a) the formula for r is r = (a/p - 1)/r
b) The interest rate for the principal is $1000, the time is 2 years and simple inters $1080 is 0.04
c) The formula for p is p = a/1+rt
Simple Interest:
Simple interest is the process of multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given,
the amount a of money in an account after simple interest has been earned is given by the formula
=> a = p + prt
where
p is the principal,
r is the annual interest rate in decimal form, and
t is the time in years.
Here we need to find the following:
a. solve the formula for r
b. the amount of money in an account after interest has been earned is $1080, the principal is $1000, and the time is 2 years. what is the annual interest rate?
c. solve the formula for p.
a) The formula for r is calculated by moving the other elements and hold on r.
Then, the given formula,
=> a = p + prt
=> a = p (1 + rt)
=> a/p = 1 + rt
=> a/p - 1 = rt
=> r = (a/p - 1)/r
b) The given values are
p = $1000
t = 2
a = $1080
Now apply the values on the formula r to find the value of it,
=> r = ([1080/1000] - 1)/2
=> r = (1.08 - 1) /2
=> r = 0.08/2
=> r = 0.04
c) The formula for p can be derived as follows:
=> a = p + prt
=> a = p(1+rt)
=> p = a/1+rt
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3y+4x=9
I have to find the literal solution
Answer:
Step-by-step explanation:
3−4x/3 this is for x
y = -4/3x + 3 this is for why I’m not sure which one your trying to solve for
Find the greatest common factor for each problem.use the t-chart to slow?
16 and 40
Gcf:
The required GCF is 8.
The greatest common factor is that greatest number from the factors which divides the number completely.
For example take numbers 12 and 16.
The factors of 12 are 2×2×3.
And the factors of 16 are 2×2×2×2.
We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.
Here it is given to find the greatest common factor of 16 and 40.
Factors of 16 = 2×2×2×2
Factors of 40 = 2×2×2×5
We can see clearly the common factors are 2×2×2 which gives 8.
So, 8 is the greatest common factor.
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What is it asking for??
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
Using exponent properties, the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
What is the equivalent expression?The original expression is:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]
When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]
The negative exponent at the numerator goes to the denominator, hence:
[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]
The negative outer exponent means that we have to exchange the numerator and denominator, hence:
[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
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Answer:
y^18/x^18
Step-by-step explanation:
A snail moves at a pace of 2 ft/min. how fast does the snail move in inches/hour?
The snail move at the pace in 1440in/hr.
Speed:
Speed is measured as the ratio of distance to the time in which the distance was covered.
Speed is a scalar quantity as it has only direction and no magnitude.
Given,
A snail moves at a pace of 2 ft/min.
Here we need to find how fast does the snail move in inches/hour.
We know that,
1 ft/min = 720.00 in/h
So, here we have 2 feet/minute.
That is equal to
=> 2 x 720.00 in/h
When we multiply it then we get the value of,
=> 1440 in/hr
Therefore, the snail move at the pace in 1440in/hr.
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Classify the angle as acute , obtuse , right , or straight
Answer:
1. straight
2. right
3. obtuse
4. acute
Step-by-step explanation:
Simplify: 3/4y - 2/4y + 7 = 2/4y - 1. Show your work.
help please
I'm assuming the equation is
[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]
Let me know if the equation is different so I can update the solution.
-----------------
Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").
If we multiply both sides by 4, then all the denominators of 4 will cancel.
We'll have these steps:
[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]
Final Answer: y = 32Answer:
[tex]y=32[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]
Therefore "y = 32."
Hope this helps.
A point that is Interior to an Angle is found on the Exterior of the Angle
Select the correct response:
True
False
True
the sum of interior angles is equal to exterior
A point that is Interior to an Angle is found on the Exterior of the Angle
The statement is false
How do we explain?
A point that is interior to an angle is located within the angle, not on the exterior. The interior of an angle refers to the region enclosed by the angle's sides.
A point that is interior to an angle is located within the angle, not on the exterior. When we refer to the interior of an angle, we are referring to the space enclosed by the angle's sides and vertex.
In geometric terms, an angle consists of two rays that share a common endpoint called the vertex. The interior of the angle is the region between these two rays while on the other hand, the exterior of an angle refers to the space outside the angle, beyond its sides.
In conclusion, a point that is interior to an angle is found within the angle itself, not on the exterior.
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Identify the slope and y intercept of the line for
each equation.
7. y = -5x - 3/4
8. y=1/4x+5
Answer:
7. Slope = -5
Y-intercept = -3/4
8. Slope = 1/4
Y-intercept = 5
Step-by-step explanation:
y = mx + b
Slope = m
Y-intercept = b
how do i solve this equation
Answer:
[tex]\frac{9b}{a^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{a^{2} }{b}(\frac{3b}{a^{2} })^{2}[/tex]
[tex]\frac{9a^{2}b^{2} }{a^{4}b }[/tex]
[tex]\frac{9b}{a^{2} }[/tex]
9x+1-x^2
write in standard form
Answer:
−[tex]x^{2}[/tex] + 9x + 1
Step-by-step explanation:
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece . find the leg of each piece
One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
Here,
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .
We have to find the leg of each piece.
What is Length, Width and height?
The length, width and height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.
Now,
If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.
And, since the other piece is 12 inches longer than your first piece, its length is x + 12.
And, when you place these two pieces back together, their lengths should add up to be 72 inches.
You can write this last statement about adding the two pieces together to get a 72 inch piece
In equation form as:
x + (x+12) = 72
2x + 12 = 72
To solve this begin by subtracting 12 from both sides;
2x = 60
Now just divide both sides by 2 to find that:
x = 30
So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
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What is
3² + √25 [2²(2² - 3)(5² - 4²) - 201]
list the variables and constants in this expression:
3x+6
Answer:
The variable is x and the constant is 6. The coefficient of the variable is 3.
Step-by-step explanation:
If the domain of the function f(x) = 3x -2 is {-1, 0, 1}, what is the range of the function?
When x = -2:
f(-2) = -3 (-2) + 1
f(-2) = 6 +1
f(-2) = 7
y = 7
When x = 0:
f(0) = -3 (0) + 1
f(0) = 0 +1
f(0) = 1
y = 1
When x = 3:
f(3) = -3 (3) +1
f(3) = -3 (3) + 1
f(3) = -9 +1
f(3) = -8
y = -8
So, the Range is {7, 1, -8}
Assignment Active
Solve and write about ratios.
Students voted for a new class president and the results What does the ratio 344:109 represent?
are shown in the table.
O Jocelyn's votes to total votes
O Rosalia's votes to Danny's votes
O total votes to Jocelyn's votes
O total votes to Danny's votes
Assignment
Candidate
Rosalia
Jocelyn
Danny
Intro
Votes
124
109
111
Who votes to who’s votes
The answer to this question is:
Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.
A ratio in mathematics shows how frequently one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of orange to lemon is eight to six (that is, 8:6, which is equal to the ratio of 4:3).
According to the question,
No. of votes Rosalia got = 124
No. of votes Jocelyn got = 109
No. of votes Danny got = 111
No. of votes received by all candidates =
= 124 + 109 + 111
= 344
So, the ratio 344:109 is the ratio of the total votes to Jocelyn's votes.
Therefore, Ratio 344:109 represents the ratio of the total votes to Jocelyn's votes.
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Abbey wants to use her savings of $1,325 to learn yoga. the total charges to learn yoga include a fixed registration fee of $35 and a monthly fee of $50. choose the inequality that would be used to solve for the maximum number of months for which abbey can learn yoga with her savings. 35x 50 ≤ 1,325 35 50x ≥ 1,325 35 50x ≤ 1,325 35x 50 ≥ 1,325
Answer:
Step-by-step explanation:
Take 1325-35=1290. 1290/30= 43. She will be able to learn 43 Yoga for 43 months.
I need help on this!!
I don’t see the lateral height, how do I solve for this??
Solve 2 (x-3) ≥-3 (−3+x).
A. x ≤2
B. x <3
C. x ≥3
D. x ≥ 2
[tex]2(x-3)\geqslant -3(-3+x)\implies 2x-6\geqslant 9-3x\implies 2x\geqslant 15-3x \\\\\\ 5x\geqslant 15\implies x\geqslant \cfrac{15}{5}\implies x\geqslant 3[/tex]
how many seconds are in 10 1/2 minutes
Answer:
630 seconds
Step-by-step explanation:
1 minute = 60 seconds
Number of minutes × Number of seconds per minute = Number of seconds in total
60 × 10 ½ = 630 seconds
Hope this helped! ^^
If f(x) = x² – 1, and
g(x) = x + 2, then
f(g(x)) = [? ]x²+[ ]x + []
CAN SOMEONE HELP ME PLEASE I don't know what -2 1/3+(-1 3/4)=? in factions
The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12
How to evaluate the fraction?The fraction expression is given as
-2 1/3 + (-1 3/4) =
Express the terms of the expression as an improper fraction
So, we have
-2 1/3 + (-1 3/4) = -7/3 + (-7/4)
Remove the bracket in the above expression.
So, we have
-2 1/3 + (-1 3/4) = -7/3 - 7/4
Take the LCM in the above expression.
So, we have
-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12
Evaluate the difference
-2 1/3 + (-1 3/4) = -49/12
Express the fraction as a mixed fraction
-2 1/3 + (-1 3/4) = -4 1/12
Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12
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1. (-32) (-3) =? 2. (79) (-2) =?
Answer:
1. = 96
2. = -158
Step-by-step explanation:
When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative
f(x) = 12x + 10 is a function which can used to to calculate a person's daily paycheck.
Which would be a reasonable domain for this function?
A: all real numbers
B: 0
C: 0
D: 0
This shows that a reasonable domain for this function is x > -5/6
Domain of a functionThe domain of a function is a value of the independent variable of the function for which it exists.
Given the equation below:
f(x) = 12x + 10
Since the function represents the expression used calculate a person's daily paycheck, then the function f(x) must be greater than zero;
12x + 10 > 0
12x > -10
x > -10/12
x > -5/6
This shows that a reasonable domain for this function is x > -5/6
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A "size 7" shoe is about 1.4 x 10-¹ meters long. The circumference of the earth is about meters 1.06 x 10^7 around the equator. How many shoes, end-to-end, would it take to wrap around the equator? Show how you expanded and used the Giant One.
Number of shoes needed to wrap around the equator = 7.57 x10⁷
The length of a size 7 shoe = 1.4 x 10-¹ m
The circumference of the Earth around the equator = 1.06 x 10^7 m
We know that here, the circumference around the equator will be equal to the number of shoes times the length of each shoe.
So to find the number of shoes, we should divide the circumference of the Earth by the length of one shoe.
Hence, number of shoes end-to-end needed to wrap around the equator = 1.06 x 10⁷ / 1.4 x 10-¹
= 7.57 x10⁷
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I need help is -2x=3/8 a literal equation?
The equation -2x=3/8 is not a literal equation.
What is a literal equation?A literal equation can be defined as an equation which primarily of letters.
It is an equation made up of several variables or letters.
Examples of literal equations are;
V = dts = ut + 1/2 at^2Area = πr²D = m/ vWe can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.
Given the equation;
-2x=3/8
We can see that there is only one variable to be worked out and hence, is not a literal equation.
Thus, the equation -2x=3/8 is not a literal equation.
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What is the mode for this problem?
Simply completely:
5y(xy^3)^2
Answer:
5y^7x^2
Step-by-step explanation:
5y (xy^3)^2
apply product rule: xy^3
5y(x^2(y ^3)^2)
multiply exponents: (y^3)^2
5y(x^2y^6)
Add exponents: y and y^6
5y^7x^2
what following is (are)the solution to(x-3)=7x-4
Answer:
Step-by-step explanation:
The X is equal to 1/6.
Meaning that the X is 1/6.
Answer:
x = 1/6
Step-by-step explanation:
(x - 3) = 7x - 4
x = 7x -1
-6x = -1
-x = -1/6
x = 1/6
Which of these is an example of a systematic random sample?
a.) selecting all the students in a class of 30.
b.) selecting 4 balls from a bag containi
An example of a systematic random sample will be selecting 4 balls from a bag containing. The correct option is B.
What is systematic random sampling?A probability sampling technique called systematic sampling involves picking people from the population at regular intervals, such as every 15th person on a list of the population. This can mimic the advantages of straightforward random sampling if the population is arranged in random order.
Here we have two options a.) selecting all the students in a class of 30.
b.) Select 4 balls from a bag containing 30 balls.
Out of the two options, a systematic random sample will be Select 4 balls from a bag containing 30 balls.
Therefore, the correct option is B.
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