It will take 15.03 years for Bentley's money to triple.
How longer for Bentley's money to triple than Camden's?For Bentley:
We have
Principal (P) = $670
Interest rate (r) = 6 7/8% = 0.06875 (compounded quarterly)
Time (t) = unknown
Amount after t years (A) = [tex]P(1 + r/4)^{4t}[/tex]
For Camden:
We have
Principal (P) = $670
Interest rate (r) = 7 3/8% = 0.07375 (compounded annually)
Time (t) = unknown
Amount after t years (A) = [tex]P(1 + r)^t[/tex]
We have to find t such that 3P_Bentley = Camden.
[tex]2010 = 2010(1 + r/4)^{4t} / (1 + r)^t[/tex]
Simplifying, we get:
[tex](1 + r/4)^{4t} / (1 + r)^t = 1/3[/tex]
Taking natural logarithm:
4t ln(1 + r/4) - t ln(1 + r) = ln(1/3)
4 ln(1 + r/4) - ln(1 + r) = ln(1/3) / t
t = (4 ln(3.88356) - 4 ln(16)) / ln(3)
Solving for t, we get:
t = 15.034752564
t = 15.03 years.
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Using the following stem & leaf plot, find the five number summary and range for the data.
1 0 2
2 1 2 5 9 9
3
4 2 2 7 9
5 0 2 3 4 8 9
6 0 7
Note that the five number summary and range for the data are given as follows:
Minimum: 102First Quartile (Q1): 225Median (Q2): 329Third Quartile (Q3): 458Maximum: 607.What is the explanation for the above response?The five-number summary and range were calculated using the given stem and leaf plot. The minimum value is 102, the first quartile (Q1) is 226, the median (Q2) is 340, the third quartile (Q3) is 492, and the maximum value is 670. The range is the difference between the maximum and minimum values, which is 568.
The range is calculated by subtracting the minimum value from the maximum value:
Range: 607 - 102 = 505
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find area of the triangle help please
The calculated area of the triangle is 7.5 square inches
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle with the following dimensions
base = 6 inches
height = 2.5 inches
Using the above as a guide, we have the following:
Area = 1/2 * base * height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 6 * 2.5
Evaluate
Area = 7.5
Hence, the area of the triangle is 7.5 square inches
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Based on a survey of 1250 employees at a software company, the average number of hours spent in meetings per week is 4.3 with a margin of error of 1.1.
What is the range of values for the actual mean numbers of hours spent in meetings in a week? Enter your answer by filling in the blanks to correctly complete the statement.
The actual mean number of hours spent in meetings in a week is between______and______hours
Answer:
Step-by-step explanation:
The margin of error represents the range of values within which the true population mean is likely to fall with a certain level of confidence. To calculate the range of values for the actual mean number of hours spent in meetings in a week, we can use the formula:
(actual mean) = (sample mean) ± (margin of error)
Substituting the given values, we get:
(actual mean) = 4.3 ± 1.1
To find the range of values, we need to compute the upper and lower bounds of this interval:
Lower bound = 4.3 - 1.1 = 3.2 hours
Upper bound = 4.3 + 1.1 = 5.4 hours
Therefore, the actual mean number of hours spent in meetings in a week is between 3.2 and 5.4 hours.
During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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Select the correct answer.
Consider functions f and g.
f(z) = log (x - 1)
g(x)
²-4
Which statement gives the best approximation of the solutions of the equation f(x) = g(z)?
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642
-3.464 and z≈ 3.642.
OB.
The solutions are where the graphs of the functions cross the x-axis at z
O C.
The solutions are where the graphs of the functions intersect at
-3.464 and z≈ 3.464
O D.
The solutions are where the graphs of the functions cross the x-axis at z ≈ -4 and ≈ 0.422
The statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
option A. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
How did we get the value?To find the solutions of the equation f(x) = g(x), set f(x) = g(x) and then solve for x. Using the given functions, we have:
log(x - 1) = (⅓x² - 4)
Exponentiating both sides:
x - 1 = e^(⅓x²-4)
Solve for x:
x = e^(⅓x²-4) + 1
Therefore, the solutions to the equation f(x) = g(x) are given by the values of x for which the graphs of the functions intersect. To find these points of intersection, plot the graphs of the functions and look for the points where they intersect. In other way round, solving for x numerically:
Based on the given functions, it is clear that g(x) is an upward-facing parabola with its vertex at (0, -4) and x-intercepts at (-2√3, 0) and (2√3, 0). The function f(x) is defined only for x > 1, and its graph is a monotonically increasing curve that approaches infinity as x approaches 1 from the right.
Therefore, there is only one point of intersection between the graphs of f(x) and g(x), which occurs to the right of x = 1. This point of intersection can be found numerically using a calculator or computer software, and it is approximately x ≈ 3.642.
Thus, the statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
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Mia is designing a cake for a birthday party. She plans for a total of 20 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?
The square cake can be distributed in such a way that each person out of 15 guest may get 8 , with the least amount left over .
The Correct option is (1).
What is Volume of any shape?
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.
First find the volume of square cake,
Volume = l x b x h
= 8 x 8 x 2
=128
Now there are total 15 guests, Each of get
=
= 8.533
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume=
=
=
=28.26
Now there are total 15 guests, Each of get
=
= 1.884
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume=
=
=
=50.24
Now there are total 15 guests, Each of get
=
= 3.349
4. Volume = l x b x h
= 6 x 9 x 2
=108
Now there are total 15 guests, Each of get
=
= 7.2
According to question each person may get 8 .
Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .
Find the length of the missing side
Answer:
24
Step-by-step explanation:
10^2+x^2=26^2
x^2=26^2-10^2
x^2=576
x=[tex]\sqrt{576}[/tex]=24
College Level Trigonometry Question!
The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.
How to find the force ?The formula for finding the force parallel to the incline:
= mass of the monolith x acceleration due to gravity x sin( slope angle )
Mass in kg :
= 57 tons x 1000
= 57, 000 kg
Force parallel to the incline:
= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )
= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )
= 32, 120.52 Newtons
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A triangle has side lengths of (6.2x - 9.4y) centimeters, (6.2x - 2.5z)
centimeters, and (8.3z + 1.4y) centimeters. Which expression represents the
perimeter, in centimeters, of the triangle?
O-3.2xy +3.7xz +9.7yz
O 12.4x8y + 5.8z
O-10.5yz +20.7xz
O-1.1z + 12.4x - 1.1y
Submit Answer
The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.
Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.
We know that, perimeter of triangle is sum of all the sides.
Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y
= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)
= 12.4x-8.0y+5.8z
Therefore, option C is the correct answer.
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Work out the value of fg^2 when:
f = -5 and g = -4
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a diamond
Answer: The odds against selecting a diamond are 3:1 (or 3/4)
Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.
The rectangles in the figure below are folded along the dotted lines at 90 * angles to make a completely closed rectangle box with no overlap. What is the volume of the resulting box?
The Volume of the resulting rectangular box is calculated as: 72 cubic units.
What is the Volume of a Rectangular Box?A rectangular box's volume can be calculated using the formula expressed below:
Volume = length * width * height.
Using the image of the net of the rectangular box, when folded, the dimensions of the box would be:
Length = 6 units
Width = 10 - 6 = 4 units
Height = 11 - 4 - 4 = 3 units
Plug in the values:
Volume of rectangular box = 6 * 4 * 3 = 72 cubic units.
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A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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Which of the following is not a linear transformation?
Select one:
Rotation in geometry
Projection in geometry
None of the options
Reflection in geometry
A survey asked students whether they have any siblings and pets. The survey
data are shown in the relative frequency table.
Pets
No pets
Total
Siblings
0.3
0.45
0.75
OA. 30%
OB. About 67%
O C. 75%
D. 40%
Given that a student has a sibling, what is the likelihood that he or she also
has a pet?
The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.
Let A denote the event that a student does not have a sibling.
Let B denote the event that a student has a pet.
Then A∩B will denote the event that the student does not have a sibling but he has a pet.
Let P denote the probability of an event in this question.
Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.
P(B|A)
We know that:
[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]
Also from the table, we have:
P(A)=0.25
and P(A∩B)=0.15
Hence,
[tex]P(B|A) = \frac{0.15}{0.25}[/tex]
[tex]P(B|A) = \frac{3}{5}[/tex]
[tex]P(B|A) = 0.6[/tex]
which in percentage is:
0.6 * 100 = 60 %
Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.
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A pole that is 3m tall cast a shadow that is 1.15m long at the same time a nearby building cast a shadow that is 40.75m long. How tall is the building
Answer:
The heights and shadows of the objects are legs of similar right triangles. We can use these similar triangles to set up a proportion to solve for the height of the building.
2.9 / 1.26 = x / 47.25
x = 108.75 m
1. Convert the following Mayan numbers to decimal (base 10).
b)
||:
:|| || ()
The given Mayan number which is: :|| :|| in decimal (base 10) is 42.
How to solveThe Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).
In order to obtain the decimal equivalent (base 10) of a Mayan numeral, it is imperative to comprehend the positional significance of each constituent symbol.
The numerical system employed here assigns a weight to each digit that corresponds to a certain power of 20. Specifically, the weight associated with the least significant digit is 20 raised to the exponent of 0, while the weight of the digit to its immediate left is 20 raised to the exponent of 1, and so forth.
The Mayan number given, : :|| :||, can be broken down as follows:
The leftmost position has no symbol, which represents a value of 0.
The second position from the left has two shell-like symbols (:), which represent a value of 2x20¹ = 40.
The third position from the left has two horizontal bars (||), which represent a value of 2x20⁰ = 2.
The given Mayan number in decimal (base 10) is 40 + 2 = 42.
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‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️
The area of the composite figure is equal to 75.5 square meters
How to calculate for the area of the figureThe composite figure can be observed to be made up of a big rectangle, a smaller rectangle, a triangle and a smaller triangle. We calculate for the area of the four shapes and sum the results to get the total area of the composite figure as follows:
area of the big rectangle = 6 m × 4 m = 24 m²
area of the smaller rectangle = 7 m × 2 m = 14 m²
area of the big triangle = 1/2 × 10 m × 6 m = 30 m²
area of the smaller triangle = 1/2 × 5 m × 3 m = 7.5 m²
total area of the composite figure = 24 m² + 14 m² + 30 m² + 7.5 m²
total area of the composite figure = 75.5 m²
Therefore, the area of the composite figure is equal to 75.5 square meters
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200 000+40 000+8 000+10+8 in standard form
Answer:
240 8018
Step-by-step explanation:
two hundred forty eight thousand and eighteen
MODELING REAL LIFE About 5.2% of a population
contracted the flu last year. A test used to diagnose the
flu was 92% accurate for people who had the flu and
85% accurate for people who did not have it. Find and
interpret the ratio of true positives to false positives.
The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .
Here. we have,
First, find the number of people who have the flu:
= 5. 2 % x 10, 000
= 520 people
Those who don't have it:
= 10, 000 - 520
= 9, 480 people
True positive :
= 92 % x 520
= 478 people
False negatives:
= 8 % x 520
= 42 people
False positives:
= 15 % x 9, 480
= 1, 422 people
The ratio of true positives to false positives is therefore:
478 : 1, 422
239 : 711
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Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
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Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
Bad gums may mean a bod mood. Researchers discovered that 85% of people who have suffered a bad mood had periodontal disease. Only 29% of healthy people have this disease. Suppose that in a certain community bad moods are rare, occuring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have bad mood?
Answer:
24.6%
Step-by-step explanation:
denote B: bad mood; H: healthy; D: periodontal disease
P(B|D)
=P(B,D) / P(D)
=P(B,D) / [P(D,B)+P(D,H)] ### law of total probability ###
=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]
=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]
=0.245664739
Algebra substitution y=-3x+5 2x+y=6
The solution to the system of equations y=-3x+5 and 2x+y=6 is (x,y) = (-1,8).
To solve the system of equations using substitution, we can substitute the expression for y in the second equation with the expression for y in the first equation:
2x + y = 6
2x + (-3x + 5) = 6 (substitute y = -3x + 5)
2x - 3x + 5 = 6
-x + 5 = 6
-x = 1
x = -1
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y:
y = -3x + 5
y = -3(-1) + 5
y = 8
We can check our solution by verifying that it satisfies both equations:
y = -3x + 5 => 8 = -3(-1) + 5 => 8 = 8 (true)
2x + y = 6 => 2(-1) + 8 = 6 => 6 = 6 (true)
Thus, our solution is correct.
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can someone help me do these qustions ( sorry if its hard to see) -(geometric sequence)
1. The geometric sequence is B. -1, 2, -4, 8.
2. The sixth term is 8192.
3. The next three terms are 1, 1/2 and 1/4.
4. The 10th term is 4374.
5. The eight term is 1/16.
6. The next three terms in the geometric sequence are -1/36 1/216, and - 1/1296
7. The 8th term or the sequence will be 4.
8. The 6th term of the geometric sequence is 2048.
How to calculate the valueThe 6th term of the sequence is:
a₆ = -2 * 4⁵ = -2 * 1024 = -2048
The common ratio of the sequence is:
r = 8/16 = 4/8 = 2/4 = 1/2
16 * (1/2) = 8
8 * (1/2) = 4
4 * (1/2) = 2
Therefore, the next three terms in the geometric sequence are 8, 4, and 2.
The common ratio of the sequence is:
r = 6/(-36) = -1/6
-1/6 * (1/6) = 1/36
1/36 * (1/6) = 1/216
-1/216 × 1/6 = -1 /1296
Therefore, the next three terms in the geometric sequence are -1/36, 1/216 and 1/1296.
The 8th term or the sequence will be:
= 512 × 0.5 × 0.5 × 0.5 × 0.5⁴
= 4
The 6th term of the geometric sequence is:
= 2 × 4 × 4 × 4 × 4 × 4
= 2048
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Suppose that the function is defined as follows.
Answer:
Step-by-step explanation:
Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 14, 9, 9, 6, 10, 19 Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
HELP ASAP PLEASE 20 POINTS!!!!!
Answer:
5.6 mi
Step-by-step explanation:
1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that
A side of an equilateral triangle is 20 cm long. What is the area of the triangle
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
Answer: 18.75
Step-by-step explanation:
small greeting cards = 1.80
large greeting cards = 3.85
1.80 x 4 = 7.20
3.85 x 3 = 11.55
7.20 + 11.55 = 18.75
Pleas help and I will mark your brainliest. It is simple matrix work!
The inverse of matrix C is C⁻¹ = [1/9 4/27] [1/27 -5/27].
How to determine inverse of matrix?To find the inverse of matrix C, use the following formula:
C⁻¹ = 1/det(C) × adj(C)
where det(C) = determinant of matrix C and adj(C) = adjugate of matrix C.
To find the determinant of C, use the following formula for a 2x2 matrix:
|a b|
|c d| = ad - bc
So:
det(C) = |5 1|
|12 -3| = (5)(-3) - (1)(12) = -27
Find the adjugate of C, which is the transpose of the matrix of cofactors of C, which is:
|-3|
| 1| = -(-3) = 3
So the upper left cofactor is 3, which is:
|12|
|-3| = -(12) = -12
So the upper right cofactor is -12, which is:
| 1|
|-3| = -(1) = -1
So the lower left cofactor is -1, which is:
|5|
|1| = 5
So the lower right cofactor is 5. Putting the cofactors into a matrix and transposing it gives the adjugate of C:
adj(C) = [ 3 -12]
[-1 5]
Now find the inverse of C:
C⁻¹ = 1/det(C) × adj(C)
= -1/27 × [ 3 -12]
[-1 5]
= [1/9 4/27]
[1/27 -5/27]
So the inverse of matrix C is:
C⁻¹ = [1/9 4/27]
[1/27 -5/27]
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