What is the circumference and area of this circle? (Use 3.14 for pi)

Answer:

Step-by-step explanation:

570.675

The score of z when x = 72,

z = 1.273

The mean is = 58

∴ x = 72 is the 1.273 standard deviation to the right of the mean.

According to the data given in the above question,

John's average words = 58

Standard deviation = 11

⇒ X-N(58,11)

∴ John types 72 words per minute in a typing test on Sunday.

The z- score when x= 72,

X ≅ N(μ = 58 , σ = 11)

The z- score could be given by using the formula,

z = x - μ / σ

since

x = 71

μ = 58

σ = 11 ( standard deviation )

Putting the values in the formula of z-score,

z = \(\frac{72 - 58}{11}\)

z = 1.273

Therefore, the score of z when x = 72,

z = 1.273

The mean is = 58

∴ x = 72 is the 1.273 standard deviation to the right of the mean.

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Multiply both sides by \(x^{-3}\) to get a homogeneous equation.

\((2xy^2 - x^3) \, dy + (y^3 - 2yx^2) \, dx = 0 \\\\ \implies \left(2\dfrac{y^2}{x^2} - 1\right) \, dy + \left(\dfrac{y^3}{x^3} - 2\dfrac yx\right) \, dx = 0\)

Substitute \(y=vx\) and \(dy = x\,dv + v\,dx\). This makes the equation separable.

\((2v^2 - 1) (x\,dv + v\,dx) + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (2v^3 - v) \, dx + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (3v^3 - 3v) \, dx = 0\)

Separate the variables.

\(x (2v^2 - 1) \, dv = (3v - 3v^3) \, dx\)

\(\dfrac{2v^2-1}{3v-3v^3} \, dv = \dfrac{dx}x\)

\(\dfrac13 \dfrac{1 - 2v^2}{v(v-1)(v+1)} \, dv = \dfrac{dx}x\)

Expand the left side into partial fractions.

\(\dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac av + \dfrac b{v-1} + \dfrac c{v+1} \\\\ \dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac{a(v^2-1) + bv(v+1) + cv(v-1)}{v(v-1)(v+1)} \\\\ 1-2v^2 = (a+b+c) v^2 + (b-c) v - a\)

Solve for the coefficients \(a,b,c\).

\(\begin{cases} a + b + c = -2 \\ b-c = 0 \\ -a = 1 \end{cases} \implies a=-1, b=c=-\dfrac12\)

Thus our equation becomes

\(\left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \dfrac{dx}x\)

Integrate both sides.

\(\displaystyle \int \left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \int \dfrac{dx}x\)

\(\displaystyle -\frac13 \ln|v| - \frac16 \ln|v-1| - \frac16 \ln|v+1| = \ln|x| + C\)

Solve for \(v\) (as much as you can, anyway).

\(\displaystyle -\frac16 \left(2\ln|v| + \ln|v-1| + \ln|v+1|\right) = \ln|x| + C\)

\(\displaystyle \ln\left|\frac1{\sqrt[6]{v^2(v^2-1)}}\right| = \ln|x| + C\)

\(\displaystyle \frac1{\sqrt[6]{v^4-v^2}} = Cx\)

\(\sqrt[6]{v^4-v^2} = \dfrac Cx\)

\(\left(\sqrt[6]{v^4-v^2}\right)^6 = \left(\dfrac Cx\right)^6\)

\(v^4-v^2 = \dfrac C{x^6}\)

Put the solution back in terms of \(y\).

\(\left(\dfrac yx\right)^4-\left(\dfrac yx\right)^2 = \dfrac C{x^6}\)

\(y^4 - x^2y^2 = \dfrac C{x^2}\)

\(\boxed{x^2y^4 - x^4y^2 = C}\)

which is about as simple as we can hope to get this.

Answer:

Step-by-step explanation:

1. 882/24 = 36.75 or 37 crates of milk

2. 3712 x 6 = 1902 yoghurts were sold

3. 94291 - 63512 = 30779

4. 91429 is greater by (91429-42929) = 48500.

10. 7 hours 55 mins

1 month and 3 days or 33 days.

Next bus would pass at 8:15am

Answer:

Magic Land and Land of Make Belive

Step-by-step explanation:

they are 15 miles apart, while the other one is 11 miles.

Answer:

Land of make believe and Magic Land

Step-by-step explanation:

1 times 2 is equal to 2.

Multiplication is a mathematical operation that combines two numbers (known as "factors") to produce a third number (known as the "product"). It is represented using the symbol "x" or the asterisk (*).

For example, consider the multiplication of the numbers 2 and 3:

2 x 3 = 6

Here, 2 and 3 are the factors, and 6 is the product. Multiplication is a type of arithmetic operation that can be used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

In summary, multiplication is a mathematical operation that combines two numbers to produce a third number, and it is represented using the symbol "x" or the asterisk (*). It is an important operation in mathematics, used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

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Answer:

21x² - 19x + 4

Step-by-step explanation:

Step 1: Write factors

(7x - 4)(3x - 1)

Step 2: FOIL (First Outside Inside Last)

21x² - 7x - 12x + 4

Step 3: Combine like terms

21x² - 19x + 4

Answer:

21 cups of sugar

Step-by-step explanation:

so it gives you the ratio for cups of sugar(or as i'm going to use it, COS) and cups of flower(COF), which is 3:2, so if you have 14 cups of flower, you would divide 14 by the COF part of the ratio, which is 2, which gives you 7, then you would multiply the COS part of the ratio, which is 3, by 7 to get the number of cups of sugar needed for 14 cups of flower.

Answer:

20cm

Step-by-step explanation:

Given data

Radius= 4cm

Circumference= 20π

Let CD be the diameter of circle A

C= 2πr

20π= 2πr

10= r

Diameter= 2*r

D= 20cm

Hence the diameter CD= 20cm

Answer: positive 7

Step-by-step explanation:

Cardinal number of the set containing all negative integers greater than −8 is 7.

In mathematics,cardinal numbers or cardinals for short, are generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number: the number of elements in the set.

Now the given set is all negative integers greater than -8.

Let S be the set,so

S = {-7,-6,-5,-4,-3,-2,-1}

now to find the cardinality, we see that set S has 7 elements.

Cardinality of Set S is 7.

Hence, cardinal number of the set containing all negative integers greater than −8 is 7.

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The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Answer:

Hi

Please mark brainliest ❣️

Answer:

8/18 and 9/18

Step-by-step explanation:

Answer:

44 cupcakes

Step-by-step explanation:

Tammy baked a total of 20 cupcakes.

\( \therefore \) Daniella baked 4/5 of 20 cupcakes;

⟼ \( \sf \: \frac{4}{5} \times 20\)

⟼\( \sf \: \frac{4}{5} \times \frac{20}{1} \)

⟼\( \sf \frac{4}{ \sout{5}} \times \frac{ \sout{20}}{1} \)

⟼\( \sf\frac{4}{1} \times \frac{4}{1} \)

⟼\( \sf \: 4 \times 4\)

⟼ \( \sf \: = 16\)

Daniella baked 16 cupcakes

Since miko baked 1/2 of daniella

⟼ 1/2 * 16

⟼ 16/2

⟼ 8

Miko baked 8 cupcakes

Altogether they baked 8 + 16 + 20

⟼ 44 cupcakes

The 3 girls bake altogether 44 cupcakes if Tammy baked a batch of 20 cupcakes and Daniella baked 4/5 as many cupcakes as Tammy.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Tammy baked a batch of 20 cupcakes.

Daniella baked 4/5 as many cupcakes as Tammy.

Miko baked 1/2 as many cupcakes as Daniella.

Number of cupcakes Daniella baked = 4/5 of 20

Number of cupcakes Daniella baked = (4/5)20

Number of cupcakes Daniella baked = 16

Number of cupcakes Daniella baked = 1/2 of 16

Number of cupcakes Daniella baked = (1/2)16

Number of cupcakes Daniella baked = 8

Total number of cupcakes = 20 + 16 +8

Total number of cupcakes = 44

Thus, the 3 girls bake altogether 44 cupcakes if Tammy baked a batch of 20 cupcakes and Daniella baked 4/5 as many cupcakes as Tammy.

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After evaluating the given integral by changing to polar coordinates we get \(7 e^8-31\)

As per the details shared in the above question it is given that,

\($x^2+y^2=64$\)

\((x, y)=r(\cos \theta, \sin \theta)\)

\(d A=r d r d \theta.\)

Further solving above we get,

\(r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2\)

The polar coordinate,

\(\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta\)

\(& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r\)

\(=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .\)

\(=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8\)

Now substituting the value we get,

\(7 e^8-31\)

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Note the correct question should be ,

Evaluate the given integral by changing to polar coordinates.

\(\iint_R y e^x d A\) , where R is the region in the first quadrant enclosed by the circle  \(x^2+y^2=64\).

Answer:

essentially the question is if

\( \frac{14}{8} or \ \: \frac{12}{7} \)

is more

we can express the two fractions as 98/56 and 96/56

(56 is just 7*8)

now we can see that 14/8 is slightly more than 12/7, Drink a is your answer

Answer:

Air conditioners are rated by the number of British Thermal Units (BTU) of heat they can remove per hour. Another common rating term for air conditioning size is the "ton," which is 12,000 BTU per hour.

Each air conditioner has an energy-efficiency rating that lists how many BTUs per hour are removed or “pulled out” for each watt of power it draws.

The efficiency rating for room conditioners is the Energy Efficiency Ratio, or EER.

The efficiency rating for central air conditioners, is the Seasonal Energy Efficiency Ratio, or SEER.

These ratings are posted on an Energy Guide Label, which must be conspicuously attached to all new air conditioners. Energy Star-labeled appliances mean that they have high EER and SEER ratings

Answer:

19.5+24+7.5=51

19.5+7.5+24=51

19.5+24+7.5=51

I hope this help.

Answer:

Step-by-step explanation:

the 1st number of this series is x

because this series has 384 consecutive odd integers => this is a arithmetic sequence with d = 2

=> the sum of this series = \(384x+384(384-1) =384x+147072\)

but this series has a sum that is the perfect fourth power of a positive integer

=> 384x + 147072 = k^4 ( k is a positive integer)

to have the smallest sum => x must be the smallest odd integer.

+) with the sum = 104 976 => x isnt a integer => unreasonable

+) with the sum = 20 736 => x = -329

+) with the sum = 10000 =>x isnt a integer => unreasonable

+) with the sum = 1296 =>   x isnt a integer => unreasonable

+) with the sum = 38 416 => x isnt a integer => unreasonable

=> the smallest sum is 20 736

Answer:

The smallest sum is 20 736!

Step-by-step explanation:

Hope this helps!!! :))

After solving the expression, the value is negative 7 over 24 times k plus negative 6. Therefore, option C is correct.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given statement for the expression,

-(5/8)k - 8 + 2 + (1/3)k

Take LCM as 24 and solve the equation,

(-7k - 144) / 24

= (-7/24)k - 6

Therefore, this concludes that option C is correct.

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\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, \(\omega=14\ rev/min\)

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

\(\omega=14\ rev/min=1.46\ rad/s\)

Radius, r = 11.5 feet

Let v is the velocity. So,

\(v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s\)

Hernce, the correct option is (d) "16.86 ft/s"

Step-by-step explanation:

\( \frac{1000000}{10} \\ cancel \: one \: zero \: from \: nominator \: and \: denominator \\ = \frac{100000}{1} \\ = 100000\)

Answer:

Step-by-step explanation:

If the large Jar is $4.10 for 540g

and  small jar  $2.81 for 360 g

You need to show how much it cost for 1 g,so you can compare how much it cost per gram. You would divide the total cost by the grams to see how much it is for 1 g.

Large jar.   $4.10/540 = $.0076  for 1 gram

Small Jar.   $2.81/360 =$.0078 for 1 gram

Because the large jar is cheaper to buy per gram, the large jar is the best value for the money.

Answer:

432 = 2 square × 3 cube

Step-by-step explanation:

yan po ang alam ko...