Answer:
All answers in this set can be written in the form y=f(x).
Use the following information to determine your answers: The typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. Suppose last night you slept for 5 hours. How many standard deviations are you from the mean? Please round to the second decimal point.
We have been given that the typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. Suppose last night you slept for 5 hours.
We will use z-score formula to solve our given problem as z-score tells a data point is how many standard deviation from the mean.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{5-7.5}{1.3}[/tex]
[tex]z=\frac{-2.5}{1.3}[/tex]
[tex]z=-1.923076923[/tex]
Upon rounding to two decimal places, we will get:
[tex]z\approx -1.92[/tex]
Therefore, you are [tex]-1.92[/tex] standard deviations from the mean or 1.92 standard deviation below mean.
A North American company manufactures rivets for use in car production. A sample of forty rivets from the production line had mean 6.803 and standard deviation 0.275 (both in 1/100 of an inch). On communicating these results to the company headquarters in Europe, a request is made for the summary statistics to be converted into millimeters. Given that one inch is 2.538 centimeters, find the mean and standard deviation of the sample in millimeters. What is the mean in millimeters
Answer:
Mean = 1.73 mm
Standard deviation = 0.0698 mm
Step-by-step explanation:
Given:
Sample size, n = 40
Mean, u = 6.803
Standard deviation = 0.275
a) Given that one inch is 2.538 centimeters, to find the mean in millimeters we have:
[tex] 6.803 * \frac{1}{100} [/tex]
Converting to cm, we have:
[tex] 6.803 * \frac{1}{100} * 2.538 = 0.173 cm[/tex]
Converting to mm, we know 1cm = 10 mm,
0.173 * 10 = 1.73 mm
b) Given that one inch is 2.538 centimeters, to find the standard deviation in millimeters we have:
[tex] 0.275 * \frac{1}{100} [/tex]
Converting to cm, we have:
[tex] 0.275 * \frac{1}{100} * 2.538 = 0.00698 cm[/tex]
Converting to mm, we know 1cm = 10 mm,
0.00698 * 10 = 0.0698mm
In this exercise we have to use the knowledge of statistics to calculate the car production, so we have to:
Mean: [tex]1.73mm[/tex]Standard deviation: [tex]0.0698 mm[/tex]Given the following information, we have:
Sample size n = 40 Mean u = 6.803 Standard deviation = 0.275A) Find the convertion to the mean in milimeters, will be:
[tex]6.803*(1/100)*2.538=0.173 cm\\=1.73 mm[/tex]
B) Find the convertion to the stardard deviation in milimeters, will be:
[tex]0.275*(1/100)*2.538=0.00698\\=0.0698 mm[/tex]
See more about statistics at brainly.com/question/10951564
Many demographers predict that the United States will have zero population growth in the coming decades, in contrast to the historical average population growth of about 1 percent per year. Use the Solow model to forecast the effect of this slowdown in population growth on the growth of total output and the growth of output per person. Consider the effects both in the steady state and in the transition between steady states.
Answer:
Check the explanation
Step-by-step explanation:
Other things being constant, a slowdown in population growth will lead to an increase in the availability of capital per worker and output per worker.
At the steady state, output per worker will grow at the rate of g while. Thus, steady state per person output growth will be same, however total output will increase at the rate n+g.
In case of transition between steady states, during the transition phase, output per worker will grow at a rate greater than g. Overtime in the long run with a fall in population growth, total output will fall while output per worker will increase.
Differentiate the function:
y=x^3+2x-1
Answer:
y' = 3x² + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
y = x³ + 2x - 1
Step 2: Differentiate
Basic Power Rule: y' = 3x³⁻¹ + 1 · 2x¹⁻¹ - 0Simplify: y' = 3x² + 2Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
1.
Find the midpoint of MN given M(3,-1) and N(11,-9)
The height (in feet) of a rocket from ground level is given by the function f(t) = -16t2 + 220t. What is the instantaneous velocity of the rocket 12 seconds after its launch?
Answer:
-164 ft/second.
Step-by-step explanation:
The instantaneous velocity is given by the derivative;
f(t) = -16t^2 + 220t
V = f'(t) = -32t + 220
So at 12 seconds:
V = -32*12 + 220
= -164 ft/second ( It is negative because it is descending).
The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. LaTeX: X_1=X 1 = number of product 1 produced in each batch LaTeX: X_2=X 2 = number of product 2 produced in each batch MAX: LaTeX: 150\:X_1+250\:X_2150 X 1 + 250 X 2 Subject to: LaTeX: 2\:X_1+5\:X_2\le2002 X 1 + 5 X 2 ≤ 200 LaTeX: 3\:X_1+7\:X_2\le1753 X 1 + 7 X 2 ≤ 175 LaTeX: X_1,\:X_2\ge0X 1 , X 2 ≥ 0 How much profit is earned per each unit of product 2 produced?
Answer:
250
Step-by-step explanation:
It appears your profit function is ...
150x1 +250x2
This tells us the profit for each unit of product 2 is 250.
what is the length of leg s of the triangle below?
Answer:
the answer would be 10
Step-by-step explanation:
256 divided by -16 with steps.
Answer:
256÷-16=16
Step-by-step explanation:
The complete expression is 256 divided by -16 is -16
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
256 divided by -16 = what
When represented as an equation, we have
Result = 256 divided by -16
Make the result the subject of the formula
So, we have
Result = 256/-16
Rewrite as
Result = -256/16
Evaluate the quotient
Result = -16
Hence, the number is -16
Read more about expressions at
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Write a description of how you would calculate the area of the shaded space include the answer.
Answer:
The area of shaded region is 25.5 units³
Step-by-step explanation:
Step 1 , you have to find the area of rectangle and triangle using the formulas :
Rectangle :
[tex]area = length \times width[/tex]
Let length = 5 units,
Let width = 6 units,
[tex]area = 5 \times 6[/tex]
[tex]area = 30 \: \: {units}^{2} [/tex]
Triangle :
[tex]area = \frac{1}{2} \times base \times height[/tex]
Let base = 3 units,
Let height = 3 units,
[tex]area = \frac{1}{2} \times 3 \times 3[/tex]
[tex]area = \frac{1}{2} \times 9[/tex]
[tex]area = 4.5 \: \: \: {units}^{2} [/tex]
Step 2 , in order to find the shaded region, you have to substract the area of triangle from the area of rectangle (As the triangle is not shaded) :
[tex]area = 30 - 4.5[/tex]
[tex]area = 25.5 \: \: \: {units}^{2} [/tex]
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
a is the correct option pls mark me as the brainliset
A. It is a proven fact that sometimes drawing it down will help you remember.
C. You could just write it down, simple as that.
F. People always doublecheck-it helps them go over to see if they made a mistake or anything.
Please, Brainliest?
Hope this helps.
Consider the following parametric equation. x equals (t plus 5 )squared; y equals t plus 8; negative 10 less than or equals t less than or equals 10 (a) Eliminate the parameter to obtain an equation in x and y. (b) Describe the curve and indicate the positive orientation. (a) Eliminate the parameter to obtain an equation in x and y. Choose the correct equation below. A. y equals StartRoot x plus 3 EndRoot B. y equals (x plus 3 )squared C. y equals x squared plus 3 D. y equals 3 plus or minus StartRoot x EndRoot (b) Describe the curve and indicate the positive orientation. A. -15 15 -5 15 x y
Answer:
a) D. y = 3 ±√x
b) parabola opening to the right
Step-by-step explanation:
(a) Solving for t in the equation for y:
y = t+8
t = y -8 . . . . subtract 8
Substituting into the equation for x, we have ...
x = ((y -8) +5)^2 = (y -3)^2
Solving for y, we get
±√x = y -3 . . . . . take the square root
y = 3 ±√x
__
(b) The equation describes a parabola that opens to the right.
The answer plz hurryyy
Answer:
The answer is that the y-coordinate should be -3 1/2.
Step-by-step explanation:
First, look at the graph. On the x-axis, the dot is at -5, since it is 5 units to the left of the origin. On the y-axis, the dot is at -3 1/2. It is between -3 and -4, not -4 and -5. Therefore, the answer is that the y-coordinate should be -3 1/2, not -4 1/2. You can also check by seeing if -4 1/2 is reasonable. -4 1/2 would mean the dot would be more than 4 units below the origin. On the graph, the dot is clearly above the -4 mark, so the -4 1/2 must not be correct.
Convert the degrees measure 180° to radian measure.
Answer:π
Step-by-step explanation:
180°=π
Complete the five-number summary for the data set: 5, 2, 1, 3, 3, 6, 4, 2, 7.
you type in the answer
Answer:
NOOO OYU TYPE INTHE ANSWER
Step-by-step explanation:
a population is growing continuously at a rate of 5%. if the population is now 3400, what will it be in 17 years?
Answer:
7793
Step-by-step explanation:
3400 x 1.05^17 = 7792.862
Answer:
The population would be 7792.86 or when rounded would be 7793
Step-by-step explanation:
This question is an example of a repeated percentage change
To work this out you would first have to convert the percentage of 5 into a decimal. You can do this by dividing 5 by 100, this gives you 0.05. This is because percentages are out of 100.
The next step is to add 0.05 to 1, which gives you 1.05. This is because we are increasing the amount by 5% annually.
The final step is to multiply the amount of 3400 by 1.05 to the power of 17, this gives you 7792.86. This is because we are finding 5% and adding it to the amount and finding 5% of that new amount, this will continue 17 times.
1) Divide 5 by 100.
[tex]5/100=0.05[/tex]
2) Add 0.05 to 1.
[tex]0.05+1=1.05[/tex]
3) Multiply 3400 by 1.05 to the power of 17.
[tex]3400*1.05^{17} = 7792.86[/tex]
4) Round to the nearest whole number.
7793
what is the cube root of 1
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
Idk what it is asking.
Answer:
Jumbo burger with fried is 75%
chicken with salad is 65%
Step-by-step explanation:
you first split the burger and sides. You add up the sides to find the salad. Then add up the sides and burgers
Answer:
What is the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwich with a Salad? Make an area or tree diagram to help with the problem.
Answer to question: 20% for Jumbo Burger with Regular Fries and 10.5% for Chicken Sandwich with a Salad.
Step-by-step explanation:
You are going to find the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwhich with a Salad by using a area model or a tree diagram. Although you ddin't ask me to solve it, I'm gonna help you with it anyways.
Sandwhiches:
50% - Jumbo Burger (JB)
30% - Chicken Sandwich (CS)
20% - Regular Burger (RB)
Sides:
40% - Curly Fries (CF)
35% - Salad (S)
25% - Regular Fries (RF)
Acronyms
Jumbo Burger (JB) + Curly Fries (CF) = JBCF
Jumbo Burger (JB) + Salad (S) = JBS
Jumbo Burger (JB) + Regular Fries (RF) = JBRF
Chicken Sandwich (CS) + Curly Fries (CF) = CSCF
Chicken Sandwich (CS) + Salad (S) = CSS
Chicken Sandwich (CS) + Regular Fries (RF) = CSRF
Regular Burger (RB) + Curly Fries (CF) = RBCF
Regular Burger (RB) + Salad (S) = RBS
Regular Burger (RB) + Regular Fries (RF) = RBRF
Probability of combinations:
JBCF = 0.5 x 0.4 = 0.20
JBS = 0.5 x 0.35 = 17.5
JBRF = 0.5 x 0.25 = 12.5
CSCF = 0.3 x 0.4 = 12
CSS = 0.3 x 0.35 = 10.5
CSRF = 0.3 x 0.25 = 7.5
RBCF = 0.2 x 0.4 = 8
RBS = 0.2 x 0.35 = 7
RBRF = 0.2 x 0.25 = 5
Your tree diagram should look something like this:
CF(40%)- outcome - JBCF (20%)
/
(50%)JB --- S(35%)- outcome - JBS (17.5%)
\
RF(25%)- outcome - JBRF (12.5%)
CF(40%)- outcome - CSCF (12%)
/
(30%)CS --- S(35%)- outcome - CSS (10.5%)
\
RF(25%)- outcome - CSRF (7.5%)
CF(40%)- outcome - RBCF (8%)
/
(20%)RB --- S(35%)- outcome - RBS (7%)
\
RF(25%)- outcome - RBRF (5%)
Hope this helps because this took forever :D
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
A. x - 4
D. x + 8
Step-by-step explanation:
To find the two binomial that are factors of the trinomial, you split the middle term into two:
[tex]x^2[/tex] + 4x - 32
[tex]x^2[/tex] - 4x + 8x - 32
Group:
([tex]x^2[/tex] - 4x) (8x - 32)
Take out GCF (Greatest Common Factor):
x(x - 4) 8(x - 4)
(x + 8) (x - 4)
Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 10 miles?
Answer:
70 minutes
Step-by-step explanation:
So if Petra takes 42 min to jog 6 miles, then how long would it take to jog 10 miles? What do we do?
We make a proportion, 6/42 = 10/x
We cross multiply and get an equation of 10*42 = 6*x
We simplify, 6x = 420
And divide 6 by both sides to get x= 70 min
- Hope this helped :)
Brainliest is most appreciated :)
Answer:
It would take Petra 70 minutes to jog 10 miles.
Step-by-step explanation:
There are several ways we can solve this.
As a rate:
42/6=7
One mile takes her 7 minutes.
7*10=70
10 miles takes her 70 minutes.
As a proportion:
6/42=10/x
Cross multiply.
420=6x
x=70
It would take her 70 minutes.
The function f(x)=-(x-3)^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?
A)3 square units
B)6 square units
C)12 square units
D)9 square units
Answer:
D) 9 square units
Step-by-step explanation:
The squared term will always be non-negative, so the least it can be is zero (for x=3). The squared term is subtracted from 9, so the most the function value can be is 9.
The maximum area of the rectangle is 9 square units.
Answer:
9 square units
Step-by-step explanation:
A ladder is leaning against a building. Match the values with their descriptions.
(K is up Above the G )
Answer:
The height of the building: g
Distance from the building to the base of the ladder: 57
The length of the ladder: m
Angle the ladder makes with the building: k
Angle the ladder makes with the ground: 55
Step-by-step explanation:
Based off the location of the variables and numbers, the descriptions match where they are.
Hope that helps!
A certain television is advertised as a 45-inch Tv (the diagonal length). if the width of the TV is 36 inches, how many inches tall is the TV?
Answer:
27
Step-by-step explanation:correct answer
hope this helps
plz mark me the brainliest
7.5% of what is 7.38?
Answer:
What =98.4
Step-by-step explanation:
Of means multiply and is means equals
7.5% * What = 7.38
Change to decimal form
.075 * what = 7.38
Divide each side by .075
.075 What /.075 = 7.38/.075
What =98.4
Answer:
the answer for this question is 98.4
What’s the correct answer for this?
Answer:
The first option. ∠2 and ∠4 are vertical angles.
Step-by-step explanation:
The fact that ∠2 is vertical with ∠4, proves the angles must be congruent. Vertical angles are always congruent, while adjacent angles are supplementary.
Answer:
C
Step-by-step explanation:
Angle 1 is supplementary to both 2 and 4. It's correct
Sylvia invested $500 in an account compounded annually with an interest rate of 8%. Manuel invested $600 in an account wit
72
a compound interest rate of 7.25%. Using the rule of 72, 7. who will double their money first?
Sylvia will double her money first, in approximately 9 years.
Manuel will double his money first, in approximately 10 years.
Manuel will double his money first, in approximately 9 years.
Sylvia will double her money first, in approximately 10 years.
Answer:
It’s a
Step-by-step explanation:
Got it right on edg hope this helped
Answer:
It's A
Step-by-step explanation:
Took test
1.(1 0) You measure the distance, l, a projectile travels several times using the same apparatus and find the following values (cm): 5.11, 4.89, 5.04, 4.94, 4.93, 5.06 and 5.09. Assuming that the errors are random: a) What is the mean value forl? b) What is the standard deviation for this data set? c) What is the uncertainty associated with your best estimate forl? d) How should one report the result of this measurement along with the uncertainty at the 95 % confidence level? e) If you desire to reduce the statistical uncertainty associated with the reported result using the same apparatus to be only 0.01 cm, how many measurements must be made?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Helppp.........!!!!!!
Answer:
84 centimeters of the width of the item in reality
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. Given the information, let us create a proportionality as such:
1 = 14 ⇒ x - width of item in reality (cm)
6 x
2. Now let us cross multiply, and solve through simple algebra:
14 * 6 = x,
x = 84 centimeters of the width of the item in reality
What is the value of b?
Answer:
b=24
Step-by-step explanation:
VT^2 + (2b)^2 = 67^2
VT^2 + (b+24)^2 = 67^2
-> (2b)^2 = (b+24)^2
-> 2b = b+ 24
-> b = 24
Use the Distributive Property to solve the equations. -4(x+3)=8. What does x equal?
Answer:
-5
Step-by-step explanation:
-4x-12=8
+12. +12
-4x=20
Divide -4 on both sides
20/-4
x= -5
