Using the properties of antiderivatives in theorem 6.1 to find (2 cos(r) +5sin(x))dx 1(2 cos(z) + 5 sin(x)) dx =
Answers
the integral of (2 cos(r) +5sin(x))dx 1(2 cos(z) + 5 sin(x)) dx is given by 2sin(r) + 2cos(z)x + C, where C is the constant of integration.
Using the properties of antiderivatives in theorem 6.1, we can find the antiderivative of (2cos(r) + 5sin(x))dx as follows:
1(2cos(z) + 5sin(x))dx = ∫(2cos(r) + 5sin(x))dx
We can separate the integral into two parts:
∫(2cos(r)dx) + ∫(5sin(x)dx)
Now, we can find the antiderivative of each part:
∫(2cos(r)dx) = 2∫(cos(r)dr) = 2sin(r) + C₁
∫(5sin(x)dx) = 5∫(sin(x)dx) = -5cos(x) + C₂
Combine the two antiderivatives:
2sin(r) - 5cos(x) + C₁ + C₂
Since C₁ and C₂ are constants, we can combine them into a single constant C:
2sin(r) - 5cos(x) + C
When using the properties of antiderivatives in theorem 6.1 to find (2 cos(r) +5sin(x))dx 1(2 cos(z) + 5 sin(x)) dx, the answer can be found by using the linearity of integration.
Let's first obtain the integral of (2 cos(r) +5sin(x))dx. The integral of 2cos(r) with respect to x is given by 2sin(r) + C, while the integral of 5sin(x) with respect to x is given by -5cos(x) + C.
Therefore, the integral of (2 cos(r) +5sin(x))dx is (2sin(r) - 5cos(x)) + C1
Similarly, let's find the integral of (2 cos(z) + 5 sin(x)) dx.
The integral of 2cos(z) with respect to x is given by 2cos(z)x + C, while the integral of 5sin(x) with respect to x is given by -5cos(x) + C.
Therefore, the integral of (2 cos(z) + 5 sin(x)) dx is (2cos(z)x - 5cos(x)) + C2
Thus, the integral of (2 cos(r) +5sin(x))dx 1(2 cos(z) + 5 sin(x)) dx = [(2sin(r) - 5cos(x)) + C1] + [(2cos(z)x - 5cos(x)) + C2] = 2sin(r) + 2cos(z)x + C
Where C = C1 + C2. Therefore, the integral of (2 cos(r) +5sin(x))dx 1(2 cos(z) + 5 sin(x)) dx is given by 2sin(r) + 2cos(z)x + C, where C is the constant of integration.
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Related Questions
Simplify 3.1b -7.3 - 8.2b -5.3
Answers
First, we can combine the terms with the variable b:
3.1b - 8.2b = -5.1b
Next, we can combine the constant terms:
-7.3 - 5.3 = -12.6
Putting it all together, we have:
3.1b -7.3 - 8.2b -5.3 = -5.1b - 12.6
Therefore, the simplified expression is -5.1b - 12.6.
Answer:
\( \sf \: -5.1b - 12.6\)
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 3.1b - 7.3 - 8.2b - 5.3
Let's simplify the expression,
→ 3.1b - 7.3 - 8.2b - 5.3
→ 3.1b - 8.2b - 7.3 - 5.3
→ (3.1b - 8.2b) + (-7.3 - 5.3)
→ (-5.1b) + (-12.6)
→ -5.1b - 12.6
Hence, answer is -5.1b - 12.6.
Based on experience, 60% of the women who request a pregnancy test at a certain clinic are actually pregnant.
In a random sample of 12 women
a) what is the probability that at least 10 are pregnant?
b) what is the probability that exactly 6 are pregnant?
c) what is the probability that at most 2 are pregnant?
d) what are the mean and Standard Diviation of this distrubution?
Answers
For a) the total probability of at least 10 are pregnant is 0.4509, or 45.09%. For b) the probability that exactly 6 women are pregnant are 0.2128, or 21.28%. For c) same as option b). For d) Mean is (μ) = \(n * p\) , Standard Deviation (σ) = \(sqrt(n * p * q)\).
To solve these probability questions, we can use the binomial probability formula. In the given scenario, we have:
- Probability of success (p): 60% or 0.6 (a woman requesting a pregnancy test is actually pregnant).
- Probability of failure (q): 40% or 0.4 (a woman requesting a pregnancy test is not pregnant).
- Number of trials (n): 12 ( women in the sample).
a) To find the probability that at least 10 women are pregnant, we need to calculate the probability of 10, 11, and 12 women being pregnant and sum them up.
\(\[P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)\]\)
Where X follows a binomial distribution with parameters n and p.
Using the binomial probability formula, the probability for each scenario is:
\(\[P(X = k) = \binom{n}{k} \cdot p^k \cdot q^{(n-k)}\]\)
Using this formula, we can calculate:
\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2\]\)
\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1\]\)
\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0\]\)
To find the total probability of at least 10 women being pregnant, we need to calculate the probabilities for each possible number of pregnant women (10, 11, and 12) and add them up.
Let's calculate each individual probability:
For 10 pregnant women:
\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2\]\)
For 11 pregnant women:
\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1\]\)
For 12 pregnant women:
\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0\]\)
Now, we can add up these probabilities to find the total probability of at least 10 women being pregnant:
\(\[P(\text{{at least 10 women pregnant}})\) = \(P(X = 10) + P(X = 11) + P(X = 12)\]\)
Calculating each of these probabilities:
\(\[P(X = 10) = \binom{12}{10} \cdot (0.6)^{10} \cdot (0.4)^2 = 0.248832\]\)
\(\[P(X = 11) = \binom{12}{11} \cdot (0.6)^{11} \cdot (0.4)^1 = 0.1327104\]\)
\(\[P(X = 12) = \binom{12}{12} \cdot (0.6)^{12} \cdot (0.4)^0 = 0.06931408\]\)
Adding up these probabilities:
\(\[P(\text{{at least 10 women pregnant}})\) = \(0.248832 + 0.1327104 + 0.06931408 = 0.45085648\]\)
Therefore, the total probability of at least 10 women being pregnant is approximately 0.4509, or 45.09%.
b) To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:
\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)
To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:
\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)
Let's calculate this probability:
\(\[\binom{12}{6}\]\) represents the number of ways to choose 6 women out of 12. It can be calculated as:
\(\[\binom{12}{6} = \frac{12!}{6! \cdot (12-6)!} = \frac{12!}{6! \cdot 6!} = 924\]\)
Now, we can substitute this value along with the given probabilities:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)
Evaluating this expression:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6\]\)
Calculating the values:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6 = 0.21284004\]\)
Therefore, the probability that exactly 6 women are pregnant is approximately 0.2128, or 21.28%.
c) To find the probability that at most 2 women are pregnant, we need to calculate the probabilities for 0, 1, and 2 women being pregnant and sum them up:
\(\[P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\]\)
To find the probability that exactly 6 women are pregnant, we can use the binomial probability formula:
\(\[P(X = 6) = \binom{12}{6} \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)
Let's calculate this probability:
\(\[\binom{12}{6}\]\) represents the number of ways to choose 6 women out of 12. It can be calculated as:
\(\[\binom{12}{6} = \frac{12!}{6! \cdot (12-6)!} = \frac{12!}{6! \cdot 6!} = 924\]\)
Now, we can substitute this value along with the given probabilities:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^{12-6}\]\)
Evaluating this expression:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6\]\)
Calculating the values:
\(\[P(X = 6) = 924 \cdot (0.6)^6 \cdot (0.4)^6 = 0.21284004\]\)
Therefore, the probability that exactly 6 women are pregnant is approximately 0.2128, or 21.28%.
d) The mean and standard deviation of a binomial distribution are given by the formulas:
Mean (μ) = \(n * p\)
Standard Deviation (σ) = \(sqrt(n * p * q)\)
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the measure of an angle is 166 degrees. what is the measure of of its supplementary angle?
Answers
Answer:
14°
Step-by-step explanation:
Supplementary angles add up to 180° so subtract 166 from 180.
Which of the following best describes a cubic centimeter?
A. a square with a side length of 1 centimeter and an area of 1 square centimeter
B. a square with a side length of 1 centimeter and an area of 2 square centimeter
C. a cube with a side length of 1 centimeter and a volume of 1 cubic centimeter
D. a cube with a side length of 1 centimeter and a volume of 3 cubic centimeters
Answers
hope this helped!!
evaluate x2+x-12÷y2 for x = 5 and y =2
Answers
Answer:
3
Step-by-step explanation:
A bacteria population grows at a rate proportional to its size. The initial count was 400 and 1600 after 1 hour. In how many minutes does the population double
Answers
The population grows at a rate proportional to its size approximately 15 minutes.
Since the bacteria population grows at a rate proportional to its size, we can use the exponential growth formula: P(t) = P(0) e^(kt), where P(t) is the population at time t, P(0) is the initial population, k is the growth rate constant, and e is the base of the natural logarithm.
Given that the initial count is 400, we have P(0) = 400. After 1 hour (60 minutes), the population is 1600, so P(60) = 1600.
To find the growth rate constant (k), we can substitute the values into the exponential growth formula:
1600 = 400 e^(k * 60)
Dividing both sides by 400:
4 = e^(k * 60)
Taking the natural logarithm of both sides:
ln(4) = k * 60
Solving for k:
k = ln(4) / 60
To determine the doubling time, we need to find the value of t when the population reaches twice its initial count (800):
800 = 400 e^[(ln(4) / 60) t]
Dividing both sides by 400:
2 = e^[(ln(4) / 60) t]
Taking the natural logarithm of both sides:
ln(2) = (ln(4) / 60) t
Solving for t:
t = (60 / ln(4)) ln(2)
Calculating this value, we find that the population of bacteria doubles in approximately 15 minutes.
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A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans.
Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation 4.3 + 6y = 48
models this situation, where x is the number of cars and y is the number of vans
Answers
Answer 2x and 7y
Step-by-step explanation:
Question:
Find 4 possible solutions in the context of the problem.
The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
Given the equation that models the situation expressed as:
4x + 6y = 48
We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.
If there are no cars i.e. at when x = 0
4(0) + 6y = 48
0 + 6y = 48
6y = 48
y = 48/6
y = 8
One of the solution is (0, 8)
If there are 3 cars, i.e. at when x = 0
4(3) + 6y = 48
12 + 6y = 48
6y = 48 - 12
y = 36/6
y = 6
The second solution will be (3, 6)
If there are 6 cars, i.e. at when x = 6
4(6) + 6y = 48
24 + 6y = 48
6y = 48 - 24
y = 24/6
y = 4
The third solution will be (6, 3)
If there are 9 cars, i.e. at when x = 9
4(9) + 6y = 48
36 + 6y = 48
6y = 48 - 36
y = 12/6
y = 2
The fourth solution will be (9, 2)
Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
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1.50%) the goal of the study is to compare numerical measurement of body condition (cond) between two different age groups. answer questions based on the spss outputs.
Answers
To compare numerical measurements of body condition (Cond) between two different age groups using SPSS outputs, you can follow these steps:
Import your data into SPSS and make sure the variable for age group is coded appropriately (e.g., 1 for Group 1, 2 for Group 2).
Run a descriptive statistics analysis for the variable "cond" separately for each age group.
This will provide you with the mean and standard deviation for each group.
To compare the means between the two groups, you can use an independent samples t-test.
Go to Analyze > Compare Means > Independent Samples T-Test.
Select "cond" as the Test Variable and "age group" as the Grouping Variable.
Click OK to run the analysis.
The output will provide you with the t-value, degrees of freedom, and p-value.
The t-value indicates the magnitude of the difference between the means,
while the p-value tells you if the difference is statistically significant.
If the p-value is less than your chosen significance level (e.g., 0.05),
you can conclude that there is a significant difference in body condition between the two age groups.
Remember to interpret the results in the context of your study and consider any limitations or potential confounding factors.
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find the x- and y-intercepts of the generic ellipse described by x 2 m2 y 2 n2 = 1. find a parametric description of this ellipse
Answers
One possible parametrization that traces out the entire ellipse is:
x = m cos(t)
y = n sin(t), 0 ≤ t ≤ 2π
The generic equation for an ellipse with center at the origin is given by:
x^2/a^2 + y^2/b^2 = 1
where "a" and "b" are the lengths of the semi-major and semi-minor axes, respectively.
Comparing this to the given equation x^2/m^2 + y^2/n^2 = 1, we see that the lengths of the semi-major and semi-minor axes are a = m and b = n.
To find the x-intercepts, we set y = 0 and solve for x:
x^2/m^2 = 1
x = ±m
So the x-intercepts are (m, 0) and (-m, 0).
To find the y-intercepts, we set x = 0 and solve for y:
y^2/n^2 = 1
y = ±n
So the y-intercepts are (0, n) and (0, -n).
To find a parametric description of the ellipse, we can use the parametric equations for a circle:
x = m cos(t)
y = n sin(t)
where t is the angle parameter in radians. However, these equations will only trace out one quarter of the ellipse, so we need to use different intervals of t to trace out the full ellipse.
One possible parametrization that traces out the entire ellipse is:
x = m cos(t)
y = n sin(t), 0 ≤ t ≤ 2π
This will trace out the ellipse counterclockwise, starting at the point (m, 0) and ending at the same point after a full revolution.
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What does char * s mean in C?
Answers
Char * s in C is a pointer to a character, which is a variable that stores a memory address pointing to a specific location in memory that stores a specific value.
In C, char * s is a pointer to a character. A pointer is a variable that stores a memory address. A memory address is a numerical value that points to a specific location in memory that stores a specific value. To understand char * s, it is important to understand the syntax of a pointer. Pointers are declared with the type of data they are pointing to (in this case, a char) followed by an asterisk (*) and then the name of the pointer (s). In this case, s is a pointer to a char, meaning that it points to a single character in memory.
Char * s in C is a pointer to a character, which is a variable that stores a memory address pointing to a specific location in memory that stores a specific value.
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What is the factored form of this expression?
18x2 − 50
Answers
Answer:
_14
Step-by-step explanation:
step1 18×2 -50
step2 18×2 =36_50
step3 36_50=_14
Answer:
2(9*x-25)=18×2-50
Step-by-step explanation:
the answer is in the problem since we know 1 times anything will stay the same. so just divide the other integers by 2 and put the problem in parentheses.
Find the distance between the two points.
✓ [?]
Enter the number that
goes beneath the
radical symbol.
![Find the distance between the two points. [?]Enter the number thatgoes beneath theradical symbol.](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/H2gjo3srb34pQLuWAETFCqbXa8GGaqRa.png)
Answers
Answer:
The answer is
\(\sqrt{17} \: \: \: units\)Step-by-step explanation:
The distance between two points can be found by using the formula
\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-2 , 3) and ( 2 , 4 )
The distance between them is
\(d = \sqrt{ ({ - 2 - 2})^{2} + ({ 3 - 4})^{2} } \\ = \sqrt{ ({ - 4})^{2} + ( { - 1})^{2} } \\ = \sqrt{16 + 1} \\ = \sqrt{17} \: \: \: \: \: \: \: \: \)
We have the final answer as
\( \sqrt{17} \: \: \: units\)
Hope this helps you
In the system (0 ; i,j) given the vectors : v= -2i +3j;
OA= i-2j ,
OB = 3i-4j;
OC = -i +2j
and OM = xi + y j.
1° Calculate the components of vector u = 2OB -3OC + 3BA.
Answers
The components of vector u are 3 in the i direction and -8 in the j direction.
Define vectorA mathematical object with both magnitude (or length) and direction is called a vector. Vectors are often represented as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.
To calculate the components of vector u = 2OB -3OC + 3BA, we first need to find the components of each vector:
OB = 3i - 4j
OC = -i + 2j
BA = OA - OB = (i - 2j) - (3i - 4j) = -2i + 2j
Now we can substitute these values into the equation for u:
u = 2OB - 3OC + 3BA
u = 2(3i - 4j) - 3(-i + 2j) + 3(-2i + 2j)
u = 6i - 8j + 3i - 6j - 6i + 6j
u = 3i - 8j
Therefore, the components of vector u are 3 in the i direction and -8 in the j direction.
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30% of 150 is 45 what is the base the rate and the percentage
Answers
Answer:
Step-by-step explanation:
The base is 150. The rate is 30%. The percentage is 45.
PLEASE HELP ME QUICK PLEASE!
Answers
I think the answer is option 4
Find the length of the confidence interval given the following data: O=0.6, n=81, confidence level = 95%
Answers
The length of the confidence interval is approximately 0.214.
To find the length of the confidence interval, we need to calculate the margin of error first. The formula for the margin of error in a proportion estimation is:
Margin of Error = Z * \(\sqrt{ ((p * (1 - p)) / n)\)
Where:
Z is the Z-score corresponding to the desired confidence level
p is the proportion estimate (in this case, it is the observed proportion O)
n is the sample size
Since the confidence level is 95%, we can use the Z-score associated with a 95% confidence level, which is approximately 1.96.
Plugging in the values:
Z = 1.96
p = 0.6
n = 81
Margin of Error = 1.96 * \(\sqrt{((0.6 * (1 - 0.6)) / 81)\)
Now we can calculate the margin of error:
Margin of Error = 1.96 * \(\sqrt{((0.6 * 0.4) / 81)\) ≈ 0.107
The length of the confidence interval is twice the margin of error, so:
Length of Confidence Interval = 2 * 0.107 ≈ 0.214
Therefore, the length of the confidence interval is approximately 0.214.
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We will use blue poker chips to represent cars that take some damage and yellow poker chips to represent cars that do not take some damage. We will use a total of 100 poker chips to simulate the null hypothesis model. How many of the 100 poker chips should be blue?q
Answers
We will use a total of 100 poker chips to simulate the null hypothesis model. We need to find how many of the 100 poker chips should be blue. As per the null hypothesis model 50 of the 100 poker chips should be blue and 50 should be yellow.
Null Hypothesis Model: A null hypothesis model is a statistical hypothesis that there is no significant difference between the observed and expected results. In other words, it is a statement that suggests there is no difference between two sets of data or no correlation between two variables. It is used in hypothesis testing to compare the results of an experiment to the expected results.
In this case, the null hypothesis model assumes that there is no difference between the number of cars that take damage and the number of cars that do not take damage. Hence, we can assume that the number of blue poker chips and yellow poker chips should be equal, that is, 50 each. Therefore, 50 of the 100 poker chips should be blue and 50 should be yellow.
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How many elementary events are in the sample space of the experiment of rolling three fair coins? 2 9 8 6
Answers
When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.
The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)
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How to find acceleration with velocity and distance?
Answers
What Is Velocity?
The rate of change of your position with time defines your velocity. In everyday language, velocity means the same thing as speed. However, in physics, there is an important distinction between the two terms. Speed is a “scalar” quantity, and it’s measured in units of distance/time, so in meters per second or miles per hour. Velocity is a “vector” quantity, so it has both a magnitude (the speed) and a direction. Technically, saying you’re traveling at 5 meters per second is a speed and saying you’re traveling at 5 meters per second towards the north is a velocity, because the latter has a direction too.
What Is Acceleration?
Acceleration is the rate of change of velocity with time. Like velocity, this is a vector quantity that has a direction as well as a magnitude. An increase in velocity is commonly called acceleration while a decrease in velocity is sometimes termed deceleration. Technically, since velocity includes a direction as well as a speed, a change in direction at a constant speed is still considered acceleration.
Hope this helps
A group of 29 students all order a
calculator. Calculators cost £6.75 each.
Estimate how much the total cost of the
order will be.
Pls help me tmr my homework is due in
Answers
Answer:
210
Step-by-step explanation:
we need to estimate so we don't need to use the real number but use a simplified one.
29 is approximately equal to 30
6.75 is approximately equal to 7
\(30 \times 7 = 210\)
0.072 as a multiple power of 10
Answers
Answer:
0.72 I think but not sureThank you ☺️☺️
Assume ABC= ADEF. If AB = 18, BC = 10, and AC - 25, what is the length
of DF?
• A. 25
• B. Cannot be determined
• c. 10
• D. 18
Answers
"The correct answer is B. Cannot be determined." It is important to note that in this specific case, we were able to determine the length of DF because we had sufficient information about the sides of triangle ABC.
Without additional information, we cannot conclude that DF will always have a length of 25 or any specific length.
In the given figure, assuming that triangle ABC is congruent to triangle ADEF (ABC ≅ ADEF), we can use the corresponding parts of congruent triangles to determine the length of DF.
From the information provided, we know that AB = 18, BC = 10, and AC = 25.
Since ABC ≅ ADEF, the corresponding sides are congruent. Therefore, we can conclude that DE = 18, EF = 10, and AD = 25.
To find the length of DF, we need to sum up the lengths of DE and EF:
DF = DE + EF = 18 + 10 = 28
The length of DF is 28.
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If the 1t peron ave 1/4 of total , 2nd peron ave 2/3 of total and the 3rd peron ave 1/10 which fraction i left to pay for the birthday party
Answers
Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?
The fraction left to pay for the birthday party is 17/30.
The calculation is as follows:
1 * 1/4 = 1/4 … (1)
1/4 * 2/3 = 2/12 … (2)
2/12 * 1/10 = 2/120 … (3)
Fraction left to pay:
= 1 - (1/4 + 2/12 + 2/120)
= 1 - (30/120 + 20/120 + 2/120)
= 1 - (52/120)
= 1 - 13/30
= 30/30 - 13/30
= 17/30
Thus, the fraction left to pay for the birthday party is 17/30.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
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g A high quality paintbrush can hold a surprisingly large amount of paint. Why can a good brush hold so much paint without it simply running off the bristles
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A high-quality paintbrush can hold a significant amount of paint without it running off the bristles due to its unique design and construction.
The bristles are designed to be absorbent and have a capillary action that helps retain the paint, allowing for controlled application and minimizing waste.The bristles of a good paintbrush are made of materials like natural or synthetic fibers that have absorbent properties. These materials are capable of holding and retaining a certain amount of liquid, including paint. The bristles are often packed densely, creating a large surface area for paint retention.
The capillary action plays a crucial role in preventing the paint from running off the bristles. Capillary action is the ability of a liquid to flow in narrow spaces, such as the gaps between bristles. When the brush is dipped into paint, the liquid is drawn up into the spaces between the bristles due to capillary forces. This action creates a reservoir of paint within the brush, allowing for a controlled release during painting.
The combination of absorbent bristles and capillary action enables a high-quality paintbrush to hold a substantial amount of paint without it simply running off the bristles. This design feature ensures efficient paint application, reduced drips, and better control over the painting process.
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Please help me with this! Legitimate answers only please!
Fill in the blanks with the proper/right options for the problem.
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Answer:
x= amount of subscriptions
y= total amount
m= $5 rate of change
b= $15 a starting point....
Eq: y=5x+15
PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help
Answers
Answer:
22 units
Step-by-step explanation:
Known Quantities:
AB = CD and AC = BDCalculations:
AB = 8AC = 3CD = 8BD = 3Final Calculations:
perimeter = 2 x (3+8)perimeter = 22
Show that the sequence{an} is a solution of the recurrence relation an = an−1 + 2an−2 + 2n − 9 if
a) an = -n + 2.
b) an = 5(-1)n - n + 2.
c) an = 3(-1)n + 2n - n + 2.
d) an = 7 · 2n - n + 2.
Answers
a) {\(a_n\) = -n + 2} is not a solution, b) {\(a_n\) = 5(-1)n - n + 2} is a solution, c) {\(a_n\) = 3(-1)n + 2n - n + 2} is a solution and d) {\(a_n\) = 7 · 2n - n + 2} is not a solution of the recurrence relation \(a_n\).
To show that a given sequence {\(a_n\) } is a solution of the recurrence relation \(a_n\) = \(a_{n-1\) + 2\(a_{n-2\) + 2n − 9, we substitute the given sequence into the recurrence relation and check if it holds true for all n.
a) Given \(a_n\) = -n + 2, let's substitute it into the recurrence relation:
(-n + 2) = (-n-1 + 2) + 2(-n-2) + 2n - 9
Simplifying, we get:
-n + 2 = -n - 1 + 2 - 2n - 4 + 2n - 9
Combining like terms, we have:
-n + 2 = -n - 12
Since this equation is not true for all n, the sequence {\(a_n\) = -n + 2} is not a solution of the recurrence relation.
b) Given \(a_n\) = 5(-1)n - n + 2, let's substitute it into the recurrence relation:
5(-1)n - n + 2 = 5(-1)n-1 - (n-1) + 2 + 2n - 9
Simplifying, we get:
5(-1)n - n + 2 = -5(-1)n-1 - (n-1) + 2 + 2n - 9
Combining like terms, we have:
5(-1)n - n + 2 = -5(-1)n-1 + n - 1 + 2n - 9
The equation holds true for all n, so the sequence {\(a_n\) = 5(-1)n - n + 2} is a solution of the recurrence relation.
c) Given \(a_n\) = 3(-1)n + 2n - n + 2, let's substitute it into the recurrence relation:
3(-1)n + 2n - n + 2 = 3(-1)n-1 + 2(n-1) - (n-1) + 2 + 2n - 9
Simplifying, we get:
3(-1)n + 2n - n + 2 = 3(-1)n-1 + 2n-2 - (n-1) + 2 + 2n - 9
Combining like terms, we have:
3(-1)n + 2n - n + 2 = 3(-1)n-1 + 2n-2 + n - 1 + 2n - 9
The equation holds true for all n, so the sequence {\(a_n\) = 3(-1)n + 2n - n + 2} is a solution of the recurrence relation.
d) Given \(a_n\) = 7 · 2n - n + 2, let's substitute it into the recurrence relation:
7 · 2n - n + 2 = 7 · 2n-1 - (n-1) + 2 + 2n - 9
Simplifying, we get:
7 · 2n - n + 2 = 7 · 2n-1 - (n-1) + 2 + 2n - 9
The equation does not hold true for all n, so the sequence {\(a_n\) = 7 · 2n - n + 2} is not a solution of the recurrence relation.
To summarize:
a) {\(a_n\) = -n + 2} is not a solution.
b) {\(a_n\) = 5(-1)n - n + 2} is a solution.
c) {\(a_n\) = 3(-1)n + 2n - n + 2} is a solution.
d) {\(a_n\) = 7 · 2n - n + 2} is not a solution.
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"liabilities whose book values and fair values difered.
of \( \$ 100,000 \) during that year. Muliplechoce 52000000 \( 52,05,000 \)
liablities whose book values and fair values differed:"
Answers
The liabilities whose book values and fair values differed by \$100,000 during that year are:
What is the explanation for the difference between book values and fair values of liabilities?The difference between book values and fair values of liabilities arises due to various factors. Book value refers to the value of a liability as recorded on the balance sheet, which is based on historical cost and may not reflect the current market conditions. Fair value, on the other hand, represents the estimated value of a liability in the current market.
There are several reasons why the book values and fair values of liabilities may differ.
Changes in interest rates, creditworthiness of the debtor, market conditions, and the passage of time can all contribute to these differences. If interest rates have changed since the liability was initially recorded, the fair value may be higher or lower depending on the prevailing rates.
Similarly, if the creditworthiness of the debtor has changed, the fair value may be adjusted to reflect the increased or decreased risk associated with the liability.
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Peter has 2 baseball hats. Peter and his brothers have fewer than 15 baseball hats.
Answers
Answer:
The answer is 13.
Step-by-step explanation:
Work out the product of 1 4/5 and 1 5/8
Give your answer as a mixed number.
Answers
Answer:
4 17/25
Step-by-step explanation:
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