When Wyatt commutes to work, the amount of time it takes him to arrive is normally
distributed with a mean of 45 minutes and a standard deviation of 3 minutes. Using
the empirical rule, what percentage of his commrtes will be between 36 and 54
minutes?
Answers
Answer:
Step-by-step explanation:
Using the Empirical Rule, it is found that 99.7% of his commutes will be between 36 and 54 minutes.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, considering a mean of 45 minutes and a standard deviation of 3 minutes, we have that:
36 = 45- 3 x 3
54 = 45 + 3 x 3
Within 3 standard deviations of the mean, hence, 99.7% of his commutes will be between 36 and 54 minutes.
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Related Questions
40 POINTSSS!!!!
The function g(x)=−x2+14x+39 is at a minimum when x=7.
True or False
Answers
The statement "the function g(x) = - x² + 14x + 39 is at a minimum when x = 7" is false.
What is a expression? What is a mathematical equation? What is Equation modelling ?A mathematical function is made up of terms (constants and variables) separated by mathematical operators having a dependent and independent variable. A mathematical equation is used to equate two expressions. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which y exists.
We have the following function -
g(x) = - x² + 14x + 39
We will plot the graph of the function to find the minimum value. We can see the graph is maximum when x = 7. Hence, the statement is false.
Therefore, the statement "the function g(x) = - x² + 14x + 39 is at a minimum when x = 7" is false.
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Use a protractor to draw a quadrilateral so that three of its four sides measure 3 centimeters each. The angles between these sides have measures of 80° and 85°. What is the length of the fourth side? 1. 8 cm 2. 2 cm 2. 5 cm 3 cm.
Answers
The length of the fourth side of the quadrilateral is 2.2 cm. Then the correct option is B.
What is a quadrilateral?It is a polygon that has four sides. The sum of the internal angle is 360 degrees.
A quadrilateral so that three of its four sides measure 3 centimeters each.
The angles between these sides have measures of 80° and 85°.
The following procedures are to draw the diagram will be
Make a line of 3 cm.Draw the lines of 3 cm each from the terminal points of the first line at 80° and 85°.join the terminal point of the second and third lines.The required quadrilateral is formed.The length of the fourth side of the quadrilateral is 2.2 cm
Thus, the correct option is B.
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Swimming Pool On a certain hot summer's day, 140 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The
receipts for admission totaled $214.00. How many children and how many adults swam at the public pool that day?
Answers
Answer:
88 (children) and 52 (adults).
Step-by-step explanation:
1. if the number of the children is 'x' and the adults is 'y', then total number 140 people is x+y=140, - this is the first equation;
2. if the earned money is 214 USD and 1.25 USD for child and 2 USD for adult, then this means: 1.25x+2y=214, - this is the second equation;
3. using two equations above it is possible to make up and solve the next system of two equations:
\(\left \{ {{x+y=140} \atop {1.25x+2y=214}} \right. \ => \ \left \{ {{y=52} \atop {x=88}} \right.\)
4. Finally, the answers is:
children ('x') - 88; adults ('y') - 52.
Lee recorded the number of push ups he did each each day for six days his data are listed below 68,41,58,75,48,40 what are the mean and the median of lees data set
Hleppppp please
Answers
Answer:
mean : 55; median : 53
Step-by-step explanation:
Given inputs: 68, 41, 58, 75, 48, 40
total numbers of input = 6
total value = 68 + 41 + 58 + 75 + 48 + 40 = 330
Mean → total value / total numbers of input = 330 / 6
= 55
arrange in increasing order: 40, 41, 48, 58, 68, 75
we can see that the median is between, 48 and 58,
so median → (48+58)/2 → 53
Match each expression with an equivalent radical form. One of the radical form
options will not have a match.
3 7/2
7 1/2
3 2/7
7 2/3
1. √7
2. √37
3. √3²
4. 3/72
Answers
Answer:
3^(7/2) = 2.; 7^(1/2) = 1,; 3^(2/7) = 3.; 7^(2/3) = 4.
Step-by-step explanation:
To convert the expressions to their radical form, we remember this formula:
\(b^\frac{exponent}{index}=\sqrt[index]{b^e^x^p^o^n^e^n^t}\)
Thus, for 3^(7/2), 7 is the exponent and 2 is the index, which gives us
\(\sqrt[]{3^7}\).
For 7^(1/2), 1 is the exponent and 2 is the index, which gives us
\(\sqrt{7}\).
For 3^(2/7), 2 is the exponent and 7 is the index, which gives us
\(\sqrt[7]{3^2}\).
For 7^(2/3), 2 is the exponent and 3 is the index, which gives us
\(\sqrt[3]{7^2}\)
To make tea, use 1
6
6
1
teaspoon of tea per ounce of water plus a teaspoon for the pot. Use the inverse to find the number of ounces of water needed if 7 teaspoons of tea are used.
Answers
Using the given ratio, we can set up a proportion to find the number of ounces of water needed if 7 teaspoons of tea are used. Let x be the number of ounces of water needed:
1 teaspoon / 6 ounces = 7 teaspoons / x + 1 teaspoon
Multiplying both sides by the denominator on the right side gives:
x + 1 = 7 teaspoons * 6 ounces / 1 teaspoon
Simplifying the right side gives:
x + 1 = 42 ounces
Subtracting 1 from both sides gives:
x = 41 ounces
Therefore, 41 ounces of water are needed if 7 teaspoons of tea are used.
In summary, to find the number of ounces of water needed if 7 teaspoons of tea are used, we can use the inverse of the given ratio and set up a proportion to solve for x. The resulting proportion shows that 41 ounces of water are needed to make the tea.
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Find the surface area of the polyhedra
pls!! show how you got the surface area
Answers
Answer:
164 cm.
Step-by-step explanation:
First, I solved for the bottom and top. 10 times 3 is 30. Then I doubled it because it's the same answer for the bottom and top. I got 60.
Next I solved for the sides. 4 times 3 is 12. Then I doubled it because it's the same answer for both sides. I got 24.
Lastly I solved for the front and back. 10 times 4 is 40. Then I doubled it because it's the same answer for both the front and back. I got 80.
After all this, I added everything together. 60 + 24 + 80 = 164.
Sorry, I'm not the best at explaining things.
What is the slope of the line on the graph below?
2
-2 11
1
2
3
4
5
E
7
8
x
2.
L3
4
50
46
Answers
Find the maximum and minimum values of the function f(x, y) = exy subject to x^3 + y^3 = 54
Answers
To find the maximum and minimum values of the function f(x, y) = exy subject to x^3 + y^3 = 54, we need to use the method of Lagrange multipliers.
Let's define g(x,y) = x^3 + y^3 - 54 as our constraint equation. Then, the Lagrangian function is:
L(x,y,λ) = exy + λ(x^3 + y^3 - 54)
Taking the partial derivatives with respect to x, y, and λ and setting them equal to 0, we get:
∂L/∂x = ey + 3λx^2 = 0
∂L/∂y = ex + 3λy^2 = 0
∂L/∂λ = x^3 + y^3 - 54 = 0
From the first two equations, we can solve for x and y in terms of λ:
x = (-ey/3λ)^(1/2)
y = (-ex/3λ)^(1/2)
Substituting these expressions into the third equation, we get:
(-ex/3λ)^(3/2) + (-ey/3λ)^(3/2) - 54 = 0
We can solve for λ in terms of e:
λ = e^(2/3)/(2*3^(1/3))
Substituting this back into the expressions for x and y, we get:
x = 3^(1/6)*e^(1/3)/y^(1/2)
y = 3^(1/6)*e^(1/3)/x^(1/2)
Now, we can find the critical points by setting the partial derivatives of f(x,y) = exy equal to 0:
∂f/∂x = ey(x) = 0
∂f/∂y = ex(y) = 0
From the expressions for x and y above, we see that x and y cannot be 0. Therefore, the only critical point is when e^(xy) = 0, which is not possible.
Thus, the function has no critical points in the interior of the region defined by the constraint equation. This means that the maximum and minimum values of the function must occur on the boundary of the region.
We can parametrize the boundary using polar coordinates:
x = 3^(1/3)cos(t)
y = 3^(1/3)sin(t)
Substituting these into f(x,y) = exy, we get:
f(t) = e^(3^(2/3)cos(t)sin(t))
To find the maximum and minimum values of f(t), we can take the derivative with respect to t and set it equal to 0:
f'(t) = 3^(2/3)e^(3^(2/3)cos(t)sin(t))(cos(2t) - sin(2t)) = 0
The solutions to this equation are t = π/4 and t = 5π/4.
Substituting these values back into f(t), we get:
f(π/4) = f(5π/4) = e^(3^(2/3))
Therefore, the maximum and minimum values of the function f(x,y) = exy subject to x^3 + y^3 = 54 are both e^(3^(2/3)).
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6.
The picture below shows a drawing of your garden. You put a fence around the garden and cover it
with a layer of mulch. The fence costs $1.50 per foot. One bag of mulch
covers 8 square feet and
costs $4. How much do you spend in total?
24 it
a
2 ft
2 ft
9 ft
15 ft
15 ft
Answers
2. 3
3. 3
4. 13,5
5. 22,5
6. 22,5
The function below represents the position f in feet of a particle at time x in seconds. find the average height of the particle on the given interval
f(x) = 3x^2 + 6x, [-1, 5]
Answers
Therefore, the average height of the particle on the interval [-1, 5] is approximately 33.67 feet.
To find the average height of the particle on the interval [-1, 5], we need to evaluate the definite integral of the position function f(x) = 3x^2 + 6x over that interval and divide it by the length of the interval.
The average height (H_avg) is calculated as follows:
H_avg = (1 / (b - a)) * ∫[a to b] f(x) dx
In this case, a = -1 and b = 5, so the average height is:
H_avg = (1 / (5 - (-1))) * ∫[-1 to 5] (3x^2 + 6x) dx
To evaluate the integral, we can use the power rule of integration:
∫ x^n dx = (1 / (n + 1)) * x^(n+1) + C
Applying this rule to each term in the integrand, we get:
H_avg = (1 / 6) * [x^3 + 3x^2] evaluated from -1 to 5
Now, we can substitute the limits of integration into the expression:
H_avg = (1 / 6) * [(5^3 + 3(5^2)) - ((-1)^3 + 3((-1)^2))]
H_avg = (1 / 6) * [(125 + 75) - (-1 + 3)]
H_avg = (1 / 6) * [200 - (-2)]
H_avg = (1 / 6) * 202
H_avg = 33.67 feet
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Name this triangle Acute, Scalene Obtuse, Scalene Right, Isosceles Acute, Equilateral
Answers
Answer:
Scalene
Step-by-step explanation:
The reason is because all the sides are different.
Answer:
Triangle scalene
Step-by-step explanation:
So no sides are equal and no angles are equal.
ILL GIVE BRAINLY THING!!!!Solve the equation by completing the square.
12 – 180 + 58 = 0
O A. I = 9 + V23
OB. I = 9 + V139
OC. I = -9 + V23
OD. = -9 + V139
Answers
Answer:
Step-by-step explanation:
x^2-18x+58=0
\(x^{2}\) - 18x + \((-9)^{2}\) +58 = \((-9)^{2}\)
\((x-9)^{2}\) +58 = 81
\((x-9)^{2}\) = 23
x - 9 = \(\sqrt{23}\)
x = \(\sqrt{23}\) + 9
:) there you go answer A) might be good
many subjects don’t give honest answers to questions about activities that are illegal or sensitive in some other way. one study divided a large group of white adults into thirds at random. all were asked if they had ever used cocaine. the first group was interviewed by telephone: 21% said "yes." in the group visited at home by an interviewer, 25% said "yes." the final group was interviewed at home but answered the question on an anonymous form that they sealed in an envelope. of this group, 28% said they had used cocaine.
Answers
28% is the correct answer because it is the closest to true value sine people are sensitive about information like this.
(a) Charlie bought 10 pounds of sugar for $6.
How many dollars did he pay per pound of sugar?
dollars per pound
Answers
Answer:
$0.60 per pound
Step-by-step explanation:
Dollars per pound :
No. of dollars / No. of pounds$6 / 10 pounds$0.60 per poundIf you don’t know pease be mature and don’t answer I really need the answers
What is the equation of the line that has a slope of 2 and goes through the point (4, -1)
y = 2x - 9
y = 2x - 5
y = 2x - 1
y = 2x + 9
Write the equation of the graph.
y−3=12(x+1)
y+3=−12(x−1)
y=12x+5
y−3=−12(x+1)
What is the slope of a line whose equation is 3x−4y=8
?
−43
−34
34
43
What is the equation below in slope-intercept form?
15x−3y=−12
y = -4x + 8
y = -15x -12
x = 3y - 12
x - y = 6
Answers
Answer:
1. Given the slope is 2, the equation now looks like y = 2x +b Given P (−1,4) we can solve for the b variable by substituting the x and y cordinates. 4 = 2 ⋅ (− 1) + b 4 = − 2 + b b = 6 Therefore the equation that has the slope of 2 and passes through the point (− 1,4) is y = 2x + 9 so it is d
2. i you can do that.
3. The equation for the slope of a line and the points also called point slope form of equation of a straight line is given by: y − y1 = m (x − x1) Whereas the slope-intercept form the equation of the line is given by: y = mx + b. Where b is the y-intercept.
4.In the formula,y = the y-coordinate of any point on the line,m = slope,x = the x-coordinate of any point on the line,and b = ...
Plug the slope and y-intercept into the formula. Remember,the slope is equal to the rise over the run.
You need to know these
A car dealership offers two types of discounts. a car built last year and then receive a $3,500 rebate.
• Discount 2: Take 10% off the original price of a car built this year and then receive a $1,250 rebate. A customer is deciding between two cars.
• Car R was built last year and has an original of $25,340. • Car S was built this year and has an original price of $22.860.
Based on the information, which statement is true?
F The customer would pay $19,324 for Car S.
G The customer would pay $24,073 for Car R.
H The customer would pay $21,824 for Car S.
J The customer would pay $23,107 for Car R.
Answers
Answer:
The answer would be F
Step-by-step explanation:
WILL GIVE BRAINLIEST PLS HELP
Solve for y in terms of w, x, and z.
x=zyw
y=
Answers
Answer:
y= x/zw
Step-by-step explanation:
Isolate the variable by dividing each side by the factors that dont contain the variable
x=zyw /zw
y=x/zw
1. the following question refers to the outcome of the actual experiment (described on the conclusions slides), not the data generated from your performance in particular (which may or may not have matched the real experimental results). how would you best describe the results of stroop experiment?
Answers
The correct option: b. Reaction times were the longest when people had to read words presented in colored ink.
Explain about the stroop experiment?A seemingly unimportant phenomena called the Stroop effect explains a great deal about how the brain functions.
The Stroop effect, which was first identified the dr. John Ridley Stroop in the 1930s, is our propensity to have trouble naming the physical color while it is utilized to spell out the name of both a different color. This uncomplicated discovery has significant implications for clinical psychology and psychological research.In brief, the Stroop test, a condensed version of both the original experiment, gives individuals contradictory information by having a word's color change from the color of the word printed. The Stroop test may be used to assess a person's selective attention knowledge and capabilities, processing speed, and general executive processing ability when combined with other assessments.Thus, the stroop experiment's findings most accurately represent when respondents used to have to read words given in colorful ink, reaction times tended to be the longest.
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The complete question is-
This following question refers to the outcome of the actual experiment (described on the conclusions slides), not the data generated from your performance in particular (which may or may not have matched the real experimental results).
a. Reaction times were the longest when people had to read words presented in black ink.
b. Reaction times were the longest when people had to read words presented in colored ink.
c. Reaction times were the longest when people had to name the color of colored chips/shapes.
d. Reaction times were the longest when people had to name the color of words presented in colored ink.
Jing jing works in a store and she spends some of her time organizing the stationary section. If there are nine different items on the rack, how many ways can she organize the rack so that the two most expensive items are not together?
Answers
Answer:
282240 ways
Step-by-step explanation:
number of items = 9 different items
Ranking based on worth
determine number of ways to arrange the 9 items such that the 2 most expensive are apart
first step: consider the 2expensive items as 1
∴ number of permutation = [ ( 9 - 2 ) + 1 ]! * 2!
= [ 8 ] ! * 2! = 80640
Total number of permutation/arrangement = 9! = 362880
hence to arrange the 9 items without having the two most expensive items together
= 362,880 - 80640
= 282240 ways
Pls help!!
RST ~ JIH find HI !!!!!!!!!!
Answers
The length of HI is given as follows:
HI = 15.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The proportional relationship for the side lengths in this problem is given as follows:
3/HI = 5/25
Applying cross multiplication, the length of HI is given as follows:
3/HI = 1/5
HI = 3 x 5
HI = 15.
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Alberto started out bench pressing 60 pounds. He then added 5 pounds every week. Determine whether the situation is linear or nonlinear, and proportional or nonproportional
Answers
Answer
linear
nonproportional
Step-by-step explanation:
Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.
At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.
Answer:
linear
nonproportional
Heeeelllpppssss pleeaassee.....…………
Answers
Answer:
x= -8 x=2
Step-by-step explanation:
x^2 +6x - 6 = 10
Subtract 10 from each side
x^2 +6x -16 =0
Factor what 2 numbers multiply to -16 and add to 6
8*-2 = -16
8-2 = 6
(x+8) (x-2) =0
Using the zero product property
x+8 =0 x-2 =0
x= -8 x=2
what is 5/9 in lowest terms
Answers
Answer:
5/9 it does not reduce an further unless you want a decimal in which it will be 0.56
Step-by-step explanation:
make brainliest please
What is the sum of 7, 13, and -8? *
Answers
Answer:
12
Step-by-step explanation:
7 + 13 + (-8)
Keep in mind, adding a negative number is like subtracting that number.
7 + 13 - 8
= 20 - 8
= 12
Given that R = 6x + 3y
Find y when x = 2 and R = 14
Give your answer as a fraction in its simplest form.
Answers
Answer:
y = 2/3
Step-by-step explanation:
14 = 6(2) + 3y
14 = 12 + 3y
2 = 3y
y = 2/3
Do only number 4 please
Answers
Answer:
baby formulaa for sure (wut ur school I got same question)
Step-by-step explanation:
add sum purple to yo nails
1. A manager has formulated the following LP problem. Draw the graph and find the optimal solution. (In each, all variables are nonnegative).
Maximize: 10x+15y, subject to 2x+5y ≤ 40 and 6x+3y ≤ 48.
Answers
The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.
To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.
The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.
Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.
By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.
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help me with this please
Answers
The values of a, b, c are 152°, 28°, 152° respectively.
What are angle at a point?Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.
The sum of angles at a point will give 360°.
This means that a + b + c + 28 = 360
c +28 = 180° ( angle on a straight line)
c = 180 -28
c = 152°
c = a( alternate angles are equal)
therefore the value of a = 152°
b = 28( alternate angles are equal)
therefore the value of b is 28
therefore the values of a, b, c are 152°, 28°, 152° respectively
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the nicotine content of a certain brand of cigarettes is normally distributed with a mean of 2.0 mg and a standard deviation of 0.25 mg. what is the probability that a cigarette has a nicotine content:
Answers
The probability that a cigarette has a nicotine content less than 1.8 mg is approximately 0.2119.
The probability that a cigarette has a nicotine content less than 1.8 mg can be found by using the cumulative distribution function (CDF) of the normal distribution. The CDF gives the probability of a random variable being less than or equal to a certain value.
To find this probability, we can standardize the value 1.8 mg using the formula z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have z = (1.8 - 2.0) / 0.25 = -0.8.
Next, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score.
Looking up the z-score of -0.8 in the table, we find that the corresponding probability is approximately 0.2119.
Therefore, the probability that a cigarette has a nicotine content less than 1.8 mg is approximately 0.2119.
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