled by a tee shot can be measured to any degree of precision, and there are infinitely many possible distances within the range of possible outcomes. Therefore, it is a continuous random variable.
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Factorise the following expressions
a) 9m^4-9m^3
b) 25x^9y^10-35x^7y^5
c) (x-1)(x-1)-3(x-1)
Answer:
Step-by-step explanation:
Rules:
Take out the GCF (greatest common factor)
a) [tex]9m^{4} -9m^{3}[/tex] >take out GCF, what both terms can be divided by
=9m³(m-1) >when taking out GCF, divide both terms by GCF
b) [tex]25x^{9}y^{10}-35x^{7}y^{5}[/tex] >GCF is [tex]=5x^{7}y^{5}[/tex]
[tex]=5x^{7}y^{5}(5x^{2} y^{5}-7)[/tex]
c) (x-1)(x-1)-3(x-1) >GCF is (x-1)
=(x-1) [(x-1) - 3] >within the bracket you can combine like terms
=(x-1) (x-4)
Step-by-step explanation:
A) 9m^4 - 9m^3 = 9m^3 (m - 1)
As for the number, you already took 9 out because it's common for both. As for the m, m^4 is the same as m×m×m×m. So the common between both is m×m×m = m^3.
B) 25x^9y^10 - 35x^7y^5 umm are you sure it's well written? How do you have a power in a power?
C) (x-1)(x-1)-3(x-1) = (x²-1x-1x+1) - (3x-3)
= x² - 2x + 1 - 3x + 3
= x² - 5x + 4
Mathematics help nedd
To solve the equation, we need to first simplify both sides:
(4x - 6)/5 + 1 = (x + 1)/5 - 2/5
Multiplying both sides by 5 to eliminate the denominator:
4x - 6 + 5 = x + 1 - 2
Simplifying further:
4x - 1 = x - 1
Subtracting x from both sides:
3x - 1 = -1
Adding 1 to both sides:
3x = 0
Dividing both sides by 3:
x = 0
Therefore, the solution to the equation is x = 0.
Answer: x=28
Step-by-step explanation:
Given: <A=68
Find: x
Reasoning:
<B = 2x+x
<B= 3x
<C=x they say the sides across from <C is same as other side so the
angles are the same
Solution:
All angles of a triangle =180
<A + <B + <C =180 >substitute
68 + 3x + x =180 > combine like terms
68 + 4x = 180 > subtract 68 from both sides
4x=112 >divide both sides by 4
x=28
Maria claims that any fraction located between 1/5 and 1/7 on a number line must have a denominator of 6.
Enter a fraction to show Maria's claim is incorrect.
To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.
One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.
To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:
1/5 = 7/35
1/7 = 5/35
Now we need to find a fraction between 7/35 and 5/35. One such fraction is:
6/35
This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.
Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:
1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35
As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.
Answer:
13/70
Step-by-step explanation:
In order to show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line, but does not have a denominator of 6.
Let's find the common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70 and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.
equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction between 10/70 and 14 /70. Unknown fraction is:
13/70
This fraction is located between 10/70 and 14/70 on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.
Shari bought 3 breath mints and received $2. 76 change. Jamal bought 5 breath mints
and received $1. 20 change. If Shari and Jamal had the same amount of money, how
much does one breath mint cost?
A. Each breath mint costs $0. 28.
B. Each breath mint costs $0. 49.
c. Each breath mint costs $0. 78.
D. Each breath mint costs $1. 98.
Each breath mint costs $0.78. The correct answer is C.
To solve this problem, we can use the concept of a system of linear equations. Let x be the cost of one breath mint and y be the total amount of money Shari and Jamal had.
We know that Shari bought 3 breath mints and received $2.76 change, so her equation will be:
3x + 2.76 = y
Jamal bought 5 breath mints and received $1.20 change, so his equation will be:
5x + 1.20 = y
Now we have a system of two equations with two variables:
3x + 2.76 = y
5x + 1.20 = y
We can solve for x by setting the two equations equal to each other:
3x + 2.76 = 5x + 1.20
Now, solve for x:
2x = 1.56
x = 0.78
So, each breath mint costs $0.78. The correct answer is C.
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The time it takes Alice to walk to the bus stop from her home is normally distributed with mean 13 minutes and variance 4 minutes squared. The waiting time for the bus to arrive is normally distributed with mean 5 minutes and standard deviation 2 minutes. Her bus journey to the bus loop is a normal variable with mean 24 and standard deviation 5 minutes. The time it take Alice to walk from the bus loop to the lecture theatre to attend stats class is normally distributed with mean 18 minutes and variance 4 minutes. The total time taken for Alice to travel from her home to her STAT 251 lecture is Normally distributed.
Part a) What is the mean travel time (in minutes)?
Part b) What is the standard deviation of Alice's travel time (in minutes, to 2 decimal places)?
Part c) The STAT 251 class starts at 8 am sharp. Alice leaves home at 7 am. What is the probability (to 2 decimal places) that Alice will not be late for her class?
The mean travel time is 60 minutes, the standard deviation is approximately 6.08 minutes, and the probability that Alice will not be late for her class is 0.50 or 50%.
How to find the mean time interval?To find the mean travel time, we need to add up the mean times for each stage of Alice's journey. Let's calculate it step by step:
Step 1: Alice's walking time from home to the bus stop:
Mean walking time = 13 minutes
Step 2: Waiting time for the bus to arrive:
Mean waiting time = 5 minutes
Step 3: Bus journey time from the bus loop:
Mean bus journey time = 24 minutes
Step 4: Walking time from the bus loop to the lecture theatre:
Mean walking time = 18 minutes
Now, let's calculate the total mean travel time:
Mean travel time = Mean walking time + Mean waiting time + Mean bus journey time + Mean walking time
= 13 + 5 + 24 + 18
= 60 minutes
So, the mean travel time is 60 minutes.
How to find the standard deviation?To find the standard deviation of Alice's travel time, we need to calculate the variance for each stage and then sum them up. Finally, we take the square root to get the standard deviation. Let's calculate it step by step:
Step 1: Alice's walking time from home to the bus stop:
The variance of walking time = 4 minutes squared
Step 2: Waiting time for the bus to arrive:
The standard deviation of waiting time = 2 minutes
Step 3: Bus journey time from the bus loop:
The standard deviation of bus journey time = 5 minutes
Step 4: Walking time from the bus loop to the lecture theatre:
The variance of walking time = 4 minutes squared
Now, let's calculate the total variance of travel time:
Variance of travel time = Variance of walking time + Variance of waiting time + Variance of bus journey time + Variance of walking time
= 4 + 4 + 25 + 4
= 37 minutes squared
Finally, the standard deviation of travel time is the square root of the variance:
The standard deviation of travel time = [tex]\sqrt(37)[/tex]
≈ 6.08 minutes (rounded to 2 decimal places)
So, the standard deviation of Alice's travel time is approximately 6.08 minutes.
How to find the probability?To find the probability that Alice will not be late for her class, we need to calculate the z-score for the desired arrival time and then find the corresponding probability from the standard normal distribution table. Let's calculate it step by step:
Step 1: Calculate the total travel time from home to the lecture theatre:
Total travel time = Mean travel time = 60 minutes
Step 2: Calculate the difference between the desired arrival time and the total travel time:
Time difference = 8 am - 7 am = 1 hour = 60 minutes
Step 3: Calculate the z-score using the formula:
z = (Time difference - Mean travel time) / Standard deviation of travel time
z = [tex]\frac{(60 - 60) }{ 6.08}[/tex]
z = 0
Step 4: Find the probability corresponding to the z-score from the standard normal distribution table.
Since the z-score is 0, the probability is 0.50 (or 50%).
Therefore, the probability (to 2 decimal places) that Alice will not be late for her class is 0.50 or 50%.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
what percentage is equivalent to 96/160
Answer:
60%
Step-by-step explanation:
Take 96 and divide it by 160.
(easier if done on a calculator.)
For example: Find A/B as a percentage: take "A" and divide it by "B"
The graph below shows segment FG and point P what is the first coordinate of point M
Note that the first coordinate of M is -1. (Option D)
Why is this so?
Given :- coordinates of F = (-4,-2) = (x1,y1)
coordinates of G = (2,-2) = (x2,y2)
coordinates of P = (2,-8) = (x3,y3)
and distance between point M and P is half of the distance between FG
To find :- first coordinate of point M
solution :- let the coordinate of M be (x4,y4)
as we know that distance between of the opposite point of parallel line segments are equal
so, second coordinate of M = -8
now by distance formula
FG = √(x2-x1)² + (y2-y1²)
= √[2-(-4)]² + [-2-(-2)]²
= √(2+4)² + (2-2)²
= √(6)² + (0)²
=√36
F G = 6
so, distance between point M and P = 1/2 × F G
= 1/2 × 6
= 3units
again, by distance formula
MP = √(x3-x⁴)² + (y3-y4)²
3 = √(2-x⁴)² + [-8-(-8)]²
squaring on both side
(3)² = (√(2-x⁴)² + [-8-(-8)]²)²
9 = (2-x⁴)² + [-8-(-8)]²
9 = (2-x⁴)²+(0)²
9 = (2-x⁴)²
√9 = 2-x⁴
3 = 2-x⁴
x⁴ = 2-3
x⁴ = -1
Hence the first coordinate of M is -1
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Point M is located in the third quadrant.
The distance between point M and point P is half the distance between point F and point G.
• Segment MP is parallel to segment FG. What is the first coordinate of point M?
The average depth of the Arctic Ocean is approximately 1050 meters, and the average depth of the Indian Ocean is approximately 3900 meters. To the nearest tenth, how many times as great is the average depth of the Indian Ocean compared to the average depth of the Arctic Ocean?A. 3. 7B. 3. 1C. 2. 8D. 2. 2
The average depth of the Indian Ocean is 3.7 time greater than that of Arctic Ocean. Therefore, the correct option is A.
To find how many times as great the average depth of the Indian Ocean is compared to the Arctic Ocean, we need to divide the average depth of the Indian Ocean by the average depth of the Arctic Ocean.
1: Divide the average depth of the Indian Ocean by the average depth of the Arctic Ocean:
3900 meters (Indian Ocean) / 1050 meters (Arctic Ocean) = 3.7142857
2: Round the result to the nearest tenth:
3.7
So, the average depth of the Indian Ocean is approximately 3.7 times greater than the average depth of the Arctic Ocean. The correct answer is A. 3.7.
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Ofra tried to solve an equation.
3x = 4.5
3x 4.5
3
3
=
Setting up
x = 1.5 Calculating
Where did Ofra make her first mistake?
Choose 1 answer:
Setting up
B Calculating
Ofra correctly solved the equation.
If Ofra tried to solve an equation 3x = 4.5, The statement "Ofra correctly solved the equation" is correct. So, correct option is C.
We can see this by substituting x = 1.5 into the original equation 3x = 4.5:
3(1.5) = 4.5
Simplifying the left-hand side, we get:
4.5 = 4.5
This is a true statement, which means that x = 1.5 is a valid solution to the equation 3x = 4.5.
Therefore, Ofra did not make any mistakes in solving the equation. She correctly set up the equation 3x = 4.5 by multiplying both sides by 3 to isolate x, and then calculated the value of x to be 1.5, which is the correct solution.
Option (c) is the correct answer.
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Complete question is:
Ofra tried to solve an equation.
3x = 4.5, Setting up x = 1.5 Calculating
Where did Ofra make her first mistake?
Choose 1 answer:
a) Setting up
b) Calculating
c) Ofra correctly solved the equation.
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of $25. However, movie tickets are discounted for members at $6. 00 per ticket, instead of the regular $9. 00 per ticket. Let m equal the number of movie tickets Makayla purchases in a year. Write a function to
model the amount of money Makayla spent going to the movies during the year she joined the club
The amount of money Makayla spent on the movies during the year she joined the club will be represented by (m) = 6x + 25.
We have to represent the given situation with a function. The club charges a registration fee of 55 dollars and the discount value for the club members is 6 dollars per ticket. Here, we will use x to represent the number of movie tickets.
The domain is represented by m and so it should be a whole number. It cannot be an integer as integers include negative numbers too. It cannot be a rational number because it cannot include decimals and as we know we can't buy part of a ticket. It can also not be a real number because it can't include irrational numbers.
So, our function will be (m) = 6x + 25.
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Determine the specified confidence interval. An organization advocating for healthcare reform has estimated the average cost of providing healthcare for a senior citizen receiving Medicare to be about $13,000 per year. The article also stated that, with 90% confidence, the margin or error for the estimate is $1,000. Determine the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare
the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is [$12,000, $14,000].
The estimated average cost of providing healthcare for a senior citizen receiving Medicare is $13,000 per year, and the margin of error for this estimate is $1,000 with a 90% confidence level.
To find the confidence interval, we need to add and subtract the margin of error from the estimated mean.
Lower Limit = Estimated Mean - Margin of Error
Lower Limit = 13,000 - 1,000
Lower Limit = 12,000
Upper Limit = Estimated Mean + Margin of Error
Upper Limit = 13,000 + 1,000
Upper Limit = 14,000
Therefore, the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is [$12,000, $14,000]. This means we are 90% confident that the true mean cost of providing healthcare for a senior citizen receiving Medicare is between $12,000 and $14,000 per year.
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A bracelet is now reduced to £420.this is 70% of the original price. what is the original price?
Answer:
.70p = £420, so p = £600
The original price of the bracelet is £600.
The original price of the bracelet was £600.
To find the original price of the bracelet, we need to use the information that the current price is 70% of the original price. We can use algebra to solve for the original price:
Let X be the original price of the bracelet.
70% of X is equal to £420.
We can write this as:
0.7X = £420
To solve for X, we can divide both sides of the equation by 0.7:
X = £420 ÷ 0.7
Evaluating the right-hand side gives us:
X = £600
Therefore, the original price of the bracelet was £600.
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"Please let me know if this is convergent or divergent and what
test (comparison, integral, limit, p-series, divergence test) was
used to get the answer. Please show work"
k = 1
Sum= 5^(K-1)2^(K+1)/K^k
As k goes to infinity, the expression (k / (k+1)) approaches 1. Therefore, the limit becomes: lim (k -> infinity) 10 * (1^k) = 10
Since the limit is greater than 1, the Ratio Test indicates that the series is divergent.
To determine if the given series is convergent or divergent, we can use the Ratio Test. The series is given by:
Σ(5^(k-1) * 2^(k+1) / k^k) from k=1 to infinity
First, let's find the ratio of consecutive terms, a_(k+1)/a_k:
a_(k+1)/a_k = [(5^k * 2^(k+2)) / (k+1)^(k+1)] * [k^k / (5^(k-1) * 2^(k+1))]
Now, let's simplify the expression:
a_(k+1)/a_k = (5 * 2) * (k^k / (k+1)^(k+1))
Now, let's take the limit as k goes to infinity:
lim (k -> infinity) a_(k+1)/a_k = lim (k -> infinity) 10 * (k^k / (k+1)^(k+1))
We can rewrite the expression as:
lim (k -> infinity) 10 * ((k / (k+1))^k)
As k goes to infinity, the expression (k / (k+1)) approaches 1. Therefore, the limit becomes:
lim (k -> infinity) 10 * (1^k) = 10
Since the limit is greater than 1, the Ratio Test indicates that the series is divergent.
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Find the measure of arc AD
90 + 63 = 153
this is because the pink square means that degree is 90°