Answers
a: x = 1
b: (1, -7)
c: minimum
d: (0, -8)
2.
a: x = 2
b: (2, 16)
c: maximum
d: (0, 12)
Related Questions
prove if sum of second moments is finite then series converges almost surely math.stackexchange
Answers
The second Borel-Cantelli lemma, we have P(lim sup Sn < ∞) = 0, which implies that Sn converges almost surely.
Let {Xn} be a sequence of random variables, and let Sn = X1 + X2 + ... + Xn be the corresponding sequence of partial sums. We want to show that if E(Xn²) is finite for all n, then Sn converges almost surely.
Let Yn = Xn^2. Then E(Yn) = E(Xn²) < ∞ for all n, since we are given that the second moments are finite. By the second Borel-Cantelli lemma, it suffices to show that the series ∑ P(Yn > ε) converges for every ε > 0.
Since Yn = Xn² ≥ 0, we have P(Yn > ε) ≤ P(|Xn| > √ε). Using Markov's inequality, we have:
P(|Xn| > √ε) ≤ E(|Xn|²)/ε = E(Yn)/ε.
Therefore, we have:
∑ P(Yn > ε) ≤ ∑ E(Yn)/ε = (1/ε) ∑ E(Yn) = (1/ε) ∑ E(Xn²) < ∞.
The last inequality follows from the fact that the second moments are assumed to be finite.
Thus, by the second Borel-Cantelli lemma, we have P(lim sup Sn < ∞) = 0, which implies that Sn converges almost surely.
To know more about converges refer here:
https://brainly.com/question/15415793
#SPJ11
4. Use slope and/or the distance formula to
determine the most precise name for the
figure: A(-5, -6), B(2, 0), C(11, 9), D(4, 3).
[A] parallelogram
[B] kite
[C] rhombus
[D] trapezoid
5. Use slope and/or the distance formula to
determine the most precise name for the
figure: A(-9,-4), B(-7, 1), C(1, 5), D(-1,0).
[B] rhombus
[D] quadrilateral
[A] parallelogram
[C] rectangle
Answers
Result:
1. Based on the properties, the most precise name for figure is A. parallelogram
2. From the properties, the most precise name for the figure is B. rhombus.
How to determine the precise name of the figure?We can determine the precise name of the figure calculating the slopes of AB, BC, CD, and DA using the slope formula and/or the distance formula:
1. Using the slope formula:
AB = (0 - (-6))/(2 - (-5)) = 2
BC = (9 - 0)/(11 - 2) = 9/9 = 1
CD = (3 - 9)/(4 - 11) = -6/-7 = 6/7
DA = (-6 - (-5))/( -5 -(-5)) = 0
Calculate the lengths of the sides using distance formula:
AB = [tex]\sqrt((2 - (-5))^2 + (0 - (-6))^2)[/tex] = [tex]\sqrt(7^2 + 6^2)[/tex] = [tex]\sqrt{85}[/tex]
f BC = [tex]\sqrt((11 - 2)^2 + (9 - 0)^2)[/tex] = [tex]\sqrt(9^2 + 9^2)[/tex] = 9√2)
CD = [tex]\sqrt((4 - 11)^2 + (3 - 9)^2)[/tex] = sqrt[tex]\sqrt(7^2 + 6^2)[/tex] = √85
DA = [tex]\sqrt((-5 - 4)^2 + (-6 - (-9))^2)[/tex] = [tex]\sqrt(9^2 + 3^2)[/tex] = 3√10
The slopes of AB and CD are equal (2 and 6/7, respectively), and the slopes of BC and DA are equal (1 and 0, respectively).
Therefore, opposite sides are parallel that is a parallelogram.
2. First, we can calculate the slopes of AB, BC, CD, and DA using the slope formula:
AB = (1 - (-4))/(-7 - (-9)) = 5/2
BC = (5 - 1)/(1 - (-7)) = 4/4 = 1
CD = (0 - 5)/(-1 - 1) = -5/-2 = 5/2
DA = (-4 - 0)/(-9 - (-1)) = 4/8 = 1/2
Next, using the distance formula, we calculate the lengths of the sides:
AB = [tex]\sqrt((-7 - (-9))^2 + (1 - (-4))^2)[/tex] = [tex]\sqrt(2^2 + 5^2)[/tex] = [tex]\sqrt29[/tex]
BC = [tex]\sqrt{(1 - (-7))^2 + (5 - 1)^2}[/tex] = [tex]\sqrt(8^2 + 4^2)[/tex] = 4[tex]\sqrt17[/tex]
CD = [tex]\sqrt((-1 - 1)^2 + (0 - 5)^2)[/tex] = [tex]\sqrt(2^2 + 5^2)[/tex] = [tex]\sqrt29[/tex]
DA = [tex]\sqrt((-9 - (-1))^2 + (-4 - 0)^2)[/tex] = [tex]\sqrt(8^2 + 4^2)[/tex] = [tex]\sqrt80[/tex])
The slopes of AB and CD are equal (5/2 and 5/2, respectively), and the slopes of BC and DA are equal (1 and 1/2, respectively). meaning the opposite sides are parallel.
AB and CD have the same length ([tex]\sqrt(29)[/tex]), and BC and DA have the same (4[tex]\sqrt(17}[/tex]), which means it's a rhombus.
Learn more about a parallelogram at brainly.com/question/30273259
#SPJ1
On reversing the digits of a two digit number, the number obtained is 9 less than three times the original number. If the difference of these two numbers is 45, find the original number. A 35
B 27
C 28
D 30
Answers
There is no solution to this problem. None of the answer choices (A, B, C, D) are correct.
Let's start by representing the original two-digit number as 10x + y, where x represents the tens digit and y represents the ones digit.
When we reverse the digits, we get the number 10y + x. According to the problem, this number is 9 less than three times the original number:
10y + x = 3(10x + y) - 9
Simplifying this equation, we get:
10y + x = 30x + 3y - 9
7y - 29x = -9
We also know that the difference between these two numbers is 45:
(10x + y) - (10y + x) = 45
9x - 9y = 45
x - y = 5
Now we have two equations with two variables, which we can solve using substitution or elimination. I'll use elimination:
7y - 29x = -9
-7y + 7x = 35 (multiplying the second equation by -7)
Adding these two equations, we get:
-22x = 26
x = -13/11
This doesn't make sense, since x should be a digit between 1 and 9.
Know more about number here:
https://brainly.com/question/17429689
#SPJ11
Estimate the perimeter and the area of the shaded figure.
Answers
The perimeter and area of the given polygon are:
Perimeter = 22.325 units
Area = 25 square units
How to find the area and perimeter?Using Pythagoras theorem, we can find the length of the sides of the polygon as:
a = √(1² + 3²)
a = √10
b = √(3² + 3²)
b = 2√9
c = √(3² + 3²)
c = 2√9
d = √(1² + 3²)
d = √10
e = 4
Thus:
Perimeter = 2√10 + 4√9 + 4
Perimeter = 22.325 units
Area = 2(¹/₂ * 1 * 3) + 2(¹/₂ * 3 * 3) + (4 * 3)
= 25 square units
Read more about area and perimeter at: https://brainly.com/question/19819849
#SPJ1
help! look at the picture pls math.
Answers
Check the picture below.
so if we just get the volume of the whole box, and the volume of the balls, if we subtract the volume of the balls from that of the whole box, what's leftover is the part we didn't subtract, namely the empty space.
[tex]\stackrel{ \textit{\LARGE volumes} }{\stackrel{ whole~box }{(3.5)(3.5)(12.1)}~~ - ~~\stackrel{\textit{three balls} }{3\cdot \cfrac{4\pi (1.65)^3}{3}}} \\\\\\ 148.225~~ - ~~17.9685\pi ~~ \approx ~~ \text{\LARGE 91.8}~cm^3[/tex]
suppose you are interested in using regression analysis to estimate an nba player's salary using the following independent variables: the player was traded in the last 5 years, player's age, player's height, career free throw percentage, average points per game, and the team had greater than 45 wins in the previous season. which of the following independent variables are indicator (dummy) variables? select all that apply.
Answers
Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:
- The player was traded in the last 5 years
Based on the information provided, only one of the independent variables can be an indicator (dummy) variable, which is:
- The player was traded in the last 5 years
This variable can take on a value of 0 or 1, where 0 represents that the player was not traded in the last 5 years, and 1 represents that the player was traded in the last 5 years. The other independent variables are continuous variables (e.g., player's age, player's height, career free throw percentage, average points per game) or categorical variables that do not need to be represented as dummy variables (e.g., the team had greater than 45 wins in the previous season).
Visit to know more about Variables:-
brainly.com/question/28248724
#SPJ11
what is the value of the expression
2/-3 x -1/5
Answers
Explanation
Assuming the “x” is multiply
- 2/3 x - 1/5
Multiply across
And two negatives multiplied = positive
2/15
An amount is increased by 20% 40% of the new amount is 288 Work out the original amount.
Answers
When the amount is increased by 20%, the new amount becomes 1.20x.
Then, 40% of the new amount is 0.40(1.20x) = 0.48x.
We know that 0.48x = 288, so we can solve for x:
x = 288 / 0.48
x = 600
Therefore, the original amount is $600.
Calculate the surface area.
25 square inches
120 square inches
126 square inches
132 square inches
Answers
The surface area of the figure is 132 square units.
Option D is the correct answer.
We have,
The figure has two types of shapes.
- 3 rectangles
- 2 triangles
Now,
Area of the 3 rectangles.
= 5 x 10 + 4 x 10 + 3 x 10
= 50 + 40 + 30
= 120 square units
Area of 2 triangles.
= 1/2 x 4 x 3 + 1/2 x 4 x 3
= 1/2 x 12 + 1/2 x 12
= 6 + 6
= 12 square units
Now,
Total surface area.
= 120 + 12
= 132 square units.
Thus,
The surface area of the figure is 132 square units.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
Researchers studying osteoporosis (bone loss) suspected that women over the age of 50 in the United
States are diagnosed with the disease more often than women over 50 in Mexico. They took a random
sample of 200 women over the age of 50 from each country. Here are the results:
Diagnosed with osteoporosis? US. Mexico
Yes. 40. 20
No 160 180
Total 200. 200
The researchers want to use these results to test He: pus - PM = 0 versus H₂: Pus-PM > 0.
Assume that all conditions have been met.
What is the P-value associated with these sample results?
a. P-value is greater than or equal to
0.20
b. 0.05 is less than or equal to the P-
value < 0.10
c. 0.10 is less than or equal to the P-
value < 0.20
d. P-value < 0.01
e. 0.01 is less than or equal to the P-
value < 0.05
Answers
Answer:
A P-value < 0.01
Step-by-step explanation:
Key Question #20 1. For f(x)= x, determine the average rate of change of f(x) with respect to x over each interval. a. 1
Answers
The average rate of change of f(x) = x with respect to x over the interval a = 1 is 1.
To determine the average rate of change of f(x) = x with respect to x over the interval a, we'll use the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In this case, the interval a is 1, so let's choose an interval b. We can use any value for b, but let's choose b = 2 for simplicity.
Step 1: Find f(a) and f(b)
f(x) = x, so:
f(1) = 1
f(2) = 2
Step 2: Plug the values into the formula
Average Rate of Change = (f(2) - f(1)) / (2 - 1)
Average Rate of Change = (2 - 1) / (2 - 1)
Step 3: Calculate the result
Average Rate of Change = (1) / (1)
The average rate of change of f(x) = x with respect to x over the interval a = 1 is 1.
To learn more about Rate of change
https://brainly.com/question/17214872
#SPJ11
Which data table indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant?
Answers
Answer:
Step-by-step explanation:
To determine if there is a positive linear association between the hours worked and the daily wages of waiters in a restaurant, you can create a scatter plot of the data and look for a pattern.
Once you have the data, you can use a statistical software or a spreadsheet program to create a scatter plot. You can then visually inspect the scatter plot to see if there is a clear pattern of a positive linear association between the two variables.
If there is a positive linear association, the data points on the scatter plot will form a roughly straight line that slopes upwards from left to right. The closer the data points are to the line, the stronger the association.
So, the data table that indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant is the one where the scatter plot shows a clear upward trend.
Algibra 1, unit 5! Help
Answers
Answer: -15
Step-by-step explanation:
x+y=10
y=-x+10
2x+3(-x+10)=45
2x-3x+30=45
-x=15
x=-15
frankie has a new cell phone plan. he will pay a one-time activation fee of 30$, and 45$ each month. which equation can be used to determine the total amount, t, Frankie will have spent after m months on his cell phone plan
Answers
The equation which can be used to determine the total amount, t, Frankie will have spent after m months on his cell phone plan is t = 30 + 45m.
Given that,
Frankie has a new cell phone plan.
He will pay a one-time activation fee of 30$, and 45$ each month.
One time activation fee = $30
Amount each month = $45
Amount for m months = 45m
Total amount for the plan = 30 + 45m
If t represents the total amount for the cell phone activation plan, the required equation can be written as,
t = 30 + 45m
Hence the required equation for the cell phone plan is t = 30 + 45m.
Learn more about Equations here :
https://brainly.com/question/29280354
#SPJ1
Sophia, Malcolm, and Oren are playing a money game. Their bank
balances are shown in the table. Complete the table by writing the
absolute value of each bank balance to show how much each
player owes. Who owes the greatest amount?
Bank Balance Amount Owed
-$150
- $325
- $275
Answers
Answer:
Please mark me the brainliest
Bank Balance | Amount Owed
---------------------|-------------
-$150 | $150
-$325 | $325
-$275 | $275
To find the amount owed, we simply take the absolute value of each bank balance. The player who owes the greatest amount is the one with the largest absolute value bank balance. In this case, that would be Malcolm, who owes $325.
Step-by-step explanation:
You have a combination lock that has the numbers 1-40 on the dial. You
forgot the combination, but you remember that the combination is three
numbers, the last digit of all three numbers is 6, and none of the numbers
are between 1 and 10. You make a random guess with what you know.
What is the probability that you will get the combination?
Answers
Answer:
1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)
Step-by-step explanation:
The first digit can be any of the numbers between 10 and 40, except for those that end in 6 (since the last digit of all three numbers is 6). This leaves us with 30 numbers to choose from for the first digit. Similarly, the second digit can be any of the numbers between 10 and 40, except for those that end in 6 and the one chosen for the first digit. This leaves us with 29 numbers to choose from for the second digit.
For the third digit, we have only one option since we know it ends in 6.
So the total number of possible combinations is:
30 * 29 * 1 = 870
Out of these, only one combination is the correct one. Therefore, the probability of guessing the combination correctly on the first try is:
1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)
Which of the following is NOT an assumption of the Binomial distribution?a. All trials must be identical.b. All trials must be independent.c. Each trial must be classified as a success or a failure.d. The probability of success is equal to 0.5 in all trials.
Answers
Option e. "The number of trials is not fixed" would be the correct answer.
The assumption of the Binomial distribution that is NOT included in the options provided is that the number of trials must be fixed in advance. This means that the Binomial distribution applies only to situations where there is a fixed number of independent trials, each with the same probability of success, and the interest is in the number of successes that occur in these trials. Therefore, option e. "The number of trials is not fixed" would be the correct answer.
learn more about probability
https://brainly.com/question/30034780
#SPJ11
Express in the form of a rational number: 0.1212….
Answers
Answer:
[tex]0.1212...=\dfrac{4}{33}[/tex]
Step-by-step explanation:
A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.
There are three ways to show a repeating decimal:
Several duplicates of the repeating digit or block of digits, followed by an ellipsis, e.g. 0.3333... or 0.123123...A dot or a line above a repeated digit, e.g. [tex]\sf 0.\.{3}[/tex] or [tex]\sf 0.\overline{3}[/tex]A line above a repeating block of multiple digits, e.g. [tex]\sf 0.\overline{123}[/tex]0.1212... is a repeating decimal as there are two duplicates of the repeating block of digits "12" followed by an ellipsis.
To express a repeating decimal as a rational number, begin by assigning the decimal to a variable:
[tex]x=0.1212...=0.\overline{12}[/tex]
Multiply both sides by 100:
[tex]\implies x \cdot 100=0.\overline{12}\cdot 100[/tex]
[tex]\implies 100x=12.\overline{12}[/tex]
Subtract the first equation from the second to eliminate the part after the decimal:
[tex]\begin{array}{crcr}& 100x & = & 12.\overline{12}\\- & x & = & 0.\overline{12}\\\cline{2-4} & 99x & = & 12\phantom{.12}\\\end{array}[/tex]
Divide both sides of the equation by 99:
[tex]\implies \dfrac{99x}{99}=\dfrac{12}{99}[/tex]
[tex]\implies x=\dfrac{12}{99}[/tex]
Reduce the fraction to is simplest form by dividing the numerator and denominator by 3:
[tex]\implies x=\dfrac{12 \div 3}{99 \div 3}=\dfrac{4}{33}[/tex]
[tex]\textsf{Therefore, $0.1212...$ expressed in the form of a rational number is\;$\dfrac{4}{33}$}.[/tex]
Please help me with this my quiz. Thank you :)
Due tomorrow
Answers
Answer:
dark blue
Step-by-step explanation:
- (d) When a=0.02 and n=24, X2-left =____
X2-right =_____
Answers
When a=0.02 and n=24, [tex]X_{left}^{2}[/tex] = 9.260 and [tex]X_{right}^{2}[/tex]= 41.638. In order to calculate [tex]X_{left}^{2}[/tex] and [tex]X_{right}^{2}[/tex] when a=0.02 and n=24, we need to use the chi-squared distribution table. This table provides us with the critical values for a given level of significance (alpha) and degrees of freedom (df).
To answer your question, when a=0.02 and n=24, we will find the [tex]X_{left}^{2}[/tex] and [tex]X_{right}^{2}[/tex] values using the Chi-square distribution table.
Step 1: Determine the degrees of freedom. In this case, the degrees of freedom (df) are equal to n-1, so df = 24 - 1 = 23.
Step 2: Determine the significance level (alpha) and divide it by 2. Since a = 0.02, the significance level is [tex]\frac{\alpha}{2} =0.01[/tex] for each tail (left and right) of the distribution.
Step 3: Use the Chi-square distribution table to find the critical values. Look for the values corresponding to the degrees of freedom (23) and significance level (0.01) in each tail.
According to the Chi-square distribution table:
[tex]X_{left}^{2}[/tex]= 9.260
[tex]X_{right}^{2}[/tex]= 41.638
To know more about the significance level visit:
https://brainly.com/question/30011181
#SPJ11
Annabel is comparing the distances that two electric cars can travelafter the battery is fully charged
Answers
After the battery is fully charged, Car B can go further than Car A. Car B, as compared to Car A, had lower variability measurements. After the battery is completely charged, Car B can go further than Car A since Car A has a lower mean and median. Option D is Correct.
The median splits the data in half. A lower median indicates that Car A has less mileage than Car B.
Two measurements exist.
The measure of centre reveals how closely or widely the data are dispersed around the centre.
The measurements of centre are mean, median, and mode.
Car A travelled less since it had a lower mean and median.
We can find out how data changes with a single value using the measure of variability. The data is denser at the mean when the MAD is less. The MAD in Car B is lower. Data that is closer to the centre of the data set has a smaller IQR.
IQR is lower in Car B.
Consequently, automobile B travelled steadily since its IQR and MAD were lower. Option D is Correct.
Learn more about variability visit: brainly.com/question/12872866
#SPJ4
Correct Question:
Annabel is comparing the distances that two electric cars can travel after the battery is fully charged. Car A (miles) Car B (miles) Mean 145 200 Median 142 196 IQR 8 4 MAD 6 2 Part A Use the measures of center to make an inference about the data. Use the drop-down menus to complete your answer. Car A can travel further than Car B after the battery is fully charged. Part B Based on the data, which car performs most consistently? Explain. A. Car A because the measures of center are smaller for Car A than for Car B. B. Car B because the measures of center are smaller for Car B than for Car A. C. Car A because the measures of variability are smaller for Car A than for Car B. D. Car B because the measures of variability are smaller for Car B than for Car A.
The point A is shown below.
Reflect A across the x-axis.
Then reflect the result across the y-axis.
Plot the final point.
Important: Only plot the final point in your answer.
8-1
X
5
Answers
The coordinate of final point of A after transformation is,
A'' = (0, - 7)
We have to given that;
Coordinate of A = (0, 7)
We know that;
Rule for the across the x - axis is,
(x, y) = (x , - y)
Hence, We get;
Point after transformation is,
A' = (0, - 7)
And, Rule for the across the y - axis is,
(x, y) = (-x , y)
Hence, Point after transformation is,
A'' = (0, - 7)
Thus, The coordinate of final point of A after transformation is,
A'' = (0, - 7)
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
Both of these groups started with 22, 6-sided dice and followed the same procedure for removing dice until they had no dice left. How could they end up with such different scatterplots? Does it make sense that one set of data could look so possibly linear while the other does not?
Answers
It is possible for one set of data to have a scatterplot that appears linear while the other does not, even if both groups started with the same number of dice and followed the same removal procedure.
This is because the way the dice were removed could have been different between the two groups, leading to different patterns of results. Additionally, other factors such as the order in which the dice were removed or the number of trials conducted could also affect the resulting scatterplot.
Ultimately, the scatterplot is a visual representation of the relationship between the variables being measured, and it can take on many different forms depending on the specific data and conditions being analyzed.
To learn more about scatterplot
https://brainly.com/question/1348021
#SPJ11
What is the coefficient of x^3 term in the power series expansion (or Taylor's expansion) of f(x) = e^(x) sin(x)
Answers
The coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is 1/15.
To find the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x), we need to write the Taylor series for [tex]e^x[/tex] and sin(x) and then multiply them to get the Taylor series for f(x). The Taylor series for e^x is:
[tex]e^x[/tex] = 1 + x + (x²/2!) + (x³/3!) + ...
The Taylor series for sin(x) is:
sin(x) = x - (x³/3!) + (x⁵/5!) - ...
Multiplying these two series, we get:
f(x) = [tex]e^x[/tex] sin(x) = (1 + x + (x²/2!) + (x³/3!) + ...) × (x - (x³/3!) + (x⁵/5!) - ...)
Expanding this out and collecting the terms with x³, we get:
f(x) = x - (x³/3!) + (7x³/5!) + ...
Therefore, the coefficient of x³ term in the power series expansion of f(x) = [tex]e^x[/tex] sin(x) is -1/6 + 7/120 = 1/15.
Learn more about the Power series expansion at
https://brainly.com/question/30262936
#SPJ4
x-3y= -9 slope intercept form
Answers
Answer:
[tex]\textsf{y=\frac{1}{3}x+3}[/tex][tex]y = \frac{1}{3} x+3[/tex]
Step-by-step explanation
[tex]\textsf{*slope intercept form: y = mx +b}[/tex]
---------------------------------------------
[tex]\textsf{x - 3y = -9}[/tex]
Subtract x from both sides:
[tex]\textsf{-3y = -x - 9}[/tex]
Divide both sides by -3:
-3y/-3 = -x/-3 - 9/-3
[tex]\textsf{y = 1/3x +3}[/tex]
[tex]-jurii[/tex]
Phil is a 21-year-old male. What is his life expectancy? Male Female Deaths Per 1,000 Life Expectancy (Years) Probabillity of Living to This Age Deaths Per 1,000 Life Expectancy (Years) Probabillity of Living to This Age Age 19 1.0 58.2 0.9907 0.5 62.2 0.9940 20 1.0 57.2 0.9897 0.5 61.3 0.9935 21 1.0 56.3 0.9888 0.5 60.3 0.9930 22 1.0 55.3 0.9878 0.5 59.3 0.9925A. 56.3 years B. 77.3 years C. 77.2 years D. 55.3 years
Answers
Phil's life expectancy is 56.3 years.
Based on the provided data, the life expectancy for Phil, a 21-year-old male, is 56.3 years. Therefore, the correct answer is 56.3 years.
Learn more about life expectancy: https://brainly.com/question/30036353
#SPJ11
Show work and please explain how to solve it!
Answers
The density of the ball in the air is given as follows:
d = 4 x 10^5 ounces/ft³.
How to calculate the density?The density is calculated as the division of the mass by the volume of an object, as follows:
d = m/v.
The ball in this problem is spherical with a diameter of 0.05 feet = radius of 0.025 feet, hence the volume is given as follows:
V = 4 x 3.1416 x 0.025³/3
V = 6.545 x 10^-5 ft³.
The ball in the air is inflated, hence the mass is given as follows:
m = 22.93 ounces.
Thus the density of the ball is given as follows:
d = 22.93/(6.545 x 10^-5)
d = 4 x 10^5 ounces/ft³.
More can be learned about density at https://brainly.com/question/1354972
#SPJ1
Suppose a bag contains 4 white chips and 6 black chips. What is the probability of randomly choosing a black chip, not replacing it, and then randomly choosing another black chip?
Answers
The probability of choosing a black chip and then another black chip is,
⇒ 1/3
Since, There are 4 + 6 = 10 chips in the bag.
And, 6 of them are black .
Hence, The probability that the first chip chosen will be black is,
⇒ 6/10
⇒ 3/5.
After that, there is one black chip less in the bag, so there are 9 chips in the bag, 5 of them are black.
Hence, The probability that the second chip chosen will be black is,
⇒ 5/9
Now, Multiply the probabilities to find the probability that the first chip will be black and the second chip will be black:
⇒ 3/5 × 5/9
⇒ 1/3
Thus, The probability of choosing a black chip and then another black chip is,
⇒ 1/3
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Now suppose a new highway reduces shipping costs from Plant 3 to the North region by 25%. How will this change affect the appliance company?
a. This change in shipping costs will not affect the shipping plan, but will reduce the company's shipping costs.
b. This change in shipping costs may or may not affect the company. We need additional information to determine the exact effect.
c. Due to this cost reduction, the company's shipping plan will change and they will use the shipping route from Plant 3 to the North region.
d. This change in shipping costs will not affect the company since they are not using this shipping route.
Answers
This change in shipping costs may or may not affect the company.
We need additional information to determine the exact effect.
Option B is the correct answer.
We have,
While the reduction in shipping costs from Plant 3 to the North region is significant, we need more information about the company's current shipping plan, routes, and costs associated with other plants to determine if this change will impact their overall shipping strategy.
Thus,
This change in shipping costs may or may not affect the company.
We need additional information to determine the exact effect.
Learn more about cost and effects here:
https://brainly.com/question/28448166
#SPJ11
Find the surface area of the regular hexagonal prism to the nearest tenth.
Answers
The Surface Area of the regular hexagonal prism is 92.784 square unit.
We have,
a = 2 unit
h= 6 unit
So, surface area of Prism
= 6 ah + 3√3 a²
= 6(2)(6) + 3√3 (2)²
= 72 + 12√3
= 92.784 square unit.
Thus, the Surface Area is 92.784 square unit.
Learn more about Surface Area here:
https://brainly.com/question/26330105
#SPJ1