8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answers
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46
Related Questions
Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answers
Answer:
The answer is "\(\frac{5\pi}{6}\)"
Step-by-step explanation:
Please find the graph file.
\(h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\\)
If 58% of the people at a certain conference are doctors, 44% are men, and 43% are male doctors, what is the probability that a person selected at random atthis conference is a doctor or man (or both)?Write your answer as a decimal (not as a percentage).
Answers
Given data:
Assume the following events:
Event A = person is a doctor
Event B = person is a man
P(A) = 58% are doctors
P(B) = 44% are men
P(A and B) = 43% are male doctors
Find: probability that a random person is a doctor or a man or both (A or B)
Solution:
\(\begin{gathered} P(\text{A or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=0.58+0.44-0.43 \\ P(A\text{ or B)}=0.59 \end{gathered}\)Answer: The probability that a person selected at random at
this conference is a doctor or man (or both) is 59%.
What is the perimeter of this tile? in2 N 4 in. lin
Answers
What is the equation of the following line written in general form? (The y-intercept is -1.)
-2x-y-1=0
2x+y - 1 = 0
2x-y-1 = 0
Answers
There are 2 ways that you can solve this . Either plug in the x and y value into each equation until it is right or rewrite the equation .
the equation in slope intercept form is y=2x-1
When you get y by itself in the last one it is also equal to y=2x-1
For both ways work is attached !
a) If a cube has a volume of 3375 cubic centimeters, how would you write the length of one side as a power? b) If a cube has a volume of 1527 cubic centimeters, what is the length of the sides? Round your answer to two decimal places.
Answers
Given:
The volume of the cube is
\(\begin{gathered} V1=3375cm^3 \\ V2=1527cm^3 \end{gathered}\)Required:
To find the side length of the cube.
Explanation:
The formula for volume of the cube is
\(V=a^3\)Where a is the side length.
(a)
\(\begin{gathered} 3375=a^3 \\ \\ a=\sqrt[3]{3375} \\ \\ a=\sqrt[3]{15^3} \\ \\ a=(15^3)^{\frac{1}{3}} \\ \\ a=15cm \end{gathered}\)1(b)
\(\begin{gathered} 1527=a^3 \\ \\ a=\sqrt[3]{1527} \\ \\ a=11.52cm \end{gathered}\)Final Answer:
(a) The side length is 15cm.
(b) The side length is 11.52cm.
\(\begin{gathered} \sqrt[3]{8}=2 \\ \\ And \\ \\ \sqrt[3]{8}=\sqrt[3]{2^3} \\ \\ =(2^3)^{\frac{1}{3}} \\ \\ =2 \end{gathered}\)Below is the graph of . Translate it to make it the graph of . y2468-2-4-6-8x2468-2-4-6-8
Answers
The graph of y = x^2 should be translated by 1 unit to the right and 3 units up.
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.Therefore, we have the following:
f(x) = x^2
g(x) = f(x - 1) + N
g(x) = (x - 1)^2 + 3
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Amanda tiene 4 bolitas más que Rodrigo, y Patricio tiene una bolita más que el doble de Amanda y Rodrigo juntos. Si en total tienen 103 bolitas, cuantas bolitas tiene Amanda
Answers
Las cantidades de bolitas para cada una de las tres personas son las siguientes:
Amanda: 19 bolitas
Rodrigo: 15 bolitas
Patricio: 69 bolitas
¿Cuántas bolas tienen Amanda, Rodrigo y Patricio?En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:
Amanda
x = y + 4
Rodrigo
y
Patricio
z = 2 · (x + y) + 1
Total
x + y + z = 103
A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:
x + y + 2 · (x + y) + 1 = 103
3 · x + 3 · y = 102
x + y = 34
y + 4 + y = 34
2 · y = 30
y = 15
Luego, determinamos las cantidades de bolitas de Amanda y Patricio:
x = 15 + 4
x = 19
z = 2 · (19 + 15) + 1
z = 2 · 34 + 1
z = 68 + 1
z = 69
ObservaciónEl enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.
The statement is written in Spanish and the language used in the answer is the same of the statement.
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Can someone help me plz
Answers
Answer:
iloveyou
Step-by-step explanation:
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
Answers
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answers
Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No
Which of the following is a true statement about ecology?
Ecology is the study of relationships of living organisms and their environment.
Ecology is the study how animals adapt to their environment.
Ecology studies how living organisms have changed over time.
Ecology studies the difference between living organisms.
Answers
Ecology is the study of relationships of living organisms and their environment
Step-by-step explanation:
Ecology in a simple sense is the the study of ecosystems
Explain how you can use a literal equation to solve a problem.
Answers
Answer:
To solve a literal equation means to rewrite the equation so a different variable stands alone on one side of the equals sign. We have to be told for which variable we want to solve. We started with " P = .." and ended with " W = .. ". That's what it means to "solve a literal equation."
Step-by-step explanation:
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
Answers
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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Find the exact value of sin(x/2) if sec(x) = 7/3 and 400° < x < 430°
Answers
The exact value of sin(x/2) is - √(2/7)
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
\(Sin(\frac{x}{2})= \pm\sqrt{\frac{1-cosx}{2}}\)-------------(1)
Given: sec(x) = 7/3
cos x =1/ sec(x) = 1/( 7/3) = 3/7
(1) becomes sin(x/2) = ± √( ( 1- 3/7)/2 )
= ± √[( 7-3)/7]/2 )
= ± √[(4/7)/2] = ± √(2/7)
when sin(x/2) = - √(2/7), the value of x will be between 400 and 430 degrees
The exact value of sin(x/2) is - √(2/7)
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6 Jamila uses a tape measure to find the length of her desk. It is 1 metre 8.5 centimetres. Write this in metres.
Answers
Answer:
1.085 metres
Step-by-step explanation:
1 cm = 0.01 m
8.5 cm = 0.085 m
1m+0.085m=1.085 metres
Answer:
1.085 metres
Step-by-step explanation:
100 centimetres = 1m
what about 8.5 cm?
Divide the centimetres by 100
8.5/100 = 0.085m
Then add the metre(s) you already have which is 1
thus 0.085 + 1
1.085m
I need the answer to this question
Answers
Answer:
it is not factorable
Step-by-step explanation:
There are no factors of 24 that will make -4, so it is not factorable
13. Find the arc length with the given information . centralangle = pi/4, radius = 6
14. Which angle has its terminal side in the second quadrant?
Answers
Answer:
3π/2; 3π/4
Step-by-step explanation:
The system of equations y = negative 3 x + one-half and y = one-fifth x minus 1 and four-fifths is shown on the graph below.
What is a reasonable estimate for the solution?
(0.7, –1.7)
(–1.7, 0.7)
(1.4, –3.3)
(–3.3, 1.4)
Answers
Answer:
the -1,17,0.7 but if i get it wrong i can give u free points
Step-by-step explanation:
Answer:
-1,17,0.7
Step-by-step explanation:
The angle of elevation to a nearby tree from a point on the ground is measured to be 74^{\circ} ∘ . How tall is the tree if the point on the ground is 54 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the tree whose angle of elevation is \(74^{0}\) and 54 feet tall is 188 foot.
Height of the tree= 188 foot (rounding off nearest tenth)
What is angle of elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know by trigonometric ratios,
\(tan \; \theta = \frac{P}{B}\)
\(tan \; 74^0 \;\) = \(\frac{P}{54}\)
3.48 = \(\frac{P}{54}\)
P= 3.48 x 54
= 187.92 feet
≈ 188 foot (rounding off nearest tenth)
The height of the tree whose angle of elevation is and 54 feet tall is 188 foot.
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Answer: 188.3 feet tall*
Step-by-step explanation:
the shortest side of a right triangle measures 7m. The lengths of the other two sides are Consecutive integers. What is the length of the other two sides?
Answers
The lengths of the other two sides of the right triangle are 24m and 25m, respectively.
Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we have the equation:
\(7^2 + x^2 = (x + 1)^2\)
Expanding and simplifying this equation, we get:
\(49 + x^2 = x^2 + 2x + 1\)
Now, we can cancel out \(x^2\) from both sides of the equation:
49 = 2x + 1
Next, we can isolate 2x:
2x = 49 - 1
2x = 48
Dividing both sides by 2, we find:
x = 24
Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.
Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.
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Pls help 15 points pls hurry
Answers
Answer:
5k and -3k are like variables
constants 7 and -2 are like terms
5+2k+n is equivalent expression
Step-by-step explanation:
If you were to show the followinginformation in a circle graph, howmany degrees would each sector be?C= 39 people with contactsG= 25 people with glassesN= 32 people with neither contacts or glasses
Answers
Explanation
For the given question
We are asked to determine the degrees for each of the sectors
We have that
\(\begin{gathered} C=39\text{ people with contacts} \\ G=25\text{ people with glasses} \\ N=32\text{ people with neither contacts or glasses} \end{gathered}\)We can get the answer using the fact that the sum of angles in a circle is 360 degrees
\(\begin{gathered} So\text{ that} \\ C=\frac{C}{C+G+N}\times360^0 \\ \\ C=\frac{39}{39+25+32}\times360^0 \\ \\ C=146.25^0 \end{gathered}\)Also
\(\begin{gathered} G=\frac{C}{C+G+N}\times360^0 \\ \\ G=\frac{25}{39+25+32}\times360^0 \\ \\ G=93.75^0 \end{gathered}\)Finally
\(\begin{gathered} N=\frac{N}{C+G+N}\times360^0 \\ \\ N=\frac{32}{39+25+32}\times360^0 \\ \\ N=120^0 \end{gathered}\)Therefore, we will have our answer as an option B
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Compare negative one and six tenths repeating and negative five thirds using symbols <, >, or =. negative one and six tenths repeating is less than negative five thirds negative one and six tenths repeating is greater than negative five thirds negative five thirds is equal to negative one and six tenths repeating negative five thirds is greater than negative one and six tenths repeating
Answers
Answer:
-1 6/10
is greater than
- 5/3
Step-by-step explanation:
HELP IM IN K12 AND THERS MORE OF THESE
Answers
if you know the ratio of students to teachers is 5 to 1 and you know there are 15 teachers, how many students are there?
Answers
Answer:
Ratio = 5:1
= 5 / 1
Number of teachers = 15
Lets take the number of students = x
Therefore,
5:1 = x:15
= 5/1 = x/15
x = 15 × 5
= 75 students
Hope it helps!!
HELP PLEASE NEED IT THANKS
Answers
Answer:
<
Step-by-step explanation:
1) Substitute 5 into the question
\(\frac{4(5)}{4}\)\(2(5)-3\)2) Work out the sides
\(\frac{4(5)}{4} =5\)\(2(5)-3=7\)3) Put it into an inequality
5 < 7
Hope this helps, have a great day!
Miklós is filling a questionnaire online. In the diagram, the grey colour indicates the proportion of questions he has already completed.
How many questions are left if he has answered 16 questions so far?
image of the questionnaire attached
Answers
Answer:
e=123444565666 i hope it helps :}}
Step-by-step explanation:
Two identical trains, each with 31 cars, are traveling in opposite directions. When car Number 19 of one train is opposite car Number 19 of the other, which car is opposite car Number 12?
Answers
Car 12 of Train B is also 12 cars away from Car 19 on Train B.
How to explain the informationSince each train boasts 31 cars, we can ascertain the total amount of vehicles between Car 19 and Car 12 on Train A:
31 - 19 = 12
Thus, Car 12 on Train A is a dozen units distant from Car 19 on Train A.
Nevertheless, Train B is furthermore moving in an inverring direction and has its exclusive set of automobiles between Car 19 and Car 12. We comprehend that the matching figure of cars must be amongst Car 19 and Car 12 on Train B as with Train A.
In essence, Car 12 of Train B is also 12 cars away from Car 19 on Train B.
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A serving of filleted fish is generally considered to be about 1/3 lb. How many servings can be prepared from 4 1/2 lb of fillets?
Answers
Answer:
There are several ways to solve this. If 1 serving = 1/4 pound, then 4 servings = 1 pound. 6 pounds *4=24 servings. That leaves 1/3 of a pound. 1/4 pound is less than 1/3 pound, so you get one more serving. That makes 25 servings, and 1/12 of a pound left over. How do you know it is 1/12? Well, LCD (lowest common denominator) shows that 1/3-1/4= 4/12-3/12=1/12.
Would anyone help me with this please, worth 20 pts.
Answers
Answer:
Below in bold.
Step-by-step explanation:
The perimeter = length of 3 sides of the square + 1/2 the circumference of the circle. The radius of the circle = 2.5 in and its circumference = 2π r and 1/2 of this is π r.
So the perimeter = 3*5 + π r
= 15 + 2.5π
= 22.85 in to the nearest hundredth.