Answer:
x = 2 , x = 5
Step-by-step explanation:
assuming you mean
[tex]\sqrt{9x-9}[/tex] = x + 1 ( square both sides to clear the radical )
([tex]\sqrt{9x-9}[/tex] )² = (x + 1)² ← expand using FOIL
9x - 9 = x² + 2x + 1 ( subtract 9x from both sides )
- 9 = x² - 7x + 1 ( add 9 to both sides )
0 = x² - 7x + 10 ← factor the quadratic
consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (- 7)
the factors are - 2 and - 5 , since
- 2 × - 5 = + 10 and - 2 - 5 = - 7 , then
(x - 2)(x - 5) = 0
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 5 = 0 ⇒ x = 5
As a check
substitute these values into the equation and if both sides are equal then they are the solutions.
x = 2
left side = [tex]\sqrt{9(2)- 9}[/tex] = [tex]\sqrt{18-9}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 2 + 1 = 3
left side = right side , so x = 2 is a solution
x = 5
left side = [tex]\sqrt{9(5)-9}[/tex] = [tex]\sqrt{45-9}[/tex] = [tex]\sqrt{36}[/tex] = 6
right side = 5 + 1 = 6
left side = right side, so x = 5 is a solution
passes through (0, -5) and has vertex (-1, 4)
The equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The vertex of the parabola is at (-1, 4). Then the equation is given as,
y = a(x + 1)² + 4
The equation passes through (0, -5), then we have
y = a(x + 1)² + 4
-5 = a(0 + 1)² + 4
-5 = a + 4
a = -9
Then the equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4
More about the equation of the parabola link is given below.
https://brainly.com/question/20333425
#SPJ1
a shirt was discountef from 75$ to 60$ what is the percent the shirt was reduced
Answer: 20%
Step-by-step explanation:
60 divided by 75 then times 100 = 80%
100% - 80% = 20%
Which of the following equations has infinitely many real solutions?
A.
3(x-6)= 3x + 18
B.
3(x-6)= 3x - 18
C.
3x+1=x-1
3x + 1 = 3x - 1
D.
Answer:
B: 3(x-6) = 3x-18
Step-by-step explanation:
The left and right sides of this equation are actually equal! We can see this by dividing the 3 on the left through the parentheses. This gives us [tex]3x-18[/tex], which is equal to the right-hand side of the equation!
To solidify this, we add 18 to both sides, and subtract 3x from both sides, which gives us that 0=0, so there are infinitely many solutions for x(since no matter what x is, it will result in 0=0 which is always true).
I hope this helps!
1… 1f21: 7: 4: 3a + 1 then what is 4th proportional?
B.
(8)
C
9
4
3
D.
3/4
1
9
2-Range of the data 112, 121, 184, 189, 177,190 is:
A.78 B.77 c 70 D.74
The 4th proportional of the given ratio is 4/3. option C
The range of the data 112, 121, 184, 189, 177, 190 is 78. option A
How to find 4th proportional?It follows from the concept of proportions that the ratios can be represented as follows;
21 : 7 = 4 : 3a + 1
21/7 = 4 / (3a + 1)
cross product
21 × (3a + 1) = 4 × 7
63a + 21 = 28
subtract 21 from both sides
63a = 28 - 21
63a = 7
a = 7/63
a = 1/9
So,
3a + 1
= 3(1/9) + 1
= 3/9 + 1
= 1/3 + 1
= 1 ⅓
= 4/3
21 : 7 = 4 : 4/3
Range of the data:
112, 121, 184, 189, 177, 190
Recall, the range of a dataset is the difference between the maximum and minimum data values and hence, we have;
Range = Highest data value - Lowest data value
= 190 - 112
= 78
Therefore, the range of the given set of data is 78.
Read more on ratio:
https://brainly.com/question/2328454
#SPJ1
PLEASE HELP ME BRAINLIEST IS THE REWARD
Answer:
13.3=c
Step-by-step explanation:
The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex]. For this problem, let
a=8.3
b=10.4
So,
[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]
Which constant must she add to both sides of the equation so that the left side is a perfect square?
The constant that must be added to both sides of the equation to find the perfect square is b/2a.
What is the quadratic equation?The 2nd equation in x is known as a quadratic function. Ax2 + Bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.
As per the given information in the question,
The equation for the quadratic equation is,
Ax² + Bx + c = 0
And for finding the roots,
d = b² - 4ac
Then, use the formula (-b±√d)/2a.
To know more about quadratic equations:
https://brainly.com/question/17177510
#SPJ1
Regina spent $45.50 over 61/2 months on music downloads. If she spent the same amount of money each month, how much money, in dollars, did Regina spend per month on music downlo
Answer:
She spend $7 a month on downloads.
Step-by-step explanation:
y = the total spent on downloads
x = number of months
m = the amount spent each month
y = mx
45.50 = m(6.5) Divide both sides by 6.5
7 = m
Are the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
The lines C and D are parallel.
What is a line?
In pure mathematics, a line is an infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas
Main body:
As Line LM cuts the line at C the angle made by both line is 48°
and line NP cuts the line at D , the angle made by line is 132°
we know that to make a line parallel , the sum of angle on one side of the line should be 180°
∠C +∠D = 48° +132°
= 180°
Hence , the lines C and D are parallel.
To know more about angle , visit:
https://brainly.com/question/25716982
#SPJ1
Terrence signed up for the Safe Venture driving school. He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes. When Terrence completes the 26 total hours of instruction, he will take his driver's test.
Which equation can you use to find w, the number of weeks the driving classes last?
The equation is 2w + 10 = 26.
The number of weeks the driving class lasts is 8 weeks.
With that,
Terrence signed up for the Safe Venture driving school.
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
We have to determine,
Which equation can you use to find w, the number of weeks the driving class lasts.
According to the question,
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
Then, The equation of the number of weeks the driving class lasts,
= 2w + 10
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
2w + 10 = 26
He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.
Therefore,
The number of weeks the driving class lasts,
2W + 10 = 26
2W = 26 - 10
2W = 16
W = (16/2)
W = 8
Hence, The number of weeks the driving class lasts is 8 weeks.
Iris wants to buy a necklace. The necklace is
$70.00. She has a coupon for 20% off her entire
order. What is the sale price for the necklace
Answer:56
Step-by-step explanation:20% of 70 is 14 dollars so you have to subtract 70-14=56.
Which of the following values is not an irrational number?
80, 7, 2.87, √59
80, 7, and 2.87 are not irrational numbers.
What is an irrational number?
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.
Given numbers: 80, 7, 2.87, √59
80 = It is a rational number
7 = It is a rational number
2.87 = It is a rational number
√59 = It is an irrational number.
Hence, 80, 7, and 2.87 are not irrational numbers.
To learn more about irrational numbers, visit:
https://brainly.com/question/20400557
#SPJ1
How do I find all the squares from 1 to 20?
Answer:
2.4.6.8.10
Step-by-step explanation:
that's the answer
Answer:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Step-by-step explanation:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10
a grocer can buy strawberries for 1.38 per pound
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
1 pound = $1.38
175 pounds = $241.50
The number of pounds for the strawberries order of $241.50 is
175 pounds.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cost of strawberries per pound = $1.38
The cost of a strawberry order = $241.50
The number of pounds for the order of $241.50.
1 pound = $1.38
Multiply 241.50/1.38 on both sides.
241.50/1.38 x 1 pound = $241.50
175 pounds = $241.50
Thus,
The number of pounds for the strawberries order of $241.50 is
175 pounds.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
The complete question is:
A grocer can buy strawberries for $1.38 per pound.
Write an equation relating c, the cost, and p, the pounds of strawberries.
A strawberry order cost $241.50.
How many pounds did the grocer order?
50 POINTS! PLEASE HURRY!
If you move the quadratic parent function, f(x) = x2, left 3 units, what is the equation of the new function?
g(x) = (x + 3)^2
g(x) = 3x^2
g(x) = x^2 - 3
g(x) = (x - 3)^2
The equation of the new function is: f(x) = (x- 3)²
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
We know that the function f(x+m) is equals to the function f(x) translated 'm' times to the left.
Therefore, to find the translate the function f(x) = x² twelve units to the right, we have given;
f(x- 3) = (x- 3)²
Therefore, the new function is: f(x) = (x- 3)²
Learn more about function here:
https://brainly.com/question/2253924
#SPJ1
write a polynomial function for each set of zeros
[tex]x = \sqrt{2} [/tex]
[tex] - i[/tex]
The required polynomial function is f(x) = (x + i)² which is degree 2 with the zeros x = √2 and x = -i.
We have to determine a polynomial function for each set of zeros:
x = √2, -i
To write a polynomial function with the zeros x = √2 and x = -i, we can start by setting the function equal to zero and substituting in the zeros:
f(√2) = 0
f(-i) = 0
We can then solve for the coefficients by expressing the polynomial function in terms of (x - √2) and (x + i).
For example, we can write:
f(x) = (x - √2)(x + i)q(x)
for some polynomial q(x).
Substituting in the zeros, we get:
f(√2) = (√2 - √2)(√2 + i)q(√2) = 0
f(-i) = (-i - √2)(-i + i)q(-i) = 0
Solving for q(x), we find:
q(x) = (x + i)/(x - √2)
Substituting this back into the original equation, we get:
f(x) = (x - √2)(x + i)(x + i)/(x - √2)
f(x) = (x + i)²
This is a polynomial function of degree 2 with the zeros x = √2 and x = -i.
Learn more about the polynomial here:
brainly.com/question/11536910
#SPJ1
xn+1=(xn)^3-1/4 x1=-1 what is x2
The required value of the x₂ is given as -0.500000.
Given that,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
xₙ₊₁ = [[xₙ]³ - 1]/4, x₁ = -1
put n = 2
x₂ = [[x₁]³ - 1]/4
= -1 - 1 /4
= -2/4
= -1/2 = 0.500000
Thus, the required value of the x₂ is given as -0.500000.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
The numbers x,y and z are given by x =[tex]\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} } , y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} } and z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex] . What is the value of x,y and z
The values of the expressions are x = √6, y = 2√3 and z = √2
How to evaluate the expressions?From the question, we have the following parameters that can be used in our computation:
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
We have
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
Take the square of both sides
So, we have
[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]
This gives
x² = 12 - 3√7 + 12 + 3√7 - 2√81
Evaluate the roots
So, we have
x² = 12 - 3√7 + 12 + 3√7 - 18
Evaluate the sum and the difference
x² = 6
Take the square roots of both sides
x = √6
Using the same steps above, we have
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
Square both sides
So, we have
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]
This gives
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]
Evaluate
y² = 12
Take the square root of both sides
y = 2√3
Lastly, we have
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
Square both sides
[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]
This gives
z² = 4 - 2 *1
Evaluate
z = √2
Read more about expressions at:
https://brainly.com/question/15775046
#SPJ1
question content area top part 1 a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. find the probability that a given class period runs between 50.5 and 51.25 minutes
The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.
[tex]P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15[/tex]
P = 0.15 means that the probability is 15%.
Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
To learn more about probability, visit brainly.com/question/11234923
#SPJ4
a dilation is a transformation that maps every point on a line segment to a point on a parallel line segment. the image has a length that is determined by the preimage and a scale factor, which is a fixed _[blank]_ of the original segment's length.
Answer:
multiple
Step-by-step explanation:
I had the same question and guessed and that was the answer lol
write an equation involving absolute value for each graph 24-29
Answer:
Step-by-step explanation:
24-29=-5
using the number line:)
Answer:
4-23=4b
Step-by-step explanation:
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x2 = 17.
The solution of the given quadratic equation is x = 1.37, - 1.37.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions .
Given quadratic equation:
9x² = 17
⇒ x² = (17 / 9)
⇒ x = ± √(17 / 9)
⇒ x = ± (√17) / 3
⇒ x = 1.37, - 1.37
Learn more about quadratic equation.
brainly.com/question/17177510
#SPJ4
#12: If the slope of a linear function is m = 6/5, how much
does the output change, when the input is decreased by 30?
The output changes by:
By using unitary method, it can be calculated that
When input decreases by 30, output decreases by 36
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
This is a problem on unitary method
Slope = [tex]\frac{6}{5}\\[/tex]
When input decrease by 5, output decreases by 6
When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]
When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]
When input decreases by 30, output decreases by 36
To learn more about unitary method, refer to the link -
https://brainly.com/question/24587372
#SPJ1
if each side is increased by 50℅.then find the increase percentage in its surface area
Answer:
Formula used:The surface area of cube = 6 side2
Calculation:According to the question,
Let the side of the cube be x
Each side of the cube increased by 50%.
= x(100 + 50)/100 = 1.5x
The surface area of the cube
⇒6x²
The new surface area of the cube (side = 1.5x)
⇒ 6 × 2.25x²
Increase percentage in the surface area
⇒((6 x 2.25 x²-6x²)/6 x² }× 100
⇒ 125%
The percentage increase in the surface area is 125%.Find the length indicated
Answer: 20
Step-by-step explanation:
Using the side splitter theorem yields:
[tex]\frac{?}{5}=\frac{12}{3}\\\\\frac{?}{5}=4\\\\?=20[/tex]
Answer:
20
Step-by-step explanation:
the scale factor from the little triangle to the larger triangle is 5/4
[tex]\frac{5x}{4}[/tex] = x + 5 Multiple through by 4 to clear the fraction
5x = 4x + 20 Subtract 4x from both sides
x = 20
The
approximate average distances from
the sun to Venus and Mercury are listed
below:
Venus: 1.08 x 108 kilometers
Mercury: 5.79 × 107 kilometers
How much closer to the sun is Mercury?
Express your answer using scientific
notation.
The subtraction of significant figures between the distance is 5.01 × 10⁷km
SubtractionIn this problem, we have to subtract the difference between the distance of Venus and Mercury. When subtracting significant digits, the amount of significant digits that will be in the final answer is determined by the number of significant digits present after the decimal place in the numbers we are subtracting.
The distance between Venus and Mercury can be calculated as
1.08 × 10⁸ - 5.79 × 10⁷ = 50,100,000km
To express the value in significant figures, we will have
50,100,000 = 5.01 × 10⁷km
Learn more on subtraction here;
https://brainly.com/question/17301989
#SPJ1
Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for how many days does he rent the backhoe?
To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
What is backhoe?
A backhoe, also known as a rear actor or back actor, is a type of digging apparatus, often known as a digger, that has a digging bucket attached to the end of a two-part articulated arm. Usually, it is attached to the rear of a tractor or front loader, the latter of which is known as a "backhoe loader."
$286.50/$95.50= 3
Henry is building an in-ground pool at his house. He is doing most of the work himself to save money. To dig the pool, he rents a small backhoe for $95.50 a day. If his total bill comes to $286.50, for 3 days does he rent the backhoe.
To learn more about backhoe visit:https://brainly.com/question/29666192
#SPJ1
Write the equation of the line...
through: (-3, 1) with slope: 2
y = mx + b
Answer:
Step-by-step explanation:
Step 1: Use point-slope form and substitute in the x and y values
y-y1=m(x-x1)
y-(1)=2(x-(-3))
Step 2: Simplify the expression
y-1 = 2(x+3)
Add one to the other side
y= 2(x+3)+1
Multiple 2 by (x+3)
y=2x+6+1
Add common terms
y=2x + 7
Based on this projection, which of the following is closest to the number of t-shirts Marcus needs to sell during the first month to meet his goal? (100 brainley points plsss help)
Answer:
A. 1,500
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]
The given scenario can be modelled as a geometric series.
If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:
Sum Sₙ = 15,000n = 6If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:
r = (1 + 0.2) = 1.2Substitute these values into the formula and solve for a:
[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]
[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]
[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]
[tex]\implies a=1510.586188[/tex]
Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.
Check:
Month 1 = 1511Month 2 = 1511 × 1.2 = 1813Month 3 = 1813 × 1.2 = 2176Month 4 = 2176 × 1.2 = 2611Month 5 = 2611 × 1.2 = 3133Month 6 = 3133 × 1.2 = 3760Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004
Check:
Month 1 = 1500Month 2 = 1500 × 1.2 = 1800Month 3 = 1800 × 1.2 = 2160Month 4 = 2160 × 1.2 = 2592Month 5 = 2592 × 1.2 = 3110Month 6 = 3110 × 1.2 = 3732Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000
If $42,400 is invested at an interest rate of 6% per year, find the value of the investment at the end of 5 years if interest is compounded annually, semiannually, monthly, daily, or continuously. Round to the nearest cent.
Annual=
Semiannual=
Monthly=
Daily=
Continuously=
The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.
What is compound interest?
Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.
Given, Principal (P) = $42,400
interest rate(r) = 6% per year = 0.06
time(t) = 5 years
The compound amount is given by
[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]
For compounded annually, n=1
[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76
For compounded semi-annually, n=2
[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05
For compounded monthly, n=12
[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25
For compounded daily, n=365
[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60
For compounded continuously,
[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01
Hence, these are the required values of the compound amount.
To learn more about compound interest
https://brainly.com/question/3989769
#SPJ1
The population of a city is 4786000 in 1980. In 1990 the population had increased by 1.5%. What was the population in the year 2000 if it increased a further 1.2% from 1990 (in whole people)?
Answer:
4 916 083
Step-by-step explanation:
population in 1990
1.5 : 100 = x : 4 786 000
x = 1.5 · 4 786 000 / 100
x = 1.5 · 47 860
x = 71 790
4 786 000 + 71 790 = 4 857 790
population in 2000
1.2 : 100 = x : 4 857 790
x = 1.2 · 4 857 790 / 100
x = 0.012 · 4 857 790
x = 58 293.48
4 857 790 + 58 293.48 = 4 916 083.48