The interest rate of a $16,000 investment is 7.5% and the interest rate
of $6000 investment is 8%
What is interest?Compound interest is the interest levied on the interest. The annual interest formula is I = P r t, where
1. P is the money invested
2. r is the interest rate in decimal
3. t is the time
The annual interest rate on $16,000 investment exceeds the interest
earned on $6000 investment by $830 the $16,000 investment at
0.5% higher rate of interest than the $11,000
Assume that $16,000 investment is I1 , the annual interest
Assume that $6000 investment is I2 , the annual interest
The annual interest rate on a $16,000 investment exceeds the interest
earned on $6000 investment by $830
I1 - I2 = 830
I1 = 16,000 (r1)(1)
I2 = 6000 (r2)(1)
Substitute them in the equation above
16,000 (r1)(1) - 6000(r1)(1) = 830
16,000 (r2) - 6000 (r2) = 830⇒ (1)
The $16,000 investment at 0.6% higher rate of interest then the $11,000
r1 = r2 + 0.005
Substitute equation (2) in equation (1)
16,000 ( r2 + 0.006) - 6000(r2) = 830
16,000r2 + 80 - 6000r2 = 830
Subtract 80 from both sides and add like terms in L.H.S
10000r2 = 750
r2 = 0.075
- Substitute the value of in equation (2)
∴ = 0.075 + 0.005 = 0.080
- Change them to per cent by multiplying them by 100%
The interest rate of $16,000 investment = 0.075 × 100% = 7.5%
The interest rate of $6000 investment = 0.08 × 100% = 8%
The interest rate of $16,000 investment is7.5 % and the interest
rate of $6000 investment is 8%
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Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 15 calls per hour. The arrival rate is 30 calls per hour.
How many extension lines should be used if the company wants to handle 90% of the calls immediately?
fill in the blank 1
lines should be used
What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places.
L = fill in the blank 2
What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places.
fill in the blank 3
%
The various answers to the question are:
To answer 90% of calls instantly, the organization needs four extension lines.The average number of extension lines that will be busy is FourFor the existing phone system with two extension lines, 34.25 % of calls get a busy signal.How many extension lines should be used if the company wants to handle 90% of the calls immediately?a)
A number of extension lines needed to accommodate $90 in calls immediately:
Use the calculation for busy k servers.
\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)
The probability that 2 servers are busy:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
Hence, two lines are insufficient.
The probability that 3 servers are busy:
Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)
Thus, three lines are insufficient.
The probability that 4 servers are busy:
Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)
Generally, the equation for is mathematically given as
To answer 90% of calls instantly, the organization needs four extension lines.
b)
The probability that a call will receive a busy signal if four extensions lines are used is,
\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)
Therefore, the average number of extension lines that will be busy is Four
c)
In conclusion, the Percentage of busy calls for a phone system with two extensions:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.
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Which of the following graphs represents a relation that is not a function
A jacket that normally sells for $160 is on sale for 25% off. What is the sale price of the jacket?
○ $40
○ $120
○ $135
A baker used 33 3/4 cups of flour to make
4
15 batches of cookies. How many more cups
of flour does the baker need if she wants to
make 21 batches of cookies?
The baker would need 47. 25 cups of floor
How to determine the valueWe need to know that proportion is a form of mathematical comparison with two equations made equal to each other.
From the information given, we have that;
baker used 33 3/4 cups of flour to make 15 batches of cookies
This is represented as;
Convert to improper fractions
135/4 cups = 15 batches of cookies
Then, x cups = 21 batches of cookies
cross multiply the values
15x = 708. 75
Divide both sides by the coefficient of x, we have ;
x = 708. 75/15
x = 47. 25 cups of floor
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The cost of one t-shirt is 128. How much will be the cost of 20
The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.
When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.
Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.
We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.
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pls help me on this question it is geometry
Answer:
Contrapositive
Step-by-step explanation:
Original Statement: if p then q
Negation: not p
Contrapositive: if not q then not p
Inverse: if q then p
Converse: if not p then not q
eight hundred twenty nine and six tenths as a decimal
the chart below shows the coordinates of the dragon's head when it is its original size.
I'm sorry, I can't see the chart so I can't answer this question.
Need help please its important practice
TRIANGLE 1: The missing length in the triangle is 10.4 units
TRIANGLE 2: The missing length is QR = 29 yd
How to find the missing length of the triangles?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
TRIANGLE 1
Let the missing length be x
x = √(3² + 10²) (Pythagoras' theorem)
x = 10.4 units
TRIANGLE 2
QR = √(20² + 21²) (Pythagoras' theorem)
QR = 29 yd
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Graph the system below and write its solution.
x+3y=-6
Note that you can also answer "No solution" or "Infinitely many" solutions.
Solution:
0
solution
The number of solutions of the system of equations in this problem is given as follows:
Infinitely many solutions.
How to obtain the solution of the system of equations?The system of equations for this problem is defined as follows:
x + 3y = -6.y = -x/3 - 2.Writing the second equation in standard format like the second, we have that:
x/3 + y = -2.
Multiplying by 3:
x + 3y = -6.
The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.
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Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3, 6n+2, and 6n+1.
Answer:
Use Mathpapa to find your answer.
Step-by-step explanation:
It's a good, and powerful program.
which represents the rotation of ABC toA’B’C
a:(x,y) —> (-x,-y)
b:(x,y) —> (x,-y)
c:(x,y) —> (y, -x)
Answer:
a) A (-2,-2) →A¹ ( 2, 2)
B (-5,-2) →B¹ (5 , 2)
C (-3,-4) →C¹ ( 3 ,4))
b)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-5 , 2)
C (-3,-4) →C¹ ( -3 ,4))
c)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-2 , 5)
C (-3,-4) →C¹ ( -4 ,3))
Step-by-step explanation:
a) Given the (-2,-2) is rotation 180° of counter clock wise then the transformed
to A (-2,-2) → A¹( 2, 2)
B (-5,-2) →B¹ (5 , 2)
C (-3,-4) →C¹ ( 3 ,4))
b)
Reflection about the x-axis
( x, y) → ( x, -y)
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-5 , 2)
C (-3,-4) →C¹ ( -3 ,4))
c)
( x, y) → ( y, -x)
Given (x, y) is rotation 90° of clock wise about the origin then the transformed to
A (-2,-2) → A¹( -2, 2)
B (-5,-2) →B¹ (-2 , 5)
C (-3,-4) →C¹ ( -4 ,3))
Is the point (4, -15) on the line y = -3x - 3
Answer:
yes
Step-by-step explanation:
since the format of ordered pairs is (x,y) we can plug in the values into the equation to see if they are on the line
y = -3x - 3
-15 = -3(4)-3........plug in values
-15 = -12 - 3........multiply
-15 = -15..............subtract
-15 = -15..............this is true
Answer:
yes
Step-by-step explanation:
y = -3x-3
Substitute the point into the equation
-15 = -3(4) -3
-15 =-12-3
-15=-15
This is true so the point is on the line
suppose that a test for opium use has a 2% false positive rate and a 5% false negative rate. that is, 2% of people who do not use opium test positive for opium and 5% of opium users test negative for opium. furthermore, suppose that 11% of people actually use opium.a) Find the probability that someone who tests negative for opium use does not use opium.b) Find the probability that someone who tests positive for opium use actually uses opium.
The probability that someone who tests positive for opium use actually uses opium is 0.854 .
In the question ,
it is given that , the false positivity rate is 2% .
Let the sample size be of 100 .
11% of the people actually use opium = 100*0.11 = 11.
People who do not use opium = 100 - 11 = 89.
the test for opium has a 2% false positive , that is
= 2% of 89 = 89*0.02 = 1.78
So , the True negative = 89-1.78 = 87.22
the test for opium has a 5% false negative , that is
= 5% of 11 = 11*0.05 = 0.55
So , the True positive = 11-0.55 = 10.45
Probability is calculated by favorable/total.
Total (positive) = true + false = 10.45 + 1.78 = 12.23 .
Favorable (true) = 10.45
Probability is = 10.45/12.23 = 0.854
Therefore , the required probability is 0.854 .
The given question is incomplete , the complete question is
Suppose that a test for opium use has a 2% false positive rate and a 5% false negative rate. that is, 2% of people who do not use opium test positive for opium and 5% of opium users test negative for opium. furthermore, suppose that 11% of people actually use opium.
Find the probability that someone who tests positive for opium use actually uses opium.
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se quiere pintar una pared en forma de hexágono regular y se sabe que cada lado mide 3m y que su apotema es de 2,8m ¿cual es el area que se va a pintar?
Answer:
16.8 metros cuadrados.
Step-by-step explanation:
Dado que se quiere pintar una pared en forma de hexágono regular y se sabe que cada lado mide 3m y que su apotema es de 2,8m, y que el área de un hexágono es igual al perímetro multiplicado por la apotema, y dicho resultado dividido por 2, para determinar cuál es el área que se va a pintar se debe realizar el siguiente calculo:
((6x3) x 2.8) / 2 = X
(12 x 2.8) / 2 = X
33.6 / 2 = X
16.8 = X
Así, el área que se va a pintar es de 16.8 m2.
what's an isosceles triangle; triangle with 2 equal sides; area of isosceles triangle
The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.
How big is an isosceles triangle?
If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.
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Factor each.
Please help!
Find the reference angle for a rotation of 347°
The Refernce angle is 13
Step-by-step explanation:
For example imange a coordinate plane lets say we want to draw an angle thats 144° We start on the right side of the x-axis, where three o’clock is on a clock. We rotate counterclockwise, which starts by moving up. We keep going past the 90° point (the top part of the y-axis) until we get to 144°. hope this helps!
Find the area to the right of the z-score 1.39 and to the left of the z-score 1.53 under the standard normal curve.1.2 1.3 1.4 0.00 0.01 0.02 0.03 0.8849 0.8869 0.8888 0.8907 0.9032 0.9049 0.9066 0.9082 0.9192 0.9207 0.9222 0.9236 0.9332 0.9345 0.9357 0.9370 0.9452 0.9463 0.9474 0.9484 0.9554 0.9564 0.9573 0.9582 0.04 0.05 0.06 0.070.08 0.09 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.5 1.6 1.7 Use the value(s) from the table above.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value is \(P( 1.39 < z < 1.53 ) = 0.0193\)
Step-by-step explanation:
From the question we are told to obtain the area to the of the z-score 1.39 and to the left of the z-score 1.53, this is mathematically represented as
\(P( 1.39 < z < 1.53 ) = P( z < 1.53 ) - P( z < 1.39 )\)
From the z table on the question the area under the normal curve to the left corresponding to 1.53 and 1.39 is
\(P( z < 1.53 ) = 0.9370\)
and
\(P( z < 1.39 ) = 0.9177\)
So
\(P( 1.39 < z < 1.53 ) = 0.9370 - 0.9177\)
=> \(P( 1.39 < z < 1.53 ) = 0.0193\)
The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?
Answer:
Step-by-step explanation:
First, we want to take the information we have and turn it into an equation, where x is our unknown dimension. For this problem, it would be better if x was equal to the width.
Let's write out the equation:
X is the width, 2x + 2 is the length, and we are multiplying both by two since there are two sides of the field. It will all equal to 322, because that is the perimeter.
2*x + 2(2x +2) = 322
Now, let's solve:
2*x + 2(2x + 2) = 322
2x + 4x + 4 = 322
6x + 4 = 322
6x = 318
x = 318 ÷ 6
x = 53
The width is 53 yards. To find the length, we multiply 53 by two and add two.
53 * 2 + 2 = 106 + 2 = 108 yards, as the length
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
s+(2s+3)+12 what is the expression in simplest form?
Answer:
3s+15
Step-by-step explanation:
s+(2s+3)+12
Combine like terms
s+2s +3+12
3s+15
Answer:
3(s+5)
Step-by-step explanation:
To simplify the expression, we must combine like terms.
s+(2s+3)+12
The like terms are the terms with variables (s and 2s) and the terms without variables, or the constants (3 and 12).
To combine the like terms, add them.
(s+2s)+(3+12)
3s+15
This expression can also be factored using the GCF. The GCF of 3s and 15 is 3.
3s+15
Factor out a 3
3(s+5)
Where will the images of the points in the quadrilateral that are not on the line be
Answer:
All quadrilaterals are four sided shape.
Step-by-step explanation:
Four sided shape can be:
- Square
- Trapaziod
Four sided shape can be called a quadrilateral.
Tammy bought 16 cookies for a party. She had 6 cookies decorated at an extra cost of 25 cents each. If the total cost of the cookies was $9.50, how much did each plain cookie cost?
[ACCURATE ANSWER FOR BRAINLIEST]
Answer:
one plain cookie costs $0.50Step-by-step explanation:
so 25 x 6 is the extra cost
150 cents is the extra cost
subtract that from 9.50
you are left with $8
now we know that 16 plan cookies cost $8
so one plain cookie costs $0.50
Answer:
.50c
Step-by-step explanation:
1) You take the cost of the extra cookies and subtract from the total so 6 * .25 = 1.50 then 9.50 - 1.50 = 8.00
2) you take the 8.00 then divide it by the total number of cookies which is 8.00 ÷ 16 = 0.50
I Need help pls!
What is 75% of 800?
A; 9 3/8
B; 10.66
Answer:
it's 600
Step-by-step explanation:
that's not an option there but...
10% of 800 is 80
5% of 800 is 40
80 × 7 = 560
560 + 40 = 600
The system of equations y = negative one-fifth x minus 6 and y = –2x + 3 is shown on the graph below.
On a coordinate plane, 2 lines intersect at (5, negative 7).
According to the graph, what is the solution to this system of equations?
(5, –7)
(–7, 5)
(5, 7)
(7, 5)
Answer:
According to graph, solution is (5, –7)
Answer:
A) (5, –7)
Step-by-step explanation:
I got 100%, please brainlist
Please help! Will give brainliest
\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)
we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.
Y’all should Frl help me
Answer:
Step-by-step explanation:
Plug in 6 for x for g(x) and f(x)
f(6) = 2(6)⁵ = 15,552
g(6) = 10 x 4⁶ = 40,960
15,552 < 40,960
f(6) < g(6)
What is the measure of angle AED?
Answer:
Step by step explanation:
well this is simble you just do it
solve the equation for x. -x/10=13
You have the following equation:
-x/10 = 13
in order to solve for x, proceed as follow:
-x/10 = 13 multiply by 10 both sides
x = 13(-10)
x = -130
Hence, the value of x is x = -130