B
23. Find the EXACT circumference of the circle
if AB = 2in and BC = 11in.
A
C
a. √117 in
b.
5√5π in
c.
35.1 in
d. 5√5 in

The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively

let

The equation:

8.50x + 4.50y = 79

y = x + 6

Substitute x = y + x into

8.50x + 4.50y = 79

8.50x + 4.50(x + 6) = 79

8.50x + 4.50x + 27 = 79

8.50x + 4.50x = 79 - 27

13x = 52

x = 52/13

x = 4

Recall,

y = x + 6

y = 4 + 6

y = 10

Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.

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The indicated sum for the geometric series is 121.5

The series is given as:

162 − 54 + 18 − 6 + .....

Start by calculating the common ratio of the geometric series.

This is calculated using

r = -54/162

Evaluate

r = -1/3

The indicated sum for the geometric series is then calculated as:

S = a(1 - r^n)/1 - r

Substitute the known values in the above equation

S = 162(1 - (-1/3)^7)/1 + 1/3

Evaluate the exponent and the sum

S = 162(1 + 1/2187)/4/3

Evaluate the sum

S = 162(2188/2187)/4/3

Express as products

S = 162 * (2188/2187)* 3/4

Evaluate the product

S = 162 * 547/729

Evaluate the product

S = 121.5

Hence, the indicated sum for the geometric series is 121.5

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Answer:

x>4

Step-by-step explanation:

3x - 2 >10  add 2 to both sides

3x > 12  Divide both sides by 3

x >4

Answer:

[tex]x > \bf 4[/tex]

Step-by-step explanation:

To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:

[tex]3x - 2 > 10[/tex]

⇒ [tex]3x - 2 + 2 > 10 + 2[/tex]      [Add 2 to both sides]

⇒ [tex]3x > 12[/tex]

⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex]                         [Divide both sides by 3]

⇒ [tex]x > \bf 4[/tex]

Since this is the result of the second function, hence equations I and II are inverse of each other.

Inverse of a function

Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

Given the function f(x) = 3x

Find its inverse

Replace with y with x

y = 3x

x =3y

Make y the subject of the formula

3y = x

y = x/3

Since this is the result of the second function, hence equations I and II are inverse of each other.

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Answer:

3/4

Step-by-step explanation:

Fraction of total area of the circle each color occupies in the spinner.

purple = 1/8

red = 1/4

orange = 1/8

yellow = 1/8

green = 1/4

blue = 1/8

Landing on yellow or purple: 1/8 + 1/8 = 1/4

Not landing on yellow or purple = 1 - 1/4 = 3/4

Answer:

[tex]y = -\frac{2}{3}x + 490[/tex]

gradient = = [tex]-\frac{2}{3}[/tex]

y-intercept = [tex]490[/tex]

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope,

c = y-intercept.

• We are given the equation:

[tex]2x + 3y = 1470[/tex]

To change this into the slope-intercept form, we must make y the subject:

[tex]3y = -2x + 1470[/tex]          [subtract [tex]2x[/tex] from both sides]

⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex]        [divide both sides by 3]

⇒ [tex]y = -\frac{2}{3}x + 490[/tex]

• Comparing this equation with the general form equation, we see that:

m = [tex]-\frac{2}{3}[/tex]

c = [tex]490[/tex].

This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].

Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

The perpendicular bisector of a chord passes through the center of a circle.

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.

The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.

Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.

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Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.

A linear function is modeled by:

y = mx + b

In which:

Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:

C(g) = 4g + 69.

She wants to keep her bill at $83.80 per month, hence:

C(g) = 83.80

4g + 69 = 83.80

4g = 14.80

g = 14.80/4

g = 3.7.

Sarah can use 3.7 gigabytes while staying within her budget.

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Answer:

The other person is correct!

Step-by-step explanation:

Yes

Answer:

F

Step-by-step explanation:

There are 6 digits in the repeating pattern.

279 / 6 = 46.5 remainder 3.

we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.

Answer:

9

Step-by-step explanation:

let the number be y

5×y - 7 = 3×y + 11

5y-7 = 3y+11

collect like terms

5y-3y = 11+7

2y = 18

y = 18/2

y = 9

The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44

We are told that The final line on the plan is parallel to the y-axis and passes through x = -10

Now, looking at the pattern, the lengths of each side are as follows;

1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5

Thus, the sum of the length of the overall pattern is calculated as;

1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44

Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44

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Answer:

Step-by-step explanation:

13

Answer:

read below or other answer

Step-by-step explanation:

2 [{2-2(2÷2-2)} ÷2]÷2​

2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2

2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2

2 [ { 2 + 2 } ÷ 2 ] ÷ 2

2 [ 4 ÷ 2 ] ÷ 2

2 ( 2 ) ÷ 2

4 ÷ 2

2 divided by 2

Answer: 2

Step-by-step explanation:

Answer:

  9

Step-by-step explanation:

The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.

The expanded form of the number can be written as ...

  a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...

  +10×10^68 +11×10^66 +... +43×10^2 +44×10^0

Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...

  10 mod 45 = 10

  100 mod 45 = 10

This lets us conclude that any positive power of 10 mod 45 is 10.

In short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...

  a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45

  = (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45

  = (((225 mod 45) +(901 mod 45))×10 +44) mod 45

  = ((0 +1)×10 +44) mod 45

  a_44 mod 45 = 54 mod 45 = 9

__

Additional comment

The result can be confirmed by a suitable calculator.

__

The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.

Answer: 9

Step-by-step explanation:

we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344

on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.

Answer:

3:10

10:1

8:1

100:7

Step-by-step explanation:

900:3000

300:1000

3:10

80:8

10:1

2000:750

8:1

100:7

Answer:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]

[tex]\textsf{Let }x=3 \sin \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]

Find the derivative of x and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]

[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]

[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]

[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]

[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]

[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

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Answer:

Area = (a² -5a) in²

Perimeter = (4a -10) in

Step-by-step explanation:

Let the length of the rectangle be a.

Given that, its width is 5 in less than the length.

So,

length ⇒ a

width ⇒ (a - 5)

First, let's find the area of the rectangle.

Area = length × width

Area = a ( a - 5 )

Solve the brackets.

Area = (a² -5a) in²

Now, let us find the perimeter of the rectangle.

Perimeter = 2 ( l + w )

Perimeter = 2 ( a + a - 5 )

Perimeter = 2 ( 2a - 5 )

Perimeter = (4a -10) in

❄ Hi there,

let us revise the two rounding rules before getting down to the actual process of rounding.

[tex]\sf{Rules:}[/tex]

Let's see these rules in action!

The number is – [tex]219.2[/tex].

Nearest whole number – [tex]219[/tex], which is followed by a number between 0 and 4, so we just drop that number :

[tex]\sf{219.2- > > 219}[/tex]

❄

if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.

Figuratively, we have:

If we have the following, two events A and B are said to be independent.

                            [tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]

Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.

The likelihood of the event B will then be.

                            [tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]

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I understand that the question you are looking for is:

Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{(x + 3)^0}[/tex]

[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]

[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

Formular for the area of a kite is expressed as;

A = pq/2

Where p and q are the two diagonals of the kite.

Given the data in the question;

From the diagram, we can determine line AM and line MD using Pythagoras theorem.

c² = a² + b²

First, we find line AM

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b² = 16

b = √16

b = 4

Line AM = 4

Next, we determine Line MD

c² = a² + b²

(√58)² = 3² + b²

58 = 9 = b²

b² = 58 - 9

b² = 49

b = √49

b = 7

Line MD = 7

Now, we can find the area of the kite.

Diagonal p = BC = 6

Diagonal q = AD = AM + MD = 4 + 7 = 11

Area = pq/2

Area = [ 6 × 11 ]/2

Area = 66 / 2

Area = 33cm²

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

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The slope is (B) -5/4.

To find the slope:

Therefore, the slope is (B) -5/4.

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The complete question is given below:

What is the slope of a line that is parallel to the line whose equation is y=45x−3?

A. −4/5

B. −5/4

C. 5/4

D. 4/5

Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.

Then substitute the values of p and q into p+2q to get -10

Answer:

D.

Step-by-step explanation:

Yes, because it passes the vertical line test.

Answer:

============================

Conditions we need to meet:

To get the smallest number we'd use all 10 digits in the ascending order:

Here we can't have zero in the beginning as the number becomes 9-digit.

So swapping zero with the closest digit, 1.

Our number should be even, so we should swap 9 with one even digit.

Again it should be the closest one to 9, so it is 8.

We get the following number as a result:

To test you may swap digits, any number you get will be greater than this number.

Answer:

140°

Step-by-step explanation:

The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)

20 + 120 = 140

Answer:

y= 140

Step-by-step explanation:

first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.