The equation of a circle is x^2+ y^2+8x - 10y + 5 = 0
What are the center and the radius of the circle? Show your work.

She would be able to fill only one spherical mold with a diameter of 5 cm.

To calculate the number of spherical molds with a diameter of 5 cm that Carmen can fill with the same amount of powder, we need to compare the volumes of the two different sizes of molds.

The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere.

Let's calculate the volumes of the two different sizes of molds:

For the molds with a diameter of 4 cm:

- Radius (r) = diameter / 2 = 4 cm / 2 = 2 cm

- Volume (V1) = (4/3) * π * (2 cm)^3 ≈ 33.51 cubic centimeters

For the molds with a diameter of 5 cm:

- Radius (r) = diameter / 2 = 5 cm / 2 = 2.5 cm

- Volume (V2) = (4/3) * π * (2.5 cm)^3 ≈ 65.45 cubic centimeters

Now, let's calculate the number of molds with a diameter of 5 cm that can be filled with the same amount of powder:

Number of molds = V1 / V2 = 33.51 cubic centimeters / 65.45 cubic centimeters ≈ 0.512

Since we can't have a fraction of a mold, Carmen would be able to fill 0 molds with a diameter of 5 cm with the same amount of powder. In other words, she would not be able to fill any spherical molds with a diameter of 5 cm using the given amount of powder.

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The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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Hi there!

nearest percentage=64%

1.Subtract starting value and final value:

\(1599-579=1020\)

2.Divide it by the starting value:

\(1020*1599= 0.6378986866791744840525328330206378986\)

3.Multiply the term by 100:

\(0.6378986866791744840525328330206378986\)·\(100= 63.78986866791744840525328330206378986\)

4.Round the term:

\(63.78986866791744840525328330206378986=64\)

Therefore, the decrease of the total 8 years was 64%.

Answer:

64%

Step-by-step explanation:

579 is a 63.789868667917% decrease of 1599.

Percentage of decrease = |1599 - 579|/1599 = 1020/1599 = 0.63789868667917 = 63.789868667917%

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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Answer:

d

Step-by-step explanation:

I already did this before

Answer:

it B and D

Step-by-step explanation:

Step-by-step explanation:

9/25 of 100 did not like the book.

so, (25-9)/25 of 100 liked the book (because 25/25 is the whole 100 students).

the corresponding number of students we get

(25-9)/25 × 100 = 16/25 × 100 = 16 × 4 = 64

so, 64 students liked the book.

Step-by-step explanation:

success

:)

.................

Answer:jj

Step-by-step explanation:

iuin

tan(x) = 10/60

tan(x) = 1/6

tan(x) = a -> x = arctan(a) + πn

x = arctan(1/6) + πn

x = 0.165 + πn

Best of Luck!

The 100th term of the sequence is -273

Arithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference

first term a = 222

common difference, d = -5

nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d

T100 = a + ( 100 - 1 ) d

T100 = 222 + 99 * -5

T100 = -273

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Answer: C) The graph flips over the x axis.

This is because we're multiplying the y outputs by -1, to make them flip in sign from positive to negative (or vice versa).

Let's say the point (1,2) is on the f(x) curve. Multiplying y = f(x) by -1 will make the point turn into (1,-2). Apply this logic to every point on the f(x) curve and we end up with f(x) reflected over the horizontal x axis.

The notation we could write is either g(x) = -1*f(x) or g(x) = -f(x).

\(\displaystyle\bf 4x^2+3=-7x\\4x^2+7x+3=0 \\\\D=49-48=1 \\x_1=\frac{-7+1}{8} =-\frac{3}{4} \\x_2=\frac{-7-1}{8} =-1\\\\Answer: \boxed{ x_1=-\frac{3}{4} \quad ; \quad x_2=-1}\)

Answer:

14.8%

Step-by-step explanation:

The formula for market share = Total sales of the company at a particular period/ Total sales of the market × 100%

Total sales of the company = Breyer's sales = $650,417,792

Total sales of the market = Total sales in the ice cream category market = $4.4 billion

= $650,417,792/ $4,400,000,000, × 100

= 14.782222545%

Therefore, approximately to the nearest tenth, Breyer's market share is 14.8 %

Answer:

the amount of cupcakes

Step-by-step explanation:

you said the amount of cupcakes can be represented by

For a circle with a diameter of 10 cm, the circumference would be C = π(10) = 31.4 cm. The correct option is (D) 31.4 cm.

The circumference of a circle can be calculated using the formula           C = πd, where C represents the circumference and d represents the diameter of the circle.

We have the diameter of the circle is 10 cm, we can substitute this value into the formula:

C = π * 10 cm

Calculating the circumference using an approximate value of π as 3.14:

C ≈ 3.14 * 10 cm

C ≈ 31.4 cm

Therefore, the circumference of a circle with a diameter of 10 cm is approximately 31.4 cm.

The correct answer is D) 31.4 cm.

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Step-by-step explanation:

2x+y=3

y=3-2x.....eqn (1)

x=3y+5.....eqn(2)

substituting the value of y from eqn 1

x=3(3-2x)+5

x=9-6x+5

x+6x=14

7x=14

x=14/7

x=2

substituting the value of x in eqn 1

y=3-2×2

y=3-4

y=-1

therefore,

x=2

y=-1

Answer: x = 6

Step-by-step explanation:

30 + 12 = x (5 + 2)

x (5 + 2) = 30 + 12

x (7) = 42

7x = 42

Divide both sides by 7

x = 6

Answer:

30+12=x(5+2)

or,42=7x

or,x=42÷7

So,x= 6

Answer:

Sin 5/13

Cos 12/13

Tan 5/12

Csc 13/5

Sec 13/12

Cot 12/5

Step-by-step explanation:

Answer:

5 5/8

Step-by-step explanation:

This is in the simplest form

Answer:

583 x 6% = 34.98 = approximately 35

Answer:

\(

\begin{gathered}A=\underbrace{\begin{pmatrix}1&2\\4&3\end{pmatrix}}_{M_1}\underbrace{\begin{pmatrix}6&1&5\\7&3&4\end{pmatrix}}_{M_2}\end{gathered}\)

Step-by-step explanation:

\(If AA is \: the \: matrix \: product

\begin{gathered} \: A=\underbrace{\begin{pmatrix}1&2\\4&3\end{pmatrix}}_{M_1}\underbrace{\begin{pmatrix}6&1&5\\7&3&4\end{pmatrix}}_{M_2}\end{gathered}A=M1(1423)M2(671354)\)

The volume of the solid is 63 cubic units.

To calculate the volume of a pyramid, you can use the formula:

Volume = (1/3) * Base Area * Height

In this case, the base is a regular pentagon with an area of 27 and the altitude (height) of the pyramid is 7.

First, let's find the side length of the pentagon. Since a regular pentagon has all sides and angles equal, we can use the following formulas:

Area = (5/4) * side^2 * cot(pi/5)

27 = (5/4) * side^2 * cot(pi/5)

Now we solve for side:

side^2 = (27 * 4) / ((5/4) * cot(pi/5))

side^2 = 108 / ((5/4) * cot(pi/5))

side^2 = 108 * (4/5) * tan(pi/5)

side^2 = 86.4

side ≈ √86.4

side ≈ 9.306

Now we can calculate the volume using the formula:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * 27 * 7

Volume = 63 cubic units

Therefore, the volume of the solid is 63 cubic units.

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Answer:

5 spaces right

hope this helps

The percent of data within the interval from 39 to 55 which is normally distributed is 68.26%.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.

Given in the problem mean is 47 and Standard Deviation(SD) is 8

Probability of data within 39 to 55 is

P(x<55) - P(x<39)

Let Z be the standard deviation :

\(\phi(Z) = \frac{x - mean}{SD}\).

for  X = 39

\(\phi(Z) = \phi(\frac{x - mean}{SD})\) = \(\phi(\frac{39 - 47}{8}) = \phi(-1) = 1 - \phi(1) = 1-.8413 = .1587\)

for X = 55

\(\phi(Z) = \phi(\frac{x - mean}{SD})\) = \(\phi(\frac{55 - 47}{8}) = \phi(1) = .8413\)

The percent of data within the interval from 39 to 55

(.8413 - .1587) = .6826 = 68.26%

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The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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Answer:

c = 12.2

Step-by-step explanation:

a squared + b squared = c sqared

7 squared + 10 squared = 49+ 100 = 149 = \(\sqrt{x} 149\) = 12.2

The value of x that best match y = 12 is 4. Therefore, the answer is B. 4.

A scatter plot is a set of points plotted on a horizontal and vertical axis. In other words, a scatterplot is a type of data display that shows the relationship between two numerical variables.

Therefore, the scattered plot shows the relationship between the variable x and variable y as follows:

Let's trace the value of x that best fit the value of y = 12.

Hence, the value of x that fit y = 12 is 4.

Therefore, the answer is B.

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Answer:

37

Step-by-step explanation:

Anything multiplied by 0 is 0 then you just add the 37