m = –3 and b = –3 or A
Write an equation of the line pictured in the graph.
1.4 + 2/5x = 3/15x - 0.8 How do you solve this?
An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
Final answer:
The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
Explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)Using the given information, we can plug in the values and solve for r:
$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
The interest rate, for continuous compounding, is approximately 5.775%.
To find the interest rate for continuous compounding, we can use the formula for compound interest:
[tex]\[ A = P \times e^{rt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount of money,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),
- [tex]\( t \)[/tex] is the time the money is invested for (in years),
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
Given:
- [tex]\( P = $750 \)[/tex],
- [tex]\( A = $1500 \)[/tex],
- [tex]\( t = 12 \)[/tex] years.
We need to solve for [tex]\( r \)[/tex], the interest rate.
Step 1 :**Substitute the Given Values into the Formulaa :
[tex]\[ 1500 = 750 \times e^{12r} \][/tex]
Step 2 :**Divide Both Sides by 750**:
[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]
[tex]\[ 2 = e^{12r} \][/tex]
Step 3 :**Take the Natural Logarithm of Both Sides**:
[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]
[tex]\[ \ln(2) = 12r \ln(e) \][/tex]
[tex]\[ \ln(2) = 12r \][/tex]
Step 4 :**Solve for [tex]\( r \)[/tex]**:
[tex]\[ r = \frac{\ln(2)}{12} \][/tex]
[tex]\[ r = \frac{0.693}{12} \][/tex]
[tex]\[ r = 0.05775 \][/tex]
Step 5 :**Convert the Interest Rate to a Percentage**:
[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]
[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]
So, the interest rate is approximately 5.775%.
A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
1. Fifteen is a factor of the number because both 3 and 5 are prime factors.
2. Fifteen is not a factor of the number because 15 is odd and the number is even.
3. Sixteen is a factor for the number because 2^3=8 and 16 is divisible by 8.
4. Sixteen is not a factor of the number because the exponent of 2 is not even.
Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.
Given :
Number -- [tex]2^3\times 3^2\times 5[/tex]
The following steps can be used in order to determine the correct statement:
Step 1 - Write the given number.
[tex]2^3\times 3^2\times 5[/tex]
Step 2 - Simplify the above expression.
[tex]= 8\times 9 \times 5[/tex]
Step 3 - Multiply 8 by 9 in the above expression.
[tex]= 72\times 5[/tex]
Step 4 - Multiply 72 by 5 in the above expression.
= 360
Step 5 - 15 is a factor of 360.
Therefore, the correct option is 1).
For more information, refer to the link given below:
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Write an inequality for the sentence. Then solve the inequality. Fifteen less than a number is at most 6.
pls help
The requried inequality for the sentence is x - 15 ≤ 6 and the solution to the inequality is x ≤ 21.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The inequality for the sentence "Fifteen less than a number is at most 6" can be written as:
x - 15 ≤ 6
where x represents the unknown number.
To solve for x, we will add 15 to both sides of the inequality:
x - 15 + 15 ≤ 6 + 15
Simplifying,
x ≤ 21
Therefore, the solution to the inequality is x ≤ 21.
Learn more about inequality here:
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helpppppppppppppppppppppppp
A field project superintendent earns an annual salary of $72,800, and she contributes $7900 per year to her 401(k) plan. If she has a required deduction for income taxes (federal, state, and local combined) of 28% of pretax income, how much does she have withheld in income taxes per year?
Find the value of the missing side of a triangle practice
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Answer: [tex]80.47\ m^2 [/tex]
Step-by-step explanation:
The area of a sector is given by :-
[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]
Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]
radius = 12.4 m
Then,
[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]
Can someone help me please I would appreciate it.
I well mark brainliest if u explain
Please.
WILL GIVE A BRAINLEST!!!!!!
Solve and check : c-4/c-2=c-2/c+2 - 1/2-c
The solution is c =
How many extraneous solutions are there?
The solution is c = 14
How many extraneous solutions are there? zero
Let f(x)= -5x+6. Find and simplify f(3n−5).
f(3n-5)= ?
the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed. what represents the area of the tabletop
Will mark brainliest.. There are 3 questions related to the problem in the first picture. please help thanks.
The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the number of minutes. On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer matches the graph you drew, including the correct axis labels.
The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.
What is a slope?If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of a line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The characteristics of the graph of the equation c(x) = 3x + 2.00.
The graph of c(x) = 3x + 2.00 is a straight line with a slope of 3 and a y-intercept of 2.00.
The x-axis represents the number of minutes, and the y-axis represents the cost in dollars.
The slope of 3 indicates that for every additional minute of the taxi ride, the cost increases by $3.
The y-intercept of 2.00 indicates that even if the ride was 0 minutes, there is still a flat fee of $2.00.
To learn more about the slope;
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.
The acronym CPCTC stands for “__________ parts of congruent triangles are congruent.”
calculated
congruent
corresponding
coordinated
The acronym CPCTC stands for " Corresponding parts of congruent triangles are congruent. "
Step-by-step explanation:CPCTC--
It is a rule which states that if any of the two triangles are congruent by any of the congruency such as ASA, RHS , SAS or SS then the remaining sides and the remaining angles which were not covered in the congruency are also congruent.
Also, the acronym is:
Corresponding parts of congruent triangles are congruent.
what is 1,000,000,000 x 1,000,000,000
PLEASE HELP
7.03
1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...
A) summation of one times three to the power of n from n equals zero to infinity
B) summation of one times three to the power of the quantity n plus one from n equals zero to infinity
C) summation of one times negative three to the power of n from n equals zero to infinity
D) summation of one times negative three to the power of the quantity n plus one from n equals zero to infinity
2. Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131
A) summation of the quantity negative four plus nine n from n equals zero to fifteen
B) summation of negative thirty six times n from n equals zero to fifteen
C) summation of the quantity negative four plus nine n from n equals zero to infinity
D) summation of negative thirty six times n from n equals zero to infinity
3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n2 + ...
A) summation of n squared from n equals five to infinity
B) summation of n minus one squared from n equals five to infinity
C) summation of n squared from n equals six to infinity
D) summation of n plus one squared from n equals five to infinity
4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17
A) 56
B) 63
C) -7
D) 20
5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six
A) 341
B) one divided by one hundred and ninety two
C) one divided by seven hundred and sixty eight
D) three hundred and fourty one divided by two hundred and fifty six
6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...
Does the equation x2 - 4x + y2 = -3 intersect the x-axis?
Answer:
Yes, because the center is on the x-axis.
Step-by-step explanation:
First, write the equation in standard form by completing the square.
x2 - 4x + y2 = -3
x2 - 4x + 4 + y2 = -3 + 4
(x - 2)2 + y2 = 1
The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).
Which polynomial is a quintic trinomial?
x³ + 2x² -8x + 16
x² + 4
3x⁵ + 7x² -9x⁴
-x⁴ -5x² +1
Answer:
3x⁵ + 7x² -9x⁴
Step-by-step explanation:
In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...
3x⁵ + 7x² -9x⁴
Steve ordered plastic cases for storing his baseball cards. Each case has a length of 12 centimeters, a width of 6.5 centimeters ,and a height of 1.25 centimeters, what is the volume, in cubic centimeters, of one baseball card case?
Answer:
97.5
Step-by-step explanation:
what is the slope of the line through (2,-2) and (9,3)
What is the sum of the “outer” and “inner” products as described in the FOIL method when multiplying (x + 5)(x - 6)?
A. -6x
B. -x
C. x
D. 5x
Answers anybody???????
30 POINTS + BRAINLIEST!
We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]
By using the complementary angle formula which states:
[tex] \cos (90-\Theta )=\sin \Theta [/tex]
Now,
[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]
Therefore, we get
[tex] 90-(x+22)= (2x-7) [/tex]
[tex] 90-x-22= (2x-7) [/tex]
[tex] 68=3x -7 [/tex]
[tex] 75=3x [/tex]
[tex] x=25^{\circ} [/tex]
Answer:
Lets go by a step-by-step process.
Step-by-step explanation:
\cos (90-\Theta )=\sin \Theta
Now,
\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}
Now we have...
90-(x+22)= (2x-7)
90-x-22= (2x-7)
68=3x -7
75=3x
x=25^{\circ}
A metal Fabricating Company produces 150,000 souvenir tokens each year. In a random sample of 400 tokens, 3 have stamping errors. Predict the total number of coins that will have stamping errors in a year.
Which expression is equivalent to the given expression? 17x−32x A. x(32−17) B. 17(x−32) C. 17x(1−32) D. x(17−32)
If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?
I NEED HELP SO BAD PLEASE PLEASE PLEASE
Which graph represents y – 1 = 2(x – 2)?
Answer:
The graph is attached below
Step-by-step explanation:
y – 1 = 2(x – 2)
y-1 = 2x - 4
add 1 on both sides
y = 2x - 3
To graph the given equation we make a table
Plug in some number for x and find out the value of y
x y = 2x-3
-1 2(-1)-3= -5
0 2(0) -3= -3
1 2(1) -2= -1
The point to get the graph of the given equation is
(-1,-5) (0,-3) (1,-1)
The graph is attached below
Answer:
The answer is the first graph or graph A.
BTW this is just the short answer...
Its quicker. :-)