Answers
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
Related Questions
How does deriving the formula for the surface area of a sphere depend on knowing the formula for its volume?
Answers
The formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.
Deriving the formula for the surface area of a sphere depends on knowing the formula for its volume because it involves taking the derivative of the volume formula with respect to the radius.
The volume formula for a sphere is [tex]V = (4/3)πr^3[/tex], where r is the radius, and π is a constant. If we differentiate this formula with respect to r, we get dV/dr = [tex]4πr^2[/tex], which gives us the formula for the surface area of the sphere, A = [tex]4πr^2.[/tex]
Therefore, the formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.
To know more about surface area here
https://brainly.com/question/16519513
#SPJ4
taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H&R Block.
a.What is the probability of selecting a family that prepared their own taxes?
b.What is the probability of selecting two families, both of which prepared their own taxes?
c.What is the probability of selecting three families, all of which prepared their own taxes?
d.What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block?
Answers
The probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.
a. There are a total of 10 families. 7 had taxes prepared by a local professional, and 3 by H&R Block. This means 0 families prepared their own taxes. The probability of selecting a family that prepared their own taxes is 0/10 = 0.
b. Since no families prepared their own taxes, the probability of selecting two families, both of which prepared their own taxes is 0.
c. Similarly, the probability of selecting three families, all of which prepared their own taxes is 0.
d. If we want to select two families, neither of which had their taxes prepared by H&R Block, we are looking for families that had their taxes prepared by a local professional. There are 7 such families. The probability of selecting the first family is 7/10. After selecting the first family, there are now 9 families left, 6 of which had their taxes prepared by a local professional. The probability of selecting the second family is 6/9. Therefore, the probability of selecting two families, neither of which had their taxes prepared by H&R Block is (7/10) * (6/9) = 42/90, which simplifies to 7/15.
Learn more about probability here:
brainly.com/question/27342429
#SPJ11
After 4 years, $20,000 deposited in a savings account with simple interest had earned $800 in interest. What was the interest rate?
Answers
The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.
We can use the formula for simple interest to solve the problem:
Simple interest = (Principal * Rate * Time) / 100
where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.
We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:
$800 = (20,000 * Rate * 4) / 100
Multiplying both sides by 100 and dividing by 20,000 * 4, we get:
Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%
Therefore, the interest rate for the savings account is 5%.
To know more about interest here
https://brainly.com/question/25720319
#SPJ4
Question 2 (10 points) When hydrogen is added to the structure of an oil, the melting points goes down, and the oil becomes thinner and easier to pour. True False
Answers
This statement is generally true.
When hydrogen is added to the structure of an oil through a process called hydrogenation, the oil becomes more saturated with hydrogen atoms, which reduces the amount of double bonds in the oil's molecules. This can cause the melting point of the oil to decrease and the oil to become more liquid and easier to pour. Additionally, hydrogenated oils tend to have a longer shelf life and are more stable at high temperatures, making them useful in many food processing applications.
learn more about 'organic chemistry';https://brainly.com/question/31697926
#SPJ11
5/8x + 1/2 ( 1/4x + 10)
Answers
Answer:5+3x/4
Step-by-step explanation:
Answer:2x+1
1
Step-by-step explanation:
1. An integer is chosen randomly between 1 and 1000. What is the probability that the number
picked is divisible by either 4 or 5 or both?
2. An integer is chosen randomly between 1 and 1000. What is the probability that the number
picked is divisible by 4 and not 3?
Answers
1. The probability that the number picked is divisible by either 4 or 5 or both is 0.4. 2. The probability that the number picked is divisible by 4 and not 3 is 0.167.
1. Using the principle of inclusion-exclusion. There are 250 integers between 1 and 1000 that are divisible by 4, and 200 integers that are divisible by 5.
However, some integers are divisible by both 4 and 5 (i.e., by 20), and we have counted them twice. There are 50 integers in the range [1, 1000] that are divisible by 20.
So, the number of integers between 1 and 1000 that are divisible by either 4 or 5 or both is:
250 + 200 - 50 = 400
Therefore, the probability that the integer picked is divisible by either 4 or 5 or both is:
400/1000 = 0.4
2. Using the principle of inclusion-exclusion again, there are 250 integers between 1 and 1000 that are divisible by 4, and 333 integers that are not divisible by 3.
There are 250 integers in the range [1, 1000] that are divisible by 4, and 83 integers that are divisible by 12.
So, the number of integers between 1 and 1000 that are divisible by 4 but not 3 is:
250 - 83 = 167
Therefore, the probability that the integer picked is divisible by 4 and not 3 is:
167/1000 = 0.167
Know more about probability here:
https://brainly.com/question/13604758
#SPJ11
the shape of a colony of bacteria on a petri dish is circular. find the approximate increase in its area if its radius increases from mm to mm. a) let represent the radius and represent the area. write the formula for the area of the petri dish.
Answers
The formula for the area of a circular petri dish can be represented as A = πr², where "A" represents the area and "r" represents the radius.
To find the approximate increase in the area when the radius increases from r₁ mm to r₂ mm, we can calculate the difference between the areas by subtracting the initial area (A₁ = πr₁²) from the final area (A₂ = πr₂²). This can be expressed as ΔA = A₂ - A₁ = πr₂² - πr₁².
In the second paragraph, let's explain the formula and how to calculate the approximate increase in the area of the bacterial colony on the petri dish. The area of a circular shape is given by the formula A = πr², where "A" represents the area and "r" represents the radius. By substituting the initial radius, r₁, into the formula, we can find the initial area, A₁ = πr₁².
Similarly, by substituting the final radius, r₂, into the formula, we can find the final area, A₂ = πr₂². To calculate the approximate increase in area, we subtract the initial area from the final area: ΔA = A₂ - A₁ = πr₂² - πr₁². This formula allows us to find the difference in the areas of the bacterial colony on the petri dish when the radius increases from r₁ to r₂.
Learn more about Area:
brainly.com/question/1631786
#SPJ11
6. Caleb wants to buy a skateboard that costs $73. 56. If sales tax is 7%, how much would his total purchase be?
Answers
Answer:
$78.7092
Step-by-step explanation:
He wants to buy a skateboard. The percentage value of the skateboard before any changes is 100%. So $73.56 = 100%. Now when you add a sales tax to it, the price will increase by 7% so it'll now be 107% right? You just have to find how much the 107% is equal to.
100% = 73.56
1% = 73.56÷100 = 0.7356
107 % = 0.7356 × 107 = 78.7092
A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.
If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$378,325.90
$359,978.25
$173,435.93
$137,435.93
Answers
The difference in the account balances is $138,435.93.
We have,
We can solve this problem by using the formula for the future value of an annuity:
[tex]FV = PMT \times [(1 + r)^n - 1] / r[/tex]
where FV is the future value of the annuity, PMT is the yearly contribution, r is the annual interest rate, and n is the number of years.
Using the given information, we can find the future value of the annuity if the person starts at age 35:
FV1
= $5,000 x [(1 + 0.065)^30 - 1] / 0.065
= $431,874.32
Now we can find the future value of the annuity if the person starts at age 40:
FV2 = $5,000 x [(1 + 0.065)^25 - 1] / 0.065
= $293,438.39
The difference in the account balances is:
FV1 - FV2
= $431,874.32 - $293,438.39
= $138,435.93
Therefore,
The difference in the account balances is $138,435.93.
Learn more about future value here:
https://brainly.com/question/14860893
#SPJ1
find n and m using the image of the parallelogram
n= ?
m= ?
Answers
The length of the line segments m and n which are halves of the diagonals AC and BD in the parallelogram ABCD are 6 and 11 respectively.
Diagonals of a parallelogramA parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.
For the parallelogram ABCD; the lines AC and BD are its diagonals, and they both bisect each other, that is they cut each other to form two equal parts.
So AP and PC are equal halves of the line AC, while BP and PD are equal halves of the line BD
Therefore, since PC = 6 then m = 6, and for PD = 11, then n = 11 because they form diagonals of the parallelogram ABCD.
Read more about parallelogram here: https://brainly.com/question/20526916
#SPJ1
keisha just deposited a total of 900 into savings accounts at two different banks. the 550 she deposited at bank A will earn 2.25% interest compounded anually
Answers
The total amount she earned $945.75.
We have,
P= 900
bank A deposition= 550
R= 2.25%
So, the interest from Bank A
= 550/100 x 2.25
= 12.375
and, Interest from Bank B
= (900 - 550)/100 x 3
= 350/100 x 3
= 10.5
So, total she earned
= 10.5 + 12.375 = 22.875
In 2 years she will earned
= 22.875 x 2
= 45.75
Thus, the total amount she earned
= 900 + 45.75 = 945.75
Learn more about Interest here:
https://brainly.com/question/30393144
#SPJ1
Suppose we modify the production model to obtain the following mathematical model: Max 10X s.t. ax ≤ 40 x ≥ 0 Where a is the number of hours of production time required for each unit produced. With a=5, the optimal solution is x=8. If we have a stochastic model with a=3,a=4,a=5, or a=6 as the possible values for the number of hours required per unit, what is the optimal value for x? What problems does this stochastic model cause?
Answers
The optimal value for x in the stochastic model is a range of values from x=6 to x=8. The stochastic model causes problems due to the uncertainty in the optimal solution and the assumptions.
With a=5, the optimal solution is x=8. However, with the addition of stochasticity and possible values for a of 3, 4, and 6, the optimal value for x becomes a range of values.
The expected value of a is 4.5, which means that there is a higher probability of a lower value for a, resulting in a lower optimal value for x. Therefore, the optimal value for x becomes x=6 when a=3 or a=4, x=7 when a=5, and x=8 when a=6.
The stochastic model causes problems because the optimal solution is no longer a fixed value but rather a range of values that are dependent on the probability distribution of a.
Additionally, this model assumes that the production time is the only constraint on production, which may not always be the case in real-world production scenarios. Therefore, the stochastic model may not accurately reflect the actual production process and could lead to suboptimal production decisions.
To know more about stochastic model, refer here:
https://brainly.com/question/28138551#
#SPJ11
Question 4 (1 point) On a college test, students receive 6 points for every question answered correctly and a student receives a penalty of 5 points for every problem answered incorrectly. On this particular test, Melanie answered 45 questions correctly and 33 questions incorrectly. What is her score? A
Answers
To calculate Melanie's score, we first need to find out how many total points she earned and how many points were deducted for incorrect answers.
Melanie earned 6 points for each of the 45 questions she answered correctly, which gives her a total of 6 x 45 = 270 points.
For the 33 questions she answered incorrectly, Melanie received a penalty of 5 points for each one. So, the total points deducted for incorrect answers is 5 x 33 = 165 points.
To find Melanie's score, we need to subtract the points deducted for incorrect answers from the total points earned:
Score = Total points earned - Points deducted for incorrect answers
Score = 270 - 165
Score = 105
Therefore, Melanie's score on the college test is 105.
Learn more about total points: https://brainly.com/question/23848540
#SPJ11
insect Survival Most
invertebrates produce large
numbers of offspring. Most of
these offspring die before reaching
adulthood. Suppose an insect lays
80 eggs on a plant. If 70 percent
of the eggs hatch and 80 percent
of those that hatch die before
reaching adulthood, how many
insects will reach adulthood?
Answers
The required out of the 80 eggs laid, only 11 insects are expected to reach adulthood.
If an insect lays 80 eggs on a plant, and 70% of the eggs hatch, then the number of hatched eggs is:
80 x 0.7 = 56
Now, if 80% of the hatched eggs die before reaching adulthood, then the number of insects that reach adulthood is:
56 x 0.2 = 11.2
However, we cannot have a fractional number of insects, so we need to round this to the nearest whole number. Since we are asked for how many insects will reach adulthood, we round up if the decimal is 0.5 or greater and round down if the decimal is less than 0.5. In this case, since 0.2 is less than 0.5, we round down to get:
11 insects
Therefore, out of the 80 eggs laid, only 11 insects are expected to reach adulthood.
Learn more about probability here:
https://brainly.com/question/27426680
#SPJ1
A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste Which of these is an example of descriptive statistics?
A. 80% of the people in the city where the pizza shop is located like the taste of the pizza topping
B. 80% of all the pizza shop's customers like the taste of the pizza topping,
C. 80% of all people like the taste of the pizza topping,
D. 80% of the surveyed customers like the taste of the pizza topping.
Answers
D. 80% of the surveyed customers like the taste of the pizza topping. This is an example of descriptive statistics because it describes a specific group of 50 customers who were surveyed and their response to the new topping.
Descriptive statistics are used to summarize and describe data, often by using measures such as percentages, means, and standard deviations. In this case, the percentage of customers who liked the new topping is a descriptive statistic that summarizes the data collected from the survey.
This answer represents descriptive statistics because it summarizes and describes the information collected from the specific sample of 50 customers who participated in the taste test. It does not make assumptions or predictions about the entire population or customer base, but instead focuses solely on the data collected from the sample group.
Learn more about Statistics here : brainly.com/question/31577270
#SPJ11
For the following observations 14,10,7,18, x , 10, 10, 14,5 and 15, if X = 11.6 , then median, mode and standard deviation respectively are: a. 11.5 , 10 and 3.923 b. 12.5 , 12.5 and 3.8356 c. 12.5 , 13 and 14.7 d. 11.5 , 10 and 15.38 e. 13 , 10 and 3.923
Answers
The correct answer is option b.
To find the median, we need to first put the observations in order:
5, 7, 10, 10, 10, 14, 14, 15, 18, x
Since there are 10 observations, the median is the average of the 5th and 6th observations, which are both 10. Therefore, the median is 10.
To find the mode, we need to find the observation that appears most frequently. Here, both 10 and 14 appear three times each, so the data has two modes: 10 and 14.
To find the standard deviation, we need to first find the mean of the data. We know that the sum of the observations is:
5 + 7 + 10 + 10 + 10 + 14 + 14 + 15 + 18 + x
= 103 + x
Since we know that X = 11.6, we can substitute to get:
Sum of observations = 103 + 11.6 = 114.6
The mean is then:
Mean = (Sum of observations) / (Number of observations)
Mean = 114.6 / 10 = 11.46
To find the standard deviation, we need to calculate the deviation of each observation from the mean, square each deviation, find the average of the squared deviations, and then take the square root.
Deviation of 5 = 11.46 - 5 = 6.46
Deviation of 7 = 11.46 - 7 = 4.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 10 = 11.46 - 10 = 1.46
Deviation of 14 = 11.46 - 14 = -2.54
Deviation of 14 = 11.46 - 14 = -2.54
Deviation of 15 = 11.46 - 15 = -3.54
Deviation of 18 = 11.46 - 18 = -6.54
Deviation of x = 11.46 - x
To find the standard deviation, we need to find the average of the squared deviations.
Average of squared deviations = [(6.46)^2 + (4.46)^2 + (1.46)^2 + (1.46)^2 + (1.46)^2 + (-2.54)^2 + (-2.54)^2 + (-3.54)^2 + (-6.54)^2 + (11.46 - x)^2] / 10
= (41.7316 + 19.8916 + 2.1316 + 2.1316 + 2.1316 + 6.4516 + 6.4516 + 12.5316 + 42.8916 + (11.46 - x)^2) / 10
= (136.786) / 10
= 13.6786
Finally, we take the square root of the average of the squared deviations to find the standard deviation:
Standard deviation = sqrt(13.6786) = 3.8356
Therefore, the correct answer is option b.
Learn more about standard deviation: https://brainly.com/question/24298037
#SPJ11
12. What is the volume of a can of peanuts with a height of 5 in. and
a lid that is 4 in. wide? Use 3.14 for pie. Round the answer to the
nearest tenth of an inch.
Answers
62.8 cubic inches is the volume of a can of peanuts with a height of 5 in. and a lid that is 4 in. wide
We have to find the volume of a can of peanuts with a height of 5 in. and
a lid that is 4 in. wide
Volume of cylinder =πr²h
h is height which is 5 in
r is radius of can which is 2 in
Plug in values of h and r
Volume = 3.14×4×5
=62.8 cubic inches
Hence, 62.8 cubic inches is the volume of a can of peanuts with a height of 5 in. and a lid that is 4 in. wide
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
the product of a number x and 9 is 45. translate this statement into an equation
Answers
Answer: 9x=45
Step-by-step explanation:
“product” means the result from multiplying two numbers, so if the product of the two numbers is 45, then the two numbers provided (9 and x) are being multiplied.
If we were to solve for x, we could divide both sides by 9 to get 5.
The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chaneece chooses x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions. She determines that x must be between 0 and 10 and y must be between 20 and 40. Determine if Chaneece found the correct solution. If not, state the correct solution.
Answers
Chaneece did not find the correct solution
Determining if Chaneece found the correct solutionFrom the question, we have the following parameters that can be used in our computation:
x and y are the integers
So, we have
x + y ≤ 40
x - y ≥ 20
Add the equations
So, we have
2x = 60
Divide
x = 30
Next, we have
30 + y ≤ 40
So, we have
y ≤ 10
This means that
x = 30 or between 20 and 30
y = 10 or between 0 and 10
Read more about inequality at
https://brainly.com/question/30422919
#SPJ1
Given the parabola in which the vertex is the origin and the directrix is a horizontal line passing through the point (0,-7), a student determined that the parabola opens to the right and that the equation of the parabola is y^2=28x. Evaluate the student’s answer. A. The student’s answer is correct. B. The student determined the direction of the parabola correctly but did not correctly determine the equation of the parabola. C. The student determined the equation of the parabola correctly but did not correctly determine the direction of the parabola. D. The student used the equations for a horizontal parabola instead of a vertical parabola. Both the equation and direction of the parabola are incorrect. Please select the best answer from the choices provided
Answers
The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7), and the equation is y^2 = 28x, which opens to the right. So, the correct answer is A) The student's answer is correct.
To determine if the student's answer is correct, we need to check if the equation of the parabola and the direction of its opening match the given conditions.
The given parabola has its vertex at the origin and the directrix as a horizontal line passing through the point (0,-7). Therefore, the axis of symmetry is the y-axis, and the focus is located at (0,7).
The standard equation of a parabola with the vertex at the origin and the directrix as a horizontal line passing through the point (0,-p) is y² = 4px, where p is the distance from the vertex to the directrix. In this case, p = 7, so the equation of the parabola is y² = 28x.
The coefficient of x in the equation is positive, indicating that the parabola opens to the right. Therefore, the student correctly determined the direction of the parabola as well.
Hence, the answer is A. The student's answer is correct.
To know more about parabola:
https://brainly.com/question/31142122
#SPJ1
Prove, For every integer k >= 5, k2 – 3k >=10.
Answers
Mathematical induction can be used to prove that for every integer k ≥ 5, k^2 - 3k ≥ 10.
Base Case: Let k = 5,
Then, k^2 - 3k = 5^2 - 3(5) = 10
Since 10 >= 10 is true, the base case holds.
Inductive Step: Assume that for some integer n >= 5, n^2 - 3n >= 10 is true.
We want to prove that (n + 1)^2 - 3(n + 1) >= 10 is also true.
Expanding the left-hand side of the inequality, we get:
(n + 1)^2 - 3(n + 1) = n^2 + 2n + 1 - 3n - 3
On simplifying ,we get:
n^2 - n - 2 >= 0
On factoring,we get:
(n - 2)(n + 1) >= 0
Since n >= 5, n - 2 >= 3, and n + 1 >= 6, so both factors are positive. Therefore, the inequality is true for all n >= 5.
By mathematical induction, we have proved that for every integer k >= 5, k^2 - 3k >= 10.
To learn more about integer: https://brainly.com/question/929808
#SPJ11
Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0. 02, 0. 03, 0. 07, 0. 12, 0. 30, 0. 28, 0. 18.
What is the median of the distribution?
3
3. 5
4
4. 2
Answers
1.39 is the median of the distribution
Creating a table:
X :___0 __ 1 __ 2 ___ 3 ____ 4 ___ 5 ___ 6
P(x):0.02_0.03_0.07, 0.12, 0.30_ 0.28_0.18.
The standard deviation = √(Var(x))
Var(x) = Σx²*p(x) - E(x)²
E(x) = ΣX*p(x)
E(x) = (0*0.02) + (1*0.03) + (2*0.07) + (3*0.12) + (4*0.30) + (5*0.28) + (6*0.18) = 4.21
Var(X) :
[tex]((0^2*0.02) + (1^2*0.03) + (2^2*0.07) + (3^2*0.12) + (4^2*0.30) + (5^2*0.28) + (6^2*0.18)) - 4.21^2[/tex]
19.67 - 17.7241
= 1.9459
Standard deviation = √(Var(X))
Standard deviation = √(1.9459)
Standard deviation = 1.3949551
= 1.39
Learn more about standard deviation,
https://brainly.com/question/23907081
#SPJ4
Full Question ;
Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0.02, 0.03, 0.07, 0.12, 0.30, 0.28, 0.18.
What is the standard deviation of the distribution?
1.39
1.95
2.16
4.67
Use the quadratic formula to find the roots of
Answers
The roots of the quadratic equation x² + 2x - 7 are x = -1 + 2√2 and x = -1 - 2√2
To find the roots of the quadratic equation x² + 2x - 7 using the quadratic formula, we need to first identify the values of a, b, and c in the equation.
In this case, a = 1, b = 2, and c = -7.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
We can substitute the values of a, b, and c into the formula and simplify:
x = (-2 ± √(2² - 4(1)(-7))) / 2(1)
x = (-2 ± √(4 + 28)) / 2
x = (-2 ± √(32)) / 2
x = (-2 ± 4√2) / 2
We can simplify this expression further by dividing both the numerator and denominator by 2:
x = -1 ± 2√2
The roots of a quadratic equation represent the values of x that make the equation equal to zero. The quadratic formula provides a method for finding these roots for any quadratic equation, regardless of the values of a, b, and c.
To learn more about roots click on,
https://brainly.com/question/28976388
#SPJ1
Two concentric circles form a target. The radii of the two circles measure 6 cm and 2 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected. What is the probability that the randomly selected point is in the bullseye? Enter your answer as a simplified fraction in the boxes.
Answers
The probability that the randomly selected point is in the bullseye is: 1/3
How to find the probability?We are told that there are two concentric circles.
Now, the circles that have a common centre are referred to as concentric circles and have different radii. In other words, it is defined as two or more circles that have the same centre point. The region between two concentric circles are of different radii is known as an annulus.
Now, the bulls eye diameter of 4 cm since the radius is 2 cm
Meanwhile, the outer part forms a diameter of 8 cm.
Thus:
Probability of hitting the bulls eye = 4/12 = 1/3
Probability of hitting the outer part = 8/12 = 2/3
Read more about Probability at: https://brainly.com/question/24756209
#SPJ1
Find the linearization L(x) of the function at a. F(x) = x3 - x2 + 5, a = -3 L(x) = Fl Show My Work
Answers
[tex]L(x) = 33x + 86[/tex] represents the regression of F(x) at a = -3.
We must apply the following formula to determine the regression L(x) of the equation: [tex]F(x) = x^{3} - x^{2} + 5[/tex] at a = -3: [tex]L(x) = F'(a)(x - a) + F(a)[/tex] , where a derivative of F(x) calculated at an is denoted by F'(a).
We calculate the amount of F(-3): F(-3)
[tex]= (-3)^3 - (-3)^2 + 5[/tex]
= -27 + 9 + 5 = -13
We determine F(x)'s derivative:
[tex]F'(x) = 3x^2 - 2x[/tex]
We assess F'(-3):
[tex]F'(-3) = 3(-3)^2 - 2(-3)[/tex]
= 27 + 6 = 33
Now we can change these numbers in the L(x) formula:[tex]L(x) = -13 + 33(x + 3)[/tex]. If we condense this expression, we get: L(x) = 33x + 86
We utilise the equation [tex]L(x) = F(a) + F'(a)(x - a)[/tex], to determine the linearization of an equation at a specific point, where F(a) represents the function's value at point a and F'(a) was the function's derivative calculated at point a. We can approximate the function close to point a linearly.
Learn more about regression here:
https://brainly.com/question/30011167
#SPJ4
Find The Total Surface Area Of This Triangular Prism:
Answers
The total surface area of the triangular prism is 204 square units.
To find the total surface area of a triangular prism, we need to find the areas of all its faces and add them up.
First, we need to find the area of each triangular face. We can use the formula:
Area of a triangle = 1/2 x base x height
For the triangle with base 4 and height 3, we have:
Area of triangle = 1/2 x 4 x 3 = 6
For the triangle with base 6 and height 8, we have:
Area of triangle = 1/2 x 6 x 8 = 24
Now, we need to find the area of each rectangular face. We can use the formula:
Area of a rectangle = length x width
For the rectangular face with length 6 and width 4, we have:
Area of rectangle = 6 x 4 = 24
For the rectangular face with length 8 and width 4, we have:
Area of rectangle = 8 x 4 = 32
Finally, we add up all the areas to get the total surface area:
Total surface area = 2 x (area of triangle) + 3 x (area of rectangle)
Total surface area = 2 x (6 + 24) + 3 x (24 + 32)
Total surface area = 60 + 144
Total surface area = 204
To know more about surface area here
https://brainly.com/question/16519513
#SPJ4
Find The Total Surface Area Of This Triangular Prism:
Out of people wederval for the true population proportion of people with kids Give your awer as decimals to the places
What is the correct terpretation for the confidence intervala.The true proportion of people with kids is in the above interval, 954 of the time We know this
is true because the proportion of our sample is in the interval
b.With 95% confidence, the true proportion of people with kids wit be in the above interval
c.There is a 95% chance that the true proportion of people with kids will be in the above internal
Answers
The correct interpretation for the confidence interval is that with 95% confidence, the true proportion of people with kids will be in the above interval.
This means that if we were to repeat the same survey or study multiple times, about 95% of the time, the true proportion of people with kids would fall within the given interval.
It is important to note that we cannot say with certainty that the true proportion falls within the interval, as there is always a chance for sampling error or variability.
However, we can say with a high degree of confidence that the true proportion is likely to fall within the interval. Option A is incorrect because we cannot say with certainty that the true proportion is within the interval, even though it is likely. Option c is also incorrect because the confidence level refers to the long-run proportion of intervals that will contain the true value, not a probability statement about a single interval.
To know more about the construction of a confidence interval visit:
https://brainly.com/question/31496679
#SPJ11
brenda has 40 math books and 25 science books what is the greatest number of bookshelves breanda can use
Answers
Brenda can use 1000 bookshelves.
Given that, Brenda has 40 math books and 25 science books we need to find that what is the greatest number of bookshelves Breanda can use,
So, the greatest number of books = 40 x 25 = 1000
Hence, Brenda can use 1000 bookshelves.
Learn more about permutation and combination, click;
https://brainly.com/question/13387529
#SPJ1
Find the Taylor polynomials P1,. , P4 centered at a = 0 for f(x) = cos( - 5x). Py(x) = 0 Pz(x) = 0 P3(x)= P4(x) = Determine the interval of convergence of the following power series. = (x-26 k= 1 O A. (1,3] O B. (1, 3] O C. (1,3) OD. (1,3) Express the Cartesian coordinates 573,5) in polar coordinates in at least two different ways. Write the point in polar coordinates with an angle in the range 0 50 211. (Type an ordered pair. Type an exact answer, using a as needed. ) Write the point in polar coordinates with an angle in the range - 2150<0. (Type an ordered pair. Type an exact answer, using d Find the 3rd ordere Taylor polynomial of f(x) = cos (x) at a =. OA Pow== (x-3). 4-3 OC. 349+1=(x-) 3 OD. (x) = -x + 3 / 3
Answers
Thus, the third-order Taylor polynomial for f(x) = cos(x) at a = 0 is: [tex]P_3(x) = 1 - x^2 / 2! + x^4 / 4![/tex].
Taylor Polynomials:
We have f(x) = cos(-5x) = cos(0 - 5x), so we can use the Taylor series for cos(x) centered at a = 0:
cos(x) = Σ[tex](-1)^n * x^(2n) / (2n)![/tex]
Thus, we have:
[tex]P_1(x) = cos(0) + (-5x) * (-sin(0)) = 1\\P_2(x) = 1 + 0 + (-5x)^2 / 2! = 1 + 12.5x^2\\P_3(x) = 1 + 0 + (-5x)^2 / 2! + 0 + (-5x)^4 / 4! = 1 + 12.5x^2 + 52.0833x^4\\P_4(x) = 1 + 0 + (-5x)^2 / 2! + 0 + (-5x)^4 / 4! + 0 + (-5x)^6 / 6! = 1 + 12.5x^2 + 52.0833x^4 + 136.7188x^6[/tex]
Interval of Convergence:
The power series given is:
Σ[tex](2k+1)*(x-2)^k[/tex]
Using the ratio test, we have: limit:
[tex]|(2k+3)(x-2)^(k+1) / ((2k+1)(x-2)^k)| = |x-2| lim |2k+3| / |2k+1| = |x-2|[/tex]
So, the series converges for |x - 2| < 1, or 1 < x < 3. Thus, the interval of convergence is (1, 3).
Polar Coordinates:
Using the Pythagorean theorem, we have:
r = [tex]\sqrt{(x^2 + y^2)\\\\\sqrt{(5^2 + 73.5^2) }\\[/tex]
r= 73.790
Using trigonometry, we have:
θ = arctan(y/x) = arctan(73.5/5) = 1.493 rad = 85.758°
In the range 0 ≤ θ < 2π, this point can be expressed in polar coordinates as (73.790, 85.758°) or (73.790, 445.242°).
In the range -π < θ ≤ π, this point can be expressed in polar coordinates as (73.790, -94.242°).
Third-Order Taylor Polynomial:
The Taylor series for cos(x) centered at a = 0 is:
cos(x) = [tex]1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ...[/tex]
Taking the first four terms, we have:
[tex]P_3(x) = 1 - x^2 / 2! + x^4 / 4! = cos(x) + x^6 / 6![/tex]
Learn more about Taylor polynomials visit: brainly.com/question/2533683
#SPJ4
A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
If you select two marbles from the bag in a row without replacing the first marble, what is the probability that the first marble is blue and the second marble is green?
Note: you are not replacing any marbles after each selection.
PLS SHOW ALL WORK!
Answers
The probability of selecting blue marble and green marble is 1/13.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%.
Probability = sample space/total outcome
total outcome = 13
The probability of picking blue in the first pick = 6/13
since there is no replacement, the total outcome for the second pick = 12
The probability of picking green in the second pick = 2/12 = 1/6
Therefore the probability of selecting blue and green marble = 6/13 × 1/6
= 1/13
learn more about probability from
https://brainly.com/question/24756209
#SPJ1