Mr. Harold invested $1,600 in an account
that paid him 3.25% simple interest. What
will be the balance of his account after
32 years, including interest?
A) $1,664.00
C) $16,640.00
B) $1,536.00
D) $3,264.00
The sum of 3 consecutive even numbers is 54 what’s the largest number
The largest number is 20 .
What is largest ?
There is a big number—a googolplex—that exists. It consists of 1 and 10100 zeros (googol). A googolduplex, which is an even larger number, is also present. It is 1 and over a googol zeros after that.
Let 'n' be any number, odd or even.
2n will always be even number. This is because, 2n has 2 as common factor. So, 2n is always even.
Eg: 2= 2×1, n=1 ; 4=2×2, n=2 etc
Numbers are even, consecutive.
Consecutive even numbers are 2n-2, 2n, 2n+2,
Eg : For consecutive even numbers, put n=2
2n-2=4-2=2
2n=4
2n+2 =4+2=6,
we get 2,4,6 which are consecutive even nos.
So, numbers are 2n-2, 2n and 2n+2
Their sum= 2n+2+2n+2n-2=6n
Sum=54
6n=54
n=54/6=9
So, n=9
Consecutive numbers are
2n-2= (2×9)-2=16
2n=2×9=18
2n+2=18+2=20.
So, numbers are 16, 18, 20. Their sum is 54.
The largest number is 20
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114=6p
x/4=16
75=y-25
answer pls
Answer:
p = 19
x = 64
y = 100
Step-by-step explanation:
114 = 6p
Divide by 6 into both sides
p = 19
x/4 = 16
Times 4 into both sides
x = 64
75 = y - 25
Add 25 to both sides
y = 100
An angle measure 8 less than the measure of its supplementary angle.what is the angle measure of each angle
Step-by-step explanation:
Let the larger angle be x.
Smaller angle = x - 8
As both angles are supplementary,
x + (x - 8) = 180°
2x - 8 = 180°
2x = 188°
x = 94°
Therefore, larger angle = 94°
Smaller angle = 94° - 8° = 86°
three students attempt to define what it means for \overleftrightarrow{ab} ab a, b, with, \overleftrightarrow, on top and \overleftrightarrow{cd} cd c, d, with, \overleftrightarrow, on top to be perpendicular. \qquad 2 lines intersecting. one line is vertical with points a and b on opposite ends. the other line is horzontal with points c and d on opposite ends. they intersect at point o in the middle of both lines. can you match the teacher's comments to the definitions?
However, the information is not complete but we can see parallel lines in general to solve it.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Define perpendicular lines.Perpendicular lines are those that cross at a straight angle of 90 degrees.
Lines that are perpendicular to one another are those that are 90 degrees apart. In light of this definition, we could conclude that for lines lll and mmm to be perpendicular, they must intersect and form a right angle (90°) to one another.
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In thi coordinate plane, the ditance between each gridline repreent 1 mile. What i the ditance, in mile, between the library and the chool? You can ue the coordinate plane to help you find the anwer by plotting the two point
The distance between the library and the school using the coordinates plane is 7.28 miles.
A coordinate plane is a two-dimensional plane which is formed by the intersection of two number lines - a horizontal number line called the x-axis and is a vertical number line called the y-axis. It is a graphing and description system for points and lines. On the provided coordinate plane, the coordinate of the library is (-3,3) and the coordinate of the school is (4, 1).
The distance formula between two coordinates is given by:
d =√((x2 – x1)^2 + (y2 - y1)^2)
Using the distance formula, the distance between the library and the school are:
d =√((-3 – 4)^2 + (3 - 1)^2)
d =√((-7)^2 + (2)^2)
d =√((-7)^2 + (2)^2)
d =√(49 + 4)
d =√53
d = 7.28 miles
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(a) how many 4-permutations are there of a set of six objects? (b) how many 2-permutations are there of a set of nine objects?
There will be a total of 720 4- permutations of a set of six objects. And there will be a total of 72 2- permutations of a set of nine objects.
The calculation for 4-permutations of a set containing six objects
P(6,4)! = 6! / (6-4)1
P(6,4)! = 6×5×4×3x2
P(6,4)! = 720
Therefore, there will be a total of 720 permutations.
The calculation for 2- permutation of a set containing 9 objects
P(9,2)! = (9,7)! = (9-2) = 9! / 7!
P(9,2)! = 9×8x7! / 7!
P(9,2)! = 72
Therefore, there will be a total of 72 permutations.
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the audit team is planning to examine a sample of control policies and procedures. assume that, based on the intended degree of reliance on internal control, the audit team wishes to control the risk of overreliance to 5%. in addition, based on prior engagements, the audit team anticipates an expected deviation rate of 2%. what would be the impact of reducing the tolerable rate of deviation from 7% to 5% on the sample size?
As per the impact of reducing the tolerable rate of deviation from 7% to 5% on the sample size is 93.
The term deviation is defined as a measure that is used to find the difference between the observed value and the expected value of a variable.
Here we have given that the audit team is planning to examine a sample of control policies and procedures. assume that, based on the intended degree of reliance on internal control, the audit team wishes to control the risk of overreliance to 5%.
And we need to find sample size.
While we looking into the given question, we know that the tolerable rate of deviation from 7% to 5% on the sample size.
Let us consider that 100 be the sample size, then the reduction in 7% to 5%, tell that there is an 2% decrement in the sample size.
Therefore, it can be calculated as,
=> 100 x 2/100
=> 2
Here we already know that the risk of overreliance to 5%.
Then the total value is
=> 5 + 2 = 7.
Then the sample size is
=> 100 - 7
=> 93.
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Peter receives a salary of rs 14 250 per month plus a commision of 6 % on all sales. find his totasl sales, given that he receives a gross salary of rs 26 250.
let x as the total sales
26 250 = 14 250 + 0.06x
26 250 - 14 250 = 14 250 - 14 250 + 0.06x (subtract 14 250 both sides)
12 000 = 0.06x
x = 200 000
CHECKING:26 250 = 14 250 + 0.06(200 000)
26 250 = 14 250 + 12 000
26 250 = 26 250
Therefore, Peter have total sales of RS 200 000.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-19a - 6 = 4a please help me solve this! this is due in two days and the entire paper has 50 questions, this is only question 27!!
Answer:
a=6/15
Step-by-step explanation:
19a-6=4a
(19-4)a=6
a=6/15
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Answer:
a= 2/5 =0.4
Step-by-step explanation:
19a−6=4a
Subtract 4a from both sides.
19a−6−4a=0
Combine 19a and −4a to get 15a.
15a−6=0
Add 6 to both sides. Anything plus zero gives itself.
15a=6
Divide both sides by 15.
a= 6/15
Reduce the fraction 6/15 to lowest terms by extracting and canceling out 3.
a=2/5
three less than twice an integer is greater than 1
2x - 3 > 1
x represents an integer and 3 is less than twice an integer which is 2x. So it's 2x - 3.
2x - 3 is greater than 1.
So therefore, the answer is 2x - 3 > 1
Answer:
2x-3>1
Step-by-step explanation:
lets say x is the interger
so twice an interger would be 2*x or 2x
and three less than that would be 2x-3
and 2x-3 is greater than one
so, 2x-3>1
julian's transcript shows a grade point average of 3.00, with a standard deviation of 0.25. what fraction of his total credits were certain to have a grade point average between 2.00 and 4.0?
At least 75% of his total credits were certain to have a grade point average between 2.00 and 4.0.
By looking at the standard deviation of 0.25, we can calculate the range of the grade point averages which are within two standard deviations away from the mean. In this case, the mean is 3.00, so two standard deviations away would be 2.00 (3.00 - 0.25 x 2) and 4.00 (3.00 + 0.25 x 2). Since the grade point averages within this range are certain to have a grade point average between 2.00 and 4.0, at least 75% of the total credits are certain to have a grade point average between these two numbers.
Lower limit (2 standard deviations away from the mean):
3.00 - (0.25 x 2) = 2.00
Upper limit (2 standard deviations away from the mean):
3.00 + (0.25 x 2) = 4.00
Therefore, at least 75% of the total credits have a grade point average between 2.00 and 4.00.
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A teacher recorded unit 4 test scores from her class.
58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.
Find the percentile rank of a score of 71 on this street -
Victor is in the 60th percentile, what was his score?
The percentage score for a 71 on the test is 27, and the winning score is 71.
What is Statistics?The science of statistics focuses on creating and researching strategies for gathering, evaluating, interpreting, and reporting empirical data.
As per the given information in the question,
The given scores are:
5, 4, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, and 96.
A percentage is a number in a range of one to 100 that represents the percentage of a range that falls inside or above it.
Formula for calculating percentile rank on a test score of 71,
R₁₀₀ = [100(N <) + 1/2]/N
=100 × 4 + 1/2(1)/15
=400 + 0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60th percentile.
60 = Score/15
Score = 71
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What is the equation of the line that passes through the points (-2,10) and (-9,-5)? Write your answer in slope intercept form
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}[/tex]
Is the data set approximately periodic?
If so, what are its period and amplitude?
Hour
Number of bikes
O
O
not periodic
1 2 3 4 5 6
7
5 19 14 4 19 15 6
8 9 10 11 12
5 20 16
22 15
periodic with period of 3 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 7.5
periodic with period of 4 and amplitude of about 5
The data is A. periodic with period of 3 and amplitude of about 7.5
How to illustrate the data?From the information, we are given the number of hours as well as the number of bikes. It should be noted that we can see that ty values are periodic as it repeats every third value.
Also, the amplitude will be the:
= Larger value - Smallest value / 3
For the first set it is 7.
For the second set it is 7.5
For the third set it is 8
For the fourth set it is:
= (20 - 5)/2
= 7.5
Therefore, the amplitude is 7.5
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Johan buys a backpack for $41. He has to pay 8% sales tax. How much is the tax?
pls help asap tysm
Answer: The tax is $3.28.
Step-by-step explanation:
8% is equal to 0.08.
If you multiply 41 x 0.08 you get 3.28.
a liner function contains the following points. what are the slope and y-intercept of this function (0,2) (-3,4)
The function is actually (0,-3)(2,4)
Slope:
slope = y2-y1 = 4-(-3) = 7/2
x2-x1 2-0
y intercept: (0,-3)
click all of the graphs that do not pass the vertical line test.
PLease help me!!!!!
Answer:
Below
Step-by-step explanation:
1 2 and 3 do not pass the vertical line test because you can draw a vertical line that will cross the graph two times
Given that f(x) = 2x^2 + 9x and p = f(-3), what is the value of 3p?
Answer:
–27
Step-by-step explanation:
f(x) = 2x² + 9x
f(–3) = 2(–3)² + 9(–3)
= 2(9) + –27
= 18 – 27
= –9
since p= f(–3) = –9
3p = 3 × – 9 = –27
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The heights of the starting 5 players (not including the libero) on a volleyball team like karasuno high school are 60 inches, 67 inches, 64 inches, and 65 inches. If the balance point of the players is 65, what is the height of the 5th player?.
The height of the 5th player would be 69 inches
To find the Height, first, we have to calculate the mean value.
No. of players=5
The height of 4 players is 60 inches, 67 inches, and 64 inches, 65 inches.
Mean =Sum of observations/No of observations
Mean of the 5th players=65
To find, Height of 5th player
As we know,
Assuming the height of the 5th player is x
Mean =Sum of observations/No of observations
65=(60+67+64+65+x)/5
65*5=60+67+64+65+x
325=256+x
x=69
Thus, the height of the 5th player is 69 inches.
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Which of the following terms represents the situation shown in the graphic below?
a glide a reflection a glide reflection
None of these choices are correct.
The term that represents the situation shown in the graphic below is B. a reflection
What is a a reflection?A glide reflection or transflection is a symmetry operation in two-dimensional geometry that combines a reflection over a line with a translation along that line into a single operation.
An exchange of points from one side of a line with points on the other side of the mirror at the same distance from the mirror occurs when a mirror line is fixed in the plane. There is a mirror line in every reflection. A mirror reflection is followed by a translation that is parallel to the mirror to create a glide reflection.
Here, the shape is mirrored in the reflection. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
In conclusion, based on the information given, it should be noted that the correct option is B.
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DISTANCE The graph represents the distance y in miles Roland is from home as a function of time x in hours. Which could very likely be true?
WHAT IS DISTANCE?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria
You need to write complete questions in order to get good and exact answers. Here you haven't provided any graph so I could help you giving you my own graph. The relationship between speed, time and distance is as follows:
Where:
[tex]d=v t[/tex]
[tex]Where :[/tex]
[tex]d: Distance[/tex]
[tex]v:speed[/tex]
[tex]t : time[/tex]
So [tex]v[/tex] represents slope of a line that passes through the origin. In this case:
d matches the y-axis
t matches the x-axis.
So:
[tex]y=m x \rightarrow d=v t[/tex]
[tex]Where:[/tex]
[tex]\begin{aligned}& y \rightarrow d \\& m v \rightarrow v\end{aligned}[/tex]
[tex]x \rightarrow t[/tex]
The graph below (Car A) comes from the following equation:
[tex]y=\frac{5}{3} x[/tex]
And the equation for car B is:
[tex]y=\frac{5}{6} x[/tex]
By comparing them, car A moves faster than car B because:
[tex]\frac{5}{3} > \frac{5}{6}[/tex]
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Samantha has a total of 12 chickens.if she has 3 times as many chickens as dogs write and sole an equation to determine the number of dogs she has.
Answer:
Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs. The correct answer is 3x = 12; x = 4.
How did we figure this out?Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs. First you have to divide by 3 on both sides.
⇒ 3x = 12 ⇒ x = 4 This is your answer, x = 4Therefore, Samantha has a total of 12 chickens. if she has 3 times as many chickens as dogs. The correct answer is 3x = 12; x = 4.
Determine the value for x in the given diagram, with a || b.
35°
55°
125°
None of these choices are correct.
Answer:
125°
Step-by-step explanation:
the given problem is related to co-interior angle
so.
please show your work
d) [tex]\frac{48y^{10} }{x^{9} }[/tex] is the answer to your question
Exponents:
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64.In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.The symbol used for representing the exponent is ^. This symbol (^) is called a carrot. For example, 4 raised to 2 can be written as 4^2 or 42. Thus, 4^2 = 4 × 4 = 16Adding exponents while maintaining the same base is the rule for multiplying like bases.exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.To know more about Exponents:
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Graph the line whose equation is given in Point slope form. y+7=2(x-4)
Some of the coordinates on the graph are (0, -15), (1, -13), (2, -11).
The graph of the equation is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of the equation y + 7 = 2 (x - 4).
y + 7 = 2 (x - 4)
y = 2(x - 4) - 7
y = 2x - 8 - 7
y = 2x - 15
For x = 0,
y = - 15
(0, -15)
For x = 1,
y = 2 - 15 = -13
(1, -13)
For x = 2,
y = 4 - 15 = -11
(2, -11)
And so on...
Thus,
The graph of the equation is given below.
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which graph represent 5x-2y=3
Answer:
The answer is below; I have put the equation and graphed it!
Step-by-step explanation:
Graph the line whose equation is given in Point slope form. y+7=2(x-4)
Some of the coordinates on the graph are (0, -15), (1, -13), (2, -11).
The graph of the equation is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of the equation y + 7 = 2 (x - 4).
y + 7 = 2 (x - 4)
y = 2(x - 4) - 7
y = 2x - 8 - 7
y = 2x - 15
For x = 0,
y = - 15
(0, -15)
For x = 1,
y = 2 - 15 = -13
(1, -13)
For x = 2,
y = 4 - 15 = -11
(2, -11)
And so on...
Thus,
The graph of the equation is given below.
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The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4600 MB. How many downloads of the standard version were there?
Answer:
The number of downloads of the standard version is 230.
Step-by-step explanation:
Let x be the number of downloads of the standard version.
The number of downloads of the high-quality version is 4x.
The total size downloaded for the standard version is 2.8x MB.
The total size downloaded for the high-quality version is 4.3(4x) = 17.2x MB.
The total size downloaded for both versions is 2.8x + 17.2x = 4600 MB.
Combining like terms, we have 20x = 4600 MB.
Dividing both sides by 20, we have x = 230 downloads of the standard version
The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?.
The coordinates of the recycle bin will be = ( -1, 2.5 )
According to the information given in the question,
The coordinates of the vertices of the park are,
( 1, 1 ), ( 1, 4 ), and ( -3, 4 )
We have to find the coordinates of the recycle bin.
Let us consider the equation of the circle,
[tex]x^{2} +y^{2}+Dx + Ey+ F =0[/tex]
So putting the values of the coordinates into the equation,
First Equation,
[tex]1^{2}+1^{2} + D + E + F = 0[/tex]
Second Equation,
[tex]1^{2} +4^{2} +D + 4E + F=0[/tex]
Third Equation,
[tex](-3)^{2} + 4^{2} - 3D+4E+F=0[/tex]
Subtracting the first equation from the second,
[tex]1^{2} +4^{2} +D + 4E -E=0[/tex]
15 + 3E = 0
3E = -15
E = -5
Subtracting the third equation from the second,
1 + 16 - 9 - 16 + D + 3D = 0
4D = 8
D = 2
Putting the values of E and D in the first equation,
1 + 1 + D + E + F = 0
F = -2 - D - E
F = 1
So now the equation of the circle becomes,
[tex]x^{2} +y^{2}+2x - 5y+ 1 =0[/tex]
By expanding the above equation we can find the standard equation,
[tex]x+2x+1^{2} +y^{2} -5y+ 2.5^{2}- 1^{2} -2.5^{2} +1 =0[/tex]
[tex](x+1)^{2} + (y - 2.5)^{2} = 1^{2} + 2.5^{2} -1[/tex]
[tex](x+1)^{2} + (y - 2.5)^{2} = 2.5^{2}[/tex]
So the required circumcenter will be = ( -1, 2.5 )
Therefore, the coordinates of the recycle bin will be = ( -1, 2.5 )
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A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1,4), and (-3,4). The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?