The interest is 16% compounded semi-annually, is Rs. 121,179.10.
To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.
Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)
So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:
Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.
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Find the Sine, Cosine and Tangent.
The Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318
How to find the Sine, Cosine and Tangent.From the question, we have the following parameters that can be used in our computation:
The triangle
Where, we have
tan(28) = 21/x
This means that
x = 21/tan(28)
Evaluate
x = 39.49
using the above as a guide, we have the following:
tan(28) = 21/39.49
tan(28) = 0.5318
Also, we have
sin(28) = 21/√(39.49² + 21²)
sin(28) = 0.4695
Lastly, we have
cos(28) = 39.49/√(39.49² + 21²)
cos(28) = 0.8829
Hence, the Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318
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At a certain college, 49% of the students are male and 51% are female. In addition, 20% of the men and
10% of the women are taking Japanese classes. The student is selected at random. If the selected student
attends Japanese lessons, what is the probability that the student is female?
Answer:
0.339, or approximately 33.9%
Step-by-step explanation:
We can solve this problem using Bayes' theorem. Let F denote the event that the selected student is female, and J denote the event that the selected student is taking Japanese classes. We want to find the probability of F given J, which we can write as P(F|J).
Using the law of total probability, we can decompose the probability of J as follows:
P(J) = P(J|F)P(F) + P(J|M)P(M)
where M denotes the event that the selected student is male. We can calculate the probabilities on the right-hand side of this equation as follows:
P(J|F) = 0.1 (from the problem statement)
P(F) = 0.51 (from the problem statement)
P(J|M) = 0.2 (from the problem statement)
P(M) = 0.49 (from the problem statement)
Plugging in these values, we get:
P(J) = 0.10.51 + 0.20.49 = 0.149
Now we can use Bayes' theorem to find P(F|J):
P(F|J) = P(J|F)P(F) / P(J)
Plugging in the values we calculated earlier, we get:
P(F|J) = 0.1*0.51 / 0.149 = 0.339
Therefore, the probability that the selected student is female given that they attend Japanese classes is 0.339, or approximately 33.9%.
Hope this helps!
A ladder 25m long leans against a vertical wall 7m height. How far is the foot of the pole away from the wall
Answer:
24m
Step-by-step explanation:
If we imagine this situation as a right angled triangle, 25m is the hypotenuse, 7m is the height and we need the base length
so by Pythagoras thorium we can say that [tex]\sqrt[2]{25^2 -7^2}[/tex]= base length
which is= 24
y = x²
y = 1,002x - 2,000
If (x₁, y₁) and (x2, y2) are distinct
solutions to the system of equations
shown, what is the sum of ₁ and ₂?
X1
Answer:
To find the sum of x₁ and x₂, we need to solve the system of equations:
y = x² ...(1)
y = 1,002x - 2,000 ...(2)
Since both equations are equal to y, we can set them equal to each other:
x² = 1,002x - 2,000
To solve this quadratic equation, we can rearrange it into standard form:
x² - 1,002x + 2,000 = 0
Now, we can factorize the equation:
(x - 2)(x - 1,000) = 0
Setting each factor equal to zero, we get two solutions:
x - 2 = 0 => x = 2
x - 1,000 = 0 => x = 1,000
Therefore, the values of x₁ and x₂ are 2 and 1,000, respectively.Therefore, the values of x₁ and x₂ are 2 and 1,000, respectively.The sum of x₁ and x₂ is:Therefore, the values of x₁ and x₂ are 2 and 1,000, respectively.The sum of x₁ and x₂ is:x₁ + x₂ = 2 + 1,000 = 1,002The sum of distinct solutions x₁ and x₂ to the system of equations y = x² and y = 1,002x - 2,000 is 1,002.
Explanation:The problem here involves finding the solutions to the system of equations. Those equations are y = x² and y = 1,002x - 2,000. To solve this system of equations, we can set the two equations equal to each other, because they both equal y.
So, we have: x² = 1,002x - 2,000. Rearranging, we get x² - 1,002x + 2,000 = 0. This is a quadratic equation, and we can solve for x using the quadratic formula: x = [1,002 ± sqrt((1,002)² - 4*1*2,000)] / (2*1). This will yield 2 solutions for x, let's call them x₁ and x₂.
The question asks for the sum of x₁ and x₂. In a quadratic equation ax² + bx + c = 0, the sum of solutions is given by -b/a. Here, a = 1 and b = -1,002, so the sum of solutions x₁ and x₂ is -(-1,002)/1 = 1,002.
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Solve the triangle 15 points
The measure of the angle B is 32. 0 degrees
How to determine the measuresTo solve the given triangle, we need to know the different trigonometric identities and their ratios.
We have that these identities are;
sinetangentcotangentsecantcosecantcosineFrom the information given, we have that;
Opposite side of angle B = 5
Hypotenuse side = 9.43
Using the sine identity, we get that;
sin B = 5/9.43
Divide the values, we have;
sin B= 0.5302
Find the inverse value of the sine identity and then substitute
B = 32. 0 degrees
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The measure of angle D of the given Kite is: 127°
How to find the angle of the Kite?From the diagram, the figure represents a kite.
Properties of a kite are:
- Two pairs of adjacent sides are equal.
- Two diagonals intersect each other at right angles.
- The longer diagonal bisects the shorter diagonal.
- The angles opposite to the main diagonal are equal.
Thus:
The angle B = the angle D
The sum of all angles of a quadrilateral = 360
Given: ∠A = 36 and ∠C = 70
Thus:
2∠D = 360 - (36 + 70)
2∠D = 254
∠D = 127°
So, the measure of angle D = 127°
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Let P(x) = -50x+20,000x-1,5000,000 represent the profit function for manufacturing a particular model of recreational
vehicle (RV) and x represent the number of RVS produced monthly. Use a compound inequality to state the range of the
number of RVs that need to be sold each month for the company to make a profit.
O 0
100
200
none of the answer choices
O 0
O 100
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.
The profit function is given by P(x) = -50x + 20,000x - 1,500,000.
To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:
-50x + 20,000x - 1,500,000 > 0.
Combining like terms, we have:
19,950x - 1,500,000 > 0.
Now, let's solve this inequality for x:
19,950x > 1,500,000.
Dividing both sides by 19,950, we get:
x > 1,500,000 / 19,950.
Simplifying the right side, we have:
x > 75.
The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
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A league is a nautical measurement equal to about 3 miles. If a ship travels 2,000 leagues, about how many miles does the ship travel?
Answer: 600000
Step-by-step explanation: just multiply it man
A party is attended by n > 2 people. Prove that there will always be two people in attendance who have
the same number of friends at the party.
(The relation “is a friend of” is symmetric.)
It should be noted that there will always be two people in attendance who have the same number of friends at the party using the pigeonhole principle.
How to explain the informationThe pigeonhole principle states that if you have n pigeons and m pigeonholes, and n > m, then at least one pigeonhole must contain more than one pigeon.
In this case, we have n people at the party, and there are m = n - 1 possible numbers of friends that a person can have. This is because a person can either know 0, 1, 2, ..., or n - 1 other people.
Since n > m, the pigeonhole principle tells us that at least two people at the party must have the same number of friends.
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1. Solve and show your work for each question.
(a) What is 0.36-- (line on 3&6) expressed as a fraction in simplest form?
(b) What is 0.36- (line on 6) expressed as a fraction in simplest form?
(c) What is 0.36 expressed as a fraction in simplest form?
The decimal 0.36 can be represented as a fraction in simplest form as 9/25. It can also be expressed as a repeating decimal using a variable.
a) 0.36 can be represented as a fraction in simplest form by using place value to identify the denominator. The number 3 is in the hundredths place value position.
Thus, the denominator is 100. 36 is in the numerator position.
Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.
b) 0.36 can be represented as a fraction in simplest form by identifying the denominator based on place value.
In this case, 6 is in the thousandths place value position, so the denominator is 1000. 36 is in the numerator position. Thus, 0.36 in fraction form is 36/1000 which can be simplified to 9/250.
c) To write 0.36 as a fraction in simplest form, the place value of each digit needs to be considered. 3 is in the tenths place value position and 6 is in the hundredths place value position.
Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.The decimal 0.36 can be represented in fraction form as 36/100 or 9/25.
To determine the fraction in simplest form, the denominator must be reduced to its lowest possible value without changing the numerator. The decimal 0.36 with a line on top of 3 and 6 represents a repeating decimal.
To express this number as a fraction, a variable is used.
In this case, the variable x is equivalent to 0.36. By setting up a proportion and solving for x, the answer can be found.
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Explain the process you would use to find the area of the shaded region. Then calculate the shaded region.
You may leave your answer in terms of m or round to the nearest tenth.
Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.
To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.
Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.
Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.
Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:
Rectangle: Area = length × width
Triangle: Area = (base × height) / 2
Circle: Area = π × radius²
Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.
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Henry is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
Answer:
446.95m²
Step-by-step explanation:
10+9+13.45=32.5
32.5x11=356.95
9x10=90
356.95+90=446.95
Help thanks asapjhshd
A graph that represents the absolute function f(x) = |x + 4| - 3 is shown on the coordinate plane attached below.
What is an absolute value function?In Mathematics and Geometry, an absolute value function is a type of function that contains an expression, which is placed within absolute value symbols, and it measures the distance of a point on the x-axis to the x-origin (0) of a graph.
By critically observing the transformed absolute value function f(x) = |x + 4| - 3, we can reasonably infer and logically deduce that the parent absolute value function g(x) = |x| was vertically shifted (translated) downward by 3 units and horizontally shifted (translated) to the left by 4 units, in order to produce it as follows;
g(x) = |x|
f(x) = |x + h| - k
f(x) = |x + 4| - 3
In conclusion, we would use an online graphing tool to plot the given absolute value function f(x) = |x + 4| - 3 as shown in the graph attached below.
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Match each letter to its correct term. Efficiency Unobtainable Impossible Inefficiency Underutilization 1. A 2. B 3. C
Each letter should be matched to its correct term as follows;
1. A ⇔ Efficiency.
2. B ⇔ Impossible.
3. C ⇔ Inefficiency.
What is a production possibilities curve?In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;
Technology is fixed.Resources are fixed.Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;
A ⇔ Efficiency: it represent points on the production possibilities curve.B ⇔ Impossible: it represent points outside the production possibilities curve.C ⇔ Inefficiency: it represent points on the interior of a production possibilities curve.Read more on production possibilities here: brainly.com/question/26460726
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Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are , , , , , and , by rounding each price to the nearest dollar and then adding.
a.
The estimated total cost of the grocery items is $36.
b.
The actual total cost of the grocery items is $35.82.
How do we calculate?for part a.
We will round each price to the nearest dollar:
$5.12 = $5
$3.07 = $3
$7.11 = $7
$1.67 = $2
$13.18= $13
$5.67 = $6
Summing them up, we have:
$5 + $3 + $7 + $2 + $13 + $6 = $36
the estimated total cost of the grocery items is $36.
for part b.
We will calculate the actual total cost of the grocery items by using a calculator:
$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82
In conclusion, we will find the actual total cost of the grocery items as $35.82.
The complete question is added as an image
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50 POINTS, pls hurry
Answer: it stand for 3 million or 3,000,000
Step-by-step explanation:
Answer:
million
Step-by-step explanation:
millions always have six 0's behind it
the sum of triple the number j and 21
The expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.
To find the sum of triple the number "j" and 21, we need to multiply "j" by 3 and then add 21 to the result.
Let's break it down step by step:
Multiply "j" by 3: This can be represented as 3 * j, or simply 3j.
Add 21 to the result: We take the product from step 1 (3j) and add 21 to it, resulting in 3j + 21.
In summary, the expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.
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Which is the most suitable to measure the length of a rugby field?
Answer:
12 km (565m)
Step-by-step explanation:
PLEASE HELP I KEEP GETTING DIFFERENT ANSWERS.
I don’t understand what find three ratios for the marked angle but do not solve means.
For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA
How to determine the ratio of the given triangle above?For question 3.)
To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;
Sine rule:
a/sinA = b/sinB = c/sinC
where;
a = 8
A = sinA
b = 5
B = SinB
c = 9.45
C = Sin 90°
The three ratios;
= 9.45:sin90°; 5:sinB; 8:sinA
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20 26 28 25 28 18 23 15 17 26 29 24 29
29 17 15 17 20 30 29 16 21 22 28 19
Find Q1
Find Q2
Find Q3
Find the minimum and maximum value,
Based on the information, the minimum value is 15, and the maximum value is 30.
How to calculate the valueTo find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).
Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)
Take the average of the values at positions 6 and 7 to find Q1.
Q1 = (18 + 19) / 2 = 18.5
To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).
Position = (22 + 1) * (50 / 100)
= 11.5 (rounded to 12)
The value at position 12 is the median.
Q2 = 21
To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).
Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)
Take the average of the values at positions 17 and 18 to find Q3.
Q3 = (28 + 29) / 2 = 28.5
The minimum value is 15, and the maximum value is 30.
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