find the coordinates of point p along the directed line segment from j(-4,12) to k(10,-9) that partitions the segment in a ratio of 3:4

The statements that complete the proofs are; One half the measure of their intercepted arcs; mARC CDE = 2·m∠CFE and mARC CFE = 2·m∠CDE

The two column proof that ∠CFE and ∠CDE are supplementary is presented as follows;

Statement                                                              Reason

Quadrilateral CDEF is inscribed is circle A         Given

m<CDE + m<CFE = 360°                           Measure of angle round a circle

∠CFE and ∠CDE are inscribed angles                Given

∠CFE  + ∠CDE = 1/2 × ( m<CDE + m<CFE )     Inscribed angles are (i) one half the measure of their intercepted arcs

2 × (∠CFE  + ∠CDE) = (m<CDE + m<CFE )

So, (ii)  = 2 × m∠CFE and  = 2 × m∠CDE From the inscribed angle theorem above (See attached drawing)

2·m∠CFE + 2·m∠CDE = 360°      Using substitution property of equality

(2·m∠CFE + 2·m∠CDE)/2 = 360°/2 → m∠CFE + m∠CDE) = 180°                 Dividing both sides by 2

m∠CFE and m∠CDE) are supplementary   Angles that sum up to 180°

The statements that complete the proofs are;

(i) One half the measure of their intercepted arcs

(ii) mARC CDE = 2·m∠CFE and mARC CFE = 2·m∠CDE

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Complete question:

Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?

Quadrilateral CDEF is inscribed in circle A, so mARC CDE + mARC CFE= 360°. ∠CFE and ∠CDE are inscribed angles, which means that their measures are _________________. So, _________________. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.

The constant of proportionality in the equation 3y = 2x is 2/3.

Two or more expressions with an Equal sign is called as Equation.

if y is directly proportional to x, this is expressed as:

y ∝ x

y = kx .................... 1

k = y/x

Given the expression 3y = 2x

Divide both sides by 3

3y/3 = 2x/3

y = 2/3 x ................ 2

Compare equation 1 and 2 to find "k"

kx = 2/3 x

k = 2/3

Hence,  the constant of proportionality in the equation 3y = 2x is 2/3.

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Let k denote the event that the card drawn is king. Then , p(k) = 5 / 52 is the probability as we have drawn 5 cards from 52 cards.

P( k1/k) is the probability of a second king with the condition that one king has already been drawn. Now there are 3 kings in (52−1)=51cards

P( k1/k) = 4 / 51

P( k2/k) is the probability of a third king with the condition that two kings have already been drawn. Now there are 2 kings in (52−2)=50cards

P( k2/k) = 3/50

P( k3/k) is the probability that three kings have already been drawn. Now there are 2 kings in (52−3)=49cards

P( k3/k) = 2/49

P( k4/k) is the probability that three kings have already been drawn.Now there are 2 kings in (52−4)=48cards.

P( k4/k) = 1 / 48

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The complete question is :

suppose that 5 cards are drawn from a 52-card deck and the first one is a king. what is the probability of at least one more king?

Answer:

see below

Step-by-step explanation:

becaues the angles on the top are the same

also the ratios of the 2 sides given are of the same ratio

9/6=1.5

7.5/5=1.5

Answer:

31.3%

Step-by-step explanation:

So today's % price at $21

Yesterday, the original 100% price was $16

Using a ratio

$16. 100%

------. =. --------

$21. x

Now we can cross multiply and divide

Cross multiplication gets you...

16x = 2100

Dividing both sides by 16 to get x alone

x = 2100/16

x = 131.25

Now to find the percent we subtract this from 100

131.25 - 100 = 31.25 which equals 31.3%

Answe4.7

Step-by-step

The dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.

What is a cuboid?

A closed three-dimensional geometric shape called a cuboid is surrounded by six rectangular plane sections.

Given that, the dimensions of the first two cuboids are 1,1,16 and 1,2,8.

Note that the volume of each cuboid is the same, therefore, the multiplication of the dimensions should be the same for each cuboid.

Therefore, the dimensions of cuboid C and Cuboid D are:

Cuboid C: 1,4,4 Since 1 ×4×4=16.

Cuboid D: 2,4,2 as 2×4×2 = 16

Hence, the dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.

40% of the coins are pennies. To calculate the percentage, divide the number of pennies by the total number of coins and multiply by 100:

(240 / 600) * 100 = 40.

Esteban has a container loaded up with a lot of coins in his room and he needs to understand which level of the coins are pennies. There are 600 coins altogether and 240 of them are pennies. To figure out the level of pennies, we really want to do a straightforward estimation. We partition the quantity of pennies by the all out number of coins and afterward increase the outcome by 100. The response we get is 40%, and that implies that 40 out of 100 coins picked haphazardly from the container would be pennies. At the end of the day, close to half of the coins in the container are pennies. This data can provide us with a smart thought of the conveyance of coins in the container.

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Answer:

the answer is 717

Step-by-step explanation:

given

55*11+7*(2+14)

according to BODMAS

=55*11+7*16

=605+112

=717✔️

If the builder does not build houses with three-car or more garages, then the probability that the buyer will select no garage home is 0.1.

Probability is a measure of likelihood that a certain event occurs. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of ways the event A can occur

n(S) = number of all possible outcomes.

Suppose there are 3 possible outcomes, A, B, C, then:

P(S) = P(A) + P(B) + P(C) = 1

In the problem, let's define the events:

A = buyer will select a one-car garage

B = buyer will select a two-car garage

C = buyer will select no car garage

We have:

P(A) = 0.2

P(B) = 0.7

Hence,

P(A) + P(B) + P(C) = 1

0.2 + 0.7 + P(C) = 1

P(C)  = 1 - 0.9 = 0.1

Therefore, the probability that the customer will choose no garage option is 0.1

Your question is incomplete, most likely it was:

In building new homes, a contractor finds that the probability of a home buyer selecting a two-car garage is 0.7 and of selecting a one-car garage is 0.2. Find the probability that the buyer will select no garage. the builder does not build houses with three-car or more garages

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For Gail to receive a b in the course, her final exam score range must be between x = 79 and x = 84.

There would be a total of 10 examinations, including the ones listed, if the final exam was worth six test scores. The sum must be 800 in order to divide it by 10 to obtain the lowest average of 80, and it must be 830 in order to obtain the maximum average of 83. The following two equations are necessary in order to obtain the final exam scores that determine these averages:

84 + 76 + 83 + 83 + 6x = 800

and

84 + 76 + 83 + 83 + 6x = 830

So, in each equation, we can add like terms and get

326 + 6x = 800

and

326 + 6x = 830

6x = 474 and 6x = 504

x = 79 and x = 84.

The complete question is:

Gail needs to earn a b in her algebra class. Her current test scores are 84, 76, 83, and 83. Her final exam is worth 6 test scores . In order to get a b Gail average must lie between 80 and 83 inclusive. What range of scores can Gail receive on the final exam to earn a b in the course.

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The inequality of the graph of the solution -4/3x<-8 be 0 < x < 1/6.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤ or ≥ are used to denote an inequality, when the two expressions aren't always equal.

There are four fundamental types of inequality: less than, larger than, less than or equal to, and greater than or equal to.

A mathematical comparison of expressions is known as an inequality. The characters, >, <, ≤ or ≥ are present. In order to place the inequality sign in a sentence, check for the following terms.

Let the given inequality be -4/3x<-8

Rewrite in standard form

[tex]$\frac{-4+24 x}{x} < 0$$[/tex]

Factor [tex]$\frac{-4+24 x}{x}: \frac{4(6 x-1)}{x}$[/tex]

[tex]$\frac{4(6 x-1)}{x} < 0$$[/tex]

Divide both sides by 4, we get

[tex]$\frac{\frac{4(6 x-1)}{x}}{4} < \frac{0}{4}$$[/tex]

Simplifying the above equation, we get

(6x - 1)/x < 0

Therefore, the inequality of the graph be 0 < x < 1/6.

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The speed of the person located at earth's equator traveling due to rotation is, 1670 km/hr.

The person at equator traveling due to it's rotation will cover one complete round of earth in 24 hours. Hence the distance travelled is the circumference of the earth.

The radius of the earth is, 6 378.1 kilometers.

The circumference can be calculated as, 2×π×R

Using R = 6 378.1 kilometers,

Circumference = 2×π×6 378.1 kilometers

Circumference = 40090.91 kilometers.

The distance traveled = 40090.91 kilometers.

Time taken is 24 hrs.

Hence speed = distance/time

Speed = 40090.91/24

Speed = 1670 km/hr

The speed of the person is 1670 km/hr.

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Answer:

254.34 m²

Step-by-step explanation:

[tex]A=\pi r^2 \approx (3.14)(9^2)=254.34[/tex] m²

Answer:

Each friend shovels 1/12 of 8 driveways, or 8/12 driveways = 2/3 of a driveway.

The slope of line is -3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

A line intersects the points (7, 6) and (11, -6).

So, the slope is

= [tex](y_2 - y_1)/ (x_2 - x_1)[/tex]

= (-6 - 6) / (11 - 7)

= -12 / 4

= -3

Hence, the slope is -3.

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The given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

Amount is a numerical quantity that is used to measure the size or magnitude of something. It is typically expressed in terms of a unit of measure such as a dollar, pound, or other currency.

The given k-value of 0.1459 corresponds to the rate of decay of the 9 gram sample of the substance over time. The equation for determining the amount of the sample left after a certain amount of time (t) is: N = -kt, where N is the amount of the sample left after the given amount of time, k is a positive constant that depends on the substance itself and on the units used to measure time, and t is the amount of time in days.

N = N0 e^(-kt)

for half life N/N0 = 1/2 and k = 0.1459

1/2 = e^(-0.1459t)

=> -0.1459 t = ln(0.5)

t = - ln(0.5) /0.1459

= 4.8 days       

Therefore, with the given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

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Complete question is:

A 9 gram sample of a substance that's used for drug research has a K value of 0.1459

Find the substances half-life in days, and round answer to the nearest ten. ( exponential decay )

The sample space of all the possible outcomes of rolling two six-faced dice is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), . . ., (6,5), (6,6)}, and there are 36 possible outcomes in total.

Using the Fundamental Counting Principle, the possible outcomes can be determined.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or 36 equally likely outcomes.

A simple graphical representation of this set could be a shown in a table, where the top row is the possible outcomes of the first dice, the first column is the possible outcomes of the second dice, and the inner table is all the possible outcomes when these two dice are rolled at the same time.

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In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. [Therefore proven] BD=BC.

A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides.

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

There are

As well as AB=AC, BC 2 = AC / CD.

B = C and BC = BC = AC

The notation AC BC equals BC CD, and B = C.

CA BC equals CB DC and B = C.

Thus, based on the similarity criterion of SAS, we have

△BCA∼△DCB

DC/ BC = CB /CA = DB/ BA

CB /CA = DB/ BA

CA/ BA = CB /DB

1 = CB / DB [BA=CA]

⇒ DB=CB

[Therefore proven] BD=BC.

The Complete Question.

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The growth of the population after .t. years would be [tex]y_t = 16000^{(1.06t)}[/tex].

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex].

Given, The number of students enrolled at a college is 16,000 and grows ​6% each year.

Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.

The initial amount is 16000.

So, After t number of years, the population would be, [tex]y_t = 16000^{(1.06t)}[/tex].

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Answer:

See below

Step-by-step explanation:

Keisha walks faster than Ryan so she will lap Ryan as a way of catching up to him.

LCM of 7 and 5 is 35 which is the time taken to meet up again at the starting line

Thus she will have walked 7 laps and he will have walked 5

Answer:

x = $20.40

Step-by-step explanation:

x = cost of 13 glue sticks

4 glue sticks cost $7.76, so to find the cost of 13 glue sticks, you would use the equation:

x = (13/4) * $7.76

or

x = $20.40

The result of the simplification of the difference equation is f.

The simplification of the given expression is done by factoring the numerator, summing up the like terms, and dividing the value of the denominator from the numerator.

Given that:

[tex]\dfrac{f(4.5 + h) - f(4.5)}{h}[/tex]

Factor the numerator

[tex]\dfrac{f(4.5 + h) + f(-1 *4.5)}{h}[/tex]

Factor f out of f(4.5 + h) + f(1 *4.5)

[tex]\dfrac{f(4.5 + h-1*4.5) }{h}[/tex]

[tex]\dfrac{f(4.5 + h-4.5) }{h}[/tex]

[tex]\dfrac{f(h) }{h}[/tex]

= f

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The shaded fraction of the square is equal to option c. 1/4 or 2/8.

From the attached figure of the shaded square we have:

Shaded fraction of the square is equal to

= ( number of shaded triangles)/ ( total number of triangles formed in the square)

= ( 2 ) / ( 8 )

Which is equivalent to

= 1 / 4

Option c. 1/4 or 2/8 represents the correct shaded fraction.

Therefore, the correct shaded fraction of the  square is given  by

Option c. 1/4 or 2/8.

The above question is incomplete , the complete question is:

What fraction of the square is shaded?

a. 3/4 or 1/8    

b. 1/4 or 5/4

c. 1/4 or 2/8

d. 2/8 or 4/4

Figure is attached.

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The actual perimeter of the triangular face will be B. 18 1/2 feet.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

PQ + QR + PR

= 12 + 15 + 10

= 37 inches

Therefore, the actual perimeter of the triangular face will be:

= 37 / 2

= 18.5

The correct option is B.

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The expected population in an additional 4 years is 15,125.

The expected population can be found by using the formula for uninhibited exponential growth.

Uninhibited exponential growth is modeled by the formula

P(t) = P₀ * e^(rt)

where P₀ is the initial population, e is the base of natural logarithms (approximately equal to 2.718), r is the growth rate, and t is the time elapsed.

We can first find the growth rate by using the formula

r = (ln(P/P₀)) / t

where P is the final population and t is the time elapsed. In this case, P₀ = 8000, P = 12000, t = 7 years, so we have:

r = (ln(12000/8000)) / 7

= 0.4055 / 7

= 0.0579

Next, we can use this growth rate to predict the population in an additional 4 years. Let t' = t + 4, so we have:

P(t') = P₀ * e^(r * t')

= 8000 * e^(0.0579 * (7 + 4))

Using a calculator, we can find that P(t') ≈ 15,125.

So, the expected population in an additional 4 years is approximately 15,125.

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Approximately 41 truck loads are needed to hold it.

Given that,

A builder is 243 cy backfilling. assuming each truck has a 162 cubic feet capacity

To find : What number of truckloads are required?

The quantity of trucks required serves as an example of rates.

There are 42 trucks required.

How to calculate the quantity of trucks

The backfill's size is specified as follows: 243 CY

A vehicle may carry as much as 162 CF.

The required number of trucks is then determined as follows:

n = 243 / 162

Convert n = 243 * 27 /162 from CY to CF.

Fix n = 40.5.

n is approximately 41.

So, to hold it, roughly 41 truck loads are required.

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From the given graph we can see that the graphical representation of the function has an open dot on -1. Hence, the function has no solution for f(-1).

An open dot on a number line graph denotes that the given number cannot be a solution, whereas a solid dot on the graph suggests that the supplied number should be considered as a potential solution. For instance, if you graph x > 7, you would put an open dot there because that is not a correct response (7 is not greater than itself).

From the given graph we can see that the graphical representation of the function has an open dot on -1. Hence, the function has no solution for f(-1).

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The perception of the Olympic logo as interlocking circles is due to the human brain's tendency to simplify and organize visual information.

This is known as "gestalt psychology," where our brain perceives objects as a whole rather than individual elements. The circles provide a clear and recognizable shape that is easy for our brain to process, whereas a series of complex shapes might be harder to understand and remember.

The circles are a consistent and repeated shape in the design, further emphasizing their perception as the main element. In conclusion, it's the brain's innate pattern recognition ability and our cultural familiarity with the design that lead us to see the Olympic logo as interlocking circles.

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