The scale factor for 7 millimeters to 5 meters is 0.0014.
What is the scale factor?The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.
We can compute the scale factor (scaled-down) using the following formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
1 meter = 1,000 millimeters
5 meters = 5,000 millimeters (1,000 x 5)
The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)
The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)
Thus, the scale factor is 0.0014.
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Question Completion:What is the scale factor?
7
The product of (a - b)(a - b) is a perfect square trinomial. (1 point)
Sometimes
Always
Never
Find the product of (x + 5)². (1 point)
Ox²-10x+25
Ox²-25
O x²+25
Ox²+10x+25
Product of (a - b)(a - b) is never a perfect square trinomial, the product of (x + 5)² is x² + 10x + 25.
An algebraic expression is what?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
The algebraic expression (a + b) (a b) should be multiplied.
(a + b) = a² - ab + ba - b² (a + b)
(a + b) = a² - b² (a b) [ - ab + ba = 0 ]
Since there are only 2 terms in the final formula, a² - b² is a binomial.
As a result, the result of (a + b) (a b) is not a trinomial with a perfect square.
product of (x + 5)²
⇒ (x+5)(x+5)
⇒ x² + 5x + 5x + 25
⇒ x² + 10x + 25
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Consider the problem of predicting Y using another variable, X, so that the prediction of Y is some function of X, say g(X). Suppose that the quality of the prediction is measured by the squared prediction error made on average over all predictions, that is, by E{[Y – g(x)]?}. This exercise provides a non-calculus proof that of all possible prediction functions g, the best predic- tion is made by the conditional expectation, E(Y|X). a. E(Y|X), and let u = Y – û denote its prediction error. Show that E(u) = 0. (Hint: Use the law of iterated expectations.) b. Show that E(uX) = 0. c. Let Ỹ = g(x) denote a different prediction of Y using X, and let v = Y Ỹ denote its error. Show that E[(Y – Ỹ)?] > E[(Y - Ỹ)2]. [Hint: Let h(X) = g(x) – E(Y|X), so that v = [Y - E(Y|X)] - h(X). Derive E(v2).] a. Let û =
E(Y|X) is the conditional expectation of Y given X. We can use the law of iterated expectations to show that E(u) = 0.
This law states that E(E(X|Y)) = E(X). Therefore, E(u) = E(Y - E(Y|X)) = E(Y) - E(E(Y|X)) = E(Y) - E(Y) = 0.
b. We can use the law of iterated expectations again to show that E(uX) = 0. This law states that E(E(XY|Z)) = E(X)E(Y|Z). Therefore, E(uX) = E(YX - E(YX|X)) = E(YX) - E(E(YX|X)) = E(YX) - E(Y)E(X) = 0.
c. Let Ỹ = g(x) denote a different prediction of Y using X and let v = Y - Ỹ denote its error. We can use the equation h(X) = g(x) - E(Y|X), so that v = [Y - E(Y|X)] - h(X). Using this equation, we can derive E(v2) = E[(Y - E(Y|X))2] - 2E[(Y - E(Y|X))h(X)] + E[h(X)2]. Since E(Y - E(Y|X)) = 0, this reduces to E(v2) = E[h(X)2] < E[(Y - Ỹ)2], which shows that E[(Y - Ỹ)?] > E[(Y - Ỹ)2].
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inquiry HOW can you use a bar diagram to show a percent of change?
A bar diagram can be used to show a percent of change by the method of comparing two bars.
What is a bar diagram?
Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
A bar diagram can be used to show a percent of change by comparing the size of two or more bars. The bars can represent the original value and the final value, and the difference in size between the two bars will indicate the percent of change.
For example, if the original value is represented by a bar that is 10 units tall and the final value is represented by a bar that is 12 units tall, the percent of change would be 20% (the difference in height between the two bars divided by the original value).
The percent of change can also be labeled or annotated on the graph.
Therefore, bar graph is helpful in denoting the percent of change.
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The density function for the random variable, T, that denotes the life time of a bulb (in years) is given by: 6 - t f(t) = 12,0
A continuous random variable takes on an uncountably infinite number of possible values. For a discrete random variable X that takes on a finite or countably infinite number of possible values, we determined p(X=x) for all of the possible values of X and called it the probability mass function ("p.m.f").
For continuous random variables, as we shall soon see, the probability that X takes on any particular value x is 0. That is, finding p(X=x) for a continuous random variable X is not going to work. Instead, we'll need to find the probability that X falls in some interval a,b that is, we'll need to find.
We will do that using a probability density function ("p.d.f."). We'll first motivate a p.d.f. with an example, and then we'll formally define it.
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a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation. note: your answer should be in the form of one or more fractions multiplied together
The missing part of the equation should be like 1000 g / 1 kg × 100 cm / 1 m
Given,
The set of units used in the final response is different. In particular, kilogram (kg) and meters (m) are converted to gramm(g) and centimeter (cm), respectively (cm). You must multiply the initial value by proportions to achieve this adjustment.
It is crucial to organize these proportions in a way that permits unit cancellation when writing them down. As an illustration, since kg and m are both in the numerator, they must be in the denominators of the conversions.
Proportions:
1 kg = 1,000 g
1 m = 100 cm
Here,
The complete equation is like;
-4.3 × 10⁴ (kg × m / s) × (1000 g / 1 kg) × (100 cm / 1 m) = ? (g × cm / s)
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Complete question is attached
The expression (8)(2)(−1.5) represents the change in the scuba diver’s elevation after 8 minutes.
Find the change in elevation.
The change in elevation of the scuba diver after 8 minutes is -24.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.
The expression (8)(2)(-1.5) represents the change in the scuba diver's elevation after 8 minutes.
To determine the change in elevation, we need to evaluate the expression.
(8)(2)(-1.5) = (16)(-1.5) = -24
Thus, the change in elevation is -24.
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At what rate was an investment made that obtains $50.40 on $210 over four years?
Answer:
Rate=6
Step-by-step explanation:
First multiply the interest by 100
50.40×100=5040
then multiply the investment by the number of years
210×4=840
then divide the two answers together
5040÷840=6
Set up an equation and solve each of the following problems. The total surface area of a right circular cylinder is 54π square inches. If the altitude of the cylinder is twice the length of a radius, find the altitude of the cylinder.
The altitude of the cylinder is 6 inch.
what is surface area of cylinder?The surface area of a cylinder is given by 2πr(r + h) , where r is the radius of the base and h is the height of the cylinder. It is the sum of the areas of the two circular bases and the lateral surface.
The formula for surface area of cylinder is given by:
surface area = 2πr(r+h)
where r is radius of the cylinder and h is the altitude of the cylinder
given h = 2r
so , surface area = 2πr(r+2r)
=> 6πr²
given 6πr² = 54π
=> r² = (54π)/(6π)
=> r² = 9
=> r = 3
so the altitude of the cylinder = 2r
=>2*3
=> 6
so the altitude of the cylinder is 6 inch.
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nora's grandfather lived to be 87, and her father is still alive at the age of 98. nora concludes that longevity is inherited and anticipates a very long life. nora should know that . question 38 options: the lifespans of fraternal twins are just as similar as the lifespans of identical twins, indicating that longevity is probably not a heritable trait there is no reliable data on the heritability of longevity, so the cumulative effects of random events probably contributed to the long lives of her relatives the heritability of longevity is high, ranging from .75 to .95 for age at death, indicating that longevity is directly related to genetic factors rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or lat
Nora should know that rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later. Hence, the correct answer is option C.
The given problem here requires knowledge of both biology and mathematics in order to solve the question. The mathematical component of this question is the probability of someone inheriting logetivuty or risk factors in their life.
The biological factor here is the inheritance of a trait. The traits in question are either longevity or risk factors. The probability of someone inheriting longevity is far less compared to the probability of inheriting a health condition that might be a risk factor for the person in the long run. Hence, option C is the correct answer.
The complete question that you might be looking for is given below-
Nora's grandfather lived to be 87, and her father is still alive at the age of 98. Nora concludes that longevity is inherited and anticipates a very long life. Nora should know that __________.
A) there is no reliable data on the heritability of longevity, so the cumulative effects of random events probably contributed to the long lives of her relatives
B) the lifespans of fraternal twins are just as similar as the lifespans of identical twins, indicating that longevity is probably not a heritable trait
C) rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later
D) the heritability of longevity is high, ranging from .75 to .95 for age at death, indicating that longevity is directly related to genetic factors
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a system of linear equations is graphed. which ordered pair is the best estimate for the solution to the system?
The best estimate for the solution to a system of linear equations can be found by using the Substitution Method.
To solve for the solution, the equations must be written in the form y = mx + b. The slope, m, and the y-intercept, b, of each equation can then be calculated. The x-coordinate of the solution can be found by setting the two equations equal to each other to create an equation in one variable. This equation can then be solved for x. The y-coordinate of the solution can be found by substituting the x-coordinate into one of the original two equations. The ordered pair that is the estimated solution can then be formed.
For example, consider the system of equations y = 3x + 2 and y = -x + 5. The slope of the first equation is m1 = 3, and the y-intercept is b1 = 2. The slope of the second equation is m2 = -1, and the y-intercept is b2 = 5. Setting the two equations equal to each other yields 3x + 2 = -x + 5. Solving for x gives x = 3. Substituting this x-coordinate into either of the original equations yields y = 3(3) + 2 = 11. The ordered pair that is the estimated solution to the system is (3, 11).
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by examining birth records, it has been determined that 12% of people are born in the winter (w), 28% are born in the spring (sp), 42% are born in the summer (su), and 18% are born in the fall (f). suppose we select a person at random. find each probability. p(w and f)
The probability of selecting a person at random is p(w and f) is 0.0216 or 2.16%.
The probability of an event occurring and another event occurring is found by using the multiplication rule of probability, which states that the probability of two events occurring together is equal to the product of the probabilities of each event occurring independently.
In this case, we are looking for the probability of a person being born in the winter (p(w)) and the probability of a person being born in the fall (p(f)), so we would calculate:
p(w and f) = p(w) * p(f)
Using the information provided, we know that:
p(w) = 12% = 0.12
p(f) = 18% = 0.18
So, to find p(w and f), we would multiply:
p(w and f) = 0.12 * 0.18 = 0.0216 or 2.16%
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Answer:
0
0.30
0.82
0.70
Step-by-step explanation:
a model of a car is 4 inches long. if the actual car is 10 feet long, find the scale of the model. a. 4 in
Scale of the model is found to be 1 : 30 using the ratio method.
A model of a car is 4 inches long.
The actual car is 10 feet long.
4 in. = 10 ft. ( since given )
Divide both sides by 4, we get
∴ 1 in. = 2.5 ft.
We use the ratio here to compare the lengths of the actual car and its model.
A ratio scale is a quantitative measurement scale that is used to compare numbers.
The model is 4 inches long while the actual car is 10 feet long.
One foot is equal to 12 inches. Therefore the car in terms of inches is:
10 feet × 12 inches = 120 inches
The ratio scale is the length of the model of the car : length of the actual car
= 4 : 120
= 1 : 30
Therefore the scale of the model is 1: 30.
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if a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
The student's final grade is 78.9.
The final grade of the student is determined using the weight average. A weighted average refers to a type of mean that gives differing importance to the values in a dataset. It is used when the relative significance of values in a dataset are to be considered. The formula for finding the weighted average is the sum of all the variables multiplied by their weight, then divided by the sum of the weights.
Based on the provided information, as student score 84 on quizzes with weighted 30%, 72 on exams with weighted 40%, and 83 on final exam with weighted 30%, hence
Final grade = (84*0.3 + 72*0.4 + 83* 0.3)/(0.3 + 0.4 + 0.3) = (25.2 + 28.8 + 24.9)/1 = 78.9
Note: The question is incomplete. The complete question probably is: For a chemistry class, a student's grades are weighted as follows: quizzes are 30%, exams are 40%, and the final exam is 30%. If a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
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Answer:
79.6
Step-by-step explanation:
(86x.3)+(73x.4)+(82x.3)
Three equal mass satellites A, B, and C are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are LA, LB, and LC. Which of the following statements is correct? (A) LA > LB > LC (B) LC > LB > LA (C) LB > LC > LA (D) LB > LA > LC (E) The relationship between the magnitudes is different at various instants in time
(B) LC > LB > LA is the correct statement for satellites
The magnitudes of the angular momenta of the satellites as measured about the planet are LA, LB, and LC.
The angular momentum of each satellite is conserved independently so we can compare the orbits at any location. Looking at the common point between orbit A and B shows that satellite A is moving faster at that point than satellite B, showing LA > LB. A similar analysis at the common point between B and C shows LB > L A because three equal mass satellites are in coplanar orbits around a planet
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a customer service representative must sped different amounts of time with each customer to resolve various concerns the amount of time spent with each customer can be modeled by the following distribution find the percentile
The value of [tex]P$$(2 < x < 10)$[/tex] is 0.5350
What is meant by percentile?A score at or below which a given percentage falls is known as the k-th percentile in statistics, as is a score below which a given percentage k of scores in the frequency distribution falls. A percentile is the difference between a given score and the scores of the other members of a group. The proportion of other scores that a given score outperformed is displayed. In the 85th percentile, for instance, signifies that your test result of 75 is higher than the scores of 85% of other students.The exponential distribution is the probability distribution of the interval between events in a Poisson point process, that is, an event-producing process where events happen continuously and independently at a fixed average rate. It is an example of the gamma distribution.As per the Function, [tex]$P(x < x)=1-e^{-m x}$[/tex]
Where [tex]$x \sim E x p(0.2)$[/tex]
Therefore, [tex]$m=0.2$[/tex]
[tex]$$P(2 < x < 10)=P(x < 10)-P(x < 2)$$[/tex]
Applying all data
[tex]& \mathrm{P}\left(2 < \mathrm{x} < 10=\left(1-e^{0.2 \times 10}\right)-\left(1-e^{0.2 \times 2}\right)\right. \\[/tex]
=0.6703-0.1353=0.5350
The complete question is,
A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be
modelled by the following distribution: X-Exp(0.2)
Find [tex]$P(2 < x < 10)$[/tex].
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Anna bought a bike horn. She paid $11.59 and received $9.67 in change. How much did the bike horn cost?
Answer:
$1.92
Step-by-step explanation:
$11.59 - $9.67 = $1.92
SAVE ME WITH MY MAAAAAAATH
Answer:
14.75
Step-by-step explanation:
If Shenelle has $25 and wants to see a $10.25 regular admissions showing of a 3D movie, she will have $14.75:
[tex]x + 10.25 \leq 25[/tex]
[tex]x \leq 14.75[/tex]
A formula for calculating the magnitude of an earthquake is M=23log(EE0)
that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9
on the MMS. If a second earthquake has 700
times as much energy as the first, find the magnitude of the second quake.
Round to the nearest hundredth.
The magnitude of the second earthquake was
The magnitude of the second earthquake is given as follows:
5.80.
How to obtain the magnitude of the second earthquake?The magnitude of an earthquake is given by the equation presented as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
The first earthquake has a magnitude of 3.9, hence it's energy is obtained as follows:
[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]
As the power of 10 is the inverse function of the logarithm, we have that:
[tex]\frac{E}{E_0} = 10^5.85[/tex]
[tex]\frac{E}{E_0} = 707946[/tex]
[tex]E = 707946E_0[/tex]
The second earthquake has 700 times as much energy as the first, hence the energy is of:
[tex]E = 700 \times 707946E_0[/tex]
[tex]E = 495562049E_0[/tex]
Then the magnitude of the second earthquake is given as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{495562049E_0}{E_0}\right)}[/tex]
[tex]M = \frac{2}{3}\log{(495562049)}[/tex]
M = 5.80.
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Let f be the function given by f(t) =3/1+t^2 a. Find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0. b. Given g(x)=ſ8(t)dt , find the first four nonzero terms and the general term for the power series expansion of g(x) about x=0. c. Find the interval of convergence of the power series for g(x).
a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
What is a function?
A function is a mathematical relationship between two variables, often denoted as "f(x)" or "y = f(x)". A function assigns a unique output to each input within its domain. In other words, for every value of x, there is a corresponding value of y, and each value of x can only correspond to one value of y.
a. To find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0, we need to find the Taylor series of f(t) centered at 0. The general term of a Taylor series is given by:
f(t)^(n) / n! * (t-0)^n
The Taylor series of f(t) = 3/(1+t^2) centered at 0 is:
f(t) = 3 - 3t^2 + 3/3t^4 - 3/5t^6 + ...
The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b. To find the first four nonzero terms and the general term for the power series expansion of g(x) = ∫f(t)dt about x=0, we need to integrate the Taylor series of f(t) term by term.
g(x) = ∫f(t)dt = (3t - 3/3t^3 + 3/5t^5 - ...) from 0 to x
g(x) = 3x - 3/3x^3 + 3/5x^5 - ...
The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7
c. The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence for g(x), we can use the ratio test.
The ratio test states that if the limit of |a(n+1)x^(n+1)|/|a(n)x^n| as n approaches infinity is less than 1, the series converges for all x.
|3/7x^7|/(|3/5x^5|) = |x^2|/(|3/5|) < 1 when |x| < sqrt(5/3)
So, the interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
Hence,
a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
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Before women were allowed to vote, both men and women organized, protested, and marched. Finally, in 1920, the 19th Amendment to the Constitution gave women the right to vote.
How does this example support the author's main purpose in the book?
It shows how citizens' actions affect today's issues.
It analyzes how citizenship was different in the past.
It explains what an amendment to the Constitution is.
It shows that citizens' actions can change society.
Answer:
it analyses how citizenship was different in the past
A stunt motorcyclist makes a jump from one ramp 20 feet off the ground to another ramp 20 feet off the ground. The jump between the ramps can be modeled by y=-1/640 x to the power of 2 + 1/4 x + 20 where x is the horizontal distance (in feet) and y is the height above the ground (in feet).A) what is the motorcycle's height r when it lands on the ramp?B) what is the distance d between the ramps?C) what is the horizontal distance h the motorcycle has traveled when it reaches its maximum height?D) what is the motorcycle's maximum height k above the ground?
A) 20 ft B) 80 ft C) 40 ft D) 24 ft. The equation y=-1/640 x2 + 1/4 x + 20 can be used to calculate the height, distance, maximum height, and horizontal distance of the stunt motorcyclist's jump.
A) The motorcycle's height when it lands on the ramp is 20 feet. This can be calculated by plugging 0 in for x in the equation y=-1/640 x2 + 1/4 x + 20. When you plug in 0 for x, you get y=-1/640 (0)2 + 1/4 (0) + 20, which simplifies to y=20. This means that when the motorcycle lands on the ramp, it is 20 feet off the ground.
B) The distance between the ramps is 80 feet. This can be calculated by finding the value of x when y=20. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=20. When you solve this equation, you get x=80. This means that the distance between the ramps is 80 feet.
C) The horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet. This can be calculated by finding the value of x when y=24. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=24. When you solve this equation, you get x=40. This means that the horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet.
D) The motorcycle's maximum height above the ground is 24 feet. This can be calculated by finding the maximum value of y in the equation y=-1/640 x2 + 1/4 x + 20. When you calculate the maximum value of y, you get y=24. This means that the motorcycle's maximum height above the ground is 24 feet.
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A 300g ball collides with a wall. The figure(Figure 1)shows the ball's velocity and the force exerted on the ball by the wall. What is vfx, the ball's rebound velocity?
The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).
Using the equation vfx = 2vix - viy, the rebound velocity of the ball is calculated as follows:
vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s
1. Identify the initial velocity, vix, of the ball along the x-axis, which is 4.0 m/s.
2. Identify the initial velocity, viy, of the ball along the y-axis, which is -2.0 m/s.
3. Use the equation vfx = 2vix - viy to calculate the rebound velocity of the ball, vfx.
4. Calculate vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s.
The rebound velocity of the ball is 10.0 m/s.
The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).
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Erik has $17,531 in a savings account that earns 14% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
Answer:
$2454.34 in interest in a year
Step-by-step explanation:
Turn 14% into a decimal (0.14)
17,531x0.14 = 2453.34
determine whether the relation represents y as a function of x. x^2 + y^2 = 25
Answer: The relation x^2 + y^2 = 25 does not represent y as a function of x. This is because for a given value of x, there are multiple values of y that would satisfy the equation. For example, for x = 3, y = 4 and y = -4 both satisfy the equation. In a function, each value of the independent variable (in this case, x) must correspond to only one value of the dependent variable (in this case, y).
It's an equation of a circle with a center (0,0) and a radius of 5.
Step-by-step explanation:
What is the solution to the equation? 3|x| − 1 = 8
x = 3 or 9
x = −9 or 9
x = −3 or 3
x = −3 or −9
please help
Answer:
x = 3
Step-by-step explanation:
3|x|- 1= 8
=3x = 8 + 1
=3x = 9
=3x/3 = 9/3
x = 3.
Answer:
The equation is 3|x| - 1 = 8. To solve this equation, we first need to consider the absolute value of x.
The absolute value of x is defined as |x| = x for x ≥ 0, and |x| = -x for x < 0.
We have 3|x| - 1 = 8, so we have to consider two cases:
x ≥ 0: in this case, |x| = x and we have 3x - 1 = 8, which gives x = 3 or x = 9.
x < 0: in this case, |x| = -x and we have 3(-x) - 1 = 8, which gives -3x - 1 = 8, and then x = -3 or x = -9.
So the solution to the equation is x = 3 or 9 or x = -3 or -9.
Step-by-step explanation:
5. Sadie drew a number line diagram to find the number
of fluid ounces in 4 cups. What numbers for fluid
ounces will complete the diagram?
cups 0
fluid ounces 0
8
2
3
4
Fluid ounces are usually measured in milliliters, but if Sadie is using ounces, then the numbers she will need to complete the diagram are 32, 64, 96, and 128.
What is number?Number is a mathematical concept that represents a quantity or amount. It is used to count, measure, and label objects and phenomena in the physical and natural world. Number can be divided into two categories: cardinal numbers and ordinal numbers. Cardinal numbers are used to denote the total number of items in a set, while ordinal numbers are used to indicate the position of an item within a set. Number is also used to represent relationships between quantities, such as addition, subtraction, multiplication, and division. Number is an essential part of mathematics and is used in a variety of ways in the real world.
This is because 1 cup is equal to 8 fluid ounces, and 4 cups is therefore equal to 32 ounces, which is the same as 64 milliliters. Similarly, 2 cups is equal to 16 ounces, or 96 milliliters, and 3 cups is equal to 24 ounces, or 128 milliliters.
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can you find the slope intercept???
the slope intercept form is y=mx+b m is the slope and b is your y intercept
The set S={1,2,3,….,12} is to be partitioned into three sets A,B,C of equal size, thus A∪B∪C=S, A∩B=B∩C=A∩C=ϕ. Thus number of ways to partition S is
The number of ways to partition set S into three sets A, B, and C of equal sizes is 495.
The number of ways to partition S into three sets of equal sizes can be calculated using the formula: nPr=n!/(r!(n−r)!), where n is the total number of elements in the set and r is the number of elements in each partitioned set.
In this case, n=12 and r=4. Therefore, the number of ways to partition S into three sets A, B, and C of equal sizes is 12P4 = 12!/(4!(12−4)!) = 495.
In calculation way step by step,
We know that n = 12 and r = 4.
Calculate 12!.
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479001600
Calculate 4!.
4! = 4 x 3 x 2 x 1 = 24
Calculate (12 - 4)!
(12 - 4)! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
Calculate nPr.
nPr = n!/(r!(n - r)!) = 479001600/(24 x 40320) = 495
Thus, the number of ways to partition set S into three sets A, B, and C of equal sizes is 495.
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use differentials to estimate the amount of cubic meters of paint needed to apply a coat of paint 0.18 cm thick to a hemispherical dome with diameter 60 meters.
It requires 10.1833 cubic meter of paint to apply a coat of paint on the hemispherical shell.
What is volume of hemisphere?The volume of a hemisphere is (2/3)πr³, where r is the radius of the hemisphere. It is half of the volume of a sphere with the same radius.
Formula for Volume of a hemisphere, V = (2/3)πr³
radius = diameter/2
=>60/2
=>30 m
dr = 0.18 cm = 0.0018 m
dV/dr = (2*3)/3 * πr²
=> dV/dr = 2πr²
=> dV = 2πr² dr
so dV = 2π*(30)²*0.0018
=> 10.1833
So , it requires 10.1833 cubic meter of paint.
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Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Tanzanian blend with the Gazebo blend, but always in the same proportion. Yesterday, you mixed 80 pounds of the Tanzanian blend with 24 pounds of the Gazebo blend. Today, there is 20 pounds of the Tanzanian coffee left in stock. How many pounds of the Gazebo coffee should you mix with it to get your secret blend?
6 pounds of Gazebo blend is required to be mixed with Tanzanian blend to get the secret blend.
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: A secret coffee blend requires 80 pounds of Tanzanian blend with 24 pound of Gazebo blend.
Now, A proportion is an equation in which two ratios are set equal to each other. Ratio of the required secret blend is 80:24=10:3
Amount of Tanzanian blend left in stock is 20 pounds and let x pounds of Gazebo blend be required to make the secret blend thus to preserve the proportion we must have;
10/3=20/x
x/3=20/10
x=6
Hence, 6 pounds of Gazebo blend is required to get the secret blend.
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