Answer:
40 hours
26.09 hours
Step-by-step explanation:
What is the driving time for a 1800-mile trip if you drive at an average speed of 45 miles per hour?
1800 / 45 = 40 hours
What is the driving time at 69 miles per hour?
1800 / 69 = 26.09 hours
Step-by-step explanation:
The driving time for a 1800-mile trip at an average speed of 45 miles per hour can be calculated as
Driving time = Total distance / Average speed
Driving time = 1800 miles / 45 miles per hour = 40 hours
Similarly, the driving time at an average speed of 69 miles per hour can be calculated as:
Driving time = 1800 miles / 69 miles per hour = 26 hours
So if you drive at an average speed of 45 miles per hour, the driving time for a 1800-mile trip would be 40 hours, and if you drive at an average speed of 69 miles per hour, the driving time would be 26 hours.
8m
6m
10m
5m what is the area of this shape
Answer:
68 m²Step-by-step explanation:
we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.
6 * 8 + 4 * 5 = remember PEMDAS
48 + 20 =
68 m²
BRAINLIEST if correct, 5th grade geometry
Answer:
EF, GH
Step-by-step explanation:
both go on forever from one point
Answer:
A and B
Step-by-step explanation:
Because they go infinitly in one direction and end in another.
I need help answering this
The domain of the function for this situation is given as follows:
B. All whole numbers greater than or equal to 0 and less than or equal to 7.
How to obtain the domain of a function?The domain of a function is the set that contains all the values assumed by the input of the function.
Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.
The values that compose the domain of the graph are given as follows:
0, 1, 2, 3, 4, 5, 6 and 7.
Which is best described by option B.
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I will give brainliest and ratings if you get this correct
The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.
What is the firm short-run total cost curve and short-run average cost curve functionA. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:
TC = wL + rK,
where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.
To calculate the short-run average cost curve, we need to divide the total cost by the level of output:
SAC = TC / Q
Where Q is the level of output.
B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:
SMC = dTC / dQ
At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:
TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150
So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:
Q = 2 * sqrt(KL)
Taking the derivative with respect to L, we get:
dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))
Substituting the values, we get:
SMC = 4 + (1 / (sqrt(100 * 12.5)))
At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:
TC = 4 * 100 + 1 * 100 = 400
So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:
Q = 2 * sqrt(KL)
Taking the derivative with respect to L, we get:
dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))
Substituting the values, we get:
SMC = 4 + (1 / (sqrt(100 * 100)))
SMC = 4.01
C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.
D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.
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Find the sum of the infinite geometric series, if possible. (Round your answer to three decimal places.)
∞
Σ
n = 0 6(0.75)n
STEP 1: Determine the first term of the infinite geometric series.
a1 =
24
STEP 2: Find the common ratio of the infinite geometric series.
r =
STEP 3: Based on your results from Step 1 and Step 2, the Sum of an Infinite Geometric Series Formula may be applied to this series. What guarantees the formula will work in this case?
The common ratio has an absolute value less than 1.
The first term of the series has an absolute value less than 1.
The common ratio has an absolute value less than the first term of the series.
The common ratio is less than the first term of the series.
The common ratio is less than one.
The first term of the series has an absolute value greater than the common ratio.
The first term of the series is positive.
STEP 4: Compute the sum of the series using the Sum of an Infinite Geometric Series Formula. Round your answer to three decimal places.
Sn =
STEP 1: a1 = 6.
STEP 2: r = 0.75
STEP 3: The common ratio is less than one.
STEP 4: The sum of the Sum of the Infinite Geometric series is Sn = 24
How to find the sum of the infinite geometric series?Since we have the expression for the sum of the infinite geometric series
[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]
STEP 1:
The first term of the infinite geometric series is 6. Thus, a1 = 6.
STEP 2:
The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75
STEP 3:
The common ratio is less than one.
Because Sn = a/(1 - r) is the formula we use when the common ratio is less than 1.
STEP 4:
Sn = a/(1 - r)
Sn = 6/(1 - 0.75) = 24
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Select the correct answer.
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
A.
30
B.
240
C.
2,400
D.
3,000
Answer:
The total possible outcomes that exist are:
2400
Step-by-step explanation:
We are given four dices:
first is a standard 6-faced die.
The second die has 4 faces.
Third dice has 10 faces.
Fourth dice has 10 faces.
Now when all the dice are thrown together then the total number of possible outcomes are:
( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)
The answer is:
2400
Which is true about the function y=−2x?
It is a nonlinear function because its graph passes through the origin.
It is a nonlinear function because its graph is a straight line.
It is a linear function because its graph passes through the origin.
It is a linear function because its graph is a straight line.
The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.
Which answer choice represents a true statement?It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?
On this note, since the graph of the equation is such that g
it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.
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A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.
The probability that at least 1 of the 4 cards drawn is a face card is 0.6.
How to find probability of 4 cards drawn?A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.
Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.
A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:
P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).
The likelihood that none of the four draws will produce a face card is:
P(no face cards are present) = (10/13)4 = 0.432
As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:
P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568
The chance, rounded to one decimal place, is roughly 0.6.
Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.
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What is 7/8 of sixteen times a half of 30
7/8 of sixteen times a half of 30 is 210.
What is a PEMDAS rule?
PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
Start with the expression inside the parentheses: half of 30 is 15.
Multiply 16 by 15: 16 times 15 is 240.
Find 7/8 of 240:
7/8 of 240 = (7/8) x 240
= 210
Hence, 7/8 of sixteen times a half of 30 is 210.
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answer all pls get 100 pointa
a).The function1 changes at greater rate of 45.
b). At x = 1; the function1 = 45 and function2 = 50.
c).The functions are equal to 90 at x = 2.
What is a function in the form y = mx + cA function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.
The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.
For the function1, when y = 0 and x = 0, we can solve for c and m as follows:
0 = 0m + c
c = 0
when y = 90 and x = 2;
90 = 2m + 0
m = 45
Hence, the function1 with y = 45x changes at a greater rate of 45.
At x = 1:
for function1;
y = 45(1) + 0 = 45
for function2;
y = 40(1) + 10 = 50.
At the point when x = 2:
for function1;
y = 45(2) + 0 = 90
for function2;
y = 40(2) + 10 = 90.
Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.
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what happend if you do rise over run
PLEASE GIVE BRAINLIEST
thank you and have a good day :)
Answer:
You figure out the slope
Step-by-step explanation:
Rise/Run is a formula that calculates the slope. This determines the direction of the line and how steep it is.
Answer:
its a math term yw my boy
Step-by-step explanation:
Question 10 Part 1 of 3
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium
population continues to grow for a while, but then stops growing and begins to decline. The size of
the population at time t (hours) is b=8^6 +8^3t-8^2 t^2. Find the growth rates at t=0 hours,
t=4 hours, and t=8 hours.
The growth rate at t=0 hours is _____bacteria per hour
The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is 1,000,016.
How to calculate the number of bacteria over time?To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.
0 hours:
Population = 10^6 + (10^4)0 -(10^3)0^2
Population = 10^6 - 10^3
Population = 10^3 or 1,000
4 hours:
Population = 10^6 + (10^4)4 -(10^3)4^2
Population= 10^6 + 40,000 - 16,000
Population= 1,000,024
8 hours:
Population = 10^6 + (10^4)8 -(10^3)8^2
Population= 10^6 + 80,000 - 64,000
Population= 1,000,016
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Question 2
Answer: y =
<
-
Find the equation of the line with Slope = passing through the point (-35,10). Write your answer
in the form y = mz+ b.
I+
Submit Question
>
5
7
Write your answers as integers or as reduced fractions in the form A/B.
Question Help: Video Message instructor
An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 10 = -5/7(x - (-35))
y - 10 = -5/7(x + 35)
y - 10 = -5x/7 - 25
y = -5x/7 - 15
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Rewrite the equation in Ax+By=C form
y-6=5(x+2)
the equation of a curve is given by
y=x^3/3+7x^2/2+10x+d, where d is a
constant. Find the possible values of d
when the x-axis is tangent to the curve
v=x^3/3+7x^2/2+10x+d.
Answer: A tangent to the x-axis means that the y-coordinate of the point of tangency is 0. So, we can find the possible values of d by setting y = 0 and solving for x:
0 = x^3/3 + 7x^2/2 + 10x + d
This is a cubic equation, so it can be solved using various methods such as factoring, completing the square, or using a numerical method such as the Newton-Raphson method. If the equation can be factored or the method used is numerical, there might be multiple possible values of d. If the method used is completing the square, there would be only one possible value of d.
However, without a specific method, it's not possible to find the exact value(s) of d. The possible values of d will depend on the specific solution method used to solve the equation.
Step-by-step explanation:
what is the equation of a line that is parallel to the line that is given by the equation x=-4?
The equation of the line which is parallel to the line x = -4 will be x = -3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is x = -4. The y-intercept is zero for the line.
The equation of the line parallel to the equation will be,
x = -3
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A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answer:
285.76 kilograms 1.1 cubic yard
Step-by-step explanation:
Answer:
1.11121 cubic yards.
Step-by-step explanation:
First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:
1 lb = 0.45359237 kg
42 lbs = 42 * 0.45359237 kg = 19.05 kg
So, the weight of 1 bag of garden soil is 19.05 kilograms.
Next, let's find the weight of 15 bags of garden soil:
15 bags * 19.05 kg/bag = 285.75 kg
So, 15 bags of garden soil weigh 285.75 kilograms.
Next, let's find the volume of 15 bags of garden soil in cubic yards:
1 cubic foot = 0.037037 cubic yards
2 cubic feet * 15 bags = 30 cubic feet
30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards
So, 15 bags of garden soil have a volume of 1.11121 cubic yards.
four times the sum of the three consecutive even intergers is 240 more than six times the smallest integer.
Answer:
Step-by-step explanation:
Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".
Now we can set up the equation for the problem:
4 * (x + (x + 2) + (x + 4)) = 240 + 6x
Expanding the parentheses on the left side:
4 * (3x + 6) = 240 + 6x
Simplifying the left side:
12x + 24 = 240 + 6x
Subtracting 6x from both sides:
6x + 24 = 240
Subtracting 24 from both sides:
6x = 216
Dividing both sides by 6:
x = 36
So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.
someone pls help with this question
a² y² - 2aby + b²
Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet
SA = 2π(2.6)2 + 2.6π(4.4) square feet
SA = 2π(2.6)2 + 1.3π(4.4) square feet
SA = 2π(1.3)2 + 1.3π(4.4) square feet
SA = 2π(1.3)2 + 2.6π(4.4) square feet
Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet
The surface area of cylinder is given by the formula =2πrh+2πr²
The radius is Diameter/2
2.6/2=1.3
The radius is 1.3
Surface area =2π(1.3)(4.4)+2π(1.3)²
So =2.6π(4.4)+2π(1.3)²
Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.
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Answer:
Step-by-step explanation:
Find the area of the figure pictured below.
The area of the composite figure is 41 ft square.
How to find the area of a figure?The figure is a composite figure. A composite figure is a figure that has two or more shapes.
Therefore, the area of the composite figure is the sum of the individual area of the shapes.
Therefore,
area of the figure = area of rectangle 1 + area of rectangle 2
area of rectangle 1 = lw
where
l = lengthw = widthTherefore,
area of rectangle 1 = 2 × 4 = 8 ft²
area of rectangle 2 = 11 × 3 = 33 ft²
Hence,
area of the figure = = 8 + 33
area of the figure = 41 ft²
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The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image
The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.
The new coordinates of B will be:
x-coordinate: 4 x (-2) = -8
y-coordinate: 4 x (-1) = -4
So the new vertex B' is (-8, -4).
The new coordinates of C will be:
x-coordinate: 4 x (2) = 8
y-coordinate: 4 x (-2) = -8
So the new vertex C' is (8, -8).
The new coordinates of D will be:
x-coordinate: 4(1) = 4
y-coordinate: 4(2) = 8
So the new vertex D' is (4, 8).
Therefore, the image of the resultant figure is given in the image below.
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Grayson is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Grayson need to invest, to the nearest dollar, for the
value of the account to reach $15,000 in 5 years?
Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
What is continuously compounded interest?
Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.
The formula for continuous compounding is given by:
[tex]A = Pe^{rt}[/tex]
where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.
We want to find P when A = $15,000, r = 0.04, and t = 5 years.
Substituting these values into the formula, we get:
[tex]15000 =Pe^{0.04*5}[/tex]
Simplifying the right-hand side, we get:
[tex]15000 =Pe^{0.2}[/tex]
Dividing both sides by e^(0.2), we get:
[tex]P= \frac{15000}{e^{0.2}}[/tex]
Using a calculator, we get:
P ≈ $10,994
Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
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Enter each answer as a whole number or a faction, or DNE forDoes Not Exist
The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;
[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]
[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7
[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE
What is a piecewise function?A piecewise function is a function that has rules or definition based on the interval of reference of the function.
The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;
The points on the line of the graph are;
(1, 1), and (3, 3)
The slope of the graph as x tends to 2⁺ is therefore;
Slope = (3 - 1)/(3 - 1) = 1
The equation of the line is therefore;
y - 1 = x - 1
y = f(x) = x
Therefore;
f(x) - 4 = x - 4
f(x + 3) = x + 3
[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]
[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{2 - 4}{2 + 3} =\underline{-\frac{2}{5}}[/tex]The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;
f(f(x) + 4) = f(x + 4) = x + 4
[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;
[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = 3 + 4 = 7[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;
The equation of the function at x = 2 is; y = f(x) = x
f(2 + h) = 2 + h
f(2) = 2
Therefore;
[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h
[tex]\lim \limits_{h\to 0} \frac{f(2 + h)-f(2)}{h} = \frac{0}{0}[/tex] DNE (Does Not Exist)Learn more about the piecewise functions here: https://brainly.com/question/14390119
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NAME
12. Ling wants to buy a sleeping bag.
The sale price is $9. What was the
original price if the sale price was 30?
Scenario #1: Raul.
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account, which earns 1.5% interest per year.
1. what is the total balance in the account after 40 years?
2. how much of a total did Raul contribute himself?
3. how much money did Raul make through compound interest in this savings account?
4. identify one way Raul could have increased the total amount of money he made over 40 years. Explain your reasoning..
After 40 years, the account has a total balance of $49.450.80.
Why is there an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
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A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score?
A. B in 3 three-credit classes
B. D in 1 three-credit class
C. in 1 four-credit class
D. C in 1 two-credit class
Weighed averages show that the student has a grade point average of 2.33.
How is the grade point determined?The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.
A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.
B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.
C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.
D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.
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What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
The measure of each angle in the regular polygon is 154.3 degrees
How to determine the measure of each angle in a regular polygonFrom the question, we have the following parameters that can be used in our computation:
Number of sides, n = 14
The measure of each angle is calculated as
Angle = ( n − 2 ) × 180/n
substitute the known values in the above equation, so, we have the following representation
Angle = (14 − 2) × 180/14
Evaluate
Angle = 154.3
Hence, the angle is 154.3
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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 400 grams and a standard deviation of 20grams. Find the weight that corresponds to each event.
(Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.)
a. Highest 20 percent
b. Middle 60 percent to
c. Highest 80 percent
d. Lowest 15 percent.
Answer:
a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.
b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weights:
Weight Lower Bound = Mean + (z-score * Standard Deviation)
Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g
Weight Upper Bound = Mean + (z-score * Standard Deviation)
Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.
c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.
d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (-0.9332 * 20) = 346.64 g
So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.
Step-by-step explanation:
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
What is Variability of data?Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.
The range is the best measure of variability for the data shown, and its value is 45.
The range is defined as the difference between the largest and smallest values in a set of data.
In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.
The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.
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