After participating in a track meet, athletes were given the option to drink a sports drink or water. The results showed that 85 athletes chose a sports drink, 62 athletes chose water, and 14 athletes chose not to drink anything. Of those that chose water or a sports drink, 27 athletes choose to drink both.

How many athletes did not choose water?
1.) 99
2.) 85
3.) 72
4.) 58

By definition of linear independence, the vectors in the set {a, b, c} are independent if

[tex]k_1\vec a+k_2\vec b+k_3\vec c=\vec0[/tex]

can only be obtained with the choice of k₁ = k₂ = k₃ = 0.

This vector equation corresponds to the system of linear equations

[tex]\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}[/tex]

The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).

The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.

The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:

5 inches x 4 = 20 inches

4 iches x 4 = 16 inches

20 + 20 + 16 +16= =72 inches

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Step-by-step explanation:

11.

As all the exterior angles of a pentagon add up to 360, [ because exterior angle of a polygon = n(360/n) where n = no. Of sides, As the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.]

THEN,

56 + 2x + 85 + 57 + 4x = 360

6x + 198 = 360

6x = 360 - 198

X = 162/6 = 27

Ans : x = 27

12.

Let the missing angle be x,

As we know that all exterior angles in a pentagon add up to 360 ( Write the same thing written above),

Then,

83 + 83 + 26 + 46 + x = 360

238 + x = 360

X= 360 - 238

X = 122

Answer : the fifth exterior angle = 122°

Hope this helps

Answer:

162.50

Step-by-step explanation:

6500 *  5/12 * .06 =

Answer:

Step-by-step explanation:

Heroes in Greek Mythology were men or women of special strength, courage, or ability. They were often of divine ancestry and noted for superhuman courageous acts.

What makes a hero in Greek Mythology?

Answer:

X and 127 are co-interior angles and X and Y are straight angle

Answer:

Y=127°

X=53°

Step-by-step explanation:

Y is 127 bcs it is correspoding to the 127° it has given u in the question. But you know that half a circle is 180° now that you have 127 as y u minus 180- 127 which equals X that is 53 hope u understood

Th anwse is d) :B k .............

Answer:

B

Step-by-step explanation:

EZ

Answer:

17.3

Step-by-step explanation:

area of paralellogram=base x height

height=sin(60) x 4= [tex]2\sqrt{3}[/tex]

area = 5 x [tex]2\sqrt{3}[/tex]

        = [tex]10\sqrt{3}[/tex] = 17.3(to nearest tenth)

[tex] \huge \mathfrak \red{HeY \: ThErE♡}[/tex]

No. of mangoes sid has = 15

No. of apples sera has = 6

Total no. of fruits Sidra will have = 15 + 6 = 21

[tex] \huge \mathfrak \red{HoPe \: It \: HeLpS♤}[/tex]

Answer:

l+s≥300

2.5l+2.1s≤670

Step-by-step explanation:

If you know what y = x², you can make the parabola more narrow by scaling this by some constant greater than 1 or smaller than -1. For example, y = 2x² or y = -5x². Note that if you pick a negative constant, you would end up reflecting the parabola across the horizontal axis.

To get a wider graph, you would instead scale by some constant between -1 and 1. For example, y = -1/2 x² (scaling by -1/2, or equivalently scaling by 1/2 and reflecting).

Taking the aformentioned details together, you can (1) reflect and (2) narrow the graph by multiplying y = 3x² by a negative constant larger than 1 in magnitude. For example, y = -15x², where we scale by -5.

A) y − 4

Four less than an unknown value

B) b + 4

Four more than some number

C) a^4

Some number to the power of four

D) 4x

Four times an unknown value

E) z ÷ 4 =

Quotient of a variable and four

Answer:

5a + 1

Step-by-step explanation:

3a + 2a = 5a

2 - 1 = 1

So now we rewrite the problem.

5a + 1

combine like variables and combine whole numbers

2+3a-1+2a

2-1 is 1

and 3a+2a is 5a

so this is 5a+1

Hope this helped

Step-by-step explanation:

Let the number of phones sold in 1987 is k.

The rate of decrease is

The function to represent the number of phones P sold after x years after 1987 is

Answer:

[tex]f(x)=a(0.86)^x[/tex]

where:

Step-by-step explanation:

General form of an exponential function:

  [tex]f(x)=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given:

If the number of phones decreased by 14% each year, then each year the number of phones will be 86% of the previous year
(100% - 14% = 86%)

Therefore, b = 86% = 0.86

Substitute the given and found values into the general form of the function to create a function to represent the number of home phones sold:

   [tex]f(x)=a(0.86)^x[/tex]

where:

Answer:

15

Step-by-step explanation:

let the number=x

⅔x=18

2x=54

x=27

Now 5/9 of the number=5/9×27

=5×3=15

Answer:

6/2(1+2)

First lets simplify whats in the parentheses

6/2(3)

So thats 6/2 * 3

6/2 = 3

3*3 =

9

Answer:

9

Step-by-step explanation:

first, you do (1+2) which is 3 and then you do 6/2 which is 3 then 3x3 is 9

Y=mx+b form:

y<2/5x+2

y ≥ -1/2x+3

I forgot how to do the inequalities :)

Step-by-step explanation:

The volume of the hopper bin is the amount of feed in it

The given parameters are:

Start by calculating the radius (r) of the cones.

r = D/2 -------- because the cones and the cylinder have equal diameters.

So, we have:

r = 36/2 = 18

The height (h) of the cones is:

tan(θ) = h/r

This gives

tan(52) = h/18

Make h the subject

h = 18 * tan(52)

Evaluate

h = 23.04

The volume is then calculated as:

Volume = Volume of cylinder + 2 * Volume of cone

This gives

Volume = πr^2H + 2 * 1/3πr^2h

Volume = πr^2H + 2/3πr^2h

Factor out πr^2

Volume = πr^2(H + 2/3h)

Substitute known values

Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)

Evaluate

Volume = 35973.85 cubic feet

Hence, the volume of the hopper bin is 35974 cubic feet

The given parameters are:

For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:

Weight = 22 * 35974 pounds

Weight = 791428 pounds

At 85% full, the weight wuld be:

Weight = 85% * 791428 pounds

Weight = 672713.8 pounds

672713.8 pounds is greater than the weight limit of 500000 pounds.

Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit

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The probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).

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]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

For this case, we've got:

Each coin flip is a bernoulli distribution as it has two possible outcomes (assuming any other outcome like coin landing standing straight etc ignored). Take success = getting head in a flip, and failure = not getting success= not getting head = getting tail as the outcome of the flip.

Now, each of those 8 flips are independent in terms of result of each other (assuming coin stays unbiased).

If we take:

X = number of heads out of those 8 flips = number of successes in those 8 bernoulli trials, then:

[tex]X \sim B(n = 8, p)[/tex]

where p is the probability of success = P(Getting head in an unbiased coin with head or tail as only possible outcomes) = 1/2 = 0.5 (as head can come in 1 way, and total outcomes is 2, all equally likely).

Thus, we get:

[tex]X \sim B(n = 8, p=0.5)[/tex]

Now, P(Exactly 5 heads in those 8 flips) = P(X = 5)

Using the probability function of the binomial distribution, we get:

[tex]P(X = 5) = \: ^8C_5(0.5)^5(0.5)^{8-5} = \dfrac{8\times 7\times 6\times 5\times 4}{5 \times 4 \times 3\times 2 \times 1} \times (0.5)^8 \approx 0.219[/tex]

Thus, the probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).

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Answer:

Step-by-step explanation:

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

x/3 + (x+2y)/3 = 14

Multiply first equation by 6

3(x+y) - (x - y) = 96

2x + 4y = 96

x + 2y = 48       (A)

Multiply second equation by 3

x  + x + 2y = 42

x + y = 21         (B)

Subtract  A - B:-

y = 27

So:

x + 27 = 21

x = -6.

The quadratic relation

is f(x) = a(x - 27)(x + 6)

=   a(x^2 - 21x - 162)     where a is some constant

Vertex form:

f(x) = a[(x - 10.5)^2 - 110.25 - 162]  

f(x)  = a[(x - 10.5)^2 - 272.25]

f(x) = a[(x - 10.5)^2 -  272.25a.

Answer:B

Step-by-step explanation: Because the  science math Spanish and art. Science: MAD of 1.14, Math: of 1.6, Spanish: MAD of 1.2 Art: MAD of 1.93 In which class were his scores the closest together

Answer:

spanish

Step-by-step explanation:

Answer:

B and D.

Step-by-step explanation:

4(2n) + n

= 8n + n

= 9n.

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✟\:Important\: point's✟ }}}[/tex]

→ Your given expression:- 4(2n)+n

☆ Hence option b (9n) is right ans

[tex]\pink{\underline{ \underline{ \boxed{ \sf{✰\: Option.\:B✓ }}}}}[/tex]

Hope it helps !

to get the LCD we should start by doing a quick prime factoring of each denominator, as you see in the picture below.

the factors in red are the common factors to all values, and they are used in the LCD only once, the other not common factors in blue, they're used in the LCD.

The pressure to the nearest tenth at the time of the first measurement  for this case was 1.82 atm approximately.

According to the Boyle's law, the pressure of a gas tends to drop as the capacity of the container increases. We can write it symbolically as:

[tex]P_1V_1 = P_2V_2[/tex]

where we have:

[tex]P_1[/tex] and [tex]V_1[/tex] are first pressure and first volume, and:

[tex]P_2[/tex] and [tex]V_2[/tex] are second pressure and second volume.

The complete question is:

" According to Boyle's law, PV = k, what was the pressure to the nearest tenth at the time of the first measurement given the following information?

V₁ = 7,450 mL, P₂ = 8.25 atm, V₂ = 1,645 mL"

So, using the Boyle's rule, we get:

[tex]P_1V_1 = P_2V_2\\\\P_1 = \dfrac{P_2V_2}{V_1}\\\\P_1 = \dfrac{8.25 \times 1645}{7450} \approx 1.82 \: \rm atm[/tex]

Thus, the pressure to the nearest tenth at the time of the first measurement  for this case was 1.82 atm approximately.

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Answer:

~12 meters per second is your answer

Step-by-step explanation:

You need to do these specific things in order to convert.

Kilometers to meters - Multiply by 1000

Minutes to Seconds - Multiply by 60.

_______________________________________________________

First, do 20 kilometers multiplied by 1000

20 x 1000 = 20,000 meters

Do 29 minutes multiplied by 60.

29 x 60  = 1,740 seconds

_______________________________________________________

Now that we have everything converted, you need to divide it to find the speed.

Speed is Distance over Time.

20,000 meters / 1,740 seconds = Speed

Do 20,000 divided by 1,740

11.494252873563218390804597701149 That is your number.

You need to round that to the nearest whole number.

~12 meters per second is your answer

Answer: 6/11

Step-by-step explanation:

28 - 7 = 21

16 + 11 - 21 = 6

11 - 6 = 5

16-6 = 10

10 + 5 15

P (a) = 16/28

p (b) = 11/28

A I B = 6/28/11/28 = 6/11

Answer: 10

Step-by-step explanation: