In a triangle, two of the angles measure 56° and 72°. Find the measure of the third angle.

Answers

Answer 1
Answer: In a triangle, the three interior angles always add to 180°.

56° + 72° + x° = 180°

128° + x° = 180°    |subtract 128° from both sides

x° = 52°

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Elliott has 4 columns of marbles. He has 3 marbles in each column. How many marbles does he have in all? *

Answers

Answer:

3*4=12

Step-by-step explanation:

the answer is 12

Final answer:

To find out how many marbles Elliott has in total, we multiply the number of columns by the number of marbles in each column, resulting in 12 marbles in total.

Explanation:

To find out how many marbles Elliott has in total, we can multiply the number of columns by the number of marbles in each column. In this case, Elliott has 4 columns with 3 marbles in each column. So, we can calculate the total number of marbles by multiplying 4 and 3, which equals 12. Therefore, Elliott has 12 marbles in total.

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What temperature in Fahrenheit is 50 degree celsius? (Enter numeric value only. If rounding is necessary, round to the nearest whole number.)

Answers

Step #1: Subtract 32. Step #2: Mutliply by 5. Step #3: Divide by 9... 50-32 = 18; 18 * 5 = 90; 90 / 9 = 10 degrees celsius.

A plan has scale 1:22. what is the actual length, in cm, represented by 101 cm ?

Answers

The ratio of the scale of the plan to the actual length is 1:22.

This means that every 1 cm on the plan represents 22 cm for the actual length.

Therefore, to find the actual length of 101 cm on the plan, we just have to multiply 101 * 22.  This equals 2222 cm.

Therefore, the actual length is 2222 cm.

Find the percent of the area under the normal curve between the mean and 0.83 divisions of the mean.

Answers

0.296730608171932
= 29.6731%

The ratio of D's to A's in the school was 4 to 72. If there were 1080 A's in the school this term, how many D's were there? Write your answer in a complete sentence.

Answers

Answer:

To find the number of D's in the school, we can use the given ratio of D's to A's and the number of A's provided.

The ratio of D's to A's is given as 4 to 72. This means that for every 4 D's, there are 72 A's.

We are also given that there are 1080 A's in the school this term.

To find the number of D's, we can set up a proportion using the ratio:

4 D's / 72 A's = X D's / 1080 A's

Cross-multiplying, we get:

4 * 1080 = 72 * X

Simplifying further:

4320 = 72X

Dividing both sides by 72:

X = 4320 / 72

X = 60

Therefore, there were 60 D's in the school.

Step-by-step explanation:

Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 19y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

Answers

Answer:

1.92 yd  x 3.83 yd  x 2.58 yd

Step-by-step explanation:

We have given a rectangular base, that its twice as long as it is wide.

It must hold 19 yd³ of debris.

Lets minimize the surface area, subject to the restriction of volume (19 yd³)

The surface is given by:

S=2(w*h+w*2w+2wh)=2(3wh+2w^2)

The volume restriction is:

V=w*2w*h=2w^2h=19\n\nh=(9.5)/(w^2)

replacing h in the surface equation, we have:

S=2(3wh+2w^2)=6w((9.5)/(w^2))+4w^2=57w^(-1)+4w^2

Derivate the above equation and set it to zero

dS/dw=57(-1)w^(-2) + 8w=0\n\n57w^(-2)=8w\n\nw^3=57/8=7.125\n\nw=\sqrt[3]{7.124} =1.92

The height will be:

h=9.5/w^2=9.5/(1.92^2)=9.5/2.69=2.58

Therefore,The dimensions that minimize the surface are:

Wide: 1.92 yd  

Long: 3.83 yd

Height: 2.58 yd