Step-by-step explanation:
circular permutations of n objects =(n-1)!
One leg of a right triangle is 14 centimeters longer than the other leg. The length of the is 26 centimeters. What are the lengths of the legs?
The length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.
Explanation:
Let x be the length of the shorter leg of the right triangle.
According to the problem, the longer leg is 14 centimeters longer than the shorter leg, so its length is x + 14.
We also know that the length of the hypotenuse of the right triangle is 26 centimeters.By the Pythagorean theorem, we have:
x^2 + (x + 14)^2 = 26^2
Simplifying the left side:
x^2 + x^2 + 28x + 196 = 676
Combining like terms:
2x^2 + 28x - 480 = 0
Dividing by 2:
x^2 + 14x - 240 = 0
Factoring:
(x + 20)(x - 6) = 0
Therefore, x = -20 or x = 6.
Since the length of a side cannot be negative, we reject x = -20 and conclude that x = 6.
So the length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.
tammy spends $15 each time she travels the toll roads. she started the mount wit $210 in her toll road account. the amount, A( in dollars), that she has left in the account after t trips on the toll roads is given by the following function
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe. Write the equation for the relationship that has constant of proportionality greater than 1.
Answer:
r/p = 2
Step-by-step explanation:
The proportional relationship between the amount of raisins and the amount of peanuts can be expressed as:
r/p = k
where k is the constant of proportionality.
To find an equation with a constant of proportionality greater than 1, we simply need to choose a value of k that is greater than 1. For example, if we choose k = 2, the equation becomes:
r/p = 2
To check that this equation is correct, we can use the original ratio of 4 cups of raisins for every 6 cups of peanuts:
4/6 = 2/3
This confirms that the constant of proportionality is indeed 2, and that the equation for the relationship with a constant of proportionality greater than 1 is:
r/p = 2
In a study of the effects of college student employment on academic performance, two random samples (one from students who worked and the other from students who did not work) were selected from college students at a large university. The following summary statistics for GPA were reported.
Employed students
sample size 114
Mean GPA 3.15
Std deviation 0.485
Non-employed students
Sample size 114
Mean GPA 3.23
std deviation 0.524
Compute a 90% confidence interval for the mean GPAs of non-employed students. Assume that the normal condition is met.
a. Identify the variables needed to solve the problem.
b. Find the standard deviation.
c. Calculate the point estimate and margin of error.
d. Calculate the confidence interval
Therefore the 95% confidence interval is,
(219.25, 534.75)
How to solveHere sample standard deviation is given but the sample size is large. Therefore we use z table to find the critical value.
Therefore the 90% confidence interval for the mean GPA for students at the University who are employed and who are not employed is,
(0.112, 0.308)
For the next problem,
We follow the same procedure as we have done in the first problem.
And here the data is different and we construct 95% confidence interval.
Therefore the 95% confidence interval is,
(219.25, 534.75)
And we interpret this confidence interval as,
We are 95% confident that the true difference in the mean daily caorie intake for teens who do eat fast food on a typical day and those who do not falls within this interval.
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The graph of a quadratic function F has zeros of -8 and four and a maximum at -2, 18 what is the value of “a” in the function equation?
Answer:
Since the given quadratic function has zeros of -8 and 4, we know that the factors of the quadratic equation are (x + 8) and (x - 4).
The maximum of the function occurs at the midpoint between the zeros, which is (-8 + 4)/2 = -2. So, the x-coordinate of the vertex is -2.
We also know that the y-coordinate of the vertex is 18. So, the vertex of the quadratic function is (-2, 18).
Using the vertex form of the quadratic function, we can write:
F(x) = a(x + 2)^2 + 18
Since the function has zeros of -8 and 4, we can write:
F(x) = a(x + 8)(x - 4)
a(x + 2)^2 + 18 = a(x + 8)(x - 4)
ax^2 + 6ax - 128a - 576 = ax^2 + 16ax - 32a
10ax - 96a - 576 = 0
10a(x - 6) = 0
a = 0 or x = 6.
Since the vertex is a maximum and the coefficient of the x^2 term is positive, we know that a > 0. Therefore, we can conclude that x = 6 and a = 3.
Hence, the value of "a" in the function equation is 3.
i need help with this trig question part A and B
Answer:
Part A: ∠A ≈ 27.7 °
Part B: c ≈ 8.75
Step-by-step explanation:
Part A:
Use the Law of Cosines.
Cosθ =
[ a² + b² - c² ] / [ 2ab ]
Sub in all the information where θ is A.
A = cos⁻¹ { [10² + 7² - 5²] / [2×10×7]
A ≈ 27.7 ° (1 decimal place)
Part B:
Use the Law of Cosines, but instead the unknown is the side c.
Rearrange to isolate c:
c² = a² + b² - 2ab×cosθ
c = √(5² + 6² - 2×5×6×cos(105°))
c ≈ 8.75 (2 decimal places)
A stock can go up, go down, or stay unchanged . How many possibilities are there if you own 9 stocks?
7
MTR
12345 6 7 8 9 10 x
Tickets
mowing lawns in you
How
much do you earn when you mow 17 lawns?
(See Example 4.)
48. MODELING REAL LIFE It costs $35 a month for membership at a wholesale store. Write and
graph an equation that represents the monthly cost (in dollars) of a membership. What is the
cost of a membership for an entire year?
Name:___________ Period:___
6-1 Populations & Samples
LT: I can ________________________________________________
_______________________________________________________.
Population: An ________ group of objects - _________, _________, _____________ - from which _________ can be collected.
Sample: A _____________ of the ______________.
Why use a sample?
When you ask a ____________ question about a _____________, it is often more efficient to gather data from a _____________ of the ______________.
Representative Sample: Accurately reflects the _________________ of the entire ______________.
(It has the __________ characteristics as the _________________.)
Random Sample:
→ Each ___________ of the population has an _________ chance of being ____________.
→ Tends to be a ___________________ __________of a population.
How might you generate a random sample? Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
If x = 3 units, y = 5 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
The area of the rhombus by decomposition is
32 square unitsHow to find the area o the rhombsThe rhombus is decomposed into simpler elements which are
2 triangles and a parallelogramArea of 2 triangles
= 2 * 1/2 * base * height
= 2 * 1/2 * x * h
= 2 * 1/2 * 3 * 4
= 12 square units
Area of a parallelogram
= base x height
= y * h
= 5 * 4
= 20 square units
Area of the rhombus
= 20 square units + 12 square units
= 32 square units
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Find the weighted mean. Round your answer to one decimal place.
Deliveries Per Week Frequency
4 7
8 2
12 5
16 6
Weighted mean =
deliveries per week
Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive.
What is the probability that the number will be more than 6 or odd? (Enter your probability as a fraction.)
Start by putting the possible integers your friend can select
[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]
Then, call the 2 possible events as A and B, and what are the possible integers in each event:
A = Be more than 6
B = The number is odd
[tex]\text{A}=\{7,8,9,10\}[/tex]
[tex]\text{B}=\{1,3,5,7,9\}[/tex]
The probability of the union of two events can be calculated as:
[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]
Then,
[tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A)}=\dfrac{4}{10}[/tex]
[tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(B)}=\dfrac{5}{10}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]
Finally,
[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]
[tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]
Answer:
the probability that the number will be more than 6 or odd is: 7/10
Start by putting the possible integers your friend can select
[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]
Then, call the 2 possible events as A and B, and what are the possible integers in each event:
A = Be more than 6
B = The number is odd
[tex]\text{A}=\{7,8,9,10\}[/tex]
[tex]\text{B}=\{1,3,5,7,9\}[/tex]
The probability of the union of two events can be calculated as:
[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]
Then,
[tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A)}=\dfrac{4}{10}[/tex]
[tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(B)}=\dfrac{5}{10}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]
[tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]
Finally,
[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]
[tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]
Answer:
the probability that the number will be more than 6 or odd is: 7/10
Work sheet is pretty hard giving 20 points
Part A: The Table for the data set above and it's title are attached accordingly.
Part B:
1) The shortest marker in the data set is Marker 1, which has a length of 4.00 inches.
2) The longest marker in the data set is Marker 14, which has a length of 6.75 inches.
3) The range of the data set is 2.75 inches, calculated by subtracting the shortest marker (4.00 inches) from the longest marker (6.75 inches).
4) To find the median, we need to arrange the data set in order from smallest to largest:
4.00, 4.25, 4.75, 5.00, 5.00, 5.25, 5.50, 5.50, 5.625, 6.00, 6.25, 6.25, 6.25, 6.50, 6.75
The median is the middle value, which is 5.50 inches.
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Which expressions are equivalent to the one below? Check all that apply.
log2 2 + log2 8
A. 4
B. log₂ (2^4)
C. log2^16
D. log 10
The expressions B and C are equivalent to the given expression:
B. log₂ (2^4) = log₂ 16C. log₂ 16What are logarithmic functions?A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.
How to find the equivalent expressions?Simplify the expression using logarithmic property,
log m + log n = log (m.n)
Expression can be written as,
log₂(2) + log₂(8) = log₂(2x8)
= log₂ 16
simplify further,
log₂16 = log₂(2)⁴
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How many solutions does the equation sin(4x) = 1/2 have on the interval
(0, 2π]?
The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.
The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π].
The first solution occurs when 4x = π/6, or x = π/24. This corresponds to an angle of π/24 radians, or 7.5°.
The second solution occurs when 4x = 5π/6, or x = 5π/24. This corresponds to an angle of 5π/24 radians, or 112.5°.
Therefore, the equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.
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What do you know about this data before finding the range or the interquartile range?
187, 191, 202, 209, 218, 1984
The values are not in order.
The outlier will have no affect on the range.
The data has an outlier, therefore the interquartile range is much greater than it would be without the outlier.
The data has an outlier, therefore the range will be much greater than it would be without the outlier.
Answer:
D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.
Step-by-step explanation:
The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.
Answer:
d got it right in edge.
Which type of car had the largest range in monthly sales? Explain how you came up with your answer
Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.
Answer:
Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.
Step-by-step explanation:
Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.
Solve in order 10 points
A) The speed of the object is 6.71 units per second.
B) , the equation of the line is y = -3x + 9
C) The magnitude of the resultant force is 4.36N
How can one compute the above?a) The position of the object at time t is given by:
(x, y) = (4, -3) + t (-3 , 6)
v = (dx/ dt, dy/dt) = (-3, 6)
So the velocity vector is ( -3, 6).
For speed of the object, we need to find the magnitude of the velocity vector....
|v| = √((-3)^2 + 6^2)
= √(45)
= 3 √(5)
= 6.71 units
B
The equation given as (x, y) = (4, -3) + t (-3, 6)
Written in form of y=mx + b we have:
y = -3 t + 9
Thus,
EQuation is y = -3x + 9
C)
The angle between the two forces can be calculated as 90 ° - 30° = 60°.
To find the magnitude of the resultant force using the law of cosines, we can use the formula.....
c ² = a ² + b ² - 2ab cos(C)
In this case, we have...
a = 3N
b = 5N
C = 60 degrees
c ² = 3 ² + 5 ² - 2(3)(5) cos(60)
c ² = 9 + 25 - 30(0.5)
c ² = 19
c = √(19)
c = 4.35889894354
c ≈ 4.36
So it is right to state that the magnitude of the resultant force is 4.36N
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brainest if correct look at picture
Answer:
i'm pretty sure its c, but if not then sorry
Step-by-step explanation:
Answer:
The equation of the line in the point-slope form is y+3=2/3(x−5)
Step-by-step explanation:
B
Find the volume for each figure. Use 3.14 for Pi
1.
r=21 ft-
35 ft
Answer:
V = 16155.3 cubic feet
Step-by-step explanation:
The formula for volume (V) of a cone is
[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.
In the diagram, we're shown that the radius is 21 feet and the height is 35 feet. Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:
[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]
The five number summary of a dataset was found to be:
0, 5, 8, 16, 20
An observation is considered an outlier if it is below:
-11.5
Correct
An observation is considered an outlier if it is above:
32.5
Correct
That's correct. An observation is considered an outlier if it is more than 1.5 times the interquartile range (IQR) above the third quartile (Q3) or below the first quartile (Q1).
How to further determine the value?The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
In this case, the first quartile Q1 is 5 and the third quartile Q3 is 16. So the IQR is:
IQR = Q3 - Q1 = 16 - 5 = 11
An observation is considered an outlier if it is more than 1.5 times the IQR above Q3 or below Q1.
To find the upper outlier bound, we add 1.5 times the IQR to Q3:
Upper outlier bound = Q3 + 1.5(IQR) = 16 + 1.5(11) = 32.5
So any observation above 32.5 is considered an outlier.
To find the lower outlier bound, we subtract 1.5 times the IQR from Q1:
Lower outlier bound = Q1 - 1.5(IQR) = 5 - 1.5(11) = -11.5
So any observation below -11.5 is considered an outlier.
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Help me pleaseee! I need help with this problem
Answer:
Step-by-step explanation:
In the given figure, the triangle ABC is a right triangle with a right angle at C. We need to find the length of the side AB.
Using the Pythagorean theorem, we know that in a right triangle with sides of length a, b, and c (where c is the hypotenuse), we have c^2 = a^2 + b^2.
In this case, we have AC = 4 and BC = 3. So, applying the Pythagorean theorem, we get:
AB^2 = AC^2 + BC^2
AB^2 = 4^2 + 3^2
AB^2 = 16 + 9
AB^2 = 25
Therefore, AB = 5.
What is the quotient of 4 1/2÷2/3
The value of the quotient of 4 1/2 ÷ 2/3 is,
⇒ 27/4
We have to given that;
The expression is,
⇒ 4 1/2 ÷ 2/3
Now, We can simplify as;
⇒ 4 1/2 ÷ 2/3
⇒ 9/2 × 3/2
⇒ 27/4
Thus, The value of the quotient of 4 1/2 ÷ 2/3 is,
⇒ 27/4
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Consider the following equation.
-(3/2)^x+12 = 2x- 3
Approximate the solution to the equation above using three terations of successive approximation. Use the graph below as a starting point.
A. X=35/8
B. X=33/8
C. X=69/16
D. X=71/16
The solution of the graph is approximately
D. X=71/16What is solution of the graphThe solution of a graph depends on the type of graph and the problem being represented. In general, a solution of a graph refers to a point or set of points that satisfy the conditions or constraints of the problem.
For the problem, the solution of the graph is the point where the two graphs intersects.
Deducing from the graph this is at point x approximately 4.455 the closest value to this point in the option is x = 71/16
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Faber Kozlowski had 6 times as much money as Theriault Luigi. After Faber Kozlowski spent 1/3 of his money and Theriault Luigi spent 4/5 of his money, they had a total of $1155 left.
(a) How much money did Faber Kozlowski and Theriault Luigi have altogether at first?
(b) Theriault Luigi spent 3/4 of his remaining money on a hoodie. What fraction of his original amount of money did he spend on the hoodie?
Answer:
Step-by-step explanation:
Let's use variables to represent the amount of money each person had at first.
Let x be the amount of money that Theriault Luigi had.
Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.
After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.
After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.
Together, they had a total of $1155 left, which means:
4x + (1/5)x = 1155
Multiplying both sides by 5 to eliminate the fraction gives:
20x + x = 5775
Combining like terms gives:
21x = 5775
Dividing both sides by 21 gives:
x = 275
Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.
So, the answer to (a) is $275 + $1650 = $1925.
For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.
Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.
Answer:
(a) $1925
(b) 15%
Step-by-step explanation:
(a)
Let f = original amount of money Faber had.
Let t = original amount of money Theriault had.
"Faber Kozlowski had 6 times as much money as Theriault Luigi. "
f = 6t
"After Faber Kozlowski spent 1/3 of his money"
He has now: 2/3 f
"and Theriault Luigi spent 4/5 of his money"
He has now: 1/5 t
"they had a total of $1155 left"
2/3 f + 1/5 t = 1155
f = 6t
2/3 f + 1/5 t = 1155
2/3 (6t) + 1/5 t = 1155
4.2t = 115
t = 1155/4.2
t = 275
f = 6t = 6(275) = 1650
f + t = 275 + 1650 = 1925
Part (a) answer: $1925
(b)
Original amount: t = 275
He first spent 4/5 of the original amount, so he had 1/5 left.
275/5 = 55
He spent 3/4 of $55 on the hoodie.
3/4 × $55 = $41.25
$41.25/$275 × 100% = 15%
Part (b) answer: 15%
Dolls were sold for ₱42,356 gross, with returns amounting to ₱3,479. The cost of the dolls sold is ₱27,212. What is the gross profit?
Answer:
To find the gross profit, we need to subtract the cost of the dolls sold from the gross sales revenue (after returns have been deducted).
First, we need to calculate the net sales revenue, which is the gross sales revenue minus the returns:
Net sales revenue = Gross sales revenue - Returns
Net sales revenue = ₱42,356 - ₱3,479
Net sales revenue = ₱38,877
Next, we can calculate the gross profit:
Gross profit = Net sales revenue - Cost of goods sold
Gross profit = ₱38,877 - ₱27,212
Gross profit = ₱11,665
Therefore, the gross profit from the sale of the dolls is ₱11,665.
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Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
The x y-coordinate plane is given. The curve starts at the point (0, 2.5), goes down and right, changes direction at the point (4, 0), goes down and left, changes direction at the point (0, −2.5), goes up and left, changes direction at the point (−4, 0), goes up and right, continuing until it reaches its starting point.
The standard form equation of the ellipse as described in the task content is;
x²/4² + y²/(5/2)² = 1.What is the standard form equation of the ellipse as described?It follows from the task content that the standard form equation of the ellipse is to be determined.
Recall, the equation of an ellipse takes the form;
(x - h)²/a² + (y - k)²/b² = 1
where (h, k) is the center and a represents the distance of the center to each vertex on the major axis and b represents the distance from the center to each vertex on the minor axis.
Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;
x²/4² + y²/(5/2)² = 1
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What is the value of sin-1(1)?
ㅠ
0 -플
ㅇㅇ
ㅇ플
ㅇ TT
Answer:
Step-by-step explanation:arcsin(1) = pi/2
Benjamin is doing some remodeling at his home. He currently has a triangular patio that has a base that is four times as long as its height. He wants to increase the length of the base of the patio by 2 feet and the length of the height of the patio by 9 feet. If x represents the height of the patio, which of the following functions will give the area of the new patio?
Answer:
[tex] a_{old} = \frac{1}{2} (x)(4x) = 2 {x}^{2} [/tex]
[tex] a_{new} = \frac{1}{2} (x + 9)(4x + 2)[/tex]
[tex] = (x + 9)(2x + 1)[/tex]
[tex] = 2 {x}^{2} + 19x + 9[/tex]
Which of the following is equal to
OA. Speed
OB. Displacement
OC. Velocity
OD. Acceleration
distance
time
SUBI
Answer:b
Step-by-step explanation: