Answer: The equation of the circle is [tex]x^2+y^2=r^2.[/tex]
Step-by-step explanation: We are given to write the equation of a circle centered at the origin.
We know that the standard equation of a circle with center at the point (g, h) and radius 'r' units is given by
[tex](x-g)^2+(y-h)^2=r^2~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The co-ordinates of the origin are (0, 0).
So, if the center of the circle is at the origin, then we have
(g, h) = (0, 0).
Therefore, from equation (i), we have
[tex](x-0)^2+(y-0)^2=r^2\\\\\Rightarrow x^2+y^2=r^2.[/tex]
Thus, the required equation of the circle is [tex]x^2+y^2=r^2.[/tex]
Identify the Asymptotes for the graphs below help pls!
Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?
50.00 rupees
56.00 rupees
63.76 rupees
76.63 rupees
Ria will need 2677920 Rupees to pay her tuition fees
Data;
Tuition fee = $42,000$1 = 63.76 rupees$1 rupees = $0.015How Many Rupees will she need to buy a Dollar?We need to convert the currency from dollars to rupees
From the data given in the question, $1 is equivalent to 63.7 Rupees.
This information can further be used to determine how many Rupees she needs to pay her Tuition fees.
[tex]\$1 = 63.76 Rupees\\\$42,000 = x\\x = 42000 * 63.76\\x = 2677920[/tex]
Ria will need 2677920 Rupees to pay her tuition fees
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Which of the following is the contrapositive of the conditional below?
If 3 + 4 = 6, then 2 · 5 = 10.
A. If 2 · 5 = 10, then 3 + 4 = 6.
B. If 3 + 4 ≠ 6, then 2 · 5 ≠ 10.
C. If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
D. If 3 + 4 ≠ 6, then 2 · 5 = 10.
Answer: If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
Step-by-step explanation:
Because a contrapositive is the contradiction the hypothesis and conclusion of something given and interchanging them. For example: "if not-B then not-A " is the contrapositive of "if A then B "
Answer:
If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
Step-by-step explanation: Hope This Helps You!!! :)))
6-ounce bag of rice noodles makes 5 servings. at that rate, find how many ounces of noodles are needed for 88 servings, to the nearest ounce
Write a 10 digit number such that the first digit tells how many zeros
If (a+b)^2=25, and a^2+b^2=17, then what is a*b equal to? Thanks.
a rectangle is three centimeters.longer than it is wide. if its length were to be decreased by two centimeters, its area would decrease by thirty square centimeters.
A) what are the dimensions?
B) what is it’s area?
Show your work using an equation
If 3 (x+1) =7 find the value of 3x
Find two numbers whose sum is 49 and whose product is 544
The two numbers are 16 and 33. They satisfy the conditions that their sum is 49 and their product is 544, as verified by setting up and solving a system of equations.
To find two numbers whose sum is 49 and whose product is 544, we can set up a system of equations based on the information given. Let's call the two numbers x and y. So, we have two equations:
x + y = 49xy = 544By solving these equations simultaneously, we can find the values of x and y.
The easiest way to solve this might be to express y in terms of x from the first equation: y = 49 - x. Then, substitute this into the second equation:
x(49 - x) = 544
This simplifies to a quadratic equation:
x^2 - 49x + 544 = 0
Factoring this quadratic equation, we get:
(x - 16)(x - 33) = 0
Which gives us two possible values for x:
x = 16x = 33Plugging these back into the equation for y, we get:
y = 49 - 16 = 33y = 49 - 33 = 16So the two numbers are 16 and 33.
I conceived on september 27 when will the test show the results
If molly walks 4 miles in 70 minutes, then molly will walk how far in 100 minutes if she walks at the same speed the whole time? if necessary, round your answer to the nearest tenth of a mile.
Sales fall from 300 per week to 270 per week what’s the percentage change
What is the value of the function at x=−3?
y = 4
y = 3
y = 0
y=−3
Answer:
y=4
Step-by-step explanation:
Evaluate the expression below when x = 5.
3x(2x - 7)
A.) 0
B.) 24
C.) 45
D.) 143
a person mailing postcards earns a fixed amount for each postcard he mails yesterday his hourly wage was $14 an hour if he worked 5 hours yesterday and mailed 300 postcards how much does he earn for each postcard mailed? show you work
For each postcard person gets $14/60 or $0.2333.
What is ratio?Ratio is basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, there ratio will be a:b .
Given that,
Wage for 1 hour = $14,
Since,
The person mailed 300 postcards in 5 hours,
therefore, in 1 hour 60 postcards will be mailed.
Person gets $14 for 60 postcards ,
So for 1 postcard person will get $14/60 or $0.2333 .
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What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units
On Call 3.5 hours: $10 Talk Time 1/2 hours: $1.25 What is the unit rate in dollars per hour for each company?
Rearrange the formula v = GM r for r.
The correct formula for [tex]\( r \)[/tex] rearranged from [tex]\( v = \frac{GM}{r} \) is \( r = \frac{GM}{v} \)[/tex].
To rearrange the formula [tex]\( v = \frac{GM}{r} \)[/tex] to solve for [tex]\( r \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[ v = \frac{GM}{r} \][/tex]
2. Multiply both sides of the equation by [tex]\( r \)[/tex] to get rid of the denominator:
[tex]\[ vr = GM \][/tex]
3. Divide both sides of the equation by [tex]\( v \)[/tex] to isolate [tex]\( r \)[/tex]:
[tex]\[ r = \frac{GM}{v} \][/tex]
This gives us the rearranged formula for [tex]\( r \)[/tex] in terms of [tex]\( G \), \( M \), and \( v \)[/tex]
"in how many ways can 6 people be lined up to get on a bus?"
in a simple random sample of 48 men, the mean wrist circumference of the men is 19.3 centimeters with a standard deviation of 1.2 centimeters. Round your answer to the nearest hundredth.
Which interval is the 95% confidence interval for the mean wrist circumference for all men?
18.99,19.61
18.96, 19.64
12.85, 19.75
19.14, 19.46
The 95% confidence interval for the mean wrist circumference for all men is 18.91 to 19.69 centimeters.
Explanation:To calculate the confidence interval for the mean wrist circumference, we can use the formula: CI = x ± t(s/√n), where CI is the confidence interval, x is the sample mean, t is the t-value corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 19.3 centimeters, the sample standard deviation is 1.2 centimeters, and the sample size is 48. We can find the t-value for a 95% confidence level using a t-table or calculator. Assuming a normal distribution, the t-value is approximately 1.96. Plugging in these values into the formula, we get:
CI = 19.3 ± 1.96(1.2/√48) = 19.3 ± 0.3956
Therefore, the 95% confidence interval for the mean wrist circumference is approximately 18.91 to 19.69 centimeters.
If 5kg more than 3 times mac’s mass is decreased by twice his mass the result is 60 kg. What is mac’s mass?
Mac's mass can be found by setting up the equation 3m + 5kg - 2m = 60kg, simplifying to m + 5kg = 60kg, and solving for m to get m = 55kg. Therefore, Mac's mass is 55kg.
The equation, according to the problem statement, is: 3m + 5kg - 2m = 60kg. This simplifies to m + 5kg = 60kg, from which we can subtract 5kg from both sides resulting in m = 55kg. So, Mac's mass is 55kg.
Steps to solve the problem:
Let m represent Mac's mass.
Write the equation according to the problem statement: 3m + 5kg - 2m = 60kg.
Simplify the equation: m + 5kg = 60kg.
Subtract 5kg from both sides: m = 55kg.
Conclude that Mac's mass is 55kg.
Janine has two important tests to study for. If she plans to divide her study time equally between both tests, how long should she spend studying for each test if she wants to study for at most 90 minutes?
the probability that it will rain today is 0.3 what is the probability that it will not rain?
Answer: 0.7
Step-by-step explanation: 1-0.3 = 0.7
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing is available, find the largest total area that can be enclosed.
What time is 3 hours and 30 minutes before 5:00 P.M.?
What is the first step in solving an equation by completing the square?
A line contains the points (34, 12)(34, 12) and (32, 48)(32, 48) .
What is the slope of the line in simplified form?
What proportion of a normal distribution corresponds to z scores greater than 1.04?
Final answer:
The proportion of a normal distribution for z scores greater than 1.04 is 0.1492, which is found by subtracting the area to the left (0.8508) from the total area under the curve (1).
Explanation:
To find the proportion of a normal distribution that corresponds to z scores greater than 1.04, we must look up the area to the left of the z-score using a z-table or a standard normal distribution table. Once we have the area to the left, we can calculate the area to the right by subtracting this value from 1 (since the total area under the curve is 1). For a z-score of 1.04, the z-table shows that the area to the left is approximately 0.8508. Therefore, the proportion that is greater than a z-score of 1.04 is 1 - 0.8508, which equals 0.1492.
The standard normal distribution (Z~N(0,1)) has a total area of 1 under the curve, and it is symmetric about the mean, which is 0. Z-scores give us a way to determine how many standard deviations an observation is from the mean. Additionally, common z-scores used to determine confidence intervals or the proportion of observations within a certain range are tied to the percentage areas under the curve. For example, a z-score of ±1 encompasses approximately 68% of the data, ±2 about 95%, and ±3 approximately 99.7%.
How to determine the probability of an event with a small chance repeating?
A polynomial function P(x) has a degree n. If n is even is the number of turning points of the graph of p(x) even or odd? What can you say about the number of turning points if n is odd?
The number of turning points if n is odd if A polynomial function P(x) has a degree n, is even.
What is polynomial?A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.
Given:
A polynomial function P(x) has a degree n,
A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.
For example, if the degree is 2 then the number of turning points will be 1
The general formula is, the number of turning points = n - 1
Thus, for odd n, the turning point will be even.
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