Here we will use the formula of compound interest which is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
A=amount
P=principal
r=rate of interest
n=number of times interest is compounded in a year
t=time
We are given,
r=2% or 0.02
t= 5 years
n =4( compounded quarterly)
A= $300
Let us plug these in the formula to find Principal
[tex]300=P(1+\frac{0.02}{4})^{4*5}[/tex]
[tex]300=P(\frac{4.02}{4})^{4*5}[/tex]
[tex]300=P(1.005)^{20}[/tex]
[tex]300=P(1.105)[/tex]
Principal = $271.49
Answer: Mark earned $271.49 during odd jobs.
To calculate the original amount Mark earned, the compound interest formula is used with the given interest rate, compounding frequency, future amount, and time period. After solving for the principal amount, it's determined that Mark originally earned approximately $271.73.
In order to determine how much Mark originally earned, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Given that the final amount A is $300.00, the annual interest rate r is 2%, the interest is compounded quarterly (so n is 4), and the time t is 5 years, we can plug these values into the formula and solve for P:
300 = P(1 + 0.02/4)⁴*⁵
300 = P(1 + 0.005)²⁰
300 = P(1.005)²⁰
To find P, we divide both sides by (1.005)²⁰:
P = 300 / (1.005)²⁰
Using a calculator, we can find that:
P ≈ 300 / 1.10408
P ≈ 271.73
Therefore, Mark originally earned approximately $271.73 doing odd jobs last summer.
Which of the binomials below is a factor of this trinomial x^2+13x+42
If 5 friends wanted to share 1.25 of a pizza evenly how much each person get
0.25 = [tex]\frac{1}{4}[/tex]
1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
there are 5 quarters thus each person woud get one quarter
Given the formula for the perimeter of a rectangle where l represents the length and w represents the width.
2(l + w)
What does the 2 represent in this formula?
A) The 2 represents the perimeter.
B) The 2 represents the two width pairs.
C) The 2 represents the two length pairs.
D) The 2 represents the two sets of length and width pairs.
For this one, I would go with D.
D makes the most sense, giving that there is two sets of each and, that it is just a shorter way to say "add all the sides."
B and C would only give us half or part of the perimeter and then A does not make much sense.
D would be the answer through process of elimination.
Negative one fourths times negative six elevenths
You multiply fractions simply by multiplying numerators and denominators with each other:
[tex] -\dfrac{1}{4} \times \left(-\dfrac{6}{11}\right) = \dfrac{1 \times 6}{4 \times 11} = \dfrac{6}{44} = \dfrac{3}{22} [/tex]
What does it mean if a check was skipped on a bank statement? A. The check may not have been cashed or deposited yet. B. The check was written for more money than was available in the account. C. The account holder wasted money by not using a check. D. The bank will charge a fee for the skipped check.
Answer:
A. The check may not have been cashed or deposited yet.
Step-by-step explanation:
Our bank statements contains all our transactions like the debits or withdrawals, credits or deposited amounts and checks deducted etc.
And all the transactions are ordered date wise.
So, if a check was skipped on a bank statement, that means the check has not been cashed yet.
Answer:
A for plato
Step-by-step explanation:
An oven temperature is set to 329 degrees f. What is this setting closest to in degrees celsius?
It is 165 degrees celcius
Find r if (r, 6) and (5, -4) are two points on a line with a slope of 5/7 (Hint: use the slope formula)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]
Substitute
[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]
Please help with one question. A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 10x - 0.025x² The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?
The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
For maximum r, r'(x) = 0
It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]
= [tex]10-0.5x=0[/tex]
[tex]x=\frac{10}{0.05}[/tex]
x= 200
Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]
Solving it we get,
r(200) = 1000
Hence, maximum revenue is $1000.
When you multiply 2.54 by 0.2 how may digits are behind the decimal in the answer
Given the graph of a line y=−x. Write an equation of a line which is parallel and goes through the point (−8,2).
y = -x - 6
the equation of a line in ' slope- intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
y = - x is in this form with m = - 1 and c = 0
note that parallel lines have equal slopes thus
the partial equation is y = - x + c
To find c substitute ( - 8, 2 ) into the partial equation
2 = 8 + c ⇒ c = 2 - 8 = - 6
y = - x - 6 ← is the equation of the parallel line
If it is 11:30, what time would it be in 40 minutes?
in 40 minutes it will be 12:10
Which graph represents the solution set of the system of inequalities?
{ x+y<1
2y ≥ x-4
Answer:
The graph in option (c) is the correct answer.
Step-by-step explanation:
The line corresponding to the inequality [tex]x+y<1[/tex] represents the dashed line and the line corresponding to the inequality [tex]2y\geq x-4[/tex] represents the solid line.
In order to figure out the correct shaded region, we test one point from each of the four possible regions and figure out the point at which both the inequalities bold true. The region containing that point would be the correct shaded region.
Let us test the point (0,0).
First inequality [tex]0+0<1[/tex], that is, [tex]0<1[/tex] holds true.
The second inequality [tex]2(0)\geq 0-4[/tex] that is, [tex]0\geq -4[/tex] as well holds true.
Since both the inequalities hold true at point (0,0), therefore, region containing origin is the correct answer. Thus, the correct answer is forth option. Since the options are not labeled, I have attached the correct graph with my solution in order to make sure you get the correct answer.
PLEASE HELP! The high school band wants to sell two types of cookies, chocolate chip and peanut butter, as a fundraiser. A dozen chocolate chip cookies requires 2 cups of flour and 1 egg. A dozen peanut butter cookies uses 3 cups of flour and 4 eggs. The club has 90 cups of flour and 80 eggs on hand. The profit on the chocolate chip cookies is $1 per dozen and on the peanut butter is $1.50 per dozen. If they want to offer both types of cookies, how many of each cookie should the club make to maximize profits?
a.
infeasible solutions
c.
24 dozen chocolate chip
14 dozen peanut butter
b.
30 dozen chocolate chip
25 dozen peanut butter
d.
20 dozen chocolate chip
18 dozen peanut butter
Answer:
24 dozen chocolate chip
14 dozen peanut butter
Step-by-step explanation:
x = number of dozen chocolate chip cookies
y = number of dozen peanut butter cookies
Total number of cups of flour is:
2x + 3y ≤ 90
Total number of eggs is:
x + 4y ≤ 80
Total profit is:
P = x + 1.5y
Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.
But let's try solving this algebraically. x and y are positive integers, and we want them to be as large as possible.
Let's start by assuming the solution is on the line 2x + 3y = 90.
x + 4y ≤ 80
2x + 8y ≤ 160
90 − 3y + 8y ≤ 160
5y ≤ 70
y ≤ 14
If y = 14, x = 24, and P = 45.
Now let's assume the solution is on the line x + 4y = 80.
2x + 3y ≤ 90
2 (80 − 4y) + 3y ≤ 90
160 − 8y + 3y ≤ 90
70 ≤ 5y
14 ≤ y
Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.
Which construction is illustrated above?
A. a parallel line to a given line from a point not on the line
B. an angle congruent to a given angle
C. the bisector of an angle
D. a perpendicular to a given line from a point on the line
Construction of an angle congruent to a given angle.
.What are congruent angles?Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
For two angles to be congruent their measurements must be equal.
Therefore, we can conclude that the construction above is angle congruent to a given angle.
Learn more about congruent angles here
https://brainly.com/question/28262429
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An angle congruent to a given angle construction is illustrated in the figure. Option B is the right choice.
Congruent angles share an identical measure, establishing equality between their angular dimensions.
In the realm of geometry, the fundamental criterion for angles to be considered congruent is that their measurements are precisely equal. This equality in angular magnitude implies that the angles exhibit indistinguishable orientations and positions.
Consequently, when engaging in geometric constructions, if a constructed angle aligns in measurement with a given angle, it is deemed congruent to the specified angle.
This fundamental concept is pivotal in geometric reasoning and problem-solving, providing a basis for establishing equivalences between angles and facilitating precise angular constructions. In summary, congruent angles signify an equality in measurement, forming a cornerstone in geometric analyses and constructions.
Option B is the right choice.
For similar question on congruent
https://brainly.com/question/29789999
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I need help, can anyone help?
What is the slope of the line that passes through (1, 4) and (1, −3)?
Always remember (y2-y1)/(x2-x1) for finding slope
So (-3)-4 / 1-1=
-7 / 0
So undefined
4. Find mQ
A.) 76
B.) 104
C.) 66
D.) 114
See the attached picture for the solution:
Answer:
76=R
R=76
180-76-38=66
Step-by-step explanation:
Find two consecutive internet's whose sum is 75
37 and 38
consecutive integers have a difference of 1 between them
let n and n + 1 be the consecutive integers, then
n + n + 1 = 75 ( subtract 1 from both sides )
2n = 74 ( divide both sides by 2 )
n = [tex]\frac{74}{2}[/tex] = 37
the integers are 37 and 37 + 1 = 38
Beth has 250 comic books in her collection. She begins to sell 20 of them each week. Martin has 80 comic books in his collection. He begins buying 15 new comic book each weeks
And Whats the question here?!?!
Which values are possible rational roots of 9x^3+14x^2-x+18=0 according to the rational root theorem? Select each correct answer. ±3 ±1/18 ±1/3 ±1/2
ANSWER
The possible rational roots are [tex]\pm3[/tex] and [tex]\pm\frac{1}{3}[/tex]
EXPLANATION
According to the rational roots theorem, the possible rational roots of
[tex]9x^3+14x^2-x+18=0[/tex]
is given by all the possible factors of [tex]18[/tex] which are
[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]
expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is [tex]9[/tex] which are
[tex]\pm1,\pm3,\pm9[/tex]
in their simplest form.
One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.
This will give us
[tex]\frac{\pm9}{\pm3} =\pm3[/tex].
Another possible rational root is
[tex]\pm \frac{1}{3}[/tex].
Hence the correct options are
A and C.
Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.
The possible rational roots of the polynomial 9x^3+14x^2-x+18=0, according to the Rational Root Theorem, are ±3 and ±1/3. The other given options, ±1/18 and ±1/2, do not meet the criteria set by the theorem.
The question asks for the possible rational roots of the polynomial 9x^3+14x^2-x+18=0 according to the Rational Root Theorem. The Rational Root Theorem states that if a polynomial has a rational root p/q, where p and q are integers and q is not zero, then p is a factor of the constant term and q is a factor of the leading coefficient.
The constant term here is 18 and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 9 and its factors are ±1, ±3, and ±9. According to the theorem, we divide each factor of the constant term by each factor of the leading coefficient to determine the potential rational roots:
±1/1, ±1/3, ±1/9
±2/1, ±2/3, ±2/9
±3/1, ±3/3, ±3/9
±6/1, ±6/3, ±6/9
±9/1, ±9/3, ±9/9
±18/1, ±18/3, ±18/9
Out of the list, the values that match the options given in the question are ±3 and ±1/3. The other options, ±1/18 and ±1/2, are not rational roots because 1/18 is not a factor of 9 (leading coefficient), and 2 is not a factor of 18 (constant term) when considering the reduced form.
Which division expression is equivalent to
The correct answer would be A. 13/3 Divided by -5/6
The total answer would be negative 5 1/5
because you do 4x3+1=13 over the denominator that is already there so 13/3 then you do KCF a.k.a keep change and flip you keep 13/3 change the division sign into multiplication sign then you flip the -5/6 to -6/5 then multiply straight across and reduce this is the way my teacher taught me how to remember - to positive kind of things:
when a negative thing or bad thing happens to a good person is that good or bad in this case thats bad because if you think about it if a bad thing happend to someone you care about that would be bad. then that same idea goes for each pattern another example could be a good thing (+) happens to a good person (+) it is good (+)
(+) (+)=+
(-) (-)=+
(+) (-)= -
(-) (+)= -
Hope this helps. Have a good day! :)
WILL GIVE 5 STARS!!
Marshall uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 8² = 64.
What values can Marshall use for x and y?
Answer: C
Step-by-step explanation:
(x - y)²
we want (8)², so need: x - y = 8
There are many options that satisfy x - y = 8 but of the options provided to you, 10 - 2 is the only one that works.
A) 2 - 6 = -4
B) 64 - 0 = 64
C) 10 - 2 = 8
D) 8 - 64 = -56
g(t)=t^3-5t^2
h(t)=-t+5 find
(g/h)(t)
Please help
50pts who ever gets it
Answer:
Step-by-step explanation:
(g/h)(t) = g(t) / h(t)
=( t³-5t² ) /(t+5) we cannot simplify this further so
(g/h)(t) = ( t³-5t² ) /(t+5)
=
Answer:
The awnser is C and trust me
Step-by-step explanation:
11 = − 3k − 22 − 8k
K equals what?
11 = -3k - 22 - 8k
11 = -11k - 22 added like terms (-3k and -8k)
+22 +22
33 = -11k
[tex]\frac{33}{-11} = \frac{-11k}{-11}[/tex]
-3 = k
Answer: k = -3
Ankur estimated the quotient of 15 1/3 divided by -4 2/3 to be 3. Which best describes his error?
Ankur multiplied the compatible numbers 15 and –3.
Ankur found that the quotient of a positive number and a negative number is negative.
Ankur found that the quotient of a positive number and a negative number is positive.
Ankur added the compatible numbers 15 and –3.
When dividing a positive number by a negative number, the result is negative.
A better estimation would be -3.
Solution:
As the two numbers [tex]15 \frac{1}{3} {\text{and} -4\frac{2}{3}[/tex] are mixed fractions.
[tex]15 \frac{1}{3}= \frac{46}{3} \\\\ -4\frac{2}{3}= \frac{-14}{3}[/tex]
Now, [tex]\frac{ \frac{46}{3}}{\frac{-14}{3}}[/tex] = - 3
Ankur's answer= 3
The mistake he has committed , while dividing two fractions , he must have forgot that one of the fraction which is in the denominator bears negative sign before it.
So, [tex]\frac {+}{-}= -[/tex].
Ankur forgot to put negative sign before 3.
So, The correct option which describes ankur's error is : Ankur found that the quotient of a positive number and a negative number is positive.
Option 3 is right choice.
What are the outliers in this data set 78, 87, 81, 16, 64, 100, 88, 10, 87, 110, 108, 149
Answer: 10 & 16
Step-by-step explanation:
Triangle KLM was dilated according to the rule DO,0.75 (x,y). What is true about the image △K'L'M'? Check all that apply. DO, 0.75 (x,y) = (0.75x, 0.75y) LM is parallel to L'M'. KM is shorter than K'M'. The vertices of the image are closer to the origin than those of the pre-image. The distance from M' to the origin is exactly half the distance from M to the origin.
Answer: The correct statements are 0.75 (x,y) = (0.75x, 0.75y) , LM is parallel to L'M' and "the vertices of the image are closer to the origin than those of the preimage".
Explanation:
It is given that the triangle ABC was dilated according to the rule DO,0.75 (x,y)
DO, 0.75(x,y) represents the rule of dilation. Where both x- and y-coordinates are multiplied by 0.75 the dilation is about the origin has a scale factor of 0.75. The notation for this dilation would be,
[tex](x,y)\rightarrow (0.75x,0.75y)[/tex]
Therefore, the first statement is true.
Since both x- and y-coordinates are multiplied by 0.75, therefore the sides of image and preimage are parallel but the sides of image are 0.75th of the side of preimage.
Therefore, the second statement "LM is parallel to L'M'" is true but the third and fifth statement is false.
The scale factor is 0.75 which is less than 1, so the vertices of the image are closer to the origin than those of the pre-image.
Therefore, the forth statement "The vertices of the image are closer to the origin than those of the pre-image" is true.
Answer: 124
Step-by-step explanation:
What needs to happen for the equation CH4 + O2 → CO2 + H2O to be balanced?
A. A coefficient of 2 must be added before both products.
B. A coefficient of 2 must be added before the second reactant and the second product.
C. Nothing, the equation is already balanced.
D. A coefficient of 2 must be added before both products and reactants.
Geoff has a bag that contains 4 red marbles and 6 blue marbles. He chooses two marbles at random and does not replace them. What is the probability that the first marble is blue and the second marble is red? A. B. C. D.
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
First pick (blue) and Second pick (red)
[tex]\frac{6}{10}[/tex] x [tex]\frac{4}{9}[/tex]
= [tex]\frac{6(4)}{10(9)}[/tex]
= [tex]\frac{2(2)}{5(3)}[/tex]
= [tex]\frac{4}{15}[/tex]
Answer:
The answer is 4/15 hopefully this helps!
Name the complex conjugate. Then find the product. 1. -8i
You seem to be missing some information here.
Complex conjugate example:
2 - 16i >> 2 + 16i
Are you sure this is the entire question?
For this case we have a complex number of the form:
[tex]a + (b) (i)\\[/tex]
Where:
a: It's the real part [tex](b) (i)[/tex]: It is the imaginary partThus, given 1-8i, its complex conjugate is given by:
[tex]1 + 8i\\[/tex]
On the other hand, the product of both is given by:
[tex](1 + 8i) (1-8i) =\\\\(1 ^ 2-8i + 8i-64 (i ^ 2)) =\\\\1-64 (-1) =\\\\1 + 64 = 65\\[/tex]
Answer:
Conjugate complex: [tex]1 + 8i\\[/tex]
Product: 65
What is the equation of the line with a slope of 3/4 that goes through the point (4,1) in slope-intercept form ?
The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
We have
[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute:
[tex]y-1=\dfrac{3}{4}(x-4)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
Solve for y:
[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]
Answer: D.