The amount his account will have after 3 months be $ 759.38.
Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.
we have to find the amount in the account after 3 months,
So, the amount he made is,
Amount = 750(1 + 5/100)^0.25
Amount = 759.38
So, the amount his account will have after 3 months be $ 759.38.
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Let A be the set of numbers that are multiples of 3 between 1 and 16 and B be the set of even natural numbers up to and including 20. Find A∪B.
Write your answer in proper set notation.
Make sure each element is only listed once.
========================================================
Work Shown:
A = set of multiples of 3 between 1 and 16
A = {3, 6, 9, 12, 15}
B = set of even natural numbers up to and including 20
B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {3, 6, 9, 12, 15, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}
---------------
Explanation:
The U stands for "set union". It's where we combine two or more sets together to form a larger set. The duplicates are tossed out. This is what your teacher meant when writing "Make sure each element is only listed once". Writing A u B indicates "the set of values in either set A, set B, or both".
In this case, the duplicates are "6" and "12" since they are found in set A and B simultaneously. They are in the overlapped area of both sets. It might help to draw out a Venn Diagram.
Common convention is to sort the items in the set. Though technically a set like {1,2,3} is the same as {3,1,2}.
Don't forget about the curly braces to indicate to the reader that this is a set of values.
LCD for 9/8 and 11/12
The Least Common Denominator (LCD) of 9/8 and 11/12 is 24.
The two given fractions are -
9/8 and 11/12
We have to find out the Least Common Denominator (LCD) of 9/8 and 11/12.
Firstly, we have to check if we can simplify the two given fractions. In this case, we have 9/8 and 11/12 which cannot be simplified further.
Now, we have to multiply the denominators with natural numbers until they there is a first common number in the denominators of the two given fractions.
Multiplying 8 with 2 gives 16. However, there 16 is not a multiple of 12,
Multiplying 8 with 3 gives 24. 12 when multiplied with 2 also gives 24.
So, the Least Common Denominator (LCD) of 9/8 and 11/12 is 24.
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PLEASE BE FAST I HAVE 5 MIN LEFT!! <3
Step-by-step explanation:
Original prices of the office equipments
Computer = £650
Calculator = £27.75
Telephone = £69.50
45. The computer has a discount of 15%
[(100 - 15)/100]% × £650
85/100 % × £650
=£552.5
46. The calculator has a discount of 20%
[(100 - 20)/100]% × £27.75
80/100 % × £27.75
=£22.2
47. The telephone has a discount of 10%
[(100 - 10)/100] % × £69.50
90/100 % × £69.50
=£62.55
48. The saving for the computer is
= £(650 - 552.5)
= £97.5
49. The saving for the calculator is
= £(27.75 - 22.2)
= £5.55
50. The saving for the telephone is
= £(69.50 - 62.55)
=£6.95
Differentiate the following functions from first principles
(i) Y=10 x^4+3 x+50(4marks)
The solution of the differentiated equation is dy/dx = 40x³+ 3
How to differentiate the equation?From the question, we have the following equation that can be used in our computation:
Y=10 x^4+3 x+50
Rewrite properly
So, we have
y = 10x⁴ + 3x + 50
The rule of first principle of differentiation is represented as
If y = axⁿ, then dy/dx = naxⁿ⁻¹
Using the above as a guide, we have
dy/dx = 4 * 10x⁴⁻¹ + 1 * 3x¹⁻¹ + 0 * 50
Evaluate
dy/dx = 40x³+ 3
Hence, the equation result is dy/dx = 40x³+ 3
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What sorts of follow up questions about the statistics might you ask that person in order to obtain the data needed to make a decision about the validity of that statement? Be sure to use concepts and vocabulary from this week to guide your response.
The follow up questions about the statistics that you might ask in order to obtain the data needed to make a decision about the validity of that statement include:
How was the information gathered?Was the experiment under control?How big were the control and placebo groups?Was it a double-blind or blind test?Were extreme outliers removed from the data before the experiment was run?What is statistics?Statistics is the science that studies and develops methods for collecting, analyzing, interpreting, and presenting empirical data.
Statistics is the study and manipulation of data, which includes methods for gathering, reviewing, analyzing, and drawing conclusions from data. Statistics is divided into two categories: descriptive statistics and inferential statistics. Such questions can be asked to gain a better understanding of the statement's validity.
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I don’t know the answer
After 15 years, Zephan will have a balance of $13181.07 in his savings account.
Given,
In the question:
Compound Interest is given by the formula.
A = P(1 + r)^t
Zephan invested $5500 in a savings .
Rate of interest is 6%
Time = 15 years
Now, According to the question:
We know that :
P = 5500
r = 6%
n = 1
t = 15
Compound Interest is given by the formula.
A = P(1 + r)^t
Substitute the values in above formula.
A = 5500. [tex](1+\frac{6}{100}/1 )^1^5[/tex]
Evaluate the equation/expression:
A = 13181.070062
Round 13181.070062 to the required place
= 13181.07
Hence, After 15 years, Zephan will have a balance of $13181.07 in his savings account.
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x + 20 ≤ -10 please help progress leraning
The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
It is given that the expression is,
x + 20 ≤ -10
Rearrange the expression as
x≤ -10-20
x≤ -30
Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
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Use the equation below to find a, if b=6 and c=13.
a=35-b-c
a
1
X
Ś
The value of a = 16
The process of making something less complicated and hence easier to accomplish or understand, or the thing that arises from this process: The organization offers advice on how to simplify trade procedures. Simplification is classified into two types: You must be conversant with both sorts of simplification questions, the first of which is 'Finding the missing number.' The second type of simplification difficulty is 'the relationship between the numbers and simplifying the numbers using simplification principles.'
Given that b= 6 and c= 13
Given equation is a = 35-b-c
Now substitute b and c values in the given equation
A = 35 - 6 -13
A = 35 – 19
A = 16
Therefore the value of a = 16
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I WILL GIVE BRAINLYEST FOR ANSWER Rewrite the equation y=5-4/3x in standard form
Answer:
4x+3y=15
Step-by-step explanation:
y=-4/3x+5
4/3x+y=5
4x+3y=15
:]
Use the graphs off and g to describe the transformation from the graph off to the graph g.
f(x) = -1/2x-5
g(x) = f(x-3)
The graph of f(x) is transformed 6 units horizontally to get the graph g(x). g(x) is a transformation form of the graph of f(x).
What is the reciprocal function?
The typical instance of reciprocal functions that we might run into is y = a/x, where a is a real number. Accordingly, reciprocal functions are those that have an algebraic expression in the denominator and a constant on the numerator.
Given functions are:
f(x) = -1/(2x-5)
g(x) = f(x-3)
The points on the graph f(x) = -1/(2x-5) are:
When x = 0, f(x) = 1/5
When x = 1, f(x) = 1/3
When x = -1, f(x) = 1/7
The graph of f(x) is added.
Putting x = x-3 in f(x) = -1/(2x-5) to find the function g(x):
g(x) = -1/(2x-6-5)
g(x) = -1/(2x-11)
The points on the graph g(x) = -1/(2x-11) are:
When x = 0, g(x) = 1/11
When x = 1, g(x) = 1/9
When x = -1, g(x) = 1/13
The graph of g(x) is added.
The graph g(x) is translated 6 units horizontally.
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4. Which of the following exponential functions matches the graph
←
a.
b.
(-1, 10)
11
+
)
5
(0, 2)
1
5
2 4
X
C.
y=2
5
d. y = 2(5)*
X
The equation y=2(1/5)ˣ is satisfy the graph with points (-1,10) and (0,2).
Given that,
In the picture we have a graph with two points (-1,10) and (0,2).
We have to find the equation of the graph from the given equation.
Basic Functions Graphing. if possible, identifying the shape. A line would be the graph of a linear function of the type f(x) = ax + b, for instance; a parabola would be the graph of a quadratic function.
We check by substituting the points in the equation of the option a,b,c and d.
The option c.
y=2(1/5)ˣ
The point (-1,10)
10=2(1/5)⁻¹
10=2(5)
10=10
The point (0,2)
2=2(1/5)⁰
2=2(1)
2=2
Therefore, The equation y=2(1/5)ˣ is satisfy the graph with points (-1,10) and (0,2).
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an arctic explorer reached the north pole and decided to erect the national flag . his eyes was 1.6 m from the ground and the angle of elevation to the top of the 3 m flagpole was 28. how far from the base of the flagpole did he stand?
The explorer stood 2.63m away from the flag pole.
What is Angle of Elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
If the pole is 3m high, and his eye is 1.6 meters from the ground.
Then distance from the top of the pole and his eyes would be 3 - 1.6 = 1.4m
The angle of elevation between the line of sight and the horizontal = 28°
so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.
Let the distance of the explorer from foot of pole be x,
so that,
tan 28 = 1.4/x
by cross multiplying,
x tan28 = 1.4
x = 1.4/tan28
x = 1.4/0.5317
x = 2.63m
In conclusion, the distance of the explorer to the base of the flagpole is 2.63m
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If a + b = 5 and ab = 6, find the value of a³ + b³
The value of a³ + b³ is 64.184
Here,
a + b = 5 .........(1)
and ab = 6
a = b/6
Substitute above value of 'a' in equation(1)
b/6 + b = 5
7b/6 = 5
7b = 30
b = 30/7
b = 4.28
So, a = 5 - 4.28
a = 0.72
We know that the formula of a³ + b³
a³ + b³
= (a + b)(a² + b² - ab)
= 5 * (0.72² + 4.28² - 6)
= 5 * 12.8368
= 64.184
Therefore, the value of a³ + b³ is 64.184
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The number of ways in which 6 pictures can be hung from 8 picture nails on the wall is a) 6^8 b) 20160 c) 8^6 d) None of these
only for mathdud
The number of ways in which 6 pictures can be hung from 8 picture nails on the wall is b) 20160.
Given:
The number of ways in which 6 pictures can be hung from 8 picture.
Number of ways = [tex]8_C_{6}[/tex]*6!
[tex]8_C_{6}[/tex] = 8!/(8-6)!6!
= 8!/2!*6!
= 8*7*6! / 2*1*6!
= 56/2
= 28
6! = 6*5*4*3*2*1
= 30*4*3*2*1
= 120*3*2*1
= 360*2*1
= 720*1
= 720
[tex]8_C_{6}[/tex]*6! = 28*720
= 20160
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Answer:
answer is 20160 ..........
If $100 is borrowed and the interest after 6 months is $8, what is the annual interest rate for a simple interest loan?
Answer:
48
Step-by-step explanation:
I=prt
8/100= 0.08
I=100(6)(0.08)
48
Solve the following word problems. Show your work in the space below.
19. Demetrius bought 6 boxes of colored pencils. There were 15 pencils in each box.
How many colored pencils were there altogether?
6 Boxes of colored pencils
15 Pencils in each box
Total Number of colored pencils : 15 x 6 = 90 Pencils
con tubos de 4,5 metros de largo se desea conducir agua a lo largo de 18 km. ¿cuantos tubos serán necesarios?
Answer:
Serán necesarios:
4000 tubos
Step-by-step explanation:
1 km = 1000 metros
18 km = 18*1000 = 18000 metros
Entonces:
18000/4.5 = 4000
Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How many leaves did she collect by the end of the week?
Answer:
49 leaves
Step-by-step explanation:
7 days x 7 leaves per day = 49 leaves in total
work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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Name the property used to justify the equation. (-2+5) +-7 = -2 + (5 +-7)
(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
The probability that they two people are chosen and travel by different transport is 47/144
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
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What is a common denominator for 3/5 and 2/3
Answer:30
Step-by-step explanation:
What is the ordered pair for Point T?
(1,5)
(0,5)
(5,0)
(5,5)
Answer:
B
Step-by-step explanation:
point T is on the y-axis with x- coordinate 0 and y- coordinate 5, then
the ordered pair for point T is (0, 5 )
What would $1000 become in a saving account at 3% per year for 3 years when the interest is not compounded (simple interest: p*r*
$1000)?
What would the same amount become after 3 years with the same rate but compounded annually?
S
Do NOT type dollar signs or commas.
Round to the nearest hundredth
Blank 1:
Blank 2
The required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
Given that,
$1000 become in a saving account at 3% per year for 3 years when the interest is not compounded.
Simple interest is defined as the percentage of earning on the lending for a period of time
Here,
Simple interest earned = P × r × t /100
= 1000 × 3 × 3 /100 = 90
Amount = P + SI = 1000 + 90 = $90
Now, when interest is compounded annually,
Amount = 1000(1.03)³
Amount = $1092.72
Thus, the required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
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f(x) = 3x + 2, what is f(5)
f(5)=17
Step-by-step explanation:
f(5)=3(5)+3
=15+2=17....
please help this is inverse functions algebra 2
Se me da mal algebra pero la b tiene buena pinta porque no se
For a given right triangle, if
Sin(3x - 7) = Cos(x + 1)
Find x:
A:24
B:3
C:4
D:46.8
Responses
If ΔABC ≅ ΔFDE, which of the following statements is true? (1 point)
∠A ≅ ∠E
∠B ≅ ∠F
∠A ≅ ∠D
∠B ≅ ∠D
Simplify.
8.4c-4.3c.
Answer:
4.1c
Step-by-step explanation:
8.4-4.3 is 4.1, and because you can combine like terms its 4.1c.
The assets and liabilities of a veterinarian are listed below.
Home Value $490,986
Mortgage $89,100
Credit Card Balance $6,691
Owned Work Equipment $98,820
Car Value $44,186
Investments $34,417
Office Equipment Loan $214,744
What is the value of the veterinarian's liquid assets?
$34,417
$44,186
$78,603
$98,820
Answer:
$34,417
Step-by-step explanation:
Hello,
As we can see liquid assets are things that can be easily converted to cash.
So, noting my previous statement we can see that investments are a liquid asset since it can be quickly or easily converted to cash.