Based on the information given, we know that the roots of the equation 5x + 13x + k = 0 are reciprocal of each other. This means that if one root is represented by r, the other root can be represented by 1/r.
Using the sum and product of roots formula, we can find that the sum of the roots is: r + 1/r = -13/5
Multiplying both sides by r, we get: r^2 + 1 = -13/5r
Multiplying both sides by 5r, we get: 5r^3 + 5r = -13
Simplifying, we get: 5r^3 + 5r + 13 = 0
This is a cubic equation that can be solved using the cubic formula. However, we do not need to solve for r to find the value of k.
We know that the product of the roots is: r * 1/r = 1
Using the product of roots formula, we can find that the product of the roots is: k/5 = 1
Multiplying both sides by 5, we get: k = 5
Therefore, the value of k is 5.
Learn more about roots of equation here, https://brainly.com/question/776122
#SPJ11
If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)=151-x/10. a. Find an expression for the total revenue from the sale of x thousand candy bars. b. Find the value of x that leads to maximum revenue. c. Find the maximum revenue.
Answer:
(a) The total revenue from the sale of x thousand candy bars is equal to the product of the price charged for a candy bar and the number of candy bars sold. If p(x) is the price charged for a candy bar in cents, then the revenue R(x) in dollars is given by:
R(x) = (p(x) * 1000x) / 100
R(x) = (151 - x/10) * 100x
R(x) = 15100x - 1000x^2
Therefore, the expression for the total revenue from the sale of x thousand candy bars is R(x) = 15100x - 1000x^2 dollars.
(b) To find the value of x that leads to maximum revenue, we need to find the value of x for which R(x) is maximum. We can do this by finding the derivative of R(x) with respect to x, setting it equal to zero, and solving for x. So:
R'(x) = 15100 - 2000x
Setting R'(x) equal to zero, we get:
15100 - 2000x = 0
Solving for x, we get:
x = 7.55
Therefore, the value of x that leads to maximum revenue is 7.55 thousand candy bars.
(c) To find the maximum revenue, we substitute x = 7.55 into the expression for R(x):
R(7.55) = 15100(7.55) - 1000(7.55)^2
R(7.55) = $57042.50
Therefore, the maximum revenue is $57,042.50 when 7.55 thousand candy bars are sold.
Step-by-step explanation:
The maximum revenue from the sale of candy bars in the city is $84,375. a. The expression for total revenue from the sale of x thousand candy bars can be found by multiplying the price per candy bar by the number of candy bars sold:
Total revenue = p(x) * x
Substituting the given equation for p(x), we get:
Total revenue = (151 - x/10) * x
b. To find the value of x that leads to maximum revenue, we need to take the derivative of the revenue function and set it equal to zero:
d/dx (151x - x^2/10) = 0
Simplifying and solving for x, we get:
x = 750
c. To find the maximum revenue, we substitute the value of x obtained in part (b) into the revenue function:
Total revenue = (151 - 750/10) * 750 = $84,375
Therefore, the maximum revenue from the sale of candy bars in the city is $84,375.
Learn more about revenue here:
brainly.com/question/1842659
#SPJ11
A corporation has 30 manufacturing plants. Of these, 23 are domestic and 7 are located outside of the country. Each year a performance evaluation is conducted for 4 randomly selected plants. What is the probability that the evaluation will include no plants outside the country? What is the probability that the evaluation will include at least 1 plant outside the country? What is the probability that the evaluation will include no more than 1 plant outside the country? The probability is. (Round to four decimal places as needed.) The probability is. (Round to four decimal places as needed.) The probability is. (Round to four decimal places as needed.)
The probabilities are:
(a) P(X = 0) ≈ 0.3139
(b) P(X ≥ 1) ≈ 0.6861
(c) P(X ≤ 1) ≈ 0.9862
We can model this situation using the hypergeometric distribution.
Let's define:
N = total number of manufacturing plants = 30
D = number of plants outside the country = 7
n = number of plants in the performance evaluation = 4
(a) Probability of including no plants outside the country:
We want to find P(X = 0), where X is the number of plants outside the country in the performance evaluation. This can be calculated using the hypergeometric distribution formula:
P(X = 0) = (C(23, 4) * C(7, 0)) / C(30, 4) = (23 choose 4) / (30 choose 4) ≈ 0.3139
(b) Probability of including at least 1 plant outside the country:
We want to find P(X ≥ 1). We can use the complement rule and find the probability of including no plants outside the country and subtract it from 1:
P(X ≥ 1) = 1 - P(X = 0) = 1 - (C(23, 4) * C(7, 0)) / C(30, 4) ≈ 0.6861
(c) Probability of including no more than 1 plant outside the country:
We want to find P(X ≤ 1). This can be calculated as the sum of P(X = 0) and P(X = 1):
P(X ≤ 1) = P(X = 0) + P(X = 1) = (C(23, 4) * C(7, 0)) / C(30, 4) + (C(23, 3) * C(7, 1)) / C(30, 4) ≈ 0.9862
Therefore, the probabilities are:
(a) P(X = 0) ≈ 0.3139
(b) P(X ≥ 1) ≈ 0.6861
(c) P(X ≤ 1) ≈ 0.9862
To learn more about hypergeometric visit:
https://brainly.com/question/15187088
#SPJ11
The following population data of a basic design of a product are given as:
1. Base product
average length - 90 cm
with a standard deviation of the length - 7 cm
2. A modifications was made to this product and a sample of 12 unit was collected. The sample is shown in the table to the right:
3. Test at a=0.01 whether there is difference between standard deviations (+/-) of this product's length between the base and the modified product?
a) What is/are the critical value(s)? b) What is/are the test statistic(s)? c) Was there a difference? Yes or No
a) The critical value for a two-tailed test with a significance level of 0.01 and 11 degrees of freedom is 3.11 (found using a t-distribution table).
b) The test statistic for comparing two standard deviations is the F-statistic. The formula for calculating it is [tex]F = \frac{s1^2}{s2^2}[/tex], where s1 is the sample standard deviation of the first group (base product), s2 is the sample standard deviation of the second group (modified product), and the larger standard deviation is always in the numerator. Using the sample data given, we find:
s1 = 7 cm (from the base product)
s2 = 6.5 cm (from the modified product)
[tex]F = \frac{(7)^{2} }{(6.5)^{2} } = 1.223[/tex]
c) To determine if there is a difference between the standard deviations, we compare the calculated F-statistic to the critical value we found in part a. Since our calculated F-value (1.223) is less than the critical value (3.11), we fail to reject the null hypothesis. Therefore, we conclude that there is not enough evidence to suggest that there is a significant difference between the standard deviations of the two products.
To know more about "standard deviation" refer here:
https://brainly.com/question/23907081#
#SPJ11
4. Samantha plans to deposit $175 in an account at the end of each month for the next seven
years so she can take a trip. The investment will earn 5. 4 percent, compounded monthly.
a. How much will she have in the account after the last $175 deposit is made in
seven years?
b.
How much will be in the account if the deposits are made at the beginning of each
month?
a) Samantha will have $20,359.68 in the account after the last $175 deposit is made in seven years.
b) Samantha makes 175-dollar deposits at the beginning of each month for seven years, she will have $21,372.77 in the account after the last deposit is made.
We can use the formula for the future value of an annuity with monthly compounding to solve this problem. The formula is:
FV = [tex]P * (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]
Where:
FV is the future value of the annuity
P is the regular payment or deposit
r is the annual interest rate
n is the number of compounding periods per year (12 for monthly compounding)
t is the total number of years
a. If Samantha makes 175-dollar deposits at the end of each month for seven years, the total number of deposits she will make is:
7 years x 12 months/year = 84 deposits
The regular payment or deposit is P = $175, the annual interest rate is r = 5.4%, and the number of compounding periods per year is n = 12. The total number of years is t = 7.
Using the formula above, we can calculate the future value of the annuity:
FV = [tex]$175 *[/tex] [tex](((1 + 0.054/12)^(12*7) - 1) / (0.054/12))[/tex]
FV = [tex]$175 *[/tex] (((1.0045)[tex]^84 - 1[/tex]) / (0.0045))
FV =[tex]$175 * (116.2269)[/tex]
FV = $20,359.68
Therefore, Samantha will have $20,359.68 in the account after the last $175 deposit is made in seven years.
b. If Samantha makes 175-dollar deposits at the beginning of each month for seven years, we need to adjust the formula above to account for the timing of the deposits. One way to do this is to use the formula:
[tex]FV = P * (((1 + r/n)^(n*t) - 1) / (r/n)) * (1 + r/n)[/tex]
Where the additional factor (1 + r/n) accounts for the fact that the deposits are made at the beginning of each month.
Using this formula, we get:
FV = [tex]$175 * (((1 + 0.054/12)^(12*7)[/tex] - 1) / (0.054/12)) * (1 + 0.054/12)
FV = [tex]$175 * (((1.0045)^84 - 1)[/tex] / (0.0045)) * 1.0045
FV = $175 * (122.2837)
FV = $21,372.77
Learn more about compounding
https://brainly.com/question/2760551
#SPJ4
Seth weighed 8 pounds when he was
born. How many ounces did Seth weigh
when he was born?
Answer: 132 Ounces.
Step-by-step explanation: 1 pound = 16 ounces. 8 1/4 or 8.25 x 16 = 132
Seth weigh 132 ounce when he was born.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example,Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
We have,
Seth weighed 8 pounds when he was 8 1/4 pounds born.
So, the weight in ounce
= 8 1/4 x 16
= 33/4 x 16
= 33 x 4
= 132 ounce
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
you are testing the claim that having lights on at night increases weight gain (abstract). a sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. test the claim using a 6% level of significance. assume the population variances are unequal and that the weight changes are normally distributed. give answers to 3 decimal places.
To test the claim that having lights on at night increases weight gain, we can conduct a two-sample t-test with unequal variances.
Let μ1 be the population mean weight change for mice living in bright light and μ2 be the population mean weight change for mice living in a normal light/dark cycle. The null hypothesis is H0: μ1 - μ2 = 0 (there is no difference in weight gain between the two groups) and the alternative hypothesis is Ha: μ1 - μ2 > 0 (mice in bright light gain more weight).
Using the given data, we can calculate the sample means and standard deviations:
x1 = 2.312 kg, s1 = 1.052 kg (for the sample of 10 mice in bright light)
x2 = 1.062 kg, s2 = 0.598 kg (for the sample of 8 mice in normal light/dark cycle)
We can then calculate the test statistic t:
t = (x1 - x2) / √(s1^2/n1 + s2^2/n2) = (2.312 - 1.062) / √(1.052^2/10 + 0.598^2/8) = 2.840
The degrees of freedom for the t-test is approximately given by the Welch-Satterthwaite equation:
df = (s1^2/n1 + s2^2/n2)^2 / (s1^4/(n1^2*(n1-1)) + s2^4/(n2^2*(n2-1))) = (1.052^2/10 + 0.598^2/8)^2 / (1.052^4/(10^2*9) + 0.598^4/(8^2*7)) = 14.867
Using a t-distribution table or calculator with df = 14.867 and a one-tailed test at α = 0.06 (equivalent to a critical t-value of 1.796), we find the p-value to be p = 0.006. Since this p-value is less than the significance level of 0.06, we reject the null hypothesis and conclude that there is evidence to support the claim that mice in bright light gain more weight than those in a normal light/dark cycle.
Note that the 6% level of significance is not a commonly used level and may be too liberal or too conservative depending on the context. It is important to consider the practical significance of the result and the potential for type I and type II errors.
To learn more about Test statistic - brainly.com/question/14128303
#SPJ11
please answer this know
Q3) A soccer coach wants to choose one starter and one reserve player for a certain position. If the candidate players are 8 players, in how many ways can they be chosen and ordered?
Using permutation, the soccer coach can choose one starter and one reserve player for the certain position in 56 different ways.
The coach wants to choose and order two players from a group of 8. This is a permutation problem since order matters.
To find the number of ways to choose one starter and one reserve player from 8 candidate players, you can use the following steps:
The formula for the number of permutations of n objects taken r at a time is nPr = n!/(n-r)!.
Using this formula, we can calculate the number of ways the coach can choose and order two players:
8P2 = 8!/(8-2)! = 8!/6! = 8x7 = 56
Therefore, there are 56 ways the coach can choose and order a starter and reserve player for the position from a group of 8 candidates.
Know more about permutation here:
https://brainly.com/question/1216161
#SPJ11
A bridge connecting two cities separated by a lake has a length of 4.042 mi.
Use the table of facts to find the length of the bridge in yards.
Round your answer to the nearest tenth.
The length of the lake of 4.042 miles in yards is 7113.92 yards
How long is the length in yards?From the question, we have the following parameters that can be used in our computation:
Lake has a length of 4.042 mi.
This means that
Length = 4.042 miles
From the table of values:
To convert inches to feet, we multiply the length value by 1760
So, we have
Length = 4.042 * 1760 yards
Evaluate
Length = 7113.92 yards
Hence, the length is 7113.92 yards
Read more about metric units at
https://brainly.com/question/28234927
#SPJ1
what is the average rate of change of f(x)=3x^2-4 between x=2 and x=4?
The value of the average rate of change is,
⇒ f ' (x) = 14
We have to given that;
The function is,
⇒ f (x) = 3x² - 4
Now, We can formulate;
The value of the average rate of change as;
⇒ f ' (x) = f (4) - f (2) / (4 - 2)
⇒ f ' (x) = (3 × 4² - 4) - (3 × 2² - 4) / 2
⇒ f ' (x) = 44 - 16 / 2
⇒ f ' (x) = 28/2
⇒ f ' (x) = 14
Thus., The value of the average rate of change is,
⇒ f ' (x) = 14
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ1
Let CD be a line segment of length 6. A point P is chosen at random on CD. What is the probability that the distance from P to C is smaller than the square of the distance from P to D? Hint: If we think of C as having coordinate 0 and D as having coordinate 6, and P as having coordinate, then the condition is equivalent to the inequality < (6 − x)²
The probability that the distance from P to C is smaller than the square of the distance from P to D is 1/3.
Given a line segment CD of length 6.
A point P is chosen at random on CD.
Let C(0, 0) and D (6, 0).
Any point in between C and D will be of the form (x, 0).
So let P (x, 0).
Then using distance formula,
CP = √x² = x
PD = √(6 - x)² = 6 - x
CP < (PD)²
x < (6 - x)²
x < 36 - 12x + x²
x² - 13x + 36 > 0
(x - 9)(x - 4) > 0
x - 9 > 0 and x - 4 > 0
x > 9 and x > 4
x > 9 is not possible.
Hence x > 4.
Possible lengths are 5 and 6.
Probability = 2/6 = 1/3
Hence the required probability is 1/3.
Learn more about Probability here :
https://brainly.com/question/29381779
#SPJ1
|x+3| if x>5 don't use the absolute value symbol
The possible values of the expression when the inequality is true, are:
(8, ∞).
How to find the possible values of the expression?
Here we have the absolute value expression:
A = |x + 3|
And we know that x > 5, replacing that in the inequality, we will see that the lower bound of the possible values is:
A >|5 + 3|
A > 8
Then the values allowed for the expression are all the values in the range (8, ∞).
Learn more about inequalities.
https://brainly.com/question/24372553
#SPJ1
88 x 45 please help worth a lot
The product of two term 88 x 45 would be equal to 3960.
Since Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
When an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that 88 x 45
We need to simply multiply the term;
88 x 45
= 3960
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ1
BRAINLIEST FOR THE BEST ANSWER!!!! HELP ASAP
find the surface area of this triangular prism.
the surface area of the shape is 1. ____ 2. ____ inches.
1. 24, 48, 96, 108
2. square, cubic
Answer:
The surface area of the shape is 1. 96 2. square inches.
1. 96
2. square
Step-by-step explanation:
We can see that the given right triangular prism is composed of the following regular 2D shapes whose areas add up to the total surface area of the prism
A vertical rectangle of size 6 in. x 2 in.Total surface area of triangular prism = 12 + 16 + 20 + 48
= 96 square inches
Answer:
96 square inches
Step-by-step explanation:
To figure out how much surface area a right triangular prism has, you gotta break it down into a few 2D shapes. There's a tall rectangle that's 6 inches wide and 2 inches tall, which is 12 square inches. Then there's a wide rectangle that's 8 inches wide and 2 inches tall, which is 16 square inches. There's also a rectangle on the diagonal part of the prism that's 2 inches wide and 10 inches tall, which is 20 square inches. And don't forget the two triangles on the sides! Each triangle is 6 inches tall and 8 inches wide, which is 24 square inches each, for a total of 48 square inches. Add all those areas up and bam, you've got the total surface area of the triangular prism - which in this case is 96 square inches.
Please mark as brainliest
A train travels 75 feet in 44 second. At the same speed, how many feet will it travel in 5 seconds?
If a train travels 75 feet in 44 seconds. At the same speed, it travels 8.52 feet in 5 seconds
To find out how many feet the train will travel in 5 seconds at the same speed, first, we need to determine the speed of the train.
The train travels 75 feet in 44 seconds. To find the speed, we'll divide the distance traveled (75 feet) by the time taken (44 seconds):
Speed = Distance / Time
Speed = 75 feet / 44 seconds
Now, we can calculate the distance the train will travel in 5 seconds at the same speed:
Distance = Speed × Time
Distance = (75 feet / 44 seconds) × 5 seconds
The "seconds" unit cancels out, and we're left with:
Distance = (75 feet / 44) × 5
Now, we can calculate the distance:
Distance ≈ 8.52 feet
So, at the same speed, the train will travel approximately 8.52 feet in 5 seconds.
Learn more about speed here:
https://brainly.com/question/22255844
#SPJ11
Suppose the incubation period for certain types of cold viruses are normally distributed with a population standard deviation of 8 hours. Use Excel to calculate the minimum sample size needed to be 99% confident that the sample mean is within 4 hours of the true population mean.Be sure to round up to the nearest integer.
The minimum sample size needed to be 99% confident that the sample mean is within 4 hours of the true population mean is 27.
To calculate the minimum sample size needed to be 99% confident that the sample mean is within 4 hours of the true population mean with a population standard deviation of 8 hours, follow these steps:
1. Identify the desired confidence level: In this case, it is 99%.
2. Find the corresponding Z-score for the confidence level: For a 99% confidence level, the Z-score is approximately 2.576.
3. Identify the population standard deviation: In this case, it is 8 hours.
4. Identify the margin of error: In this case, it is 4 hours.
5. Use the following formula to calculate the sample size:
Sample size (n) = (Z-score^2 * population standard deviation^2) / margin of error^2
Plugging in the values, we get:
n = (2.576^2 * 8^2) / 4^2
n = (6.635776 * 64) / 16
n = 26.543104
Since we need to round up to the nearest integer, the minimum sample size needed is 27.
Know more about mean here:
https://brainly.com/question/1136789
#SPJ11
An integer divided by 7 gives a result-3.What is that integer
Answer:
- 21
Step-by-step explanation:
let the integer be n , then
[tex]\frac{n}{7}[/tex] = - 3 ( multiply both sides by 7 to clear the fraction )
n = 7 × - 3 = - 21
that is the integer is - 21
X³ + 3x² + 3x + 1 ÷ x - 1/2
We have found that the remainder when x³ + 3x² + 3x + 1 is divided by x + 1 is 0.
How do we describe the Remainder theorem?The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a).
Given:
f(x) = x³ + 3x² + 3x + 1
We first calculate the remainder of polynomial f(x) when divided by (x + 1).
We apply the Remainder theorem, the remainder of f(x) when divided by (x - r) is f(r).
we then determine the value of f(-1).
Substituting value of x = -1 is given polynomial f(x).
f(x) = x³ + 3x² + 3x + 1
f(-1) = (-1)³ + 3(-1)² + 3(*-1) +1
f(-1) = 0
In conclusion, the remainder when x³ + 3x² + 3x + 1 is divided by x + 1 is 0.
Learn more about Remainder theorem at:
https://brainly.com/question/13328536
#SPJ1
Aiman is 4 years ago older than his younger brother. The product of Aiman and his younger brother's ages is equal to their father's age. The father is 48 years old and Aiman's younger brother is (p) years old. Write a quadratic equation in terms of (p).
p^2 + 4p - 48 = 0
Let's first express Aiman's age in terms of his younger brother's age. If Aiman is four years older than his younger brother, then we can write:
Aiman's age = younger brother's age + 4
Let p be the age of Aiman's younger brother. Then Aiman's age is p + 4.
The product of Aiman and his younger brother's ages is equal to their father's age, which is given as 48. So we can write:
(p + 4) * p = 48
Expanding the left-hand side:
p^2 + 4p = 48
Subtracting 48 from both sides:
p^2 + 4p - 48 = 0
This is a quadratic equation in terms of p.
learn more about 'quadratic equation';https://brainly.com/question/31697296
#SPJ11
Sharon stands on the top of a cliff 90 m high. The angle of elevation from Sharon to a flying kittiwake is 15°. The angle of depression from Sharon to a yacht on the sea is 19º.
Given that the kittiwake is flying
directly above the yacht, find the
distance between the yacht and the kittiwake.
The distance between the yacht and the kittiwake. is 160 m
How to find the distance between the yacht and the kittiwakeThe horizontal distance between Sharon and the yacht
tan 19 = 90 / distance between Sharon and the yacht
distance between Sharon and the yacht = 90 / tan 19
distance between Sharon and the yacht = 261.38 m
The horizontal distance between the Sharon and the kittiwake
tan 15 = distance between the Sharon and the kittiwake / 261.38
distance between the Sharon and the kittiwake = 261.38 x tan 15
distance between the Sharon and the kittiwake = 70.04 m
distance between the yacht and the kittiwake
= 90 + 70.04
= 160.04
= 160 m
Learn more about angle of elevation at
https://brainly.com/question/88158
#SPJ1
Which number is NOT written in scientific notation?
The notation of number 25.67 x [tex]10^{-2[/tex] is not written in the scientific notation.
Scientific notation is a way of writing very large or very small numbers using powers of 10. It has the form [tex]a X 10^n[/tex], where a is a number between 1 and 10 (or sometimes between -1 and -10), and n is an integer.
As mentioned earlier, scientific notation has the form [tex]a X 10^n[/tex], where a is a number between 1 and 10 (or sometimes between -1 and -10), and n is an integer. But is should be reduced to one decimal number.
Thus, 25.67 x [tex]10^{-2[/tex] is not written in scientific notation.
For more details regarding scientific notation, visit:
https://brainly.com/question/18073768
#SPJ1
How many people will 5 pitchers serve if 1/8 pitcher served one person
Using proportion, we can see that 5 pitchers will serve 40 people if 1/8 pitcher served one person.
Given that,
1/8 pitcher served one person.
Let x be the number of people that the 5 pitchers served.
We can find the value using the proportional method.
Using the proportional concept, the ratio of the number of pitchers served to the number of people will be proportional.
So,
(1/8) / 1 = 5 / x
1/8 = 5/x
Cross multiplying,
x = 40
Hence 5 pitchers will serve 40 people.
Learn more about Proportion here :
https://brainly.com/question/24867814
#SPJ1
what is the answer to this question -5(x+2)=5
The solution to the equation -5(x + 2) = 5 is x = -3.
What is the solution to the given equation?Given the equation in the question:
-5( x + 2 ) = 5
First, we distribute the -5 to the expression inside the parenthesis:
-5×x + 2×-5= 5
-5x - 10 = 5
Next, let's isolate the variable x by adding 10 to both sides:
-5x - 10 + 10 = 5 + 10
-5x = 5 + 10
Simplifying the left side:
-5x = 5 + 10
-5x = 15
Finally, we can solve for x by dividing both sides by -5:
-5x / -5 = 15 / -5
x = -3
Therefore, the value of x is -3.
Learn more about equations here: https://brainly.com/question/9236233
#SPJ1
The sandbox was a foot tall, but the sand only was only filled up 3/4ths of the way. How many cubic feet of sand is there in the box?
The sandbox's 3/4ths fraction is full, the volume of sand can be found by multiplying the volume of the entire sandbox (0.33 ft³) by 3/4, which gives us 0.2475 ft³ of sand.
The area given (64 cm²) is the base of the sandbox, we can find the height of the sandbox in cm using the formula for the area of a rectangle: A = l × w.
Since the area is 64 cm², and we know that the sandbox has a rectangular base, we can assume the length and width are equal and each measure 8 cm.
Next, we need to convert the height of the sandbox from cm to feet. One foot is equal to 30.48 cm, so the sandbox is 0.33 feet tall (approximately). Since the sandbox is 3/4ths full, the volume of sand can be found by multiplying the volume of the entire sandbox (0.33 ft³) by 3/4, which gives us 0.2475 ft³ of sand.
Learn more about the fraction at
https://brainly.com/question/31466821
#SPJ4
The sandbox was a foot tall, but the sand only was only filled up 3/4ths of the way with an area of 64 cm². How many cubic feet of sand are there in the box?
Given the problem
ut = uxx, 0 < x < 2, t<0
u(x, 0) = 4x(2 - x) 0 < x < 2
u(0,t) = u(2, t) = 0, t > 0 using the energy method show that the integral 2∫0 u^2 (x, t) dx is a decreasing function of t.
By using the energy method, we get integral is a decreasing function of time t.
To use the energy method, we first multiply the given PDE by u and integrate over the domain:
∫[0,2]∫[0,t] u*ut dxdt = ∫[0,2]∫[0,t] u*uxx dxdt
Using integration by parts and the given boundary conditions, we can simplify this expression to:
d/dt (∫[0,2] u^2 dx) = -2∫[0,2] u^2 dx
This shows that the integral ∫[0,2] u^2 dx is a decreasing function of t.
Therefore, the energy of the system is decreasing over time, indicating that the solution is stable.
Learn more about integral: https://brainly.com/question/30094386
#SPJ11
a bag contains 16 coins each with a different date. the number of possible combinations of three coins from the bag is
The number of possible combinations of three coins from the bag of 16 coins with different dates can be calculated using the formula for combinations, which is nCr = n! / r!(n-r)!, where n is the total number of objects, r is the number of objects to be chosen, and ! denotes factorial (the product of all positive integers up to the given number).
In this case, we have n = 16 (the total number of coins in the bag) and r = 3 (the number of coins to be chosen for each combination). Using the formula for combinations, we can calculate the number of possible combinations as follows:
nCr = 16! / 3!(16-3)!
nCr = (16 x 15 x 14) / (3 x 2 x 1)
nCr = 560
Therefore, 560 possible combinations of three coins can be chosen from the bag of 16 coins with different dates. These combinations could represent different historical events, significant dates, or other symbolic meanings depending on the dates inscribed on the coins. The calculation of combinations is an important concept in combinatorics and probability theory, and it has many real-world applications in fields such as statistics, economics, and computer science.
To learn more about Probability, visit:
https://brainly.com/question/13604758
#SPJ11
refer to the following distribution. cost of textbooks frequency $25 up to $35 12 35 up to 45 14 45 up to 55 6 55 up to 65 8 65 up to 75 20 what are the class limits for the class with the highest frequency? multiple choice 65 up to 75 64 up to 74 65 up to 74.5 65 up to 74
The class limits for the class with the highest frequency is 65 up to 75. The correct answer is A.
The frequency distribution given in the question represents the number of textbooks and their corresponding costs. The distribution is divided into several classes, each representing a range of costs. The frequency for each class indicates how many textbooks fall within that range of costs.
The question asks us to find the class limits for the class with the highest frequency. We can see from the distribution that the class with the highest frequency is "65 up to 75", which has a frequency of 20.
The class limits for a given class are the lowest and highest values included in that class. In this case, the lower limit of the class "65 up to 75" is 65 (because it is the lowest value in that range), and the upper limit of the class is 75 (because it is the highest value in that range).
Therefore, the class limits for the class with the highest frequency are 65 (the lower limit) and 75 (the upper limit), and the correct answer is "65 up to 75". The correct answer is A.
Learn more about class limit at https://brainly.com/question/29027902
#SPJ11
On a popular app, users rate hair salons as 1, 2, 3, 4, or 5 stars. Suppose a rating is randomly selected from all the ratings on the app, Let X be the number of stars of the selected rating. Here is the probability distribution of X. Value x of X 1 2 3 4 5 PIX-x) 0.25 0.19 0.09 0.21 0.26 For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars. (a) At most 2:0 5 ? (b) More than 3: D
The probability of a randomly selected hair salon rating having at most 2 stars is 0.44,
The probability of having more than 3 stars is 0.47.
We have,
(a) To find the probability that the randomly selected hair salon rating has at most 2 stars, we need to add the probabilities for 1-star and 2-star ratings.
Based on the provided probability distribution,
P(X=1) = 0.25 and P(X=2) = 0.19.
The probability of a rating having at most 2 stars.
P(X ≤ 2) = P(X=1) + P(X=2)
= 0.25 + 0.19
= 0.44
(b)
To find the probability that the randomly selected hair salon rating has more than 3 stars, we need to add the probabilities for 4-star and 5-star ratings.
Based on the provided probability distribution, P(X=4) = 0.21 and P(X=5) = 0.26.
The probability of a rating having more than 3 stars.
P(X > 3) = P(X=4) + P(X=5)
= 0.21 + 0.26
= 0.47
Thus,
The probability of a randomly selected hair salon rating having at most 2 stars is 0.44, and the probability of having more than 3 stars is 0.47.
Learn more about probability here:
https://brainly.com/question/14210034
#SPJ11
A shelf and brackets are shown below. The shelf is perpendicular to the wall.
What angle(x), in degrees, does the bracket make with the wall?
show all work
The bracket makes an angle of approximately 51.48° degrees with the wall.
First, we can use the Pythagorean theorem to find the distance between the end of the bracket and the wall:
[tex]d = \sqrt{((3.2 ft)^2 - (2.5 ft)^2) }[/tex]≈ 1.99 ft
Now we can use the definition of the tangent function to find the angle x:
tan(x) = opposite / adjacent = 2.5 ft / 1.99 ft
Taking the arctangent of both sides, we get:
x = tan⁻¹(2.5 ft / 1.99 ft) ≈ 51.48°
Therefore, the bracket makes an angle of approximately 51.48° degrees with the wall.
Learn more about trig ratios here:
https://brainly.com/question/14977354
#SPJ1
Deon rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 74 cents for each mile driven. Deon had to pay $221.49 when he returned the truck. For how many miles did he drive the truck?
Answer:
Deon drove 270 miles.
Let x be the number of miles driven.
The total cost is 20.95 + 0.74x = 221.49
Subtracting 20.95 from both sides gives 0.74x = 200.54
Dividing both sides by 0.74 gives x = 270 miles
So the answer is 270
Answer:
271 miles
Step-by-step explanation:
The equation to find the total cost is
C = 20.95 + .74 m where m is the number of miles
221.49 = 20.95 +.74m
Subtract 20.95 from each side
221.49 -20.95 = 20.95-20.95 +.74m
200.54 = .74m
Divide each side by .74
200.74/.74 = m
271 = m
A windowpane is 15 inches by 8 inches. What is the distance between opposite corners of the windowpane?
The distance between the opposite corners of the windowpane would be 17 inches.
How to find the distance ?If the windowpane is divided diagonally, we see that the distance between the opposite corners can be be the hypotenuse of a right angle triangle.
This allows us to use the Pythagorean theorem to find that distance between opposite sides. The distance is:
d ² = 15 ² + 8 ²
d ² = 225 + 64
d ² = 289
d = √ 289
d = 17 inches
In conclusion, the distance between the opposite corners is 17 inches.
Find out more on distance at https://brainly.com/question/30262410
#SPJ1