Final answer:
The original basket contained 72 mangoes, determined by working backward from the known remainder of 3 after the sequential distribution between the king, queen, and princes.
Explanation:
From a basket of mangoes, the distribution among the royal family leads to a classic fractional subtraction problem. The solution involves working backward from the known remainder. The youngest child took the remaining 3 mangoes, which indicates that this was what was left after the king, the queen, and the three chief princes took their respective shares.
Let's denote the original number of mangoes as x. The king took 1/6 of x, leaving 5/6x. The queen then took 1/5 of the remainder (5/6x), leaving 4/5 * 5/6x = 4/6x or 2/3x. Successively, the three chief princes took 1/4, 1/3, and 1/2 of their respective remainders, each action further reducing the quantity of mangoes. The problem states that after these distributions, 3 mangoes were left, which were taken by the youngest child.
To find the original number of mangoes, we begin by denoting the final 3 mangoes as the remaining half after the last prince's share, work through the inverse operations for each prior transaction, and solve for x. Through this back calculation, we find that the original number of mangoes was 72.
If events A and B are mutually exclusive, find P(A/B)
A. P(A)
B. 1
C. 0
D. P(A)/P(B)
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = cos x (3 + v5)8 dv sin x
The first part of the Fundamental Theorem of Calculus provides a method to find the derivative of a function. However, clarity is needed in the question as it has extra elements. If we consider the derivative of y = cos x (3 + √5)8 sin x, it would be f'(x) = -sin x (3 + √5)8 sin x + cos x (3 + √5)8 cos x.
Explanation:Since the question asks for the derivative of the function y = cos x (3 + √5)8 dv sin x, we'll need to use the First Part of the Fundamental Theorem of Calculus. This theorem states that if a function f is continuous over the interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral from a to b of f(x) dx equals F(b) - F(a). In this case, we have y = cos x (3 + √5)8 dv sin x which sadly is not clear due the presence of apparently extra and possibly typographical elements.
Assuming, the question intends to find derivative of y = cos x (3 + √5)8 sin x, we can proceed as follows:
Let f(x) = cos x (3 + √5)8 sin x. Then by applying the chain rule, we get: f'(x) = -sin x (3 + √5)8 sin x + cos x (3 + √5)8 cos x.
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CC=\frac{5}{9}(F - 32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how many multiple-choice questions are there?
A. t for test, q for questions
B. m for multiple choice, s for short answer
C. s for short answer, t for test
D. p for points, m for multiple choice
apex mcr
use the Pythagorean theorem to determine if a triangle with sides lengths 2 feet 4 ft 5 ft is a right triangle
Bernard weighs 7.5 pounds at birth. assuming his development proceeds normally, he should weigh about _____ pounds by his first birthday. 22.5 24.5 20.5 18.5
Given Bernard weighs 7.5 pounds at birth.The question is asking us to assume that Bernard development proceeds normally.We need to find Bernard birth after a year.
It is observed that birth of a child triples or is thrice (3 times ) the weight at birth.As Bernard is weighing 7.5 pounds so he will triple or be 3times of this weight.
Bernard weight after a year= 3x7.5=22.5 pounds.
Lindsay's watering can holds 12 quarts of water. She uses 1 pint of water on each of her flowers.
How many flowers can she water?
She can water 24 flowers using 12 quarts.
1 quart consists of how many pints?1 quart consists of 2 pints
So, 12 quarts = 12*2 =24 pints
It is given that she uses 1 pint of water on each flower.
So, 24 pints can be used to water =24*1 =24 flowers.
Therefore, She can water 24 flowers using 12 quarts.
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Which figure shows how a shape can be rotated about an axis to form the given object?
The answer is as shown in the attachment which is the first diagram (on the left) on the second row which is highlighted in the attachment
That is the only figure which when rotated about the axis will form a cylindrical form as required.
The top two will form into a solid sphere and the last would form into a solid cylinder and not the one as required.
Answer:
Option C.
Step-by-step explanation:
In this question we will go by every option.
Option A). When a circle showing in the figure is rotated then a hollow ring will be formed.
Option B). In this option when a circle like structure with two layers is rotated about an axis it will forms a ring with two layers. Inner part of the ring will be empty.
Option C). In this option when a vertical strip is rotated by the axis, it will form the cylinder similar to the object shown in the figure.
Option D). In this option when a strip attached to the axis is rotated, a sold cylinder is formed.
Therefore Option C. is the correct option.
What is the degree measure of angle A?_____ degrees
QM Q2.) Find the multiplicities of the greatest zero, second greatest zero, and the smallest zero.
A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form?
How many hours minutes and seconds are in 2165 days?
A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no fence. find the dimensions of the pasture that will produce a pasture with a maximum area.
at 6am the temperature is -5°f the temperature rises 6°f by noon what is the temperature at noon?
Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
Let be a Point of the form [tex](x,y)[/tex] that is the Terminal Side of angle [tex]\theta[/tex], in sexagesimal degrees. By Trigonometry, we know that the Cosine, Cosecant and Tangent of the Angle are, respectively:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that [tex]x = 4[/tex] and [tex]y = -7[/tex], then the exact value of all the trigonometric relations are:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\cos \theta = \frac{4}{\sqrt{4^{2}+(-7)^{2}}}[/tex]
[tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex]
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]
[tex]\csc\theta = \frac{\sqrt{4^{2}+(-7)^{2}}}{4}[/tex]
[tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex]
[tex]\tan \theta = \frac{y}{x}[/tex]
[tex]\tan \theta = -\frac{7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
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please show me how to answer this
A plane left on time at noon on Monday. It arrived at its destination at 8:16PM the same day, which was 16 minutes late. On average, how many seconds did the plane fall behind every fifteen minutes?
To find the average delay per fifteen-minute interval, convert the total delay of 16 minutes into seconds, then divide by the number of fifteen-minute intervals between noon and 8:00 PM, yielding an average delay of 30 seconds per interval.
The question asks us to calculate how much time the plane fell behind schedule, on average, every fifteen minutes. Since the plane arrived 16 minutes late, we first need to convert this delay into seconds: 16 minutes is equal to 960 seconds (16 minutes imes 60 seconds/minute). To calculate the plane's average delay per fifteen-minute interval, we divide the total delay in seconds by the total number of fifteen-minute intervals between noon and the expected arrival time at 8:00 PM, which is 32 intervals (8 hours ×4 intervals/hour). Therefore, the average delay per interval is 960 seconds \/ 32 intervals = 30 seconds per interval.
Exercise 3.8 asked you to write a method called quadratic that solves quadratic equations and prints their roots. recall that a quadratic equation is a polynomial equation in terms of a variable x of the form a x2 + b x + c = 0. the formula for solving a quadratic equation is:
If the graph of the function h is defined by = h(x)+x^2+9 is translated vertically downward by 9 units, it becomes the graph of a function g. Find the expression for
gx
Which of the following is the correct simplification of 7•4²÷ 8 -12
how much tax you need to pay on a taxable income of 40,000
14 m equals how many mm
The average weekly income of teachers in one school district is $750 with a standard deviation of $85. Find the percentage of teachers earing more than $825 a week?
SCIENCE HELP 10 POINTS!!!!!
The greenhouse effect traps heat near earth's surface. Greenhouse gases in the atmosphere—carbon dioxide, water vapor, methane, and nitrous oxide—allow the shorter waves of ultraviolet radiation from the sun to enter earth's lower atmosphere. However, these gases do not allow the longer wavelengths of infrared radiation to pass back out to the outer atmosphere. The result is that the lower atmosphere heats up.This result happens naturally, but it can be accelerated by human activities. Since the late 1800s, human activity has greatly altered the amount of greenhouse gases that enter the atmosphere. Burning fossil fuels, farming, and clearing forests, as well as industry, have all contributed to increases of carbon dioxide (CO2), methane, nitrous oxide, and other greenhouse gases in the atmosphere.The result is that temperatures in the troposphere have gone up. Many scientists identify this increase in greenhouse gas emissions as contributing directly to global warming. This suggests that human activity has had an impact on the global climate.
The author argues that in modern times, the greenhouse effect *
A.helps keep the Earth warm
B.has increased because of human activity
C.is in a natural cycle of changing
D.has changed local weather patterns
C.is in a natural cycle of changing
The beginning balance in Cash was $3,500. Additional cash of $2,000 was received. Checks were written totaling $2,500. The cash balance is Question 3 options: $2,000. $6,000. $4,500. $3,000.
A jar contains 8 large red marbles, 5 small red marbles, 7 large blue marbles, and 4 small blue marbles. if a marble is chosen at random, which of the conditional probabilities is larger, p(red|large) or p(large|red)?
A dog kennel uses 90 lb of dog food per day. How many pounds are used in a year?
Instructions:Select the correct answer from the drop-down menu. In the figure, sin ∠MQP = cos N and sin R sin R and sin N cos N and sin M cos R and sin N .
Answer:
Cos R and sin N
Step-by-step explanation:
Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4
If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, how long would it take 200 nurses to measure the blood pressure of 200 patients (in minutes)?
Final answer:
One nurse takes 2 minutes to measure the blood pressure of one patient. With 200 nurses, each assigned to one patient, it will take all nurses 2 minutes to measure the blood pressure of 200 patients.
Explanation:
The question is asking for the time it would take a group of nurses to measure the blood pressure of an equal number of patients given a scenario. It works on the principle that if the number of nurses is directly proportional to the number of patients, the time it takes for one nurse to measure one patient's blood pressure will be the same, regardless of how many nurses or patients there are, as long as the ratio remains 1:1.
If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, that means one nurse takes 2 minutes to measure the blood pressure of one patient. Therefore, if you have 200 nurses each measuring the blood pressure of one patient, it would still take 2 minutes for all 200 patients to have their blood pressure measured since each nurse is working with one patient individualy.