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2 years ago

How much of a 90% alloy must be combined with 70% gold alloy in order to get 60 ounces of an 85% gold alloy?

1 answer:

4 0

X = amount of 90% alloy
y = amount of 70% alloy

x + y = 60
0.9x + 0.7y = 0.85*60

0.9x + 0.7(60 - x) = 0.85*60
(0.9 - 0.7)x = (0.85 - 0.7)*60
x = (0.85 - 0.7)*60/(0.9 - 0.7)
x = 45 ounces

y = 60 - 45
y = 15 ounces

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In a regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample points in the sample space

posledela

Answer: a.) 40320

b.) 336

Step-by-step explanation:

since we have 8 possible positions, with 8 different candidates, then there are 8 possible ways of arranging the first position, 7 possible ways of arranging the Second position, 6 ways of arranging the 3rd position, 5 possible ways od arranging the 4th position, 4 possible ways of arranging the 5th position, 3 possible ways of arranging the 6th position, 2 possible ways of arranging the 7th position and just one way of arranging the 8th position since we have only one person left.

Hence, the Number of possible sample space for different 8 positions is by multiplying all the number of ways we have in our sample space which becomes:

8*7*6*5*4*3*2*1 = 40320.

b.) By the sample space we have, since we've been asked ti arrange for only the firat 3 positions, then we multiply just for the first 3ways of choosing the positions, this becomes:

8*7*6 = 336

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1 year ago

Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the

natulia [17]

Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.

In order to triangle JKM be a right triangle $KM^{2}=JK^{2}+JM^{2}$ .

We will find length of side KM using our right triangles JLM and JLK as $KM=KL+LM$ .

Using Pythagorean theorem in triangle JLM we will get,

$LM=\sqrt{JM^{2}-JL^{2}}$

$LM=\sqrt{8^{2}-5^{2}}$

$LM=\sqrt{64-25}$

$LM=\sqrt{39}=6.244997998\approx 6.24$

Now let us find length of side KL.

$KL=\sqrt{JK^{2}-JL^{2}}$

$KL=\sqrt{13^{2}-5^{2}}$

$KL=\sqrt{169-25}$

$KL=\sqrt{144}=12$

Now let us find length of KM by adding lengths of KL and LM.

$KM=12+6.24=18.24$

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

$KM^{2}=JK^{2}+JM^{2}$

$18.24^{2}=13^{2}+8^{2}$

$18.24^{2}=169+64$

$18.24^{2}=233$

Upon taking square root of both sides of equation we will get,

$18.24\neq 15.264337522473748$

$18.2\neq 15.3$

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.

6 0

1 year ago

Read 2 more answers

Tyler is bored in history class, so he is staring at the ceiling tiles. He notices that some tiles are perfect squares, while ot

finlep [7]

Answer:

The complete tables are shown below.

The value of x is 70.59%.

Step-by-step explanation:

Absolute frequency table:

Square Rectangle Row Total

Bright 25 10 35

Off White 23 10 33

Column Total 48 20 68

Relative frequency table

Square Rectangle Row total

Row% 71.43% 28.57% 100.00%

Bright Column% 52.08% 50.00% ____

Total% 36.76% 14.71% 51.47%

Row% 69.70% 30.30% 100.00%

Off White Column% 47.92% 50.00% ___

Total% 33.83% 14.71% 48.53%

Row% ____ ____ 100.00%

Column Column% 100.00% 100.00% 100.00%

Total% x = 70.59% 29.41% 100.00%

$\text{Value of}\ x=100.00\%-29.41\%=70.59\%$

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2 years ago

mike and mandy bought the same item mike paid 15000 mandy got a discount and paid 3000 less than mike how much of a discount did

slega [8]

She got a 20% discount

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2 years ago

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Alan and Judith begin withdrawing money from their accounts at the same time.

ELEN [110]

Answer:

Step-by-step explanation:

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2 years ago