Answers
Answer:
a)
\(2.5 = ( \frac{1 + e}{1 - e} ) \sqrt{ \frac{1.25}{5} } \)
\(2.5 = (\frac{1 + e}{1 - e} ) \sqrt{.25} \)
\(2.5 = .5( \frac{1 + e}{1 - e} )\)
\( \frac{1 + e}{1 - e} = 5\)
\(1 + e = 5(1 - e )\)
\(1 + e = 5 - 5e\)
\(6e = 4\)
\(e = \frac{2}{3} \)
b)
\(t = ( \frac{1 + \frac{2}{3} }{1 - \frac{2}{3} } ) \sqrt{ \frac{1.8}{5} } \)
\(t = 5 \sqrt{.36} = 5(.6) = 3\)
So t = 3 seconds.
c)
\( 3.5 = ( \frac{1 + \frac{2}{3} }{1 - \frac{2}{3} } ) \sqrt{ \frac{h}{5} } \)
\(3.5 = 5 \sqrt{ \frac{h}{5} } \)
\(.7 = \sqrt{ \frac{h}{5} } \)
\(.49 = \frac{h}{5} \)
\(h = 2.45\)
So h = 2.45 meters.
The value of e is 0.6, the rubber ball will bounce for 3.6 seconds when it is dropped from a height of 1.8 m and , the rubber ball was dropped from a height of 2.25 meters.
When the rubber ball is dropped from a height of 1.25m, it bounces for 2.5 seconds.
Thus, h = 1.25 m and t = 2.5 s.
Substituting these values in the formula, we get:
\(2.5 = \left(\frac{1+e}{1-e}\right)\sqrt{\frac{1.25}{5}}\)
Squaring both sides, we get:
\(6.25 = \frac{(1+e)^2}{(1-e)^2} \frac{1.25}{5}\)
Simplifying the above equation, we get:
e = 0.6
We need to find the time taken for the rubber ball to stop bouncing when it is dropped from a height of 1.8 m.
Thus, h = 1.8 m.
Substituting the value of h and e in the formula, we get:
\(t = \left(\frac{1+0.6}{1-0.6}\right)\sqrt{\frac{1.8}{5}}\)
Simplifying the above equation, we get:
t = 3.6 seconds
We need to find the height from which the rubber ball was dropped when it bounces for 3.5 seconds.
Thus, t = 3.5 s.
Substituting the value of t and e in the formula, we get:
\(3.5 = \left(\frac{1+0.6}{1-0.6}\right)\sqrt{\frac{h}{5}}\)
Simplifying the above equation, we get:
h = 2.25
Hence, the value of e is 0.6, the rubber ball will bounce for 3.6 seconds when it is dropped from a height of 1.8 m and , the rubber ball was dropped from a height of 2.25 meters.
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Related Questions
I need the slope for this
Answers
Answer:
Slope: 7
Step-by-step explanation:
y=mx+b
substitute what you know
7=m
The dominator of the fraction 4/19 i increaed by an amount o that the value of the reulting fraction i 2/11 determinin the amount by which the dinominator wa increaed
Answers
The quantity that increased the denominator of 4/19, to obtain the fraction 2/11, becomes 3.
The denominator of the fraction 4/19 was increased by 11 so that the value of the resulting fraction is 2/11. The dominator (denominator) of the fraction 4/19 was increased by an amount to make the fraction equal to 2/11. To find the amount by which the denominator was increased, we can cross multiply and solve for the unknown value.
Here's how:
4/19 = 2/11
Cross multiply:
4 * 11 = 2 * 19 + 2 * x
Simplify:
44 = 38 + 2x
Subtract 38 from both sides:
6 = 2x
Divide by 2:
x = 3
So the dominator (denominator) was increased by an amount of 3 to make the fraction equal to 2/11.
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3. let a {1,2,3,... ,9}.(a) how many subsets of a are there? that is, find |p(a)|. explain.(b) how many subsets of a contain exactly 5 elements? explain.
Answers
(a) There are 512 subsets of a.
(b) 126 subsets of a contain exactly 5 elements.
(a) To find the number of subsets of a, we can use the formula \(2^n\), where n is the number of elements in the set. In this case, n = 9. So, the number of subsets of a is \(2^9\) = 512. This is because each element in the set can either be included or excluded from a subset, giving us a total of 2 choices for each element. Multiplying these choices for all 9 elements gives us the total number of possible subsets.
(b) To find the number of subsets of a that contain exactly 5 elements, we need to choose 5 elements out of the 9 available elements. This can be done using the combination formula, which is n choose k = n! / (k!(n-k)!), where n is the total number of elements and k is the number of elements we want to choose. So, in this case, the number of subsets of a that contain exactly 5 elements is 9 choose 5, which is 9! / (5!(9-5)!) = 126.
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he
ne.
st
Simplify the following:
Holiday Bonus Problem
(5 Points)
X
{²+ + + ²x - 3X ICE +
R-X
{[(X + A)(X-A)M+A²M]E}
7
ruc
4AS
4AS
+
3X[(E+Y)²-(E-Y)²] * 3E[(Y + X)² – (Y-X)²] 3Y[(X + E)²-(X-E)²]
- BA}Y
4AS
![ofhene.stSimplify the following:Holiday Bonus Problem(5 Points)X{+ + + x - 3X ICE +R-X{[(X + A)(X-A)M+AM]E}7ruc4AS4AS+3X[(E+Y)-(E-Y)]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/6rzQQTBQ4JQrxvHD3hunxk35warOd2M8.png)
Answers
Answer:
99987766554446677765
proof by contradiction every integer greater than 11 is a sum of two composite numbers
Answers
Proof by contradiction: Every integer greater than 11 is a sum of two composite numbers.
Step 1: Assume the negation of the statement, which is "There exists an integer greater than 11 that cannot be written as a sum of two composite numbers."
Step 2: Let n be the smallest integer greater than 11 that cannot be written as a sum of two composite numbers. This means that all integers greater than n can be written as a sum of two composite numbers.
Step 3: Since n is not composite, it is either prime or 1. If n is prime, then it cannot be written as a sum of two composite numbers because the sum of two composite numbers is composite. If n is 1, then it cannot be written as a sum of two composite numbers because 1 is not composite.
Step 4: Therefore, n cannot be prime or 1. This means that n must be composite. Since n is composite, it can be written as the product of two numbers a and b, where a and b are greater than 1.
Step 5: Since a and b are greater than 1, they must be composite. Therefore, n can be written as the sum of two composite numbers, a and b. This contradicts the assumption that n cannot be written as a sum of two composite numbers.
Step 6: Therefore, the assumption that there exists an integer greater than 11 that cannot be written as a sum of two composite numbers is false. In other words, every integer greater than 11 can be written as a sum of two composite numbers.
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if two sides of a square field were increased by five feet, as seen in the diagram, the area of the field would increase by 245 ft2 . find the area of the original square
Answers
If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².
To find the area of the original square, we can use the following formula:
Area of the original square = x²
where x is the original length of the square field.
Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².
Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:
(x + 5)² = 245 + x²
Expanding the left-hand side of the equation and simplifying, we get:
x² + 10x + 25 = 245 + x²
Solving for x, we get:
10x + 25 = 245
x = 22
Plugging x = 22 into the formula, we can find the area of the original square:
Area of the original square = x² = 22² = 484 ft²
Therefore, the area of the original square is 484 ft².
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solve pls brainliest
Answers
Answer:
1)YES:This is a decimal neither terminates nor repeats
2)YES:Repeating decimal
3)NO: Terminating decimal
4)YES: this is a decimal neither terminates nor repeats.
Step-by-step explanation:
Hope it can help you lovelots
Two lines intersect. Find the value of b.
bo
42°
cº
Answers
Step-by-step explanation:
b = 42
c = 138
plz mark my answer as brainlist plzzzz if you find it useful .
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
Answers
If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120
The number q is an odd number
The median of q consecutive integers = 120
Consider the q = 3
Then three consecutive integers will be 119, 120, 121
The largest number = 121
Substitute the value of q in each options
Option A
(q-1) / 2 + 120
Substitute the value of q
(3-1)/2 + 120
Subtract the terms
=2/2 + 120
Divide the terms
= 1 + 120
= 121
Therefore, largest of these integers is (q-1) / 2 + 120
I have answered the question in general, as the given question is incomplete
The complete question is
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
a) (q-1) / 2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
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Wes and his brother Andy are moving.
Andy is carrying 6 small boxes plus 2 pounds of clothing.
Wes is carrying 3 of the same small boxes plus 3.5 pounds of clothing.
The small boxes weigh the same.
What is the weight of each small box in pounds?
Answers
Each small box weighs 0.5 pounds.
Let's assume that the weight of each small box is x pounds.
Then, we can set up two equations based on the information given:
2 + 6x = weight carried by Andy
3x + 3.5 = weight carried by Wes
Since the weight of the small boxes is the same, we can set these two expressions equal to each other:
2 + 6x = 3x + 3.5
Solving for x, we can subtract 2 and 3x from both sides:
3x - 6x = 3.5 - 2
-3x = 1.5
Finally, we can divide both sides by -3 to get x by itself:
x = -1.5/-3
x = 0.5
Therefore, the weight of each small box is 0.5 pounds.
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2
2
4 4
3
7
37
39
41
43
Answers
Answer:
39
Step-by-step explanation:
Find F'(x): F(x) = Sx 3 t^1/3 dt
Answers
The derivative of F(x) is \(F'(x) = x^{(1/3)\).
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.
Let's compute F'(x):
F(x) = ∫[0 to x] \(t^{(1/3)} dt\)
To differentiate the integral with respect to x, we'll use the Leibniz integral rule:
F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)
According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.
\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\) [applying the chain rule to the upper limit]
Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.
\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)
\(F'(x) = x^{(1/3)\)
Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).
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a bag of chocolates is labeled to contain 0.384 pounds of chocolate. the actual weight of the chocolates is 0.3798 pounds. how much lighter is the actual weight?
Answers
The actual weight is 0.0042 pounds lighter than the labeled weight.
The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.
Subtracting the actual weight from the labeled weight, we get:
0.384 pounds - 0.3798 pounds = 0.0042 pounds.
Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.
It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.
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PLEASE HELP IM STUCK
Answers
Answer:
option b is the answer of the above
ps
mymall.lausd.net Bookmarks
Gannexation - Goo...
FINAL LT 4 Assessment
9 of 10
POSSIBLE POINTS: 0.5
Draw a picture that represents the word problem. If it is not clear from your drawing, label the airplane, island and boat. Don't forget to include x in your
picture!
You are flying an airplane directly over a boat and spots an island in the distance. If the plane is flying at a height of 5,500m and you look down at the
island at an angle of 72 degrees, how far is the boat from the island?
x Clear
Undd
Redo
(720
Answers
Answer:
Step-by-step explanation:
You probably need to make your own version cause mine is super messy but here
in testing the null hypothesis h0: μ1 – μ2 == 0, the computed test statistic is z = −1.33. find the corresponding p-value.
Answers
The corresponding p-value for the computed test statistic of z = -1.33, testing the null hypothesis H0: μ1 – μ2 = 0, is greater than 0.10 (or 10%).
To find the corresponding p-value, we look at the standard normal distribution table (z-table) or use statistical software. In this case, the test statistic is z = -1.33, which represents the number of standard deviations the sample mean difference is away from the hypothesized mean difference (0).
Since the test statistic is negative, we find the area to the left of -1.33 in the standard normal distribution table.
This gives us a p-value greater than 0.10, indicating that the observed mean difference is not significantly different from the hypothesized mean difference at the conventional significance level (usually α = 0.05). Therefore, we fail to reject the null hypothesis H0: μ1 – μ2 = 0.
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Annie was given the following problem to solve by completing the square. Find the errors that she made and explain how to fix her errors.
Answers
The error made by Annie was that she failed to add the squared value of half the coefficient of x to the right hand side of the equation.
To solve using completing the square x² - 6x + 9 = 25move constant term to the right side by subtracting 9 from both sides
x² - 6x = 16
Find half the coefficient of the x term and square it
(-6/2)² = 9
Add 9 to both sides of the equation
x² - 6x + 9 = 16 + 9
x² - 6x + 9 = 25
Factorize the left hand side
(x - 3)² = 25
x - 3 = ±5
x = 3 ± 5
Therefore, the error made was that she didn't add 9 to the right side of the equation.
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Triangle UVW, with vertices U(-6,2), V(-4,6), and W(-8,5), is drawn inside arectangle, as shown below.What is the area, in square units, of triangle UVW?
Answers
Okay, here we have this:
Considering the provided vertices, we are going to calculate the requested area, so we obtain the following:
Then we will first calculate the measure of each side and later with Heron's formula we will find the area, then we have:
\(\begin{gathered} u=\sqrt{((-4-(-8))^2+(6-5)^2)} \\ u=\sqrt{4^2+1^2} \\ u=\sqrt{17} \end{gathered}\)\(\begin{gathered} w=\sqrt{(-6-(-4))^2+(2-6)^2} \\ w=\sqrt{2^2+(-4)^2} \\ w=\sqrt{20} \end{gathered}\)\(\begin{gathered} v=\sqrt{(-6-(-8))^2+(2-5)^2} \\ v=\sqrt{2^2+(-3)^2} \\ v=\sqrt{13} \end{gathered}\)Then, the area is:
\(\begin{gathered} A=\sqrt{\frac{(\sqrt{13}+\sqrt{17}+\sqrt{20})}{2}(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{13})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{17})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{20})} \\ =\sqrt{49} \\ =7 \end{gathered}\)Finally we obtain that the triangle's area is equal to 7 square units.
Since people are sad they missed my 50 points, here is 100 points for the first 2 to answer. First one gets branliest aswell.
Answers
z scores that fall below the mean are ______. a. 0 b. negative c. either positive or negative d. positive
Answers
The correct answer to the question "z scores that fall below the mean are" is "negative". Z-scores are measures of relative standing that can be used to make comparisons among the scores in the distribution by transforming raw data into standardized units.
The formula for z-score is:z = (X-μ)/σz-scores can be negative, zero, or positive numbers. A negative z-score tells us that the corresponding score is below the mean and vice versa.In addition to this, the mean of all z-scores is always zero. If the mean of all z-scores is zero, that means that z-scores are measuring deviation from the mean. If a z-score is below the mean, it means that the corresponding raw score is below the mean, which results in a negative z-score.
Z-scores that fall below the mean are negative. Z-scores are statistical values that allow analysts to transform raw data into standardized units that make comparisons possible among scores in the distribution. The formula for calculating the z-score is: z = (X-μ)/σThe z-score can be either negative, zero, or positive, depending on whether the value is below, equal to, or above the mean, respectively. Because the mean of all z-scores is always zero, z-scores can be used to measure deviation from the mean, with a negative z-score indicating that the corresponding raw score is below the mean. Z-scores allow us to compare the scores in the distribution by converting them into standard units. Negative z-scores are associated with scores that are below the mean. Conversely, positive z-scores are associated with scores that are above the mean.
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What is the slope of y=5/4x-7/4
Answers
The answer is:
5/4
Work/explanation:
Let's work out the slope of the line.
The equation is in y = mx + b form where m = slope; b = y intercept.
Similarly, in y=5/4x - 7/4, the slope is 5/4.
Hence, the answer is 5/4.A group of 4 friends are posing for a photograph. If 2 of the friends want to stand beside each other, how many ways can the picture be taken? 6,10,12,20
Answers
Answer:
6
Step-by-step explanation:
If 2 of the friends wants to stand beside each other, we can take these 2 friends like 1 option and calculated the number of ways, using the rule of multiplication as:
__ 3_____ * ____2_____ *____1____ = 6
1st place 2nd place 3rd place
Because we have 3 options (2 friends and the friends that are beside each other) for the first place of the picture, 2 options for the second and 1 option for the third.
Wylie climbs steadily down a trail that is 1,500 feet above sea level for 40 minutes. Then he takes a 10-
minute lunch break. After lunch, Wylie climbs back up the trail for 5 minutes to take a picture. Finally, he
hikes for 15 minutes until he reaches sea level. Which graph best represents this description?
о А.
OB
fy
ТУ
15
15
Elevation (100 ft)
Elevation (100 ft)
x
0 20 40 60
Time (min)
X
0 20 40 60
Time (min)
fy У
15
y
15
Elevation (100 ft)
Elevation (100 ft)
X
0 20 40 60
Time (min)
Х
0
20 40 60
Time (min)
Answers
Answer:
C
Step-by-step explanation:
Your math teacher is planning a test for you. The test will have 30 questions. Some of
the questions will be worth 3 points, and the others will be worth 4 points. There will
be a total of 100 points on the test. How many 3-point questions and how many 4-
point questions will be on the test?
Answers
Answer:
20 questions for 3 points
10 questions for 4 points
Step-by-step explanation:
20 × 3 = 60
10 × 4 = 40
60 + 40 = 100
Evaluate each expression using the values in the given table. X -3 -2 -1 0 1 2 3
f(x) -9 -7 -5 -3 -1 1 3 g(x) 3 2 1 0 -1 -2 -3 (a) (fog)(-3) =
(b) (gof)(3) = (c) (fof)(3) =
Answers
(a) (f◦g)(-3) means applying function f to the result of applying function g to -3. Given g(-3) = 3, we find f(g(-3)) = f(3) = -1.
(b) (g◦f)(3) means applying function g to the result of applying function f to 3. Given f(3) = -3, we find g(f(3)) = g(-3) = 3.
(c) (f◦f)(3) means applying function f to the result of applying function f to 3. Given f(3) = -1, we find f(f(3)) = f(-1) = -5.
Therefore:
(a) (f◦g)(-3) = -1
(b) (g◦f)(3) = 3
(c) (f◦f)(3) = -5
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plsssssssss answer it
Answers
Answer:
Answer is -7
Step-by-step explanation:
coz if -2 equal only
- answer so answer is
-7
what is the largest area of a rectangle that can be inscribed in a semicircle of radius 6? round to the nearest whole numb
Answers
The area of the largest rectangle is 46.47 square root.
Consider a semi-circle with a rectangle ABCD inscribed in it.
Let, O = centre of the semi-circle
A and B lies on the base of the semi-circle
OA = OB = x
D and C lie on the semi-circle
BC = AD = y
AB = CD = 2x
By Pythagorean theorem,
CB² + OB² = OC²
⇒ y² + x² = (6)²
⇒ y² = 36 - x²
⇒ y = √(36 - x²)
Now, area of rectangle in terms of x,
Area, A = 2x × y
= 2x × √(36 - x²)
Differentiating,
A' = 2 × √(36 - x²) - 2x²/(36 - x²)
When x = 0, y = 6 and when x = 6, y = 0, area = 0.
It implies that area is maximum when the value of x lies between 0 and 6.
This will occur where A’ = 0.
⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0
⇒ 2 × √(36 - x²) = 2x²/(36 - x²)
On simplification, we get,
⇒ 2 × (36 - x²) = 2x²
⇒ 36 - x² = x²
⇒ 2x² = 36
⇒ x² = 36/2
⇒ x = √36/2
Now, y = √(36 - x²) becomes
⇒ y = √(36 - (√36/2)²)
⇒ y = √(36 - 36/2)
⇒ y = √(96 - 36)/2
⇒ y = √60/2
Maximum area = 2xy
= 2(√36/2)(√60/2)
= 46.47
Therefore, the area of the largest rectangle = 46.47 square units.
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The domain for f (x) = 4x + 6 is {3,4,5). What is the range?
Answers
Answer:
The range is {18, 22, 26}
Step-by-step explanation:
The position of a particle moving along the x axis depends on the time according to the equation x=ct
5
−bt
7
, where x is in meters and t in seconds. Let c and b have numerical values 2.6 m/s
5
and 1.1 m/s
7
, respectively. From t=0.0 s to t=1.9 s, (a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.05. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (E) Number Units (h) Number Units (i) Number Units
Answers
The equation given is;\(x = ct^5 - bt^7\)Where \(c = 2.6 m/s^5\) and \(b = 1.1 m/s^7\)(a) Displacement is obtained by finding the difference between the initial and final position of the particle.
\(i.e At , the particle is at a distance ofDisplacement = Displacement = = - 1.57 m(b) When t = 1.0 s,\)
the velocity of the particle can be found by taking the derivative of the displacement with respect to time;i.e \(v = \frac{dx}{dt}\)\(x = ct^5 - bt^7\)\(\frac{dx}{dt} = 5ct^4 - 7bt^6\)At \(t = 1.0 s\), \(v = 5*2.6(1.0)^4 - 7*1.
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6/22, 3:45 PM
Kris said, "The Rawlings Rockets basketball team does not have any really tall players." These are the players'
heights in inches:
70, 77, 75, 68, 88, 70, and 72.
a. Which number does not seem to fit this set of data? 1
b. Do you agree or disagree with Kris?
2
Answers
Answer:
a. 88
b. I disagree with Kris
Step-by-step explanation:
88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.