Answers
The function among all options is y=30.5(0.7)ˣ.
What is the graph of a function?The graph of a function represents a set of all points in a plane. It helps to derive the nature of the function.
The function must satisfy the points that are given in the graph.
When x=0, y=21.35(0.7)ˣ=21.35(0.7)⁰=21.35.
But the given point is (0,30.5).
Hence, it cannot be the required function.
When x=0, y=30.5(21.35)ˣ=30.5(21.35)⁰=30.5.
When x=1, y=30.5(21.35)ˣ=30.5(21.35)¹=651.175.
But the given point is (1,21.35).
Hence, it cannot be the required function.
When x=0, y=30.5(1.3)ˣ=30.5(1.3)⁰=30.5.
When x=1, y=30.5(1.3)ˣ=30.5(1.3)¹=39.65
But the given point is (1,21.35).
Hence, it cannot be the required function.
When x=0, y=30.5(0.7)ˣ=30.5(0.7)⁰=30.5.
When x=1, y=30.5(0.7)ˣ=30.5(0.7)¹=21.35.
When x=2, y=30.5(0.7)ˣ=30.5(0.7)²=14.945≈14.95.
It satisfies all three given points.
Therefore, the required function is y=30.5(0.7)ˣ.
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Related Questions
if a multiple regression dataset has 3 predictors, what is the minimum number of observations needed to meet doane's rule?
Answers
Doane's rule is used for choosing the number of histogram bins, not for determining the minimum sample size needed for a multiple regression analysis.
However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.
Doane's rule is a guideline for choosing the number of histogram bins based on the sample size and skewness of the data. It suggests that the number of bins should be approximately equal to 1 + log2(N) + log2(1 + |g1|/SE(g1)), where N is the sample size and g1 is the sample skewness.
It is important to note that Doane's rule is used for determining the number of bins for a histogram, not for determining the minimum sample size needed for a multiple regression analysis.
That being said, in general, the minimum sample size needed for a multiple regression analysis depends on a variety of factors, including the number of predictors, the strength of the relationships between the predictors and the outcome variable, the desired statistical power, and the level of significance. There is no set minimum sample size that applies to all situations. However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.
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Mr. Steiner purchased a car for about $14,000. Assuming his loan was
compounded monthly at an interest rate of 4. 9% for 72 months:
p=
r=
n=
t=
A. How much will he have paid total?
B. How much more did he pay than the price of the car?
Answers
Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.
we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
here, we know that A(t) is the amount of money after t years.
P is the initial sum of money, know as principal,
r is the interest rate as a decimal value,
n is the number of times that interest is compounded per year,
and
t is the time in years for which the money is invested or borrowed.
now here we know,
P = 14000, r = 0.049, n = 12, t = 6
when we have all values we can find,
A(t) = P(1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
A(6) = 14000 (1+[tex]\frac{0.049}{12}[/tex])¹²ˣ⁶
A(6) = 18774
therefore we know that Mr. Steiner needs to pay $18774 in total.
now,
18774 - 14000 = 4774
therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.
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a game involves a two-sided coin, as well a six-sided die. to play the game, each player flips the coin once and rolls the die once. what is the number of individual outcomes from flipping and rolling one time? a.) 6 b.) 2 c.) 12 d.) 8
Answers
Option C : The number of individual outcomes from flipping and rolling one time is 12.
A permutation is a selection of items from a set where the order of the items does matter. In this case, a permutation would be an ordered pair of a heads or tails outcome from flipping a coin followed by a 1, 2, 3, 4, 5, or 6 outcome from rolling a die.
The number of possible combinations is found by multiplying the number of possible outcomes for each event. In this case, there are two possible outcomes from flipping a coin (heads or tails) and six possible outcomes from rolling a die (1, 2, 3, 4, 5, or 6), so the number of combinations is:
2 (outcomes from coin flip) * 6 (outcomes from die roll) = 12
The number of permutations is equal to the number of combinations because the order of the items in each combination does not matter. So, there are 12 individual outcomes from flipping and rolling one time.
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Write an equivalent expression by combining like terms. 8b - 4b b =5
Answers
The equivalent expression for 8b-4b is 4b.
What are like terms?In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.
Given 8b-4b. b=5
We have to combine the like terms to get an equivalent expressions.
Like terms containing variables with same power.
When combining like terms, we have to add or subtract their coefficients.
Coefficients are the numbers which are placed with variable.
Then, 8b-4b=4b.
When b=5⇒4*5=20
Hence, the equivalent expression for 8b-4b is 4b.
Complete question:
Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.
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the following data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5. what measure(s) of the typical value in a data set would be affected by this error? select all that apply.
Answers
The following measures of typical value in a data set would be affected by the error:
Mean: The mean is the sum of all the values divided by the number of values. If one value is significantly different from the rest, it can significantly affect the mean. In this case, the mean would be affected because the value of 5 is much lower than the other values in the data set, which would cause the mean to be lower than it should be.
Median: The median is the middle value in a data set. If the error is low enough, it may not affect the median, but if it is low enough to move the value of 5 to the middle of the data set, the median would be affected.
In conclusion, the mean and median of this data set would be affected by the error of recording the value of 75 as 5.
The mode, mean and median of this data set would be affected by the error of recording the value of 75 as 5.
Given that, a data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5.
so, here, due to mistake the mode, mean and the median will be affected.
Adding a data point to the set, or taking one away, can affect the mean, median, and mode.
If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase.
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Find the Slope of line LM algebraically.
L(-1,-5)M(-4,-2)
Answers
Answer:
-2+5/-4+1= -1
Step-by-step explanation:
put y2 minus y1 over x2 minus x1
What is the area of this compound figure?
Answers
Answer:
66mm
Step-by-step explanation:
What does it mean for an event to be unusual? Why should the cutoff for identifying unusual events not always be 0.05? Choose the correct answer below A. An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem. B. An event is unusual if it has a high probability of occurring The choice of the cutoff should consider the context of the problem. C. An event is unusual if it has a probability equal to 0 The choice of a cutoff should consider the context of the problem. D. An event is unusual if it has a probability equal to 1 The choice of a cutoff should consider the context of the problem.
Answers
The Correct option Will be An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem i.e. A.
What exactly is probability?The likelihood of an event is expressed by probability. The occurrence of a random event is the subject of this mathematical field of study. The value is between zero and one. In mathematics, probability is a tool for calculating the likelihood that certain events will take place.
Probability is the possibility of something happening. The probability distribution also makes use of this central concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood that a specific event will occur.
What does it mean when an event is unusual or out of the ordinary?When something unusual happens, it does not happen frequently in terms of sight or sound.
The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.
Now,
As an unusual event has low probability because it does not happen often and The same cutoff should not be used to detect unexpected events all of the time. Choosing a cutoff is subjective, and it should consider the repercussions of erroneously labelling an occurrence as rare.
Hence,
An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem.
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Suppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws.a. What is the probability that he will make both free throws? (to decimals) b. What is the probability that he will make at least one free throw? (to decimals) c. What is the probability that he will miss both free throws? (to decimals) d. Late in basketball game; team often intentionally fouls an opposing player in order to stop the game clock: The usual strategy is t0 intentionally foul the other team's worst free-throw shooter: Assume the team' worst free throw shooter makes 58% of his free throws Calculate the probabilities for this player as shown in parts (2), (b), and (c) and show that intentionally fouling this player who makes 58% of his free throws is better strategy than intentionally fouling the player who makes 89% of his free throws. Assume as in parts (a), (b), and (c) that two free throws will be awarded.1. What is the probability that this player will make both throws? (to 4 decimals) 2. What is the probability that will make at least one tlrow? (to decimals) 3. What is the probability that thils player wIll mlss bolhi Urows? (to decimals)"
Answers
The probability of both free throws is 0.7921, at least one free throw is 0.9889, missing both free throws is 0.0121. 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
The probability of making one free throw is 0.89. Therefore, the probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 2 decimals).
The probability of missing one free throw is 1 - 0.89 = 0.11. Therefore, the probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing one free throw is 0.11. Therefore, the probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 2 decimals).
For the worst free-throw shooter who makes 58% of his free throws:
The probability of making both free throws is: 0.58 * 0.58 = 0.3364 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.42 * 0.42 = 0.8236 (rounded to 2 decimals).
The probability of missing both free throws is: 0.42 * 0.42 = 0.1764 (rounded to 4 decimals).
For the player who makes 89% of his free throws:
The probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 4 decimals).
Therefore, intentionally fouling the player who makes 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
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Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
Answers
Answer:
<A=45°,<B=65°,<C=70°
Step-by-step explanation:
<A=3(x+5)=3x+15
<B=5x+15
<C=7x
sum angles in a triangle is 180°
so,<A+<B+<C=180
(3x+15)+(5x+15)+(7x)=180
C.L.T
3x+5x+7x+15+15=180
15x+30=180
15x=180-30
15x=150
divide both sides by 15
x=10
<A=3(x+5)=3(10+5)=3(15)=45°
<B=5(10)+15=50+15=65°
<C=7(10)=70°
A system of equations has one line with a positive slope and one line with a negative slope. which of the following statements is true?
A. There is not enough information to know whether the system is consistent or inconsistent.
B. The lines are parallel to each other.
C. The system is consistent.
D. The system is inconsistent.
Answers
The system is consistent.
What is meant by consistent?
A system of equations is said to be consistent when they have atleast one solution in common.
A system of equations has one line with a positive slope and one line with a negative slope
The system has 1 line with a positive slope, so a line that has a positive slope is going to be rising from left to right.
The second line that has a negative slope. So just a line ,it is decreasing. Now a negative slope means the line, falls from left to right or is downward sloping.
If 1 line has a positive slope and 1 line has a negative slope, then at some point those lines are going to intersect, which will be the solution to the system.
Hence, the system is consistent.
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a cup of soup is left on a countertop to cool. the table below gives the temperatures , in degrees fahrenheit, of the soup recorded over a 10-minute period. write an exponential regression equation for the data, rounding all values to the nearest thousandth.
Answers
Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup.
Calculate the x and y means in step one.
X's average: (0 + 10) / 2 = 5.
(95 + 88.5) / 2 = 91.75 is the mean of y.
Calculate the variance and covariance in step two.
(-5 6.5) + (5 -2.5) = 32.5 is the covariance.
X's variation is (5 0).
2 + (10 − 0)2 = 125
Calculate the regression coefficients in step three.
x = -32.5 / 125 = -0.26 where a = Covariance / Variance of x
Mean of x = 91.75 (-0.26 5) = 99.97 where b = Mean of y a Mean of x
Step 4: Compose the equation for exponential regression.
y = -0.0063e^0.16x + 99.97
Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup. We must first determine the means of x and y before we can solve the problem. By summing the first and last values of x and dividing by 2, the mean of x is 5 and the mean of y is 91.75. (calculated by adding the first and last y values and then dividing by 2).
Calculating the covariance and variance comes next. The difference between each x and the mean of x is multiplied with the difference between each y and the mean of y to determine the covariance. By squaring the difference between each x and the mean of x, the variance of x is determined. The regression coefficients a and b can be determined when the covariance and variance have been computed.
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math question|| geometry
Answers
The length TE in the parallelogram is 11 units
How to determine the length TEFrom the question, we have the following parameters that can be used in our computation:
The parallelogram QRST
The diagonals of parallelogram are equal
Using the above as a guide, we have the following:
QE =SE
Substitute the known values in the above equation, so, we have the following representation
3x + 12 = x + 16
So, we have
2x = 4
Divide
x = 2
Recall that
TE = 6x - 1
So, we have
TE = 6 * 2 - 1
Evaluate
TE = 11
Hence, the lentth is 11 units
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A recipe calls for 2 cups of water for every 1/3 cups of flour. How much water is needed if you use 7 cups of flour?
Answers
3x7= 21
21x2= 42 cups
HELPP!! please!!! asap
Answers
Answer:
6 units
Step-by-step explanation:
Since the two angles are equal, this means that the triangle is isosceles. So x+4 = 3x-8. After solving, 2x = 12, x = 6. So AC is 6 units.
Answer: 6 units
Step-by-step explanation:
Since this is an isosceles triangle lines AB and BC are congruent so
x + 4 = 3x - 8 ---- add 8 and subtract x on both sides
12 = 2x ---- divide by 2 to isolate the x
x = 6
A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 6 feet by 12 feet. The total surface area of the box is 396 square feet. What is the height of the box in feet?
Answers
Answer:
7 feet
Step-by-step explanation:
You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.
Surface areaThe formula for the surface area of a cuboid is ...
SA = 2(LW +H(L+W))
ApplicationFor the given box, this is ...
396 = 2(6·12 +H(6+12))
198 = 72 +18H . . . . . . . . . . divide by 2
126 = 18H . . . . . . . . . . . subtract 72
7 = H . . . . . . . . . . . . divide by 18
The height of the box is 7 feet.
A cylindrical jar of radius 6 cm contains water. How many iron spheres each of radius 1.5 cm are required to raise the level of water by 2 cm?
Answers
16 iron spheres each of radius 1.5 cm are required to raise the level of water by 2 cm
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, A cylindrical jar of radius 6 cm contains water.
Therefore, the volume of the cylinder is π(6²)h = 36πh.
Given, The height raises by 2cm therefore, 36π(h + 2).
We know, The volume of a sphere is, (4/3)πr³
= (4/3)π(1.5)³.
= (4/3)π×3.375.
= (13.5/3)π.
let, We need 'x' number of spheres.
Therefore, 36πh + (13.5/3)πx = 36π(h + 2).
36πh - 36π(h + 2) = - (13.5/3)πx.
36h - 36(h + 2) = - (13.5/3)x.
108h - 108(h + 2) = - 13.5x.
108(h - h - 2) = - 13.5x.
108(-2) = - 13.5x.
x = 216/13.5.
x = 16.
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What is 2 1/2 doubled
Answers
Answer:
5
Step-by-step explanation:
2 1/2
+ 2 1/2
1/2 and 1/2 makes a whole which is 1
so if you have 4 and and a whole which is 5
They can also be turned into decimals. 1/2 as a decimal is .5
so 2.5 plus 2.5 = 5
a cylinder with radius of 5ft has a volume of 314ft. Find its height
Answers
3.9979(depends on what place you need to round to
The equation is V=πr2h. First plug in what you know, 314=π5^2h. 5x5=25 and its multiplied with π. It would look like 314=25πh. Divide the 25π by both sides, leaving your h. Plug it into your calculator.
Check answer:
(I rounded the 4 to the nearest whole number) 4*25*π is approximately 314
Answer:
4 ft
---------------
Volume of cylinder formula:
V = πr²hGiven:
r = 5 ft,V = 314 ft³Find h:
314 = 3.14*5²h314 = 3.14*25hh = 314/(3.14*25)h = 4 ftNEED HELP ASAPPP
Find m/TUV.
m/TUV=
Answers
Answer: 54 degrees
Step-by-step explanation:
The angle will be half of that arc segment
A field in the shape of a rectangle has an area of 1/3 square mile. The length of the field is 2/5 mile. What is the width of the field?
Answers
If the area of a rectangle 1/3 square mile and length of the field is 2/5 mile then the width of the field is
What is Area of a Rectangle?
The quantity of unit squares that can fit inside a rectangle called its area. In other terms, the area of a rectangle is the area that it occupys. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes.
Given in the question,
Area of rectangle [tex]= \frac{1}{3} square mile[/tex]
The length of the field [tex]= \frac{2}{5} mile[/tex]
Let breadth be x.
As we know that,
Area of rectangle = [tex]length * breadth[/tex]
Now,
[tex]\frac{1}{3} = \frac{2}{5} *x[/tex]
[tex]x=\frac{1}{3} * \frac{5}{2}[/tex]
[tex]x=\frac{5}{6}[/tex]
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On Thursday a theme park sells 627 tickets. Each ticket costs
£54.99. The park has costs of £18,273 on Thursday. What is the
percentage profit that the theme park make on Thursday?
Answers
Answer: The theme park made a 46.8% profit on Thursday.
Step-by-step explanation:
Step 1: First, we need to calculate the total revenue from ticket sales:
627 tickets x £54.99 = £34,341.73
Step 2: Subtract the costs from the total revenue:
£34,341.73 - £18,273 = £16,068.73
Step 3: Calculate the percentage profit:
£16,068.73 / £34,341.73 x 100 = 46.8%
The theme park made a 46.8% profit on Thursday.
at noon, a ship leaves a harbor and sails south at 20 knots. four hours later, a second ship leaves the harbor and sails east at 15 knots. when will the ships be 100 nautical miles apart? round to the nearest minute. note that 1 knot = 1 nautical mile per hour.
Answers
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:
[tex]a^2 + b^2 = c^2[/tex]
We can use the Pythagorean theorem to find the distance between the two ships at any given time:
d² = (20t)² + (15(t-4))²
Simplifying this equation, we get:
d² = 400t² + 225(t² - 8t + 16)
d² = 625t² - 1800t + 3600
d = √(625t²- 1800t + 3600)
We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:
100 = √(625t² - 1800t + 3600)
Squaring both sides, we get:
10000 = 625t² - 1800t + 3600
Rearranging, we get:
625t² - 1800t - 6400 = 0
Using the quadratic formula, we get:
t = (1800 ± √(1800² + 46256400)) / (2*625)
t = (1800 ± 3900) / 1250
t = 3.84 or t = 8.16
So the time elapsed for the second ship is:
t2 = t + 4
t2 = 7.84 or t2 = 12.16
We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:
d = √((163.2)² + (62.4)²) = 174.9 nautical miles
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
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Mrs. Martinez and Ms. Jones' classes are competing for best average homework completion over the course of the semester.
Answers
According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.
How do average and mean differ?The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.
Comparing the median and average.By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.
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1/2 of 2/3 = 1/2 of ____ third(s) = ____ third(s)
Answers
The product of 1/2 and 2/3 is equivalent to one third
Taking the product of fractions
Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction
Given the expression below
1/2 of 2/3
This can also be written as;
1/2 of 2/3 = 1/2 of two thirds
Simplify
1/2 * 2/3 = 2/6
1/2 of 2/3 = 1/3
Hence the resulting value of the expression is one third
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HELPPPPP i don't know how to do these, I missed the first quarter of math
Answers
The domain of the relation is 0, 2, 3, and 7.
The range of the relation is 1 and 3.
How to find the domain and range of a relation?The domain of a function is the set of all possible inputs for the function. The domain of a relation is the independent variable of the relation. The domain of the relation are the x values.
Therefore, the domain of the relation are 0, 2, 3 and 7.
The range of the relation is the set of the second coordinates from the ordered pairs. The range is the output of the relation. The range are the y axis values.
Therefore, the range of the relation are 1 and 3.
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lights of america claims that the life length of one of its light bulbs, the twister 7 years bulb2, is normally distributed with a mean of 10,000 hours and a standard deviation of 1000 hours. lang selects one of these light bulbs at random and places it on accelerated life test. (i) what is the probability that the bulb that lang selects will last exactly 9950 hours? (ii) what is the probability that the bulb that lang selects will last at most 9950 hours? (iii) what is the probability that the bulb that lang selects will last at least 9950 hours? (iv) what is the probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours? (v) what is the probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively? (vi) what lifelength represents the 95th percentile?
Answers
(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.
(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5
(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.
(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668
(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is 0.6826.
(vi) The life length represents the 95th percentile is 11,645
The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.
(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.
(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.
(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.
(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.
For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5
Then the corresponding probability from Z table is written as,
=> 0.0668
(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.
For 9000 hours: z = (9000 - 10,000) / 1000 = -1
For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.
(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.
Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:
1.645 = (x - 10,000) / 1000
Multiplying both sides by 1000 and adding 10,000, we get:
x = 11,645
Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.
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Find X then find angle RB
Answers
The value of x is 11 and arc RB = 150°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
We know that,
∠RDB = 1/2(RB - EC)
So, substituting the values,
5x - 10 = 1/2(13x + 7 - 60)
10x - 20 = 13x - 53
3x = 33
x = 11
So, arc RB = 13 x 11 + 7 = 150°.
Hence, arc RB = 150°.
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Kellys last quiz scores were 79,89,86, and 93. What must her next score be to obtain an average that is more than 88
Answers
Answer: To find out what Kelly's next score must be in order to obtain an average that is more than 88, we first need to find the current average of her scores. To do this, we add up her current scores and divide by the number of scores:
(79 + 89 + 86 + 93) / 4 = 337 / 4 = 84.25
Since the current average is 84.25, which is less than 88, Kelly must score higher than 88 on her next quiz to bring the average up to more than 88. To be specific, Kelly must score at least 89 on her next quiz.
Step-by-step explanation:
State the maximum and minimum values if they exist.
Answers
The maximum and minimum values are 34.5 and 2
How to determine the maximum and minimum valuesfrom the question, we have the following parameters that can be used in our computation:
P = 2x + 7y
Subject to:
4x - 2y <= 5
x >= 1
0 <= y <= 4
Next, we plot the constraints on a graph
From the graph, we have the following vertices
(1, 0), (4, 0) and (3.25, 4)
This gives
P = 2(1) + 7(0) = 2
P = 2(4) + 7(0) = 8
P = 2(3.25) + 7(4) = 34.5
Hence, the minimum is 2 and the maximum is 34.5
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