The circumference of the circle is: 25.12 mm.
The Circumference of a CircleCircumference of a circle = 2πrGiven:
radius of circle = 4 mm
π = 3.14
Required:
Circumference of the circle
Thus:
Circumference of the circle = 2×3.14×4
Circumference = 25.12 mm
Therefore, the circumference of the circle is: 25.12 mm.
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The correct answer is the circle's circumference is approximately 25.12 millimeters.
To find the circumference of a circle, one can use the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( C \)[/tex] is the circumference, [tex]\( \pi \) (pi)[/tex] is a mathematical constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius of the circle.
Given that the radius [tex]\( r \)[/tex] is 4 millimeters, we can substitute the values into the formula:
[tex]\[ C = 2 \times 3.14 \times 4 \text{ mm} \][/tex]
Now, we perform the multiplication:
[tex]\[ C = 2 \times 3.14 \times 4 = 25.12 \][/tex]
There were 48 blue, 48 green and 48 yellow crayons. Also there were 72 red crayons and 120 colored pictures. What is the largest number of identical sets can be made of these crayons and pictures?
24 is the largest number of identical sets can be made of these crayons and pictures
What is Number system?A number system is defined as a system of writing to express numbers.
To find out the largest number of identical sets that can be made, we need to determine the common factors of the total number of crayons and pictures.
The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and since all three colors have the same number of crayons, we can say that there are 48 x 3 = 144 crayons in total.
The prime factorization of 72 is 2 x 2 x 2 x 3 x 3, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.
The common factors of 144, 72, and 120 are 2 x 2 x 2 x 3 = 24. This means that we can make 24 identical sets.
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The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 12 square cm/min. at what rate is the base of the triangle changing when the height is 4 centimeters and the area is 12 square centimeters?
When the height of a triangle is 4 cm and the area is 12 square cm, with the height increasing at 2 cm/min and the area increasing at 12 square cm/min, then the base of the triangle is changing at a rate of 5 cm/min.
Explanation:The subject of this question is Mathematics and is at the High School level. This question deals with the concept of related rates in calculus. First and foremost, remember the formula for the area of a triangle, which is A = 1/2bh, where A is the area, b is the base, and h is the height. Since we're given the rate of change of the height (dh/dt=2 cm/min) and the area (dA/dt=12 square cm/min), we can use this information in combination with the formula for the area of a triangle to derive an implicit function representing the rate of change of the base. By differentiating with respect to time t, we get dA/dt = 1/2b dh/dt + 1/2h db/dt. Plugging in the given values and solving for db/dt (the rate of change of the base length), we get db/dt = (2*dA/dt/h) - dh/dt. Then input the specific values at the given point, h = 4 cm and dA/dt = 12 square cm/min, dh/dt = 2 cm/min. The calculation results in db/dt = 5 cm/min. Therefore, the base of the triangle changes at a rate of 5 cm/min when the height is 4 cm and the area is 12 square cm.
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How would you write this equation in terms of sin and cos as well as simplify it from there?
(1+cotx)(1-cotx)-csc^2 x
can someone help me with factoring by grouping
x^3 + x^2 - 25x - 25
please show work
what is a real world triangle area problem
Final answer:
A real-world problem involving the calculation of a triangle's area could include finding the area of a triangular plot of land to determine how much grass seed is needed for landscaping. By using the formula for the area of a right-angled triangle, we can calculate the area in square meters and subsequently determine the required quantity of grass seed.
Explanation:
Real World Triangle Area Problem
Calculating the area of a triangle is a common problem in real-world applications. For instance, consider a scenario where you need to find the area of a triangular plot of land to determine how much grass seed to purchase for landscaping. If the plot is a right-angled triangle with one leg measuring 50 meters and the other leg measuring 40 meters, you can use the formula for the area of a right-angled triangle, which is ½ × base × height.
In this case, the base would be one leg of the triangle (50 meters), and the height would be the other leg (40 meters). Therefore, the area would be:
Area = ½ × 50 m × 40 m
Area = 25 m × 40 m
Area = 1000 square meters
Knowing the area of the triangular plot, you can then calculate the amount of grass seed needed, based on the recommended seeding rate per square meter. This practical example demonstrates how mathematics, specifically triangular area calculation, is applied in landscaping projects.
Hi! can someone please answer this question
NEED HELP The value of x is
.
Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i.
The first three iterates of the function f(z) = 2z + (3 - 2i) with z0 = 5i are 3 + 8i, 9 + 14i, and 21 + 26i after consecutive substitutions. The first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Explanation:To find the first three iterates of the function f(z) = 2z + (3 - 2i) with the initial value z0 = 5i, we perform successive substitutions into the function.
First iterate (f1): Substitute z0 into f(z)Second iterate (f2): Substitute f1 into f(z)Third iterate (f3): Substitute f2 into f(z)Thus, the first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Final answer:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, substitute the initial value into the function to get the first iterate. Then, substitute the first result back into the function to find the second iterate. Finally, substitute the second result back into the function to find the third iterate.
Explanation:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, we substitute the initial value into the function:
f(z0) = 2(5i) + (3 - 2i) = 10i + 3 - 2i = 3 + 8i.
Then, we substitute the result back into the function to find the second iterate:
f(3 + 8i) = 2(3 + 8i) + (3 - 2i) = 6 + 16i + 3 - 2i = 9 + 14i.
Finally, we substitute the second result back into the function to find the third iterate:
f(9 + 14i) = 2(9 + 14i) + (3 - 2i) = 18 + 28i + 3 - 2i = 21 + 26i.
Tommy has a coupon for an additional 25% off the price of any sale item at a store. The store has put a Art Kit on sale for 15% off the original price of $40. What is the price of the Art Kit after BOTH discounts?
the perimeter of a quarter circle is 14.28 KM. What is the quarter circle's radius?
Sam counted Out Loud by 6's Jorge counted Out Loud by 8s what are the first three numbers both Sam and George said
Each runner in a relay race runs one leg, or 1/8 kilometer. How many runners will it take to cover the 3/4 kilometer? Show your work.
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See attachment
It is the bottom left.
Which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5
m<1 +m<2 = 180° is the answer
Answer:
Third option is the right choice.
Step by step explanation:
We have been given an diagram and we are asked to choose the true statement about the diagram.
Let us see our all choices one by one.
1. [tex]m\angle5+m\angle6=m\angle1[/tex]
We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].
Therefore, 1st option is incorrect.
2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]
We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees. Therefore, 2nd option is also incorrect.
3. [tex]m\angle1+m\angle2=180^{o}[/tex]
We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.
4. [tex]m\angle2+m\angle3=m\angle5[/tex]
We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].
Therefore, our 4th option is also incorrect.
What is the value of X to the nearest 10th? The figure is not drawn to scale.
Answer: C: 9.26
Step-by-step explanation:
whatcis 72/90 reduced
find the unknown in the equation. Blake ×1/6=1/6+1/6+1/6
Nadia cuts 3 pieces pf equal length from 8 yards of ribbon. How long is each piece?
Answer: Each piece is 2.6 long
Step-by-step explanation: All you have to do is divide 8 and 3 and you will get 2.6
(sorry if i'm wrong)
Find two numbers, if their sum is 6 and their difference is 36
The two numbers will be 21.5 and -14.5. Addition, subtraction, multiplication, and division are the four basic math operations.
What is an arithmetic operation?Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.
Let the two numbers will be x and y
The sum of the two numbers is 7
x+y=7 ------ 1
The difference between the two numbers is 36
x-y=36 -------2
On subtracting the equation 2 by equation 1 we get;
x-y-x-y=36-7
-2y=29
y= -14.5
From equation 1
x+y=7
x-14.5=7
x=7+14.5
x=-21.5
Hence the two numbers will be 21.5 and -14.5.
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A calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. find the mean and standard deviation of the number of questions that he/she gets correct
Exhibit 4-3 x: 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 refer to exhibit 4-3. what is the mean?
carla travels on a high speed train for 30 minutes. If she travels 160 km, how many kilometers will she travel in one hour
plz help
An acute angle θ is in a right triangle with cos θ =2/3 . What is the value of sec θ?
Final answer:
The secant of an angle is the reciprocal of its cosine. Given cos θ = 2/3 for an acute angle in a right triangle, the sec θ equals 3/2.
Explanation:
In the context of trigonometry, the secant (sec) of an angle is the reciprocal of the cosine (cos) of that angle.
Given that cos θ = 2/3 for an acute angle in a right triangle, we can find the value of sec θ by taking the reciprocal of the cosine value. Hence, the value of sec θ is simply the reciprocal of 2/3, which is 3/2.
turn 1/8 into a percent
The Treasury Department auctioned $15 billion in 3-month bills in denominations of $10,000 at a discount rate of 3.750%.
What would be the effective rate of interest? (Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent.)
adding fractions with denominators of 10 and 100
4x + 3y =4 2x - y =7 in substitution
During a laboratory experiment, the average number of radioactive particles passing through a counter in 1 millisecond is 4. what is the probability that 6 particles enter the counter in a given millisecond?
The probability of exactly 6 radioactive particles passing through a counter in 1 millisecond, with an average rate of 4, is approximately 0.1041 or 10.41%.
To find the probability of a specific number of events occurring in a Poisson distribution, use the formula:
P(X = k) = [tex](e^{(-\lambda)} \times \lambda^k) / k![/tex]
Where:
P(X = k) is the probability of observing k events.
e is the base of the natural logarithm, approximately equal to 2.71828.
λ (lambda) is the average rate of events occurring in a given time period.
k is the number of events you want to find the probability for.
k! is the factorial of k.
λ is the average number of radioactive particles passing through the counter in 1 millisecond, which is 4.
So, to find the probability of 6 particles entering the counter in a given millisecond:
P(X = 6) = (e⁻⁴) × 4⁶) / 6!
Let's calculate it step by step:
Calculate 6! (6 factorial):
6! = 6 x 5 x 4 x 3 x 2 x 1
= 720
Calculate e⁻⁴:
e⁻⁴ ≈ 0.01832 (rounded to five decimal places)
Calculate 4⁶:
4⁶ = 4 x 4 x 4 x 4 x 4 x 4
= 4,096
Now, plug these values into the formula:
P(X = 6) = (0.01832 × 4,096) / 720
P(X = 6) ≈ 0.1041
Therefore, the probability that exactly 6 radioactive particles enter the counter in a given millisecond is approximately 0.1041, or about 10.41%.
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Rhono has a part-time job at the local supermarket working 3 hours after school each night and 5 hours on saturdays. His gross hourly pay is $8.75. Estimate and then calculate his next wages for the month, after 20% tax is deducted. Each month his expenses are: Entertainment $35.00, health and beauty $21.00, transport $18.00, clothing $24.00, hire purhases payments $15.75. Calculate the amount Rhono has left over at the end of each month, and how much he would have saved at the end of 12 months.
Rhono earns a net monthly pay of $560.00 after taxes, with monthly expenses totaling $113.75. This leaves him with $446.25 per month, resulting in a total savings of $5,355.00 at the end of 12 months.
Let's calculate Rhono's monthly wages first.Rhono works:
- 3 hours each night after school
- 5 hours on Saturdays
His gross hourly pay is $8.75.
To calculate his monthly wages, we need to find his total hours worked per month.In a week, he works 3 hours × 5 days from Monday to Friday and 5 hours on Saturday,
which totals 15 hours + 5 hours
= 20 hours per week.
In a month (considering approximately 4 weeks per month), he works 20 hours × 4 weeks
= 80 hours per month.
Now, let's calculate his gross monthly income before tax deductions:Gross monthly income = hourly wage × total hours worked per month
Gross monthly income = 8.75 × 80
Gross monthly income = $700
Now, let's calculate the amount of tax that will be deducted.Rhono's gross monthly income is $700, and 20% of this will be deducted.
Tax deduction = 0.20 × 700
Tax deduction = 140
Now, let's calculate his total monthly expenses:Total monthly expenses = 35.00 + 21.00 + 18.00 + 24.00 + 15.75
Total monthly expenses = $113.75
Now, let's calculate the amount Rhono has left over after tax and expenses:Net monthly income = Gross monthly income - Tax deduction - Total monthly expenses
Net monthly income = 700 - 140 - 113.75
Net monthly income = $446.25
This is the amount Rhono has left over at the end of each month.
To calculate how much he would have saved at the end of 12 months, we multiply this amount by 12:Total savings after 12 months = 446.25 × 12
Total savings after 12 months = $5,355
So, Rhono would have saved $5,355 at the end of 12 months.
Karim was planning for his vacation to the Bahamas. To cover his costs, he took out a $15,800, 4% simple discount note and paid a $40 bank discount. What was the approximate length of his loan in days? Assume a 360-day year.