Find the surface area of the sphere. Round to the nearest tenth.

7.6 mi

Given the equation x² + y² + 4x - 8y + 11 = 0, the center of the circle is (-2, 4).

The standard form of the equation of circle is given by

(x - h)² + (y - k)² = r²

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x² + y² + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h² + k² - r².

If the equation of the circle in general form is x² + y² + 4x - 8y + 11 = 0, then the coefficients are:

D = 4

E = -8

F = 11

If D = -2h and D = 4, then

4 = -2h

h = -2

If E = -2k and E = -8, then

-8 = -2k

k = 4

Hence, the center of the circle is (h, k) = (-2, 4).

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The probability of Hae 0.randomly picking a red ball from is 0.54.

Based on the given information, the odds in favor of Hae picking a red ball are 2:11. This means there are 2 favorable outcomes (picking a red ball) for every 11 unfavorable outcomes (not picking a red ball). To find the probability of Hae picking a red ball, we can use the following formula:
Probability = Favorable outcomes / (Favorable outcomes + Unfavorable outcomes)
In this case, there are 2 favorable outcomes and 11 unfavorable outcomes. So, the probability of Hae picking a red ball is:
Probability = 2 / (2 + 11) = 2 / 13
So, the probability of Hae randomly picking a red ball from the bag is 0.54.

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Answer:

1,680

Step-by-step explanation:

If the population is increasing by 60 for the next 13 years, we must multiply 60 and 13 to get 780.

Then, we just add 780 to the original population to get 1,680!

The enrollment after 13 years will be 1680.

We have a whose school population is predicted to increase by 60 students per year for the next 13 years. Current enrollment in that school is 900 ​students.

We have to determine the enrollment be after 13 ​years.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to question, we have -

Initial population P(i) = 900

Assume the population after the n years is P(n).

Number of students enrolled in 'n' years will be = 60n

Therefore, the following equation can be used -

P(n) = P(i) + 60n

For n = 13 years

P(13) = 900 + 60 x 13 = 900 + 780 = 1680

Hence, the enrollment after 13 years will be 1680.

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:

a=7300, b=1.0108.

L(t) = 7300(1.0108)^t

Step-by-step explanation:

First, we can see that L(t) = 7300(1.012)^(4t) can be rewritten as L(t) = 7300e^(4tln(1.012))

Using the properties of logarithms, we can simplify this to L(t) = 7300e^(4t(ln(1.012))

Now, we can see that the function L(t) is in the form L(t) = ab^t, where a = 7300 and b = e^(ln(1.012))

Therefore, we can write the equivalent function as L(t) = 7300e^(0.048t)

The final values rounded to 4 decimal places are a=7300, b=1.0108.

L(t) = 7300(1.0108)^t

Answer

L(t)=

7300

1.0489

7300(1.0489)

Step-by-step explanation:

Answer:

3. 33

4. g(x) = 3 (1+n)

Step-by-step explanation:

For the equation, I am not entirely sure that is what your teacher is looking for, but it definitely works! : )

To make it I just said that it looked like there were three different equal parts to the figures, and the area of the parts increases by one every time. So I just added 1 to whatever number it is which gets the area of one of the parts, and multiplied it by 3!

For number 3, I just plugged it into the equation I just made.

g(x) = 3(1+(10))

      = 3(11)

      = 33

Answer:

x = 11 explanation : " $3 subtracted from the cost of the book just number 8! " As an equation this would be : x - 3 = 8 SOLVE x - 3 = 8   + 3  + 3 x = 11 KEY x = cost of book 

hope it helps

Answer:

Step-by-step explanation:

The two numbers with a difference of 10 and the minimum product are -10 and 0. The minimum product is 0.

the equation (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions. Therefore the correct option is a.

To determine which equation(s) have both 2 and -5 as solutions, substitute these values into each equation and see if they satisfy the equation. Let's check each option:

a. \(x^2 + 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 + 3(2) - 10 = 4 + 6 - 10 = 0\)

Substituting x = -5:

\((-5)^2 + 3(-5) - 10 = 25 - 15 - 10 = 0\)

Both 2 and -5 satisfy the equation, so option a has both 2 and -5 as solutions.

b. \(x^2 - 3x - 10 = 0\)

Substituting x = 2:

\((2)^2 - 3(2) - 10 = 4 - 6 - 10 = -12\)

Substituting x = -5:

\((-5)^2 - 3(-5) - 10 = 25 + 15 - 10 = 30\)

Neither 2 nor -5 satisfy the equation, so option b does not have both 2 and -5 as solutions.

c. \(x^2 + 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 + 7(2) + 10 = 4 + 14 + 10 = 28\)

Substituting x = -5:

\((-5)^2 + 7(-5) + 10 = 25 - 35 + 10 = 0\)

Only -5 satisfies the equation, so option c does not have both 2 and -5 as solutions.

d. \(x^2 - 7x + 10 = 0\)

Substituting x = 2:

\((2)^2 - 7(2) + 10 = 4 - 14 + 10 = 0\)

Substituting x = -5:

\((-5)^2 - 7(-5) + 10 = 25 + 35 + 10 = 70\)

Only 2 satisfies the equation, so option d does not have both 2 and -5 as solutions.

In conclusion, the equation in option a (\(x^2 + 3x - 10 = 0\)) has both 2 and -5 as solutions.

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To find the slope of the tangent line and the instantaneous rate of change of the function at the point (-2,0), we first need to find the derivative of the function:

y = (x^2 + 3)(x^3 - 4x)

y' = [(2x)(x^3 - 4x) + (x^2 + 3)(3x^2 - 4)]

= 2x^4 - 8x^2 + 3x^2 - 4

= 2x^4 - 5x^2 - 4

(a) To find the slope of the tangent line at (-2,0), we substitute x = -2 into the derivative:

y' = 2(-2)^4 - 5(-2)^2 - 4 = 24

Therefore, the slope of the tangent line at (-2,0) is 24.

(b) The instantaneous rate of change of the function at (-2,0) is also given by the derivative at that point:

y'(-2) = 2(-2)^4 - 5(-2)^2 - 4 = 24

Therefore, the instantaneous rate of change of the function at (-2,0) is 24.

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Answer:

a) (2,9); b) no points of intersection

Step-by-step explanation:

a)

Set the two equations equal to each other

7x - 5 = -2x + 13

Rearrange collecting like terms and solve

9x = 18

x = 2

Sub in x = 2 into either of the equations and it should yield the same result

Eq.1 y = 7(2) - 5 = 9

Eq.2 y = -2(2) + 13 = 9

Therefore the point of intersection is (2,9)

The graph confirms this result (see graph 1 with red and blue lines)

b)

As the gradients are the same, we can tell straight away that the two lines should be parallel and never intersect, but we'll try to solve it algebraically using the same method as in part a.

3x - 1 = 3x + 2

When rearranging, the x's cancel out which can be seen when subtracting 3x from both sides

-1 = 2

This equation is clearly incorrect. This means that there are no values of x at which the two equations are equal. Graphically, this means that the two lines are parallel and there are no points of intersection (see graph 2 with purple and green lines)

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

Answer:

d. number of students wearing blue shirts

Answer:

x/8 = 21/3

x = 21/3 * 8

x = 56 m

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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Answer:

For me, it always helps to break down equations like this. Divide it up into two separate parts.

4^2*4^2=x

4^2=16

Replace both 4^2 with 16

16*16=256

Answer:11 kids were at the party

Step-by-step explanation:24 slices in all , 22 were eaten so that means 22 divided by 11 is 2 so there was 11 kids

Answer:

11 children

Step-by-step explanation:

First you have to do 8 times 3 to get the number of slices of pizza there were.

Then you have to divided that by 2. But remember, there are 2 slices left.

So, you have to take away one child to get the answer: 11 children

I feel bad for that last child. I hope this helped ;)

Let x = 0.757575... . Then

100x = 75.757575...

and so

100x - x = 75.757575... - 0.757575...

99x = 75

x = 75/99 = 25/33

Answer:

A

Step-by-step explanation:

Answer:

pretty sure its non- proportional. Sorry if in wrong!!!

there is no answer to this this is simply impossible

Answer:

The responses for the seniors are reversed.

Hope this helped!

Answer:

8990

Step-by-step explanation:

The 9 underlined is in the tens place.

8990.97 ⇒ 8990

Since you can't round up, you replace everything after the underlined 9 with 0's.

8990.00 = 8990

The statement "the San Gabriel Mountains are 60 miles lengthy, 24 miles wide, and more or less 10,000 feet high (at their highest)" is true.

The San Gabriel Mountains are a mountain range positioned in Southern California, walking east-west across los angeles County. They stretch for approximately 60 miles from the Cajon bypass inside the east to the San Fernando Valley inside the west and are around 24 miles wide.

The best peak within the range is Mount San Antonio, also referred to as Mount Baldy, that is kind of 10,000 ft high. The San Gabriel Mountains are a famous destination for out of doors sports consisting of hiking, camping, and snowboarding, and are an vital supply of water for the los angeles place.

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Answer: He did not convert the fractions into the like fraction to add.

Step-by-step explanation:Given: The distance Jonah runs on Sunday=  milesThe distance Jonah runs on Monday=  milesThe total distance he ran = Since both the fractions are not like , thus multiply 2 to the numerator and the denominator of the first fraction [to add fractions first convert them into like fractions], we get The total distance he ran = The right answer is "The total distance he ran ="

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

\(72 = 2^3 * 3^2\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\\)

The GCD of the crayons is \(2^3 * 3\), which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = \(2^3 * 3 * 5\)

The GCD of the drawing paper is also \(2^3 * 3\), which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

t = 4d + 5

Step-by-step explanation:

The answer can be obtained through trial and error method.

Checking :

(1) d = 1

t = 4d + 5

t = 4 (1) + 5

t = 4 + 5

t = 9

(2) d = 5

t = 4d + 5

t = 4 (5) + 5

t = 20 + 5

t = 25

To be 95% confident that the sample's variance is within 40% of the population's variance, the minimum sample size needed is 16.

To calculate the minimum sample size, we can use the formula:

\($n = \frac{(z_{\alpha/2})^2\sigma^2}{E^2}$\)

Where:

\($n$\)= sample size

\($z_{\alpha/2}$\)= the z-score corresponding to the level of confidence (in this case, 95%, so \(z_{\alpha/2}$ = 1.96)\)

\($\sigma$\) = population standard deviation (since we're interested in variance, we need to square it: \(\sigma^2$)\)

\($E$\) = the maximum allowable error (in this case, 40% of the population variance, so \(E = 0.4\sigma^2$)\)

Substituting these values into the formula, we get:

\($n = \frac{(1.96)^2\sigma^2}{(0.4\sigma^2)^2}$\)

Simplifying:

\($n = \frac{5.385\sigma^2}{\sigma^4/25} = \frac{134.63}{\sigma^2}$\)

Therefore, the minimum sample size needed to be 95% confident that the sample's variance is within 40% of the population's variance is \(\frac{134.63}{\sigma^2}$.\)

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