There are 6 seniors on the high school soccer team. Two of them will be chosen to be co-captains. How many ways are there to choose the co-captains? Decide if this is a permutation or a combination, and then find the number of ways to choose the co-captains.
A. Permutation; number of ways = 30
B. Combination; number of ways = 15
C. Combination; number of ways = 30
D. Permutation; number of ways = 15

Answer:

The integers are pairwise relatively prime since two of them are prime

Step-by-step explanation:

Given

[tex]25, 41, 49, 64[/tex]

Required

Determine if they are prime factors

First, we determine the gcd of the 4 numbers

[tex]25 = 1 * 5 * 5[/tex]

[tex]41 =1 * 41[/tex]

[tex]49 = 1 * 7 * 7[/tex]

[tex]64 = 1 * 2 * 2 * 2 * 2 * 2 * 2[/tex]

The common factor in the above computation is: 1

So:

[tex]gcd = 1[/tex]

Because the gcd is 1, this implies that no prime divides all the given numbers.

Hence, they are pairwise relatively prime

Answer:

0.375

Step-by-step explanation:

510 male out of a total of 1360

510/1360 = 0.375

Answer:

6.14 minutes   or   6 minutes & 8.4 seconds

Step-by-step explanation:

Initial elevation: 453 ft

Final elevation: 146 ft

Difference in elevation: 453 ft - 146 ft = 307 ft

speed = 50 ft/min

speed = distance/time

time * speed = distance

time = distance/speed

time = (307 ft)/(50 ft/min)

time = 6.14 minutes = 6 minutes + 0.14 * 60 seconds

time = 6.14 minutes = 6 minutes + 8.4 seconds

Answer:

m<3=84

m<4=96

Step-by-step explanation:

180-43-41=96

180-96=84

The measure of ∠3 is 96° and measure of ∠4 is 64°.

What is Triangle?

A triangle is a three sided polygon , which has three vertices and three angles with sum 180 degree.

Given that;

In triangle,

Measure of first angle (m ∠1 ) = 43°

Measure of second angle (m ∠2) = 41°

Let measure of ∠4 = x degree

Now, Sum of all angles in a triangle be 180 degree.

So, We can formulate;

m∠1 + m∠2 + m∠3 = 180°

43° + 41° + x = 180°

84° + x = 180°

x = 180° - 84°

x = 96°

So, measure of ∠3 = 96°

Since, The measure of ∠3 and measure of ∠4 are supplementary angles.

Hence, We get;

m ∠3 + m ∠4 = 180°

96° + m ∠4 = 180°

m ∠4 = 180° - 96°

m ∠4 = 64°

Thus, The measure of ∠3 is 96° and measure of ∠4 is 64°.

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Answer:

D. The median, 5, is greater than the mean, 4,

Step-by-step explanation:

Median: Put them from least to greatest, ( but they are) then find the middle

Mean: Add all the numbers together= 20, divide that by the numbers you added from 5:    20/5=4

5 from median is < than mean 4

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Hope this helps

Using the equation, the time the object will hit the ground after it is launched is 3.4 seconds.

To model the path of a projectile launched from ground level (h = 0), we can set h = 0 in the equation for y:

[tex]y = (v_0sin \theta)t - 16t^2[/tex]

Therefore, the parametric equations for the path of the projectile are:

[tex]x = (v_0cos\theta)t \\y = (v_0sin \theta)t - 16t^2[/tex]

Substituting θ = 40∘ and v0 = 128 feet per second, we get:

[tex]x = (128 cos 40^o)t\\y = (128 sin 40^o)t - 16t^2[/tex]

To determine the maximum height, we need to find the vertex of the parabolic path, which is given by:

t = -b/2a

where a = -16, b = 128 sin 40∘, and c = 0 (since the projectile starts and ends at ground level). Substituting the values, we get:

t = -128 sin 40∘ / (2*(-16)) = 2.3 seconds (approx)

The maximum height can be found by substituting this value of t into the equation for y:

y = (128 sin 40∘)(2.3) - 16(2.3)^2 = 230.3 feet (approx)

Therefore, the maximum height is 230.3 feet and it is reached at 2.3 seconds.

To find the horizontal distance at this point, we can substitute the value of t into the equation for x:

x = (128 cos 40∘)(2.3) = 172.8 feet (approx)

Therefore, the approximate horizontal distance the object is at this point is 172.8 feet.

To determine the time the object will hit the ground after it is launched, we need to find the time when y = 0:

[tex]0 = (128 sin 40)t - 16t^2[/tex]

Solving for t using the quadratic formula, we get:

t = 0 or t = 8 sin 40∘ / 2 = 3.4 seconds (approx)

Therefore, the time the object will hit the ground after it is launched is 3.4 seconds.

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Answer:

[tex] \displaystyle \sf h( - 1) = - \frac{ 2}{3} [/tex]

Step-by-step explanation:

we are given a function

[tex] \displaystyle \sf h(x) = \frac{2x - 6}{4 {x}^{2} + 8} [/tex]

we would like to simplify it for h(-1)

in order to do so

substitute the value of x

[tex] \displaystyle \sf h( - 1) = \frac{2 \cdot - 1- 6}{4 { (- 1)}^{2} + 8} [/tex]

by order of PEMDAS

simplify square:

[tex] \displaystyle \sf h( - 1) = \frac{2 \cdot - 1- 6}{4 { ( 1)}^{} + 8} [/tex]

simplify multiplication:

[tex] \displaystyle \sf h( - 1) = \frac{ - 2 - 6}{4 { }^{} + 8} [/tex]

simplify addition:

[tex] \displaystyle \sf h( - 1) = \frac{ - 2 - 6}{12} [/tex]

simplify subtraction:

[tex] \displaystyle \sf h( - 1) = \frac{ - 8}{12} [/tex]

reduce fraction:

[tex] \displaystyle \sf h( - 1) = - \frac{ 2}{3} [/tex]

Answer:

i believe the answer is 03.028.68

Step-by-step explanation:

hope this helps

9514 1404 393

Answer:

  C) No, Kayla is not correct, because the remainder is -49 not 149

Step-by-step explanation:

The remainder from division by x+5 can be found by evaluating the polynomial at x=-5, the value of x that makes the divisor zero.

Evaluation is often easier when the function is written in Horner form.

  ((x +2)x -4)x +6

For x=-5, this is ...

  ((-5 +2)(-5) -4)(-5) +6 = (-3(-5) -4)(-5) +6 = 11(-5) +6 = -49

Kayla is not correct; the remainder is -49.

Answer:

1/4 as decimal =0.25

and as percentage 25%

1/ 3 as decimal = 0.33

and as percentage = 33.33%

Answer:

7/8 * 3 = 21/24

1/3 * 8 = 8/24

21-8 = 13

Gail bought 13/24 pound more than Jose

Answer:

V=100ft³

Step-by-step explanation:

Answer:

B) x=5√3 y=5

Step-by-step explanation:

It’s a 30-60-90 triangle, so

B) x=5√3 y=5

Answer:

All of the questions?

Step-by-step explanation:

Answer:

i am not downloading this

Step-by-step explanation:

Answer:

Households without a vehicle were not surveyed. D

Step-by-step explanation:

I just finished with Maps testing like 10 minutes ago XD good luck!!

Anwner : 4/52

Explanation : The chance of drawing one of the four aces from a standard deck of 52 cards is 4/52; but the chance of drawing a second ace is only 3/51, because after we drew the first ace, there were only three aces among the remaining 51 cards. Thus, the chance of drawing an ace on each of two draws is 4/52 × 3/51, or 1/221.

Answer:

it is 7

Step-by-step explanation:

Answer:A

Step-by-step explanation:

I used the process of elimination. I did, 125 x .65 to get 81.25. Then, I subtracted 81.25 to 125. To get 43.75.

The original price of the dress was $125.00.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.

Given that the discount = 65%

Sale price = $43.75

Let the original price of the dress is $x.

Now, sale price = x - x * 65% = x - x * 65/100 = (100 - 65)x/100 = 35x/100

We can write

35x/100 = 43.75

i.e. x = (43.75 * 100)/35 = 4375/35 = 125

Therefore, the original price of the dress was $125.00. So, option 1 is correct.

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Answer:

model B is shaded to represent 37.5%

here,

=3÷8×100%

=37.5%

1.01 is the growth factor that would be needed to provide 1/12th of 12% interest each month.

A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.

Given, the growth factor would be needed to provide 1/12th of 12% interest each month

Remember the formulas:  

Increasing: y = a (1 + r)ˣ  

Decreasing: y = a(1 - r)ˣ

(1 ± r is the growth factor, while r is the growth rate)

In our case,

since it is an interest It will show the growth rate

Growth rate = 12% of 1/12

Growth rate = 1%

Growth rate = 0.01

Thus,

Growth factor  = 1 + r

Growth factor  = 1 + 0.01

Growth factor  = 1.01

Therefore, The growth factor will be 1.01.

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Answer:

33.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

since arc BC is 2 time the angle of A   , then

2(9x +12) = 21x +3

18x +24 = 21x + 3

21 = 3x

7 = x

x = 7

∠BAC = 9(7) +12

∠BAC = 63 +12

∠BAC = 75°

Answer:

c) [tex]\frac{x-2}{x+6}[/tex]

Step-by-step explanation:

When given that function (f) is the following,

[tex]f(x)=\frac{x+2}{x^2+4x-12}[/tex]

The wisest move to first make is to factor the expression, factoring is the process by which one rewrites a quadratic expression as the product of two linear expressions,

[tex]f(x)=\frac{x+12}{(x+6)(x-2)}[/tex]

If is given that function (g) is the following,

[tex]g(x)=\frac{4x^2-16x+16}{4x+48}[/tex]

Then one should also factor the expression,

[tex]g(x)=\frac{4(x-2)^2}{4(x+12)}[/tex]

One is asked to find the following,

[tex]f(x)*g(x)[/tex]

To do this operation, one must multiply the two functions together. It is easiest to do so when the functions are in factored form,

[tex]f(x)*g(x)[/tex]

Substitute,

[tex](\frac{x+12}{(x+6)(x-2)})(\frac{4(x-2)^2}{4(x+12)})[/tex]

Simplify, cross out like terms in the numerator and denominator,

[tex]\frac{x-2}{x+6}[/tex]

answer:

in order to construct 75°, you need to use a protractor and a compass

step-by-step explanation:

here is a step-by-step explanation from an online source

Construct 60°. Then 120°. Then construct 90° by bisecting them. Then bisect 60° and 90°. Then it will be 75°.

Answer:

P( red | large shirt ) ≠ P( large shirt)

P( Blue | large shirt ) = P( blue shirt)

P( shirt is medium and blue ) ≠ P( medium  shirt)

P( large shirt | red shirt ) ≠ P( red shirt)

Explanation:

P( red | large shirt ) = 42/77 = 0.5454 : P( large shirt)= 77/165 = 0.467

P( red | large shirt ) ≠ P( large shirt)

P( Blue | large shirt ) = 35/77 = 0.4545 : P( blue shirt)= 75/165 = 0.4545

  P( Blue | large shirt ) = P( blue shirt)

P( Shirt is medium and blue ) = 40/77 = 0.2424   : P( medium shirt)= 88/165 = 0.5333

P( shirt is medium and blue ) ≠ P( medium  shirt)

P( large shirt | red shirt) = 42/90 = 0.4667 : P( red shirt)= 90/165 = 0.5454

P( large shirt | red shirt ) ≠ P( red shirt)

P( Blue shirt | large shirt ) = P( blue shirt). Therefore, option B is the correct answer.

A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis.

P( red | large shirt ) = 42/77 = 0.5454 : P( large shirt)= 77/165 = 0.467

P( red | large shirt ) ≠ P( large shirt)

P( Blue | large shirt ) = 35/77 = 0.4545 : P( blue shirt)= 75/165 = 0.4545

P( Blue | large shirt ) = P( blue shirt)

P( Shirt is medium and blue ) = 40/77 = 0.2424 : P( medium shirt)= 88/165 = 0.5333

P( shirt is medium and blue ) ≠ P( medium  shirt)

P( large shirt | red shirt) = 42/90 = 0.4667 : P( red shirt)= 90/165 = 0.5454

P( large shirt | red shirt ) ≠ P( red shirt)

Therefore, option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

A box contains shirts in two different colors and two different sizes. The numbers of shirts of each color and size are given in the table. (See attached image for choices) box contains shirts in two different colors and two different sizes. The numbers of shirts of each color and size are given in the table Size Shirt Color Large Medium Total Red 42 48 90 Blue Total 35 40 75 88 165 77 From the data given in the table, we can infer that

P(red shirt | large shirt) =P(large shirt)

P(blue shirt | large shirt) = P(blue shirt)

P(shirt is medium and blue) = P(medium shirt)

P(large shirt red shirt) = P(red shirt)'

Answer:

x = 30°

x = 80°

Step-by-step explanation:

Recall: an inscribed angle is half the measure of the intercepted arc

Thus:

x = ½(arc cb)

Substitute

x = ½(60)

x = 30°

x = ½(arc ab)

Substitute

x = ½(160)

x = 80°

Given:

The end points of a line segment are (4,0) and (12,0).

To find:

The midpoint of the line segment.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The end points of a line segment are (4,0) and (12,0). So, the midpoint of the line segment is:

[tex]Midpoint=\left(\dfrac{4+12}{2},\dfrac{0+0}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{16}{2},\dfrac{0}{2}\right)[/tex]

[tex]Midpoint=\left(8,0\right)[/tex]

Therefore, the midpoint of the given line segment is (8,0).