Answer:
$73915.40
Step-by-step explanation:
→ Find the multiplier
( 3 + 100 ) ÷ 100 = 1.03
→ Multiply by principal amount and raise it to the power of years
55000 × 1.03¹⁰ = 73915.40
Answer: $630,513.36
Step-by-step explanation:
Making a Formula for His Salary on a Given YearLet's make a table of values to see how much he earns every year after graduation.
1 year -> $55,000
2 years -> 55,000 * 103% = $56,650
3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50
4 years -> 58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³
Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.
We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.
Using this, let's generalize this for n.
n years -> [tex]55000(1.03)^{n-1}[/tex]
Finding the Sum after Ten YearsWe are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this
[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]
This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.
Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:
[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]
where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.
[tex]a_1[/tex] -> 55000
r -> 1.03
n -> 10
Now that we have the values for each variable, let's plug them in and solve
[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]
The total income he will have received after ten years is $630,513.36.
Answer the question.
Answer:
16 boys and 8 girls
Step-by-step:
24 / 3 = 8
so 8 girls
24 - 8 = 16
and 16 boys
Find the missing side of each triangle. Leave your answers in the simplest radical form.
On solving the provided question, we can say that it is a right angle triangle x = [tex]\sqrt{5}[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here
it is a right angle triangle
so by trigonometry
Sin 90 = [tex]\sqrt{5} / x[/tex]
x = [tex]\sqrt{5}[/tex]
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I need help on this question I have attached it on this assignment. THX
Answer:
I) 5575
ii) 312.50
b) 345
Step-by-step explanation:
I)11.15(500)=5575
ii) 1.25(250)=312.50
b) 407.10/1.18 = 345
Please help me with this question
The solution to the equation cosh(t) = t does not exist
How to determine the solution to the equationThe equation is given as
cosh(t) = t
To solve the equation cosh(t) = t, we can start by expressing the equation in terms of e^t and e^-t.
So, we have"
cosh(t) = (e^t + e^-t)/2 = t.
Rewrite the above equation as
e^t + e^-t = 2t.
Using a graphing calculator, the curve of e^t + e^-t and the line of 2t do not intersect
Hence, the equation has no solution
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a flooring tile has a shape of a parallelogram Hight is 10cm and base is 24cm how many tiles do you need to fill a room with area 1080 msq
45000 tiles we need to fill a room with area 1080 m²
What is Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides.
Area of floor =1080m²
Base of parallelogram shaped tile (b) =24 cm
and corresponding height (h)=10 cm
Area of one tile=b×h
=24×10
=240 cm²
=240/10000=24/1000 m²
Number of tiles required=1080/(24/1000)
=1080×1000/24
=45000 tiles
Hence, 45000 tiles we need to fill a room with area 1080 m²
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Solve the system of equations using substitution. 3x + 2y = 7 x = 3y + 6 (0, −2) (1, 2) (3, −1) (6, 0)
Answer:
(3, −1)
Step-by-step explanation:
I did the test
Find the answer for this equation
Consider units digit as u and tens digit as t, so t=1/2 u is the right equation.
What is the answer for the equation?Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.
given : t + u=9
1/2u+u=9 by substituting the value of t
3u=18
u=6.
t=1/2*6=3.
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Reasoning with linear equations
We can rewrite one side of the given equation using distributive property.
What is distributive property?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each term enclosed in a bracket multiplies the number outside of it, and the results are added.
The given equation is: 3(x + 2) = 18
Simplifying this,
3*x + 3*2 = 18
3x + 6 = 18
Hence, we can rewrite one side of the given equation using distributive property.
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A passenger jet flies from one airport to another 1,213 miles away in 2.7 h. Find its average speed.
Answer:m/s
Step-by-step explanation:
Answer:
To find the average speed of the passenger jet, we need to divide the distance traveled by the time it took to travel that distance.
Average speed = distance / time
In this case, the distance is 1,213 miles and the time is 2.7 h.
Average speed = 1213 miles / 2.7 h = 449.6 miles/h
So the average speed of the passenger jet is 449.6 miles per hour.
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEE HELP MEEE. Which statement best describes a graph of paired points that form a proportional relationship? Responses A straight line cannot be drawn through all the points, and the line passes through the origin. A straight line cannot be drawn through all the points, and the line passes through the origin. A straight line can be drawn through all the points, and the line passes through the point (3, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point where x = 0 and y = 0. A straight line can be drawn through all the points, and the line passes through the point where , x, = 0 and , y, = 0. A straight line can be drawn through all of the the points, but the line does not pass through the origin.
A graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through
the point where, x, = 0 and, y, = 0.
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 equation of a line on a graph that forms a straight line and forms a proportional relationship will have to pass through the origin.
origin = (x, y) = (0, 0)
Thus,
The graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through the origin.
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michael and martha run a mechanic shop. in one hour michael can perform eight oil changes or change ten tires. in one hour martha can perform seven oil changes or change fourteen tires. michael and martha have the same amount of resources. given this information which of the following is true?
Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.
Absolute advantage refers to the ability of a country or firm to produce a good or service at a lower cost than another country or firm. It is a concept in international trade and economic theory.
A country or firm has an absolute advantage in a good or service if it can produce that good or service more efficiently than another country or firm.
An individual has a comparative advantage in production if it produces at a lower opportunity cost when compared with other individuals.
The opportunity cost of Michael in the changing of oil = 10/ 8 = 1.25
Opportunity cost of Michael in changing tyres = 8 / 10 = 0.8
The opportunity cost of Martha in the changing of oil = 14 / 7 = 2
The opportunity cost of Martha in the changing of tyres = 7 / 14 = 0.5
Michael has an opportunity cost in changing of oil and Martha has an opportunity cost in changing of tyres.
Absolute advantage is when an individual produces more quantity of a good or service when compared to others.
So, Michael changes more oil (8) than Martha (7). Martha changes more tyres (14) than Michael (7)
Therefore, Based on the information given the correct option is option E.) Michael has an absolute and comparative advantage in changing the oil.
The complete question is:
Michael and Martha run a mechanic shop. In one hour Michael can perform eight oil changes or change ten tires. In one hour Martha can perform seven oil changes or change fourteen tires. Given this information which of the following is true?
A) Martha has a comparative advantage in changing oil.
B) Martha has an absolute advantage in changing oil.
C) Michael has a comparative advantage in changing tires.
D)Michael has an absolute advantage in changing tires.
E.) Michael has an absolute and a comparative advantage in changing oil
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Question
Evaluate the expression when a=14 and b=6.
−8ab=
Answer:
Step-by-step explanation:
-672 would be your answer
Please help its geometry
Answer: B
Step-by-step explanation:
b is 64 because exterior angles are congruent
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation:
P = 16+4d/9
If a scientific team uses special equipment to measures the pressure under water and finds it to be 172 pounds per square foot, at what depth is the team
making their measurements?
Answer: The team is measuring at ???? feet below the surface.
Therefore , the solution of given problem of equation comes out to be
P is equal to 12 pounds per square foot.
Define equation.Comparable to a balance scale, an equation. The equation (or scale) is out of balance if we add or subtract variable from one side. We also Must keep the "scale" (or equation) balanced while solving math equations such that both parts are always equal as expression are equal.
Here,
P= p = 12 + 4/9d is the equation that describes the relationship between the pressure,
p, of sea water in some deep ocean regions and the depth, d, below the surface.
Where
In pounds per square foot, p.
in feet is d
1) At a depth, seawater has a pressure of 85 pounds per square foot.
85 = 12 + 4/9d
4.9d/9 = 85 - 12 = 73
By xing it out, it becomes
4.9d = 73 × 9 = 657
d = 657/4.9
d = 134.1 feet
2) At 85 feet just below water's surface, the pressure of saltwater is
p = 12 + 4/9 × 85 = 12 + 4/765
P is equal to 12 pounds per square foot.
Therefore , the solution of given problem of equation comes out to be
P is equal to 12 pounds per square foot.
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what is the slope of the line -3y=12x+6
Answer:
Step-by-step explanation:
uhh
Find m∠ABD and m∠DBC
Answer:
m∠ABD=116°
m∠DBC=64°
Step-by-step explanation:
The sum of the two angles given equals 180°. To find the two angle measures, use the following equation:
m∠ABD+m∠DBC=180°
For this problem, m∠ABD=(7x+67)° and m∠DBC=(8x+8)°. So,
(7x+67)°+(8x+8)°=180°
15x+75=180
15x=105
x=7
Next, substitute x=7 into the original expressions for the angle measures.
m∠ABD=(7(7)+67)°
m∠ABD=(49+67)°
m∠ABD=116°
and
m∠DBC=(8(7)+8)°
m∠DBC=(56+8)°
m∠DBC=64°
A quadratic equation has solutions of (4+i) and (4−i). Which could represent the quadratic equation?
The quadratic equation with solutions of (4 + i) and (4- i) is,
⇒ x² - 8x + 17 = 0
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The solutions of the quadratic equation are,
⇒ (4 + i) and (4- i)
Now, We know that;
A quadratic equation with roots a and b is,
⇒ x² - (a + b)x + a × b = 0
Hence, A quadratic equation with roots (4 + i) and (4 - i) is,
⇒ x² - (4 + i + 4 - i)x + (4 + i) (4 - i) = 0
⇒ x² - 8x + (4² - i²) = 0
⇒ x² - 8x + 16 + 1 = 0
⇒ x² - 8x + 17 = 0
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Carrie solved -8 = 2y - 2 and got the solution y = 3 is she correct
Answer:
No
y = –3
Step-by-step explanation:
solution
–8 = 2y – 2
–8 + 2 = 2y
– 6 = 2y
[tex] \frac{ \\ - 6}{2 } = \frac{2y}{2} [/tex]
–3 = y
y = –3
How do the interior and exterior angles of a polygon relate? *
They are congruent
O They are supplementary
O They are complementary
There is no relations
The relationship between the interior and exterior angles of a polygon is they are supplementary.
What is a regular polygon?
If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.
Here,
we have to show how the interior and exterior angles of a polygon relate to each other.
A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.
As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).
Hence, the relationship between the interior and exterior angles of a polygon is they are supplementary.
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The first term in a sequence is 5 and the fifth term 17.what is the common difference ?
Using the concept of arithmetic progression , We have t(n) = a +(n-1)d formula, The answer is 3.
What do you mean by sequence?A number sequence is a series of numbers that are listed in a particular order. The numbers in a sequence may follow a specific pattern or rule. Examples of number sequences include the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc.), the Fibonacci sequence (1, 2, 4, 8, 16, 32, etc.), and the triangular number sequence (1, 3, 6, 10, 15, etc.). Number sequences are often studied in mathematics and have many applications in fields such as computer science, engineering, and physics.
What is arithmetic progression?An arithmetic progression (AP) is a type of number sequence in which the difference between any two consecutive terms is always the same. This common difference is known as the "common ratio" of the sequence. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic progression because the common difference is 3.
t(n) = a + (n-1)d
n=5
t(5)=17
a=5
17 = 5 +(5-1)d
12=4d
d=12/4 = 3
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Name the following function.
Answer: it is not a function
Step-by-step explanation: occurs when there was an attempt to call a value from a function, but the value is not actually a function.
HELP ME PLEASE!!!!!! I NEED IT ASAP.
Answer:
14. x = 9.7 cos(17) = 9.28
15. x = cos^-1 (10/16) = 51.32
16. x = 41/tan(35) = 58.55
write an equation in slope-intercept form of the line given the slope- 1/4 pass through (-2,1).
On solving the question we can say that slope intercept form of the equation is y = -1/4x +1/2
What is Slope Intercept form ?One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.
Any location that is not on the line will not fulfill the coordinates.
This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.
The line passes through (-2,1)
slope = -1/4
The equation of the line
y = mx + c
here m is the slope and c is the intercept.
putting the point and slope in the equation
1 = -1/4 *(-2) + c
⇒ c = 1/2
So the slope intercept form of the equation is
y = -1/4x +1/2
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The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15
How to find the value of the car in 4 yearsThe value of the car is solved by using the formula for depreciation which is y = A(1 – r)t
definition of variables
where
y = current value, = ?
A = original cost, = $24,000
r = rate of depreciation, = 15% and
t = time, in years. = 4 years
substituting the variables
current value, y = A(1 – r)t
current value, y = 24000 * (1 - 0.15)⁴
current value, y = 12528.15
the depreciation is $12528.15
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Brianna has a loyalty card good for a 10% discount at her local hardware store. If the
total cost, before tax and discount, of all the items she wants to buy is c, which
expression represents the cost after the discount?
(1-0.2)C expression represents the cost after the discount
How to find discounted price?Discount pricing' refers to a range of strategies where the price of a product or service is decreased in the interest of generating interest, unloading excess inventory, or boosting sales. The effectiveness of discount pricing rests on consumers' perception that they're 'getting a good deal' for an offering.The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the presentTo learn more about discounted price refers to:
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Just a quick question!
Solve using substitution.
–3x − 4y = 17
x − y = –1
Help please!
Answer:
(-3, -2)
Step-by-step explanation:
-3x -4y = 17
x -y = -1 Can be rewritten x = y - 1
Substitute y -1 for x into the first equation
-3(y - 1) - 4y = 17 Distribute the -3
-3y + 3 -4y = 17 Combine like terms
-7y + 3 = 17 Subtract 3 from both sides
-7y = 14 Divide both sides by -7
y = -2
Substitute -2 for y in x = y -1 to solve for x
x = -2 -1
x = -3
Check
-3x -4y = 17
-3(-3) - 4(-2) = 17
9 + 8 = 17
17 = 17 checks
x -y = -1
-3 -(-2) = -1
-3 + 2 = -1
-1 = -1 checks
Select all the expressions that are equal to 89.7 divided by 10 (/=divide)
1. 897.5/100
2. 8.975/100
3.8.975/1
4.8,975/1000
5.89,750/1000
The expression that is equal to 89.7 ÷ 10 is 897.5/100
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that an expression 89.7 ÷ 10
89.7 ÷ 10 = 8.97
1. 897.5/100
= 8.97
2. 8.975/100
= 0.08975
3. 8.975/1
= 8.975
4. 8.975/1000
= 0.008975
5. 89.750/1000
= 0.08975
Hence, the expression that is equal to 89.7 ÷ 10 is 897.5/100
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Find an explicit formula for the geometric sequence 3\,,\,15\,,\,75\,,\,375,...3,15,75,375,...3, comma, 15, comma, 75, comma, 375, comma, point, point, point.
Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text.
a(n)=a(n)=a, left parenthesis, n, right parenthesis, equals
The explicit formula for this geometric sequence 3, 15, 75, 375... is aₙ = 3(5)ⁿ⁻¹.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Note: The nth term of a geometric sequence is equal to the explicit formula for the geometric sequence.
Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = 15/3
Common ratio, r = 5.
Now, we can calculate the nth term (explicit formula) of this geometric sequence as follows:
aₙ = a₁rⁿ⁻¹
aₙ = 3(5)ⁿ⁻¹
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Complete Question:
Find an explicit formula for the geometric sequence 3, 15, 75, 375...
Question content area top left
Part 1
Find the slope of the line.
Question content area bottom left
Part 1
The slope of the line is 22.
(Type an integer or a simplified fraction.)
.
.
.
Question content area right
Part 1
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
The slope of the line is -5/6 in the graph.
What is slope?The slope of a line is how steep it is going from LEFT to RIGHT. Slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change.
No matter which two points you choose for the line's starting and ending points, the slope is always constant (it never changes).
From the given picture we can verify that
x₁ and y₁ is (-4, 6) and x₂ and y₂ is (2, 1).
We know the slope formula is y₂ - y₁ = m(x₂ - x₁)
Substituting the given details in formula we get
1 - 6 = m(2 - (-4))
-5 = m(6)
m = -5/6
Thus, the slope of the line is -5/6.
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There were some fiction and non fiction books in a second hand bookstore. The number of fiction bookw was 3/5 of non fiction bookw. After an equal number of fiction and non fiction books were sold,the ratio of the number of fiction books to the number of non fiction books left was 5:9. There were 240 books altogether at first. How many books were sold altogether?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
What is equation ?Give nonfiction books an x-factor.
Since there are three times as many fiction books as nonfiction books, we have a 3x/5 ratio, according to the question.
Due to the fact that they initially only sold two of these sorts and the fact that there were 240 volumes overall,
Due to this, the equation will be framed.
3x/5+x=240
So 8x/5=240
x=150 ( Number of non fiction books) ( no of non fiction books)
90 novels are so required.
Right at the start, this was a number.
Allow the number of books sold to increase.
In light of this, the equation is
Since there were 5:9 books in each category (fiction and nonfiction),
(90-y)/(150-y)=5/9
y=15
Therefore, the answer is 15.
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