The large sphere has a diameter of 20 feet.
Which expression represents the volume, in cubic units, of
the shaded part of the sphere?
-4ft
37(109) + 37(4)
7(109) – 2014)
1(209) + (4)
7(209) – 17(43)

Answer:

y = -26

Step-by-step explanation:

[y = 2 - 2x] + [y = -16 + 2(x - 3)^2​]

y = -16 + 2x - 6^2

y = -16 + 2x - 6^2 + 2 - 2x

y = (+2x - 2x) - 16 - 6^2 + 2

y = -16 - 6^2 + 2

y = -16 - 12 + 2

y = - 28 + 2

y = -26

The number-of-times the "number-6" go into the "number-60" is exactly "10-times".

When we divide the "number 60" by "6", we are asking how many times the "number 6" can be evenly divided into "60" without any remainder.

In other words, we are searching for the quotient of the division operation.

To find the quotient, we divide the "number 60" by "6",

On dividing "60" by "6", the result is "10", which means that the "number 6" can go into "60" exactly "10 times", because "6" multiplied by "10" equals "60", with no remainder.

Therefore, exactly "10-times" the "number-6" go into "60".

Learn more about Division here

https://brainly.com/question/13753299

#SPJ4

There were 110 children and 237 adults whο swam at the public pοοl that day.

Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.

Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:

x + y = 347 ....(1)

Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:

1.75x + 2.5y = 785 ....(2)

We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.

Frοm equatiοn (1), we can express y in terms οf x as:

y = 347 - x

We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:

1.75x + 2.5(347 - x) = 785

1.75x + 867.5 - 2.5x = 785

-0.75x = -82.5

x = 110

Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:

110 + y = 347

y = 237

Therefοre, the number οf adults whο used the swimming pοοl is 237.

Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.

To know more about equatiοns here

https://brainly.com/question/29273511

#SPJ1

Question 9: Choice (A) is the answer  

    \(\frac{1}{5} * x+\frac{1}{3} =\frac{7}{15} \\\\\frac{x}{5}=\frac{7}{15} -\frac{1}{3} = \frac{7}{15} -\frac{1*5}{3*5} =\frac{7-5}{15} \\\\\frac{x}{5} =\frac{2}{15} \\\\15x = 10\\\\x = \frac{10}{15} =\frac{2}{3} ; (A)\)

Question 10: Choice (B) is the answer:

   \(\frac{4}{6}+x=\frac{11}{12} \\\\x= \frac{11}{12} -\frac{4}{6} =\frac{11}{12} -\frac{4*2}{6*2} =\frac{11-8}{12} \\\\x = \frac{3}{12} =\frac{1}{4}; (B)\)

Hope that helped!

Answer:

he already answered it for me and you.

Step-by-step explanation:

Answer:

x=2(y+7)

Step-by-step explanation:

2y−x=−14

Subtract 2y from both sides.

−x=−14−2y

The equation is in standard form.

−x=−2y−14

Divide both sides by −1.

x=2y+14

Then use the inverse property of distrubtion.

x=2(y+7)

or if you want to you can leave it as x=2y+14

Answer:

y=x/2-7

Step-by-step explanation:

Move x to the side with the constant and then divide.

1. -x from both sides

2. the divide by 2

it can also be written like

y=1/2x-7

The name of the angles are;

a. <1 and <8 = Corresponding angles

b.<1 and <7 = Same side exterior corresponding angles

c. <4 and <8 = Same side exterior corresponding angles

d. <4 and <5 = Alternate angles

e. <4 and <2 = Supplementary angles

f.  <4 and <1 = Corresponding angles

To determine the name of the angles, we need to know the following;

Learn more about angles at: https://brainly.com/question/25716982

#SPJ1a

Answer:

3(x-1)(x+2)

Step-by-step explanation:

i dont know if this what u looking for but i think:

3(x-1)(x+2)

Answer:

option 1 is the answer

Step-by-step explanation:

.......

Answer:

Option 1 and 3

Step-by-step explanation:

\(\frac{-7}{-10}\) = 0.7    this is true, two negative numbers divided becomes positive

-10 = \(\frac{-10}{-1}\)     this is not true, for a negative fraction, you can keep the negative on the numerator OR the denominator, not both

\(\frac{-1}{4}\) = \(\frac{1}{-4}\)    this is true, the fractions are the same, the negative sign can be on either numerator or denominator

\(-\frac{1}{4}\)  =  \(\frac{-1}{-4}\)  this is not true, one side becomes positive

hope this helps

Ms. Logrieco's door: 35 students per 10 minutes

Mr. Riley's door: 22 students per 8 minutes

Time Frame: 24 minutes

35 x 2 = 70

35 x 2/5 = 14

70 + 14 = 84

22 x 3 = 66

84 + 66 = 150

Thus, we can expect for 150 students to be in the cafeteria after 24 minutes.

The slope of the tangent line at t = -1 is 1/6 and the point on the curve where the tangent line is vertical is (-1, 4/3).

a) The slope of the tangent line at t = -1 can be found by taking the derivative of both x(t) and y(t) with respect to t and then evaluating at t = -1. Thus,

x'(t) = -12 and y'(t) = -2.

Therefore, the slope of the tangent line at t = -1 is given by

m = y'(t)/x'(t) = -2/-12 = 1/6.

b) To find the points where the tangent is vertical or horizontal, we need to solve for when the derivative of y with respect to x is equal to zero or undefined, respectively.

dy/dx = dy/dt / dx/dt = (-2) / (-12) = 1/6, which is never equal to zero.

Thus, there are no points where the tangent line is horizontal.

For the vertical tangent line, we need to solve for when dx/dt = 0.

dx/dt = -12 = 0 when t = 1/3.

Therefore, the point on the curve where the tangent line is vertical is

(x, y) = (3 - 12(1/3), 2 - 2(1/3)) = (-1, 4/3).

For more questions like Slope click the link below:

https://brainly.com/question/3605446

#SPJ11

Answer:

Step-by-step explanation:

Let the amount of gas be x gallons.

The product of gallons and MPG gives us the number of miles, show this as equation and solve for x:

Answer:

True

Step-by-step explanation:

I'm positive the answer is true

Basically, i kept adding 3 more days/4 more hours to see if it would still line up.

I really hope this helped :>

Answer:

3

Step-by-step explanation:

Hi there!

Slope = \(\displaystyle \frac{y_2-y_1}{x_2-x_1}\) where two points on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (10,17) and (7,8):

\(=\displaystyle \frac{17-8}{10-7}\\\\=\displaystyle \frac{9}{3}\\\\= 3\)

Therefore, the slope of the line is 3.

I hope this helps!

lower limit of the 99% interval = 3.7265

Upper limit of the 99% interval = 6.1535

What do you mean  by standard deviation?

The standard deviation is a quantity that reveals the degree of variation (such as spread, dispersion, and spread) from the mean.

Number of students, n = 11

Averange time , mean , μ = 4.94

Standard deviation , \(s_{x}\) = 1.27

Significance level , α = 1 -= 0.99 = 0.01

Degree of freedom for t-distribution , d.f. = n - 1 = 11 - 1 = 10

Critical value = \(t_{\alpha /2,d.f\) = \(t_{0.005,10}\) = 3.169

Margin of error ,E = \(t_{\alpha /2,d.f\) × \(\frac{s_{x} }{\sqrt{n} }\) = 3.169  ×\(\frac{1.27}{\sqrt{11} }\) = 3.169 × 0.38292 = 1.21347

Limits of 99% confidence intervals are given by:

a) Lower limit = μ - E = 4.94 - 1.21347 = 3.7265

b) Upper limit = μ + E = 4.94 + 1.21347 = 6.1535

Therefore, lower limit of the 99% interval = 3.7265

Upper limit of the 99% interval = 6.1535

To learn more about the stanadrd deviation from the given link.

https://brainly.com/question/475676

#SPJ4

A) The average cost function C(x) can be obtained by dividing the total cost function by the quantity x:

C(x) = (0.05x^2 + 22x + 340) / x

Simplifying this expression, we get:

C(x) = 0.05x + 22 + 340/x

Therefore, the average cost function C(x) is given by 0.05x + 22 + 340/x.

B) To find the critical values of C(x), we need to determine the values of x where the derivative of C(x) is equal to zero or is undefined. Taking the derivative of C(x) with respect to x, we have:

C'(x) = 0.05 - 340/x^2

Setting C'(x) equal to zero and solving for x, we find:

0.05 - 340/x^2 = 0

Rearranging the equation, we have:

340/x^2 = 0.05

Simplifying further, we get:

x^2 = 340/0.05

x^2 = 6800

Taking the square root of both sides, we find two critical values:

x = ± √(6800)

Therefore, the critical values of C(x) are x = √(6800) and x = -√(6800)

C) Using interval notation, we can express the domain of x where the function C(x) is defined. Given that the range of x is from 0 to 150, we can represent this interval as (0, 150).

Leran more derivative about here: brainly.com/question/29020856

#SPJ11

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

For more information about chi-square test,visit

https://brainly.com/question/17142834

#SPJ4

Answer:

C lets look at were this line starts which is in between 7 and 8 right in the middle making it 7.5 it is negative because the point is on the negative side of our graph. Where the line ends in on positive 2 on the x-axis. -Your friend, Bill Cipher

Step-by-step explanation:

Answer:

(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") ... This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

Step-by-step explanation:

Using Pythagorean theorem, the distance between them is 17 miles

To determine the distance between the two couple, we can simply use Pythagoras theorem to find the distance.

Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be represented by the equation c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

In this problem, we can substitute the values and solve.

Let x represent the distance apart.

x² = 8² + 15²

x² = 289

x = √289

x = 17

The distance apart their place of work is 17 miles.

Learn more on Pythagoras theorem here;

https://brainly.com/question/343682

#SPJ1

Answer:

64

Step-by-step explanation:

)3£56::?£

yerk

v hi is

)(5_-

The equation of the exponential function is\(4 * 3^{x}\).

What is exponential function?

An exponential function is  of the form:

\(f(x) = a^{x}\)

here "a" is a constant called the base, and "x" is the variable. The base "a" is typically a positive real number, but it can also be a negative number or a complex number. The function is called exponential because the variable "x" appears in the exponent.

We can see that as "x" increases by 1, "y" is multiplied by a constant factor of 3. This suggests that the exponential function has a base of 3. To find the equation, we can use the general form of an exponential function:

\(y = a * b^{x}\)

where "a" is the initial value or y-intercept, and "b" is the base.

We can use the given values of (x,y) to form a system of equations:

\(a * 3^{0} = 4\)

\(a * 3^{1} = 12\)

\(a * 3^{2} = 36\)

\(a * 3^{3} = 108\)

Simplifying each equation, we get:

a = 4

3a = 12

9a = 36

27a = 108

Solving for "a", we get:

a = 4

Substituting this value of "a" into the equation, we get:

\(y = 4 * 3^{x}\)

So the equation of the exponential function represented by the table is y \(= 4 * 3^{x}.\)

Tο learn more about exponential function, visit the link:

https://brainly.com/question/2456547

#SPJ1

Answer:

\(t^{4}\) + 8\(t^{2}\) + 8t - 12

Hope this helps!

Step-by-step explanation:

\(t^{4}\) - 1.5\(t^{2}\) + t - 12 + 9.5\(t^{2}\) + 7t : Combine like terms

\(t^{4}\) + ( 9.5 - 1.5 )\(t^{2}\) + ( 7t + t ) - 12

\(t^{4}\) + 8\(t^{2}\) + 8t - 12

Answer:

Step-by-step explanation:

\(\sf 4+4\div 5\)

\(\sf 4\div 5 =0.8\)

\(\sf 4+0.8\)

\(\sf 4.8\)

* Hope it helps, ty 4 pts!

* Have a good day!

Answer:

5.6 days

Step-by-step explanation:

We are given;

Initial Mass; N_o = 25 g

Mass at time(t); N_t = 25/2 = 12.5 (I divide by 2 because we are dealing with half life)

k = 0.1229

Formula is given as;

N_t = N_o•e^(-kt)

Plugging in the relevant values;

12.5 = 25 × e^(-0.1229t)

e^(-0.1229t) = 12.5/25

e^(-0.1229t) = 0.5

(-0.1229t) = In 0.5

-0.1229t = -0.6931

t = -0.6931/-0.1229

t = 5.6 days

Answer:

The answer above is correct, I got it wrong originally! Sorry for wasting this spot! ^w^

Step-by-step explanation:

Answer:

255

Step-by-step explanation:

EXPLANATION We are looking for the number of adult tickets sold. number of adult tickets sold =x We are given that there were 61 more student tickets sold than adult tickets. number of student tickets sold =+x61 The total number of tickets sold was 511.

The radius of convergence R = 1/b

The radius of convergence for a power series is given by the formula:

1/R = lim sup |bn|^(1/n)

In this case, the radius of convergence is given by:

1/R = lim sup |bn|^(1/n) = lim sup b^(1/n) = b^(1/n) as b > 0.

So R = 1/b

As for the interval of convergence, it is the set of values of x for which the series converges. The series converges when |x-a| < R, and diverges when |x-a| > R. So the interval of convergence is (a-R, a+R) which is (a-1/b, a+1/b)

To learn more about convergent series visit: brainly.com/question/15415793

#SPJ4

By using the graphs above, a graph that represent h(x), given that function h(x) = f(x) + g(x) include the following: A. graph A.

In Mathematics, the general form of a quadratic function is modeled by the following mathematical expression;

y = ax² + bx + c

Where:

Next, we would write quadratic functions that represent both f(x) and g(x) in standard form and with a leading coefficient of 1 as follows;

f(x) = (x + 3)(x + 1)

f(x) = x² + 3x + x + 3

f(x) = x² + 4x + 3

For the function g(x), we have the following:

g(x) = -(x - 3)(x - 1)

g(x) = -(x² - 3x - x + 3)

g(x) = -x² + 4x - 3

Therefore, a function that represent h(x) can be calculated as follows;

h(x) = f(x) + g(x)

h(x) = x² + 4x + 3 -x² + 4x - 3

h(x) = (x² - x²) + (4x + 4x) + (- 3 + 3)

h(x) = 8x

Read more on quadratic functions here: https://brainly.com/question/29499209

#SPJ1

According to the question The probability that a New York teenager owns a skateboard or a bicycle is 0.82.

Let's denote the event of owning a skateboard as \(\(A\)\) and the event of owning a bicycle as \(\(B\).\)

We are given:

\(\(P(A) = 0.37\)\) (probability of owning a skateboard)

\(\(P(B) = 0.81\)\) (probability of owning a bicycle)

\(\(P(A \cap B) = 0.36\)\)  (probability of owning both skateboard and bicycle)

To find the probability that the teenager owns a skateboard or a bicycle    \((\(A \cup B\))\) , we can use the formula:

\(\[P(A \cup B) = P(A) + P(B) - P(A \cap B)\]\)

Substituting the given values:

\(\[P(A \cup B) = 0.37 + 0.81 - 0.36\]\)

Calculating:

\(\[P(A \cup B) = 0.82\]\)

Therefore, the probability that a New York teenager owns a skateboard or a bicycle is 0.82.

To know more about probability visit-

brainly.com/question/29286790

#SPJ11

The two angle of the right triangle are found as 30 degrees and 60 degrees.

Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.

By using angle sum property of right angle triangle:

x + 2x + 90 = 180

3x = 90

x = 30 (one angle)

2x = 60 (Other angle)

Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.

To know more about the acute angles, here

https://brainly.com/question/10753882

#SPJ4