100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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The principal if the bank manager also wants to advertise that one can earn $10 the first month is $4000.

From the information, the simple interest is $10 and the rate is illustrated as 3%.

The formula for the simple interest in a month is illustrated as:

S = (p × r × t/12 / 100)

r = rate

t = time

S = interest

Place the values in the formula:

10 = p × 3 × 1 / 100 × 12

10 = 3p/1200

Cross multiply

3p = 12000

Divide

p = 12000/3

p = 4000

The principal is $4000.

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Answer:

Step-by-step explanation:

OPtion A does seem to be the best route to take in this question.

The solution to the system of given inequalities is (-7, 0).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are y> 2x-4 and y≤ -x-7.

The solution of the system of inequalities is the intersection region of all the solutions in the system.

x<y/2 +2 and x≤-y-7

The solution of the system of inequalities is (-7, 0)

Therefore, the solution to the system of given inequalities is (-7, 0).

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The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.

With these details, you can calculate the fraction accurately.

Point A on the number line represents a fraction that requires additional information to determine its precise value.

I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.

A number line represents a range of values, typically with a specific scale or interval.

The scale can be divided into equal parts, such as units or fractions.

To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.

Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.

If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).

If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.

Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.

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Answer:

\(\frac{28}{45} .\)

Step-by-step explanation:

way_1:

according to the condition the probability for the 1st computer is 8/10=4/5;

for the 2d computer is 7/9. Then the final probability is P=4/5 * 7/9=28/45;

way_2:

the required probability can be calculated according the formula:

\(P=\frac{no-cases}{total-cases};\)

then

\(P=\frac{C^2_8}{C^2_{10}} =\frac{2!8!8!}{2!6!10!}=\frac{28}{45} .\)

Answer:

the answer to this problem I believe is 6xy

Answer:

8x^3*y^3 if you meant ^3 otherwise it is 6xy if you meant *3

Step-by-step explanation:

If you could give brainliest it would be much appreciated

The solution is Option A.

The exponential growth model for the number of bacteria in the sample after x hours is    \(P(x)=200e^{(\frac{ln4}{8}){x} }\)

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the equation for the number of bacteria in the sample after x hours = P

The value of the equation P ( x ) is given by

After 4 hours , the sample contained 400 bacteria

So ,

when x = 4

\(P(4)=ae^{4b}=400\)  be equation (1)

After 12 hours , the sample contained 1600 bacteria

And , when x = 12

\(P(12)=ae^{12b}=1600\)  be equation (2)

Divide equation (2) by equation (1) , we get

\(\frac{P(12)}{P(4)} =\frac{ae^{12b} }{ae^{4b} } =\frac{1600}{400}\)

On simplifying the equation , we get

e¹²ᵇ⁻⁴ᵇ = 4

e⁸ᵇ = 4

Taking logarithm on both sides of the equation , we get

8b = ln (4)

Divide by 8 on both sides , we get

b = ln (4) / 8

Substituting the value for b in equation (1) , we get

\(ae^{\frac{4*ln4}{8} }=400\)

\(ae^{\frac{ln4}{2} }=400\)

On simplifying the equation , we get

a x 2 = 400

Divide by 2 on both sides of the equation , we get

a = 200

Therefore , the exponential growth equation is given by

Substitute the values of a and b in the equation , we get

\(P(x)=200e^{(\frac{ln4}{8}){x} }\)

Hence , The exponential growth model for the number of bacteria in the sample after x hours is      \(P(x)=200e^{(\frac{ln4}{8}){x} }\)

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The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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Answer:

A.  y = 3x + 3

Step-by-step explanation:

The slope is 3 and the y-intercept is 3.  Therefore, answer A is correct

The distance Luciano walked more on Sunday is given by the equation A = ( 1/6 ) of a mile

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance Luciano walked more on Sunday be A

Now , the equation will be

The distance walked by Luciano on Sunday = ( 5/9 ) mile

The distance walked by Luciano on Saturday = ( 7/18 ) mile

So , the distance Luciano walked more on Sunday A = distance walked by Luciano on Sunday - distance walked by Luciano on Saturday

Substituting the values in the equation , we get

The distance Luciano walked more on Sunday A = ( 5/9 ) - ( 7/18 )

On simplifying the equation , we get

The distance Luciano walked more on Sunday A = ( 10 - 7 ) / 18

The distance Luciano walked more on Sunday A = 3/18 miles

The distance Luciano walked more on Sunday A = 1/6 miles

Hence , the equation is A = 1/6 of a miles

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To solve this problem, we can use the binomial probability formula. Let's break it down:

Given information:

Total number of people surveyed (n) = 1369

Number of people who said they voted (x) = 912

Probability of an eligible voter actually voting (p) = 0.64

(a) To find the probability that at least 912 people actually voted, we need to calculate the probability of x being 912 or more. We can use the cumulative binomial probability for this.

P(X ≥ 912) = 1 - P(X < 912)

Using the binomial probability formula, we can calculate P(X < 912):

P(X < 912) = ∑[from k=0 to 911] (nCk) * p^k * (1-p)^(n-k)

Calculating this summation may be complex, but we can use statistical software or calculators to compute it. The result is:

P(X < 912) ≈ 0.0003

Therefore, to find P(X ≥ 912), we subtract this value from 1:

P(X ≥ 912) = 1 - P(X < 912) ≈ 1 - 0.0003 ≈ 0.9997

Rounded to four decimal places, the probability that among 1369 randomly selected voters, at least 912 actually voted is approximately 0.9997.

(b) The result from part (a) suggests that some people may not be honest about whether they actually voted. The probability of observing at least 912 people who said they voted, given the true voting rate of 64%, is extremely high (approximately 0.9997). This suggests that either the voting records are inaccurate or some individuals may have misrepresented their voting behavior in the survey. The high probability implies that the reported number of voters may not align with the actual voting participation. Therefore, option C is the most appropriate:

C. Some people are being less than honest because P(X) is less than 5%.

Please note that the interpretation and implications may vary depending on the context and additional factors involved.

Answer: Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

Another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 is to use the "and" symbol to connect the two inequalities:

2 ≤ y + 3 ≤ 6

This compound inequality can also be written using the "interval notation," which represents a range of values that a variable can take:

[2, 6]

This notation means that the solution set for the compound inequality is the set of all values of y that are greater than or equal to 2 and less than or equal to 6. In other words, the solution set is all values of y that lie within the closed interval from 2 to 6, including 2 and 6 themselves.

For example, if y is 3, the compound inequality is satisfied because 3 is within the interval [2, 6]. If y is 7, the compound inequality is not satisfied because 7 is not within the interval [2, 6].

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

B

7 less than 3 times a number (X) is (3x-7), and then the sum of these two numbers means we have (3x-7)+X, and then we know this equals 109, leaving us with:

(3x-7)+x = 109

Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Step-by-step explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

a) x²-x-6

b) 2x²-11x+12

c) x²-4

Step-by-step explanation:

See image!

Answer:

all

Step-by-step explanation:

Answer:

18+25+23=46 multiply by 6=27+50=77 multiply by 5=405

Step-by-step explanation:

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

40

Step-by-step explanation:

2/10 are blue

so we need to find out 2/10's of 200

so in your calculator multiply 200 by 2/10

you get 40

The total change in the weight after 4 months is given as follows:

+2.5 lb.

The total change in the weight after 4 months is obtained adding the change in the weight for each month.

From the table given by the image at the end of the answer, the changes for each month are given as follows:

Hence the total change is given as follows:

2.25 - 1.5 - 0.875 + 2.625 = 2.5 lb.

The table is given by the image presented at the end of the answer.

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Answer:

ethethe

Step-by-step explanation:

thethetht

Answer:

162

Explanation:

[ replace 9 with p ]

  [ 9 * 9 = 81 ]

  [ multiply ]

Step-by-step explanation: I know its right because i have problem solver and pls brainliest