Answer:
r=1/π
Step-by-step explanation:
Area of the circle is defined as:
Area = πr²
Derivating both sides
[tex]\frac{dA}{dr}[/tex]=2πr
[tex]\frac{dA}{dt}[/tex] = [tex]\frac{dA}{dr}[/tex] x [tex]\frac{dr}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : [tex]\frac{dA}{dt}[/tex] =2[tex]\frac{dr}{dt}[/tex]
Therefore,
2πr [tex]\frac{dr}{dt}[/tex] = 2 [tex]\frac{dr}{dt}[/tex]
r=1/π
Answer:
r = 1/π
Step-by-step explanation:
Here we have
Area of a circle given as
Area = πr²
Where:
r = Radius of the circle
When the area of the circle is expanding twice as fast s the radius we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt}[/tex]
However,
[tex]\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}[/tex] and
[tex]\frac{dA}{dr} = \frac{d\pi r^2}{dr} = 2\pi r[/tex]
Therefore, we have
[tex]\frac{dA}{dt} =2 \times \frac{dr}{dt} = 2\pi r \times \frac{dr}{dt}[/tex]
Cancelling like terms
[tex]1= \pi r[/tex]
Therefore, [tex]r = \frac{1}{\pi }[/tex].
what is the range of 66, 8, 12, 74, 36, 66, 7
Answer: 67.
Step-by-step explanation: To find the range of a set of numbers, all you have to do is subtract the smallest number in the set from the largest number. In this case, the smallest number would be 7 and the largest number would be 74. 74 - 7 equals 67, and so the range is 67.
Final answer:
The range is the difference between the largest and smallest numbers in the set. For the numbers 66, 8, 12, 74, 36, 66, 7, the range is 67.
Explanation:
The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 66, 8, 12, 74, 36, 66, 7, you would first identify the smallest and largest number, which are 7 and 74, respectively. Then, subtract the smallest number from the largest number: 74 - 7 = 67.
Therefore, the range of the set of numbers is 67.
do i use sin cos or tan to solve this problem
u use sin and just do sin(x)=29/34 and then use inverse sin
I need help ASAP. Will give 20 points :0 It may look easy, but it's really hard for me
The first "choose" is divide or multiply
The second "choose" is 3, 12, or 36
Answer:
divide and 12
42
Step-by-step explanation:
Hope it helps!
Answer:
divide by 12!
Step-by-step explanation:
to convert inches to feet you divide by 12. to convert feet to inches you multiply by 12
Expand: In 2a^3/b^4
In 2 + 3 In a - 4 In b
In 2 - 3 In a - 4 In b
In 2 - 3 In a + 4 In b
Answer:
ln(2) +3ln(a) -4ln(b)
Step-by-step explanation:
[tex]\ln{\left(\dfrac{2a^3}{b^4}\right)}=\ln{(2a^3b^{-4})}=\ln{(2)}+\ln{(a^3)}+\ln{(b^{-4})}\\\\=\boxed{\ln{(2)}+3\ln{(a)}-4\ln{(b)}}[/tex]
__
The applicable rules of logarithms are ...
log(ab) = log(a)+log(b)
log(a^b) = b·log(a)
Final answer:
To expand the expression In 2a³/b⁴, you apply logarithm properties to obtain In 2 + 3 In a - 4 In b, which separates the factors into individual log terms.
Explanation:
The question asks us to expand the logarithmic expression In 2a³/b⁴ using logarithm properties. The correct expansion of this expression is given by the sum of the logarithms of the numerator's factors minus the sum of the logarithms of the denominator's factors. Applying the properties of logarithms (product to sum and quotient to difference), we obtain the expansion as follows:
In 2a³/b⁴ = In 2 + In a³ - In b⁴
The logarithm of a power (such as In a³ and In b⁴) can be brought down as a coefficient:
In 2 + 3 In a - 4 In b
Thus, the correct expansion is In 2 + 3 In a - 4 In b.
what is 90 percent of 69?
Answer:
62.1
Step-by-step explanation:
90 percent means there are 90 parts from all 100 parts
90/100 × 69 = 62.1
Answer:
62.1
Step-by-step explanation:
I dont really have an explanation. sorry :(
514) 30 + 38(n +22) = -33(n +34)
expand the brackets
Answer:
CHALLENGE ACCEPTED!
Step-by-step explanation:
15420 + 38N + 836 = -33N - 1122
15420 + 836 + 1122 = -333N -38N
17378 = -371N
N = -46.8
WILL MARK BRAINLIEST
(see picture attached)
Answer choices:
4
6
12
24
Answer:
Step-by-step explanation:
24 i think so
Linear relations I need help on these two
Which ordered pair is a solution of the equation?
What is the surface area of the box formed by the
net above?
A. 162cm?
B. 244cm?
2640cm?
D. 3040cm?
Answer:
B.
Step-by-step explanation:
It just is...i got it right
what is the 25th term of the arithmetic sequence of -84, -77, -70, ...
Answer:
Your're answer is 84.
The sum of the angle measures in a triangle is 180. The angles of a
certain triangle measure x°, 2xº, and 6x° Solve for the measure of
each angle.
40°, 60° and 80°
50°, 50° and 80°
20°, 40° and 120°
30°, 50° and 100°
Answer:
20, 40, and 120
Step-by-step explanation:
x, 2x, and 6x have one thing in common: X. X is the same number throughout so if we find x we can just finish the equation by multiplying x by its coefficient.
x+2x+6x = 180. (Sum of angle measures)
9x = 180 (Add up the left side)
9x/9 = 180/9 (Divide both sides by 9 to cancel out the 9 and leave the x)
x = 20
Now we know what x is so:
Angle 1 = 20. (We know x is 20, so that one is easy.)
Angle 2 = 40 (Simply 2*x or 2*20)
Angle 3 = 120 (Simply 6*x or 6*20)
A sweater is marked down 30% off the original price. The original price was $37.50. What is the sale price of the sweater before tax?
Answer:
26.25
Step-by-step explanation:
Which values are solutions of the quadratic equation
0 = (x + 3)2 - 4? Check all that apply.
On a map of the United States, the length between NYC and Boston is 5 inches. If the scale factor is 1 inch- 48 miles. What is te actual distance between NYC and Boston? Show/ Explain your answers.
Answer:
240
Step-by-step explanation:
48*5=240
The actual straight-line distance between New York City (NYC) and Boston is calculated by multiplying the map distance of 5 inches by the scale factor of 48 miles per inch, resulting in 240 miles.
The question involves finding the actual distance between New York City (NYC) and Boston based on a map scale. The given scale is 1 inch to 48 miles, and the map shows a distance of 5 inches between the two cities.
To calculate the actual distance, we use the scale factor. Multiply the map distance by the scale factor:
Map distance between NYC and Boston: 5 inches
Scale factor: 1 inch equals 48 miles
Actual distance calculation: 5 inches x 48 miles per inch = 240 miles
Therefore, the actual straight-line distance between New York City and Boston is 240 miles.
The scale for a model car is 2 inches : 2 feet. What is the height of the
actual car in feet?
Answer:
11 ft by 5.5 ft
Step-by-step explanation:
The scale is 2in for 2 ft or 1in for 1ft
This means that you can just take the number in inches and change it to feet. Therefore 11 inches turns to 11 feet and 5.5 inches turns into 5.5 feet.
Jada traveled 135 miles in 3 hours.Andre traveled 228 miles in 6 hours.Both jada and Andre traveled at a constant speed
Answer:
(a) 45 miles
(b) 38 miles
(c) Jada travels faster than Andre.
Step-by-step explanation:
(a) First we calculate the speed at which Jada travelled:
[tex]Speed = \frac{distance}{time} \\\\\\s = \frac{d}{t}[/tex]
[tex]s = \frac{135}{3} \\\\\\s = 45 miles/hour[/tex]
Since Jada travels at constant speed throughout the journey, we can calculate the distance traveled in 1 hour:
[tex]distance = speed * time\\\\\\distance = 45 * 1[/tex]
distance = 45 miles
Jada travels 45 miles in 1 hour.
(b) We calculate the speed at which Andre travelled:
[tex]Speed = \frac{distance}{time} \\\\\\s = \frac{d}{t}[/tex]
[tex]s = \frac{228}{6} \\\\\\s = 38 miles/hour[/tex]
Since Andre travels at constant speed throughout the journey, we can calculate the distance traveled in 1 hour:
[tex]distance = speed * time\\\\\\distance = 38 * 1[/tex]
distance = 38 miles
Andre travels 38 miles in 1 hour.
(c) Jada travels faster than Andre because he has a higher speed (45 miles/hour) than Andre ( 38 miles/hour).
Find the quotient. (3.683 × 104) (7.51 × 1012) What is the solution in scientific notation?
A.4.9041 × (-9)10
B.4.9041 × 10-9
C.4.9041 × 109
D.4.9041 × 910
Answer:
B
Step-by-step explanation:
[tex]\frac{3.683 \times 10^4}{7.51 \times 10^{12}} \\=\frac{36.83 \times 10^3}{7.51 \times 10^{12}} \\=\frac{36.83}{7.51} \times 10^{3-12}\\ \approx 4.9041 \times 10^{-9}[/tex]
The quotient in the scientific notation form will be 4.9041 × 10⁻⁹. The correct option is B.
What is a scientific notation?Scientific notation can be used to indicate numbers that are either too big or too little to be conveniently stated in decimal form. It may be called scientific form.
Standard notation is the practice of writing a number using nothing but its digits. This is how numbers are usually expressed because traditional number notation does not utilize words.
Given that the two numbers are (3.683 × 10⁴) and (7.51 × 10¹²). The quotient will be calculated as:-
Quotient = (3.683 × 10⁴) ÷ (7.51 × 10¹²)
Quotient = 0.49 x 10⁻⁸
Quotient = 4.9 x 10⁻⁹
The quotient will be 4.9041 × 10⁻⁹.
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Nathan and Jorge are working on a decimal division problem in
math class. After finishing the problem, it looked like this: 4.76 ÷
2.5 = 0.19. Nathan said that the decimal is incorrectly placed in the
quotient, and Jorge disagrees. Who is right? Explain your answer.
Answer:
Nathan
Step-by-step explanation:
Because 4.76 ÷ 2.5 is 1.904
Nathan is correct about the decimal being misplaced in the quotient. The correct division of 4.76 by 2.5 should give 1.904 when rounded off to two decimal places.
Explanation:In this case, Nathan is correct in stating that the decimal is misplaced in the quotient. When rounding to two decimal places, the correct calculation should be 4.76 ÷ 2.5 = 1.904, not 0.19. The decimal point division process can be simplified as follows:
Write the division as a fraction (4.76/2.5) and change both numbers into whole numbers by moving the decimal places to the right until you have whole numbers (47.6/25 = 476/250).Next, perform the division operation as you would with whole numbers (476÷250 = 1.904).Another approach would be to simply use a calculator to confirm the correct division of 4.76 by 2.5.
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A 12 pack of soda is roughly $2.52. What is the cost per one can of soda?
Answer:
$2.52/12= $.21
the cost of one can of soda is $.21
Step-by-step explanation:
Answer:
$0.21 per can.
Step-by-step explanation:
You divide the amount of money for all 12 cans by 12.
2.52/12=0.21
If the mean salary of high school teachers In the United States is $42,335 and the standard deviation is 2,000 the probability that a randomly selected teacher will make more than $40,542 per year
Answer: The probability that a randomly selected teacher will make more than $40,542 per year is 0.82
Step-by-step explanation:
Looking at the information given, the population mean and population standard deviation are known. We would apply the formula
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = population standard deviation
From the information given,
µ = $42335
σ = 2000
x = $40542
The probability that a randomly selected teacher will make more than $40,542 per year is expressed as
P(x > 40542) = 1 - P(x ≤ 40542)
For P(x ≤ 40542),
z = (40542 - 42335)/2000 = - 0.9
Looking at the normal distribution table, the probability corresponding to the z score is 0.18
P(x > 40542) = 1 - 0.18 = 0.82
A university has 28,470 students. In a random sample of 285 students, 19 speak three or more languages. Predict the number of students at the university who speak three or more languages. The expected number of students at the university who speak three or more languages is .
Answer:
The expected number of students at the university who speak three or more languages is 1898.Step-by-step explanation:
Given that A university has 28,470 students.
In a random sample of 285 students, 19 speak three or more languages.
To find the expected number of students at the university who speak three or more languages :From the given 19 out of 285 speaks three or more languages, a expected number of students would be given by
[tex]28470\times (\frac{19}{285})[/tex]
[tex]=\frac{540930}{285}[/tex]
[tex]=1898[/tex]
∴ the expected number of students at the university who speak three or more languages is 1898Which two numbers go into the blanks so they add to be the bottom number but also multiply to be the top?
Answer:
8 and 6
Step-by-step explanation:
8 * 6 = 48
8 + 6 = 14
Joni has a box that has a mass of 67 dekagrams. She converts this to centigrams. Her work is shown below.
67 dekagrams + 1,000+ 0.067 centigrarns
Which statement explains Joni's error? Use the metric table to help answer the question.
kilo-
1.000
hecto
100
deka-
10
Metric Table
unit
1
1
deci-
0 .1
centi-
0.01
milli-
0.001
Joni should have multiplied by 10,000,
Joni should have multiplied by 1,000.
Joni should have divided by 100.
Joni should have divided by 10,000,
Mark this and return
Save and Exit
Next
Submit
Joni should have multiplied by 1,000.
Step-by-step explanation:
Mass of the box = 67 decagrams
1 decagram = 1000 centigrams
So, 67 decagrams = 67 x 1000 centigrams
= 67000 centigrams
Joni should have multiplied by 1,000.
Answer:
its A
Step-by-step explanation:
got it right on EDG
84 is what percent of 300
84 of 300 is 252.
84% × 300 =
84 ÷ 100 × 300 =
84 × 300 ÷ 100 =
25200 ÷ 100 =
252
I'm having trouble with solving logs...can anyone please explain how to solve these two?
#19
[tex]a) 3-3log30\\\\b) \frac{1}{3} log_{6} (8w^6)[/tex]
Answer:
A.) [tex]3-3\log _{10}\left(30\right)[/tex] or -1.43136... (Decimal Form)
B.) [tex]\log _6\left(2\right)+2\log _6\left(w\right)[/tex]
Explanation: I inserted image to explain how to solve the second one, but for the first one you can't go any further except writing it in standard form or changing it into a decimal.
Your welcome :3
A country's Department of Wildlife hires Elizabeth to estimate its wild goat population. Elizabeth catches 75 goats, tags them, and releases them. Then Elizabeth uses binoculars to observe a group of 260 goats, 25 of which are tagged. To the nearest whole number, what is the best estimate for the goat population?
Answer:
300
Step-by-step explanation:
if Elizabeth tagged 75 and observes 260 with 25 already taged yo need to add 260+75-25+310
since you need to round to nearest whole number it will be 300
I believe that is is 300
Multiply.
Your answer should be a monomial in standard form.
(-9n^3)(n^3)
To multiply monomials, you multiply the coefficients and add the exponents of like variables. The product of -9n^3 and n^3 is -9n^6.
Explanation:The question is about multiplying two monomials in mathematics. In this case, the two monomials are -9n^3 and n^3. To multiply monomials, you multiply the numerical coefficients and add the exponents of like variables. Here, the coefficient is -9 and the exponent 3 for the first monomial and 1 and 3 for the second monomial. When you multiply -9 by 1, you get -9. When you add the exponents 3 and 3, you get 6. So, the product of those two monomials in standard form is -9n^6.
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At an ice cream shops there are 3 different flavors of ice cream and 10 different toppings. What is the probability of the next customer ordering strawberry ice cream with sprinkles? Use a / to represent the fraction bar.
Answer:
1/30 = 3.33%
Step-by-step explanation:
There are 3 different flavors available and the favorable outcome is only strawberry flavor. There are 10 toppings and the favorable outcome is sprinkle. To calculate the probability for the two events, you just need to multiply both. The calculation will be:
P(strawberry) * P(sprinkle) = 1/3 * 1/10= 1/30
The probability of the next customer ordering strawberry ice cream with sprinkles, given that there are 3 flavors and 10 toppings, is 1/30.
The student asks about the probability of a specific ice cream order at an ice cream shop, which involves both flavor selection and topping selection. Since there are 3 different flavors and 10 different toppings, we treat these choices as independent events. The probability of selecting strawberry ice cream is 1/3, as it is one of the three available flavors. The probability of selecting sprinkles as a topping is 1/10, since it is one of ten toppings. To find the total probability of both events occurring (strawberry ice cream with sprinkles), we multiply the two separate probabilities:
Probability = Probability of strawberry ice cream times Probability of sprinkles = 1/3 times 1/10 = 1/30.
Is the following real-world scenario a Quadratic, Exponential, or Linear function?
"A library has 8000 books, and purchases 500 more books each year."
Answers
(A)Quadratic Model
(B)Exponential Model
(C)Linear Model
(D)None of the Above
Answer:
C: Linear model
Step-by-step explanation: