A volleyball league collected $2,040 for both division of volleyball teams the blue division costs &160 per team and the red division costs $180 per team.How many teams will play in each division

The ordered pair (0 , -2) lies on the line with equation 3 x - y = 2

Step-by-step explanation:

To prove that a point lies on a line

The equation of the line is 3 x - y = 2

a) Point (0 , -2)

∵ x = 0 and y = -2

- Substitute the values of x and y in the left hand side

∵ The left hand side is 3 x - y

∵ 3(0) - (-2) = 0 + 2 = 2

∴ The left hand side = 2

∵ The right hand side = 2

∴ The two sides of the equation are equal

∴ The ordered pair (0 , -2) lies on the line

b) Point (-3 , 4)

∵ x = -3 and y = 4

- Substitute the values of x and y in the left hand side

∵ The left hand side is 3 x - y

∵ 3(-3) - (4) = -9 - 4 = -13

∴ The left hand side = -13

∵ The right hand side = 2

∴ The two sides of the equation are not equal

∴ The ordered pair (-3 , 4) doesn't lie on the line

c) Point (1 , -5)

∵ x = 1 and y = -5

- Substitute the values of x and y in the left hand side

∵ The left hand side is 3 x - y

∵ 3(1) - (-5) = 3 + 5 = 8

∴ The left hand side = 8

∵ The right hand side = 2

∴ The two sides of the equation are not equal

∴ The ordered pair (1 , -5) doesn't lie on the line

The ordered pair (0 , -2) lies on the line with equation 3 x - y = 2

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Answer:

  1.047 ft

Step-by-step explanation:

The length of an arc is given by ...

  s = rθ

where s is the arc length, r is the radius, and θ is the central angle in radians. Your arc subtends an angle of 12° = (12·π/180) = π/15 radians. The length of the arc is then ...

  s = (5 ft)(π/15) = π/3 ft ≈ 1.047 ft

The weight swings through a total angle of 12°, corresponding to an arc length of approximately 1.047 feet on the circumference of the circle with radius 5 feet.

To answer this question, we need to understand that the weight swings through an arc, and this arc is a part of the circumference of a circle. Given the length of string (5 feet) is the radius, and the weight swings through 6° on either side of the vertical, we can calculate the total arc length.

Firstly, you should know that the total angle a circle encompasses is 360°. So, the weight swings through a total angle of 6° x 2 = 12°.

Secondly, recall the formula for the circumference of a circle is 2πr, or in our case 2π x 5 feet. Now, to find the length of the arc corresponding to 12°, we will use the proportion of the swing angle to the total angle, i.e., (12/360) x (2π x 5 feet).

In this way, the length of the arc travelled is almost 1.047 feet.

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Answer:

0.093 ft/min

Step-by-step explanation:

V = 4/3 π r³

Take derivative with respect to time:

dV/dt = 4π r² dr/dt

Plug in values:

141 = 4π (11)² dr/dt

dr/dt = 141 / (484π)

dr/dt ≈ 0.093

The radius is increasing at 0.093 ft/min.

The increasing rate of the radius is equal to 0.093 ft/min.

Volume is defined as the space occupied by the object in a three-dimensional space. The sphere is the shape of a circular ball.

The volume is calculated by the formula below,

V = 4/3 π r³

Take the derivative with respect to time:

dV/dt = 4π r² dr/dt

Solve the equation for the rate of change of radius of the sphere,

141 = 4π (11)² dr/dt

dr/dt = 141 / (484π)

dr/dt ≈ 0.093

Therefore, the increasing rate of the radius is equal to 0.093 ft/min.

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Answer:

  $62,490.65

Step-by-step explanation:

If we assume her deposits are at the beginning of the month, and that the interest is compounded monthly, the future value is that of an "annuity due." The formula is ...

  FV = P(1+r/n)((1+r/n)^(nt)-1)/(r/n)

where r is the APR (.0276), n is the number of yearly compoundings (12), P is the monthly payment ($280), and t is the number of years (15). Putting the numbers into the formula and doing the arithmetic, we get ...

  FV = $280(1.0023)(1.0023^180 -1)/(.0023) ≈ $62,490.65

Angelica's account balance after 15 years will be $62,490.65.

_____

If her deposits are at the end of the month, the balance will be $62,347.25.

Answer: C

Step-by-step explanation:707.10-682.87= 24.23. Similar difference can also be found in only chair which is. 161.55-137.32=24.23

Answer:

The correct answer is C on edge :) i just did the test

Step-by-step explanation:

Answer:

Optical axis

Step-by-step explanation:

Optical axis is the rotational symmetry axis of the surfaces.

A line with a certain degree of rotational symmetry is called as the optical axis in an optical system.

It is the straight line that passes through the geometric center of the lens and joins two curvature centers of its surfaces.

It is also called as the principal axis.

There are total of 32 pages in the complete book.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given is that Tyler reads 2/15 of a book on Monday, 1/3 of it on Tuesday, 2/9 of it on Wednesday, and 3/4 of the remainder on Thursday. He still has 14 pages.

Let the total number of pages in the book will be [x]. Then, we can write -

{2x/15} + {x/3} + {2x/9} + {3x/4} = x + 14

x{2/15 + 1/3 + 2/9 + 3/4} - 14 = x

259x/180 - 14 = x

1.44x - 14 = x

0.44x = 14

x = (14/0.44)

x = 32 (approx.)

Therefore, there are total of 32 pages in the complete book.

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Answer:

D= -16

E= 0

F= 0

Step-by-step explanation:

The given equation is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex]

It is also given that the circle passes through (0,0) (16,0) and (8,8).

Inserting (0,0) in the equation, it gives

[tex]0 + 0 + 0 + 0 + F = 0[/tex]

This gives F = 0 .

Now inserting (16,0) , it gives

[tex]16^{2} + 0^{2} + D(16) + E(0) + 0 = 0[/tex]

[tex]D(16) = -256[/tex]

[tex]D = \frac{-256}{16}[/tex]

D = -16

Now inserting (8,8) , it gives

[tex]8^{2} + 8^{2} + (-16)(8) + (E)(8) + 0 = 0[/tex]

[tex]-16 + E = -16[/tex]

E = 0

Thus the equation of circle is

[tex]x^{2} + y^{2} + (-16)x  = 0[/tex]

We can draw the following graph and thus verify that points (0,0) (8,8) and (16,0) lie on graph.

The equation of the circle passing through points (0, 0), (8, 8), and (16, 0) is x^2 + y^2 - 16x - 16y = 0. Solving the system of equations derived from substituting the given points into the circle equation confirms these coefficients for D and E.

To find the equation of the circle that passes through the points (0, 0), (8, 8), and (16, 0), we can use the standard form of a circle's equation:

x

2

+

y

2

+ D

x

+ E

y

+ F = 0

Because the circle passes through the origin (0,0), we know that F = 0. With the remaining points (8, 8) and (16, 0), we can substitute these coordinates into the equation to form a system of equations.

Using point (8,8), the equation becomes:

64 + 64 + 8D + 8E + F = 0

Using point (16,0), the equation becomes:

256 + 16D + F = 0

Since F = 0, the system of equations is:

Solving these equations, we get:

The equation of the circle is therefore:

To verify the result, plotting the points and the graph of the circle on a graphing utility should show that the points lie on the circumference of the circle.

Answer:

D

Step-by-step explanation:

a meter is 100 centimeters so the ratio of the real car to the model is 300 centimeters to 3 centimeters, or 100:1 so D

.---------. _

'-O------O--'

Answer:

1/8

Step-by-step explanation:

This is actually pretty easy.

First, you have the sample of the children.

You know that the family with 3 children, can only have the following children:

MMM: all males

MMF: 2 males, 1 female

MFF: 1 male, 2 females

MFM: 2 males, 1 female (different order)

FMM: 1 female, 2 males

FFM: 2 females, 1 male

FMF: 2 females, 1 male

FFF: 3 females

If you count all of these possibilities, we have 8 possible cases of family with the childrens.

In only one of them, we have only females and no males, which is the last one, all 3 females.

Therefore, the probability to select a family with no male, is only 1/8.

In the set of all possible sets of genders for three children, which is {MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF}, the event of having no male children is 'FFF'. As there are 8 possible outcomes in total, the probability of selecting a family with no male children is 1/8, or 0.125.

It seems like there is a typo in your question. It asks about the probability of selecting a family with 'nothing 6 male children', which doesn't quite make sense. However, if the question is to find the probability of selecting a family with no male children, we can certainly answer that. In your given set of outcomes, { MMM, MMF, FFM, MFF, FFM, FMF, FFM, FFF }, there seems to be a mistake as FFM is repeated three times. The correct set of equally likely outcomes for a family with three children should be { MMM, MMF, MFF, FMM, FFM, FMF, MFM, FFF }.

Each outcome is equally likely, hence, the probability of any particular outcome is 1 divided by the total number of outcomes. The total unique outcomes for the genders of three children is 2^3, or 8. The event of having no male child corresponds to the outcome 'FFF'. Since there is only one such outcome, the probability of a family with no male children is 1/8 or 0.125.

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Answer:you will  an app go to =567

x = -4 is a vertical asymptote for the function.

The graph of [tex]y=f(x)[/tex] is a vertical has an asymptote at [tex]x=a[/tex] if at least one of the following statements is true:

[tex]1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty[/tex]

The function is:

[tex]f(x)=\frac{x^2+7x+10}{x^2+9x+20}[/tex]

First of all, let't factor out:

[tex]f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq  5[/tex]

From here:

[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty[/tex]

[tex]\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty[/tex]

Accordingly:

[tex]x=-4 \ is \ a \ vertical \ asymptote \ for \\ \\ f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20}[/tex]

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Answer:

α = 13.39249775

Step-by-step explanation:

Length of the vamp = 21 ft long

Height of the vamp= 5 ft

using SOHCAHTOA

tanα = opposite /adjacent

Tan α = 5/21

α = arctan(5/21)

α = 13.39249775

Answer:

.65

Step-by-step explanation:

Strategy:

In this situation it is much easier to calculate the probability of the event we are looking for (he hits at least one target) by calculating the probability of its complement (he misses every target), and subtracting from 1.

In other words, we can use this strategy:

P(at least one hit)=1-P(miss all 10)

Calculations:

P(at least one hit)

=1-P(miss all 10)

=1-(0.9)^10

≈1-0.349

≈0.65

Answer:

P(at least one hit)≈0.65

I hope this helps!!!

The probability that Brandon will hit at least one of them is 0.65 approx.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For the considered case, as each hit is independent of each other, and there is either hit or not hit, so this situation can be modeled by binomial distribution.

For this case, we get:

Then, we get: [tex]X \sim B(n=10,p=0.1)[/tex]

The  probability that Brandon will hit at least one of them is written symbolically as:

[tex]P(X \geq 1)[/tex]

We can rewrite it as:

[tex]P(X \geq 1) = 1 - P(X < 1) = 1 - P(X = 0)[/tex]

Using the probability function of binomial distribution, we get:

[tex]P(X \geq 1) = 1 - \: ^{10}C_0(0.1)^0(1-0.1)^{10} = 1 -0.9^{10} \approx 0.65[/tex]

Thus, the probability that Brandon will hit at least one of them is 0.65 approx.

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Answer:

D: has asymmetric information.

Step-by-step explanation:

Several phones available in Barylia market are of inferior quality and it is often impossible to differentiate between a good-quality phone and a poor-quality phone.

So, we can conclude that the market for used cell phones in Barylia: has asymmetric information.

Asymmetric information or often called information failure shows the decision in transactions where one market or party has got better information than the others.

Answer:

A i think

Step-by-step explanation:

Answer: 0.5

Step-by-step explanation:

For binary distribution with parameters p (probability of getting success in each trial) and n (Total trials) , we have

[tex]\sigma=\sqrt{np(1-p)}[/tex]

We are given that ,

Total batches of televisions : n=25

The probability of defects : p= 0.01

Here success is getting defective batch .

Then, the standard deviation for the number of defects per batch will be :-

[tex]\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5[/tex] [Rounedde to the nearest tenth.]

Therefore, the standard deviation for the number of defects per batch =0.5

Answer:

Step-by-step explanation:

Jack went out for dinner at Red Lobster and his meal was $45, This is the amount that he needs to pay if there was no tax or tip.

jack wants to leave an 18% tip, The amount of tip that jack wants to leave is 18/100 × 45 = 0.18×45 = $8.1

To determine how much jack needs to pay including the tip,

Amount that jack would pay is bill + tip = 45 + 8.1 = $53.1

Another way of calculating it is,

Since the tip is 18% and his bill was 100%, we will add the percentages and multiply by the bill. It becomes

118/100 × 45 = $53.1

Answer:

No because the probability of consecutive shows starting late are not independent events

Step-by-step explanation:

Is good begin with the definition of independent events

When we say Independent Events we are refering to  events which occur with no dependency of other evnts. Basically when the occurrence of one event is not affected by another one.

When two events are independent P(A and B) = P(A)xP(B)

But for this case we can't multiply 0.97x0.97x0.97 in order to find the probability that 3 consecutive shows start on time, because the probability for shows starting late are not independent events, because if the second show is late, the probability that the next show would be late is higher. And for this reason we can use the independency concept here and the multiplication of probabilities in order to find the probability required.

Yes, you can multiply (0.97)(0.97)(0.97) because the events are independent.

Yes, you can multiply (0.97)(0.97)(0.97) to find the probability that three consecutive shows on this network start on time. This is because the events are independent; the outcome of one show starting on time does not affect the outcome of the others.

Therefore, the probability that three consecutive shows start on time is the product of the probabilities of each show starting on time:  P(all three shows start on time) = 0.97 * 0.97 * 0.97 = 0.912673.

The best statement that could be used describe a polygon is that it is a closed plane figure with three or more sides that are straight. Thus, the correct answer is A: a closed plane figure with three or more sides that are straight.

Hope this helps! :)

Answer:

It would Cost $125 for a 60 day supply of cat food.

Step-by-step explanation:

Given:

Rover eats cat food each day = [tex]\frac{3}{4}[/tex] = 0.75 can

Bono eats cat food each day = [tex]\frac{1}{2}[/tex] = 0.5 can

Each day consumption for both cats = 0.75+0.5 = 1.25 can

Each day both cats consume = 1.25 cans

For 60 days both cats consume = Number of cans in 60 days.

By Using Unitary method we get;

Number of cans in 60 days = [tex]1.25\times60=75 \ cans[/tex]

Now Cans are sold in a pack of 3.

Hence we will divide number of cans in 60 days with 3 we get;

Number of can packs required for 60 days = [tex]\frac{75}{3}=25 \ can \ packs[/tex]

Now Cost for each Can packs(3 can) = $5.00

Hence Cost for 25 Can packs (75 cans) = Price for 25 can packs(75 can)

By Using Unitary method we get;

Price for 25 can packs (75 cans) = [tex]5\times 25 = \$125[/tex]

Hence Price for 25 can packs (75 cans) which are used for 60 supply of cat food is $125.

Answer:

t=8

Step-by-step explanation:

Subtract 12t from both sides

(12t-12t) + 16 = (13t-12t) + 24

16 = 1t (or just t) + 24

Then subtract 16 from both sides, and bring "t" over the equals sign making it a negative integer.

-t = 8

t = 8

Answer:

  x³ -6x² +x +20

Step-by-step explanation:

The distributive property is useful for making sure you have all of the partial products.

  (x^2–x–4)(x–5) = x(x^2–x–4) -5(x^2–x–4)

  = (x^3 -x^2 -4x) +(-5x^2 +5x +20)

  = x^3 +(-1-5)x^2 +(-4+5)x +20

  = x^3 -6x^2 +x +20

Answer:

The total number of questions are 40

Step-by-step explanation:

let the total number of questions be "x".

percent of questions answered correctly are 80.

In fractions 80% is [tex]\frac{4}{5}[/tex]

The total number of correctly answered questions are 32.

the equation is,

[tex](\frac{4}{5})(x) = 32[/tex]

thus , x = [tex]\frac{(5)(32)}{4}[/tex]

x= 40

Answer:

The amount invested in bonds = 35,000

The amount invested in CD = 15,000.

Step-by-step explanation:

The total amount that Daniela invested is $50,000, this means if we call the amount invested in bonds [tex]b[/tex], and the amount invested in CD [tex]d[/tex], then we have:

[tex]b+d=50,000[/tex] this says the total amount Daniela invested is $50,000.

And since the amount invested in bonds [tex]b[/tex] is $5,000 more than twice the amount Daniela put into the CD, we have:

[tex]b=5,000+2d[/tex].

Thus, we have two equations and two unknowns [tex]b[/tex] and [tex]d[/tex]:

(1). [tex]b+d=50,000[/tex]

(2). [tex]b=5,000+2d[/tex],

and we solve this system by substituting [tex]b[/tex] from the second equation into the first:

[tex]b+d=50,000\\5,000+2d+d=50,000\\3d=45,000\\\\\boxed{d=15,000}[/tex]

or, the amount invested in CD is $15,000.

With the value of [tex]d[/tex] in hand, we now solve for [tex]b[/tex] from equation(2):

[tex]b=5,000+2d\\b=5000+2(15,000)\\\boxed{b=35,000}[/tex]

or, the amount invested in bonds is $35,000.

Final answer:

To find the probability that the first to arrive waits no longer than 5 minutes and the probability that the man arrives first, follow the provided detailed steps.

Explanation:

To find the probability that the first to arrive waits no longer than 5 minutes:

Man arrives first: 1/6

Woman arrives first: 1/4

Man and Woman arrive simultaneously within 5 minutes: 1/12

The probability that the man arrives first: 1/6

Answer:

[tex]a_{n}=2^{n}+3[/tex]

Step-by-step explanation:

The given sequence is not arithmetic, it's a geometric sequence, that means the sequence is obtain using powers. The faster way to find the answer is to try options that fist with a geometric sequence. If we try the last one, we'll find that's the answer.

We need to try for n=1, n=2, n=3, n=4 and n=5:

a_{1}=2^{1}+3=5

a_{2}=2^{2}+3=4+3=7

a_{3}=2^{3}+3=8+3=11

a_{4}=2^{4}+3=16+3=19

a_{5}=2^{5}+3=32+3=35

Therefore, the right answer is the last choice, because as you can observe, it fits perfectly with the given sequence.

Answer:

Step-by-step explanation:

(a) The general term of an arithmetic sequence is ...

  an = a1 + d(n -1)

If we let the sequence of population numbers be modeled by this, and we use t for the number of years, we want n=1 for t=0, so n = t+1 and we have ...

  p(t) = 854 +3(t+1-1)

  p(t) = 854 +3t

__

(b) The general term of a geometric sequence is ...

  an = a1·r^(n-1)

were r is the common ratio. Here, the multiplier from one year to the next is 1+10% = 1.10. Again, n=t+1, so the population equation is ...

  p(t) = 427·1.10^(t+1-1)

  p(t) = 427·1.10^t

Answer:

  (3√2, 1+3√2) ≈ (4.243, 5.243)

Step-by-step explanation:

The line has a slope of 1 and goes through the center of the circle, so will intersect the circle at the point ...

  (6, 6)/√2 +(0, 1) = (3√2, 1+3√2) ≈ (4.243, 5.243)

[tex] \frac{5}{3} = \frac{x}{7} [/tex]

you them cross multiply

5×7=35

3×X= 3x

35=3x

x(n)= 11.6

Answer:

n = 35/3 or 11 2/3.

Step-by-step explanation:

5/3 = n/7

Cross multiply:

3n = 5*7

3n = 35

n = 35/3