According to the solution, the Given number is not prime (7/8 or 0.875). This doesn't qualify as a prime number.
What does a prime number mean in mathematics?Prime numbers are those that have just two elements, one and themselves. For instance, the first five prime numbers are 2, 3, 5, 7, and 11. Comparatively, composite numbers are defined as having more than two elements.
How are prime numbers taught in schools?Try to divide the number by all the smaller numbers to see if your child can determine whether it is prime. It is a prime number if it can only be divided by itself and by one.
According to the given information.= 4/7+1/8+1/3
= 7/8 or 0.875
This is not a prime number.
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STUDENT ACTIVITIES The Venn diagram shows the cast members of two school musicals who also participate in the local children's theater. One of the students will be chosen at random to attend a statewide performing arts conference. Let A be the event that a student is a cast member of Suessical and let B be the event that a student is a cast member of Wizard of Oz
we can use the notation P(A) and apply the definition of probability: P(A) = P(B), P (A ∩ B), and P (A ∪ B) if we have the necessary information.
What is Vann diagram?I believe you meant to say, "Venn diagram". A Venn diagram is a type of graphical representation used to illustrate relationships between sets or groups of objects, concepts, or ideas. It consists of a series of overlapping circles or other closed shapes, with each circle representing a set or group and the overlapping areas representing the relationships or intersections between them.
by the question.
Let A be the event that a student is a cast member of Seussical, and let B be the event that a student is a cast member of Wizard of Oz. Then, we can define the following:
A ∩ B: The event that a student is a cast member of both Seussical and Wizard of Oz.
A ∪ B: The event that a student is a cast member of either Seussical, Wizard of Oz, or both.
A': The event that a student is not a cast member of Seussical.
B': The event that a student is not a cast member of Wizard of Oz.
Based on the information given, we do not know how many students are in each of these events, but we can still make some general observations. For example:
If A and B have no students in common (i.e., A ∩ B = ∅), then the number of students in A ∪ B is equal to the sum of the number of students in A and the number of students in B.
If some students are in both A and B (i.e., A ∩ B is not empty), then the number of students in A ∪ B is equal to the sum of the number of students in A, the number of students in B, and the number of students in A ∩ B. In other words, some students are counted twice when we add up the number of students in A and the number of students in B, so we need to subtract the number of students in A ∩ B to avoid double-counting.
We do not know whether the events A and B are mutually exclusive (i.e., whether A ∩ B = ∅) or not. If they are mutually exclusive, then P(A ∩ B) = 0, and we can use the addition rule of probability to find P (A ∪ B) = P(A) + P(B). If they are not mutually exclusive, then we need to use the general addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Finally, if we want to find the probability that a student chosen at random is a cast member of Seussical,
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What is the next number in the sequence 3, 4, 7, 12, 19
Answer:28
Step-by-step explanation:
Answer: 28
Explanation: Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)
Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
Use the image below to get the measure of ∠w
Answer:49
Step-by-step explanation:
Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4. 9 points. Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3. 7 points. Find Rachel's z-score, to the nearest hundredth
The z-score for Keenan is 0.71, rounded up to the hundredth.
The Z-score determines the standard deviations by which the measure deviates from the mean. After calculating the Z-score, we look at the z-score table to ascertain the p-value associated with it. This p-value represents the percentile of X or the probability that the measure's value is smaller than X. You may get the likelihood that the value of the measure is greater than X by subtracting 1 from the p-value.
The formula for calculating the z-score is as follows: The z-score is the number of standard deviations an individual's score deviates from the mean.
z = (x - μ) / σ
where the mean score is, the standard deviation is, and x is the individual's score.
About Keenan's test:
z = (80 - 77) / 4.2
z = 0.71
Keenan's z-score is 0.71 as a result, rounded to the nearest hundredth.
Any decimal number is rounded to the nearest hundredth value when it is expressed as a fraction. A hundredth is 1/100 or 0.01 in decimal form. For instance, 2.17 is the result of rounding 2.167 to the nearest tenth.
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Past studies indicate that about 60 percent of the trees in a forested region are classified assoftwood. A botanist studying the region suspects that the proportion might be greater than 0.60.The botanist obtained a random sample of trees from the region and conducted a test ofB:p=0.6 versus H, :p>0.6. The P-value of the test was 0.015. Which of the following is acorrect interpretation of the P-value?a. if it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is theprobability of obtaining a population proportion greater than 0.6.b. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the8 probability of obtaining a sample proportion as small as or smaller than the one obtained by thebotanistc. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is theprobability of obtaining a sample proportion as large as or larger than the one obtained by thebotanistd. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 isthe probability of obtaining a sample proportion as large as or larger than the one obtained by thebotaniste. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 isthe probability of obtaining a population proportion greater than 0.6.
If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.The correct answer is option C
The P-value is the probability of obtaining an outcome as extreme or more extreme than the one actually observed given that the null hypothesis is true. In this case, the null hypothesis is that the proportion of trees classified as softwood is 0.60. The P-value of 0.015 indicates that the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist is 0.015 if the null hypothesis is true.
Therefore, the P-value is an indicator of how well the sample data supports the null hypothesis. In this case, the P-value of 0.015 is lower than the commonly accepted significance level of 0.05, which indicates that the sample data does not support the null hypothesis and suggests that the proportion of trees classified as softwood is actually greater than 0.60.
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Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1,5) y P₂=(-2,-6)
Cómo resolver este ejercicio de ecuaciones lineales de dos puntos
The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)
In mathematics, how do you find coordinates?To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.
It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.
We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)
Using the values provided:
P1 = (-1.5, Y1) (-1.5, Y1)
P2 = (-2, -6) (-2, -6)
These values can be used as substitutes in the formula:
m = (-6 - Y1) / (-2 - (-1.5))
Making the denominator simpler:
m = (-6 - Y1) / (-2 + 1.5)
m = (-6 - Y1) / (-0.5)
m = 12 + 2Y1
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Question:
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1.5) and P₂=(-2,-6)
How to solve this exercise of linear equations of two points.
Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with radius 83,000,000 mi. Find the linear speed of XYZ in miles per hour. The linear speed is approximately ______ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with a radius of 83,000,000 mi. The linear speed of XYZ in miles per hour is approximately 1,093,333 miles per hour.
What is the orbit and what is the linear speed?
An orbit refers to the path taken by an object, such as a planet, as it circles around another object, such as a star. The speed of the planet is its rate of movement, measured in linear units like miles or kilometers per hour, as it travels around the orbit.
These are terms that are important to understanding the solution to the problem provided. The linear speed of XYZ in miles per hour is approximate _____ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ travels around the star ABC in a circular orbit that takes 24 hours to complete. The orbit is a circle with a radius of 83,000,000 miles.
To find the linear speed of XYZ in miles per hour, it is necessary to use the formula for the circumference of a circle.
Circumference = 2πr Circumference
=2πr Substitute 83,000,000 for r in the formula.
Circumference = 2π(83,000,000)
Circumference = 522,000,000 π
The orbit's circumference is 522,000,000 π miles.
The distance traveled by XYZ in one hour is the linear speed. The linear speed of XYZ in miles per hour is calculated as follows:
Speed = Distance/TimeSpeed
= Circumference/24Speed
= (522,000,000 π)/24
Speed = 21,750,000 π
The linear speed of XYZ in miles per hour is 21,750,000 π miles per hour.
To get an approximate answer, π is equal to 3.14.
Speed ≈ 21,750,000 (3.14)
Speed ≈ 68,295,000
The linear speed of XYZ in miles per hour is approximately 68,295,000 miles per hour. Rounded to the nearest integer, the linear speed is approximately 1,093,333 miles per hour.
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The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?
Hi!
Your answer is 11 and 4.
11 x 4 = 44
11 + 4 = 15
Hope this helps!
~~~PicklePoppers~~~
Write as a single power of 3:
27divided by 9a
Answer:
Step-by-step explanation:
27/9a
= 3^3/3^2 a
= 3/a
Which choice is an exponential function?
Of(x)=x²+6
Of(x)=5(3)*
Of(x) = 3x + 7
Of(x) = |2x+ 41
Answer:1st one
Step-by-step explanation:
Kevin made a down payment of $1,500 for his car lease. His monthly payment amount is $200 for 36 months. What is the total cost of the lease if Kevin purchases the car. The residual value at the end of the lease is $8,000?
Kevin made a down payment of $1500 for his automobile leasing. Kevin's monthly payment for a 36-month rental with an overall cost of $4,200 will be $200 if he opts to buy the vehicle outright for $16,700.
What kind of down payment is this, exactly?A deposit on a property is a typical illustration of a down payment. The down payment for a property can range from 5% to 25%, with the remaining amount being covered by a mortgage obtained from a bank or another financial institution.
A down payment or a deposit is it?A commitment is retained by a 3rd person in trust, only until date of completion when it constitutes a component of the deposit.
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The complete question is:
Kevin made a down payment of $1,500 for his car lease. His monthly payment amount is $200 for 36 months. What is the total cost of the lease if Kevin purchases the car. The residual value at the end of the lease is $8,000?
a. $14,500
b. $15,200
c. $16,700
Answer: 16,700
Step-by-step explanation:
....
please help I have attached a photo below. thanks for your time and help.
According to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.
What is a protractor?An instrument for measuring angles is a protractor, which is often made of transparent plastic or glass.
Protractors might be straightforward half-discs or complete circles. Protractors with more complex features, like the bevel protractor, include one or two swinging arms that can be used to measure angles.
Most protractors use degrees (°) to express angles.
Protractors with radian scales calculate angles.
The majority of protractors have 180 equal segments.
Degrees are further subdivided into arcminutes by some precision protractors.
They are employed in geometry, engineering, and mechanics.
So, in the given image the proctor is measuring the angle of 50°.
Therefore, according to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.
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What are the integer solutions to the inequality below?
−
4
<
x
≤
0
Step-by-step explanation:
x = +1
x = -2
x = -3
x = -4
Use number line to find the value and fit equation
3. For eacht>0, suppose the number of guests arriving at a bank during the time interval[0,t)follows a Poisson(λt). a. Denote byXthe arrival time of the first guest. What is the distribution ofX? b. Denote byYthe arrival time of the second guest. What is the distribution ofY?
Denote by X the arrival time of the first guest. The time of arrival of the first guest at a bank is modeled by the Poisson distribution, where the arrival rate is λ. Thus, the number of arrivals during time t is Poisson(λt).
Therefore, the distribution of X is Exponential(λ), which means that its probability density function is
f(x) = λe−λx, x > 0.
The expected value of X is E[X] = 1/λ and the variance is Var(X) = 1/λ².
b. Denote by Y the arrival time of the second guest.
The number of arrivals during time t is Poisson(λt). The first guest arrived at time X, so the number of arrivals from time X to time t is Poisson(λ(t - X)).
Thus, the arrival time of the second guest has the conditional probability density function:
f(y | X) = λe^(−λ(y−x)), y > x
Therefore, the unconditional probability density function of Y is obtained through the law of total probability:
f(y) = ∫f(y | x)f(x)dx
= ∫λe^(−λ(y−x))λe^(−λx)dx
= λ²e^(−λy), y > 0
Therefore, the distribution of Y is Exponential(λ), which is the same as that of X.
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is every point of every open set e c r2 a limit point of e? answer the same question for closed sets in r2
All points belonging to any closed set in R2 are limit points of that set.
What is a limit point?A limit point is a point in a metric space that can be approached arbitrarily closely by points of a sequence or a set. The definition is different from that of an isolated point, which has an open ball around it that does not include any other points of the set.
According to the definition of a limit point, every point in every open set in R2 is a limit point of the set. This is because there is always at least one other point in the open set that is within a specified distance of the point in question.
As a result, every point in every open set in R2 is a limit point of the set. We can answer the same question for closed sets in R2. A closed set in R2 contains all of its limit points. A closed set, by definition, includes its boundary.
As a result, every point in every closed set in R2 is a limit point of the set.
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use a blank number line to solve. which of the following expressions have a value that is less than 0? select all that apply. Sorry is it says i am in high school i am in 7th grade
a)-5+3
b)6+(-8)
c)5+(-3)
d)-2+5
The expressions that have values less than 0 are a) and b)
According to the question
Here's how you can use a number line to solve this problem:
Draw a blank number line with a zero in the middle.For each expression, start at zero and move to the right or left depending on the sign of the first number.Then, add or subtract the second number to get the final position on the number line.If the final position is to the left of zero, the expression has a value that is less than 0.For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.
Similarly expression b) has a value that is less than zero.
Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.
In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.
What is a number line?
A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.
What is meant by expressions?
An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.
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Solve the system of equations
n=2d+5
0. 05n+0. 10d=2. 25
Answer: THIS IS THE ANSWER
Ramona is climbing a hill with a 10 incline and wants to know the height of the rock formation. She walks 100 ft up the hill and uses a clinometer to measure the angle of elevation to the top of the formation. What is the height h of the rock formation?
Answer:
40.4026226 aka 40.403
Step-by-step explanation:
tan 22 degrees = h/100
I need help solving this question:
Answer:
The answer is letter D.
Step-by-step explanation:
Ye
Answer:
The answer is C
x -10 < -20
x < -20 + 10
x< -10
The sign won't change to the other side because the variable we were asked to find is in the positive form.
A plan for a house is drawn on a 1:40 scale. If the length of the living room on the plan measures 4.5 inches, what is the actual length of the built living room? 45 feet 25 feet 15 feet 12 feet
Answer:
actual length = 15 feet
Step-by-step explanation:
using the conversion
12 inches = 1 foot
the actual length = 40 × scale length = 40 × 4.5 = 180 inches = 180 ÷ 12 = 15 feet
An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally likely outcomes. What is the probability of rolling two 1's? Express your answer as a fraction in simplest form.
The probability of rolling two 1's is 1/18. This concludes the answer.
Why it is and what does probability mean?
Probability = No. of favorable outcomes/Total Outcomes
Here the no of favorable outcomes = 2{(2,1), (1,2) }
Total outcomes = 36
P (1 and 2) = 2/36 = 1/18
Therefore, the solution is 1/18
Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to quantify the likelihood of an event occurring, which ranges from 0 (impossible) to 1 (certain). Probability is expressed as a ratio, fraction, or percentage. The concept of probability is used in various fields such as science, economics, finance, and statistics to make informed decisions and predictions.
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f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f.
The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x)) is 1
Calculating the inverse of g(x)Given that
f(x) = 3 - 2x
Rewrite as
g(x) = -x² + x + 1
Express as vertex form
g(x) = -(x - 0.5)² + 1.25
Express as equation and swap x & y
x = -(y - 0.5)² + 1.25
Make y the subject
y = 0.5 + √(1.25 - x)
So, the inverse is
g⁻¹(x) = 0.5 + √(1.25 - x)
Calculating the value of xHere, we have
f(g(x)) = g(f(x))
This means that
f(g(x)) = 3 - 2(-x² + x + 1)
g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1
Using a graphing tool, we have
f(g(x)) = g(f(x)) when x = 1
Hence, the value of x is 1
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Complete question
f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers
Find the inverse of G and the value for x for which f(g(x)) = g(f(x)).
104.
Simplify the polynomial by writing each of its term in standard form.
12a^2 · 3ba − 2ab · 3ab^2+11aba
The simplified polynomial, with each term written in standard form, is: 36a^3b - 6a^2b^3 + 11a^2b
How to simplify the polynomialTo simplify the given polynomial, we need to expand and combine like terms.
First, we can distribute the coefficients of the first term:
12a^2 · 3ba = 36a^3b
Next, we can simplify the second term by multiplying the coefficients and adding the exponents:
-2ab · 3ab^2 = -6a^2b^3
Finally, we can combine the like terms:
36a^3b - 6a^2b^3 + 11a^2b
To write each term in standard form, we arrange the terms in decreasing order of exponents of 'a' and 'b':
36a^3b - 6a^2b^3 + 11a^2b
So, the simplified polynomial, with each term written in standard form, is:
36a^3b - 6a^2b^3 + 11a^2b
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calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. the surface area a and volume v of a spherical balloon are related by the equationA³ - 36πV² where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches.
The rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches is 4.96 square inches per second.
The surface area of a spherical balloon and the volume of the balloon are related by the equation [tex]A³ - 36πV²[/tex], where A is in square inches and V is in cubic inches. To find the rate at which the surface area of the balloon is increasing, we can use derivatives. We start by taking the derivative of the equation [tex]A³ - 36πV²[/tex] with respect to time (t).
[tex]d/dt[A³ - 36πV²] = 3A²dA/dt - 72πVdV/dt[/tex]
Given the rate at which the balloon is being inflated with gas (dV/dt) and the area and volume of the balloon (A, V) at the given instant, we can solve for the rate at which the area is increasing (dA/dt).
[tex]dA/dt = (3A² - 72πV)dV/dt / 36πV[/tex]
Plugging in the given values for A, V, and [tex]dV/dt,[/tex]we can calculate dA/dt:
[tex]dA/dt = (3(153.24)² - 72π(178.37))(18)/(36π(178.37)) ≈ 4.96[/tex]
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Suppose a large candy machine has 45% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion
pof orange candies. Find the standard deviation of the sampling distribution of
pCheck to see if the 10% condition is met.
The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.
If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).
Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.
This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.
Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.
Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.
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Simplify these radicals (ASAP!!!)
Answer:
[tex]3.\quad 2\sqrt{7}\\\\4.\quad \dfrac{2}{\sqrt{5}}[/tex]
[tex]5.\quad \dfrac{1}{\sqrt{2}}[/tex]
[tex]6.\quad\dfrac{5}{7}[/tex]
Step-by-step explanation:
To simplify radicals find the factors and simplify the square roots of the factors
#3 : √28
28 = 4 x 7
√28 = √(4 x 7) = √4 x √7 = 2 x √7 = 2√7
========================================================
[tex]\#4:\quad \sqrt{ \dfrac{4}{5}}\\\\\sqrt{ \dfrac{4}{5}} = \dfrac{\sqrt{4}}{\sqrt{5}} = \dfrac{2}{\sqrt{5}}[/tex]
========================================================
[tex]\#5\quad \dfrac{3}{\sqrt{18}}\\\text{Denominator } \sqrt{18 }= \sqrt{9 \times 2} = 3\sqrt{2}\\\\ \dfrac{3}{\sqrt{18}}= \dfrac{3}{3\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]
========================================================
[tex]\# 6 \quad \sqrt{\dfrac{25}{49}}\\\\\sqrt{25} = 5\\\\\\\sqrt{49} = 7\\\\[/tex]
[tex]\sqrt{\dfrac{25}{49}}= \dfrac{5}{7}[/tex]
Subtract (34ab – 15b + 8a) from (20ab +16b +4a)
Answer:
-14ab + 31b -4a
Step-by-step explanation:
(20ab + 16 b + 4a) - (34ab - 15b +8a)
20 ab +16b + 4a -34ab + 15b -8a
-14ab + 31b -4a
Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t) ). F(t) = t, 0 ≤ t ≤ 3 2t−3, 3 < t ≤ 4 5, 4 < t
The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).
To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.
f(t) = t, 0 ≤ t ≤ 3
f(t) = 2t - 3, 3 < t ≤ 4
f(t) = 5, 4 < t
Using the Heaviside function uc for the jump at c, we can represent each interval as follows:
f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3
f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4
f(t) = 5uc(t-4), 4 < t
Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)
Learn more about the Heaviside functions at
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