Find the angle between the diagonal of a cube of side length 15 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians. (Hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

Answer:

the angle between the diagonal is 0.6155 RADIANS

Step-by-step explanation:

Given the data in the question

as illustrated in the image below;

O is [0,0,0]

B is [15,0,15]

E is [15,15,15]

Now to find angle BOE

vector OB = [15,0,15]

vector OE = [15,15,15]

OB.OE = [15,0,15].[15,15,15] = 15 × 15 + 15 × 15 = 450 = |OB||OE|cos[angleBOE]

|OB| = √(15² + 15²) = √(225 + 225) = √450

|OE| = √(15² + 15² + 15²) = √(225 + 225 + 225) = √675

so

Angle BOE = cos⁻¹ (  450 / ( √450 × √675 )

Angle BOE = cos⁻¹ ( 0.81649 )

Angle BOE = 35.265°

Angle BOE = 0.6155 RADIANS

Therefore, the angle between the diagonal is 0.6155 RADIANS  

Which inverse operations could you use to solve the equation m/5 - 8 = -6? Select two answers.
A Add 8 to each side and then divide each side by 5
B. Add 8 to each side and then multiply each side by 5
C. Multiply each side by 5 and then add 40 to each side
D. Subtract 8 from each side and then multiply each side by 5
E Multiply each side by 5 and then add 8 to each side

Enter an estimate. Round each mixed number to the nearest half in your estimate.

5 1/2 - 4 6/7

The difference of five times a number and 11 is 39

so the question on the pic

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Statement 1: All things being equal, savers and investors expect to receive some amount of maturity premium as compensation for their deferred consumption.
Statement 2: Historical inflation rates, as opposed to expected future rates of inflation, should be used when calculating an investment’s nominal risk-free rate of return.
Statement 3: An investment that can provide a 10% return should attract more investment capital than an otherwise identical investment that can only provide a 6% return.
Statement 4: The inflation premium used to calculate the nominal interest rate on a five-year security should be equal to the rate of inflation expected in year 5 of the investment.
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A at least 19
B at least 17
C at least 16
D at least 20

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Ingredients

1.25 cup milk
1/2 cup sugar
1 ¾ tsp vanilla
⅘ cup sprinkles
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she suznsnsja. s
anna abs
s
sm

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a) Show the work to set up the problem. You may either use the percent equation, set up a proportion, or use a ratio table but SHOW YOUR WORK.






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The most common IQ tests have a standardized mean of 100 and a standard deviation of 15. Based on this information, use the empirical rule to answer the following question: If approximately 348 prospective college students are tested for their IQ, approximately what percentage of their scores will fall within one standard deviation of the mean

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2. x is greater to or equal to 100
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4. or x is greater to or equal to 134

Responses which are acquired after birth are called _____ responses.

5.
(x + 10°)
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Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain.
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43.5 47.0 51.2
39.4 40.5 40.9
41.3 38.9 37.9
46.0 46.3 45.0
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Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats. Test at a significance level of 10%.

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Required:
Find the z-score for an ACT score of 26.