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3 years ago

How many three-person relay teams can be chosen from six students?

Mathematics

2 answers:

oksano4ka [1.4K]3 years ago

6 0

2 because 6 divided by 3 is 2

hope i helped

GenaCL600 [577]3 years ago

5 0

Divide 6 evenly so you would get 3 groups of 2 so 2 three person relay teams can be chosen from 6 students

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The walnut Cove Ruritan Club sells hot dogs and drinks from a concession stand at the annual 4th of July parade. Carl bought 5 h

Naddik [55]

Answer:

The cost of one hot dog is $1.5 and the cost of one drink is $2.

Step-by-step explanation:

Let

h = the cost of a hog dog and d = the cost of a drink

We know from the information given that:

Carl bought 5 hot dogs and 3 drinks and paid $13.50. This is equal to $5\cdot h +3\cdot d=13.50$

Susan purchased 2 hot dogs and 3 drinks and was charged $9.00. This is equal to $2\cdot h +3\cdot d=9.00$

So we have a system of equations

$5\cdot h +3\cdot d=13.50\\2\cdot h +3\cdot d=9.00$

We can solve by elimination as follows:

$\mathrm{Multiply\:}5h+3d=13.5\mathrm{\:by\:}2:\\10h+6d=27\\$

$\mathrm{Multiply\:}2h+3d=9\mathrm{\:by\:}5:\\10h+15d=45$

Subtract $10h+6d=27$ from $10h+15d=45$

$(10h+15d=45) -(10h+6d=27)=\\9d=18$

$\mathrm{Solve}\:9d=18\:\mathrm{for}\:d:\\d=2$

$\mathrm{For\:}10h+6d=27\mathrm{\:plug\:in\:}\quad \:d=2$

$\mathrm{Solve}\:10h+6\cdot \:2=27\:\mathrm{for}\:h:\\h=\frac{3}{2} = 1.5$

Therefore

h = $1.5 and d = $2

8 0

4 years ago

Please answer this correctly without making mistakes

Wittaler [7]

Answer:

$7.28 per quart

Step-by-step explanation:

16 pints equals 8 quarts so divide total $ by 8

6 0

3 years ago

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the re

alukav5142 [94]

Answer:

Step-by-step explanation:

$\text{Given that:}$

$y = 1+ sec(x) \ \ y =3$

$\text{we draw the graph and the curves intersect at:}$

$x = - \dfrac{\pi}{3} \ and \ x = \dfrac{\pi}{3}$

$\text{Applying washer method;}$

$f(x) _{outer} - g(x) _{inner} --- (1)$

$V= \int ^b_a A(x) \ dx --- (2)$

$\text{outer radius = 3 - 1 = 2}$

$\text{inner radius =}$ $( 1 + sec(x) ) - 1 = sec (x)$

$A(x) = \pi ((2)^2 -(sec(x)^2) \\ \\ A(x) = \pi (4 - sec^2 (x)) ---- (3)$

$\text{The volume V =}\int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ A(x) \ dx$

$V = \int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ \pi (4- sec^2 (x) ) \ dx$

$V = 2 \pi \int ^{\dfrac{\pi}{3}}_{0}( 4 - sec^2 (x)) \ dx$

$V = 2 \pi \int ^{\pi/3}_{0} 4 . \ dx - 2 \pi \int ^{\pi/3}_{0} sec^2 (x) \ dx$

$V = 2 \pi(4) \int ^{\pi/3}_{0} 1 . \ dx - 2 \pi \Big( tan (x)\Big )^{\dfrac{\pi}{3}}_{0}$

$V = 8 \pi(x)^{\dfrac{\pi}{3}}_{0} - 2 \pi \Big( tan \dfrac{\pi}{3} -tan (0)\Big )$

$V = 8 \pi({\dfrac{\pi}{3}}-{0}) - 2 \pi \Big( tan \sqrt{3}-(0)\Big )$

$V = 8 \pi({\dfrac{\pi}{3}}) - 2 \pi \Big( \sqrt{3}\Big )$

$\mathbf{V = 2 \pi \Big(\dfrac{4\pi}{3}- \sqrt{3} \Big)}$

8 0

3 years ago

If you know how to solve this, Please answer it. Thank You

r-ruslan [8.4K]

6.5 / 12 = x / 24

x = 6.5 × 24 / 12

x = 6.5 × 2

x = 13

8 0

3 years ago

Read 2 more answers

what is the maximum height of the T-shirt after being fired from the cannon? round to the nearest tenth. Will the fans sitting i

Pie

$h(t)=-16t^2+88t+5$

Based on the given trajectory, the leading numerical coefficient is a negative number, hence, the graph of this function is a parabola opening downwards.

In a parabola opening downwards, the maximum value is the vertex of the parabola. So, in order to determine the maximum height, let's solve for the vertex of the parabola. The formula is:

$t=-\frac{b}{2a}$

where in the quadratic function is in the form of at² + bt + c = 0.

So, in the given trajectory function, a = -16, b = 88, and c = 5. Let's replace the variables in the formula above with their corresponding numerical value.

$t=-\frac{88}{2(-16)}$

Then, solve.

$t=-\frac{88}{(-32)}\Rightarrow t=2.75$

Therefore, at t = 2.75 seconds, the t-shirt reached its maximum height.

So, to determine the maximum height, replaced "t" in the trajectory function with 2.75.

$h(2.75)=-16(2.75^)^2+88(2.75)+5$ $h(2.75)=-121+242+5$ $h(2.75)=126$

Hence, after 2.75 seconds, the t-shirt reached its maximum height which is 126 feet.

Since the maximum height of the t-shirt is 126 feet, then yes, there is a chance that the fans sitting in the bleachers 90ft above the field will catch a T-shirt.

7 0

1 year ago