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A recipe requires 3 cups of flour to make 27 dinner rolls. How much flour is needed to make 9 rolls?Mandy runs 4 km in 18 min. S

Rama09 [41]

Answer:

a)1 cup of flour

b)67.5 minutes

Step-by-step explanation:

a) A recipe requires 3 cups of flour to make 27 dinner rolls. How much flour is needed to make 9 rolls?

From the above question, we know that:

27 dinner rolls = 3 cups of flour

9 dinner rolls = x

Cross Multiply

27 rolls × x = 9 rolls × 3 cups

x = 9 rolls × 3 cups/27 rolls

x = 1 cup of flour

Hence, 1 cup of flour is needed to make 9 dinner rolls

b) Mandy runs 4 km in 18 min. She plans to run in a 15 km race. How long will it take her to complete the race?

From the above question:

4 km = 18 minutes

15km = x

Cross Multiply

4km × x = 15km × 18 minutes

x = 15km × 18minutes/4km

x = 67.5 minutes

Hence, in a 15km race , it would take her 67.5 minutes to complete her race.

5 0

3 years ago

Limit xtens to 0 x^2logx^2 what is the ans of interminate forms?

GarryVolchara [31]

Rewrite the limit as

$\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}$

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

$\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}$

7 0

3 years ago

What is the trigonometric ratio for sin Z ?

Schach [20]

In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.

So, in your case, we have

$\sin(Z) = \dfrac{XY}{XZ}$

In order to find XY, we have

$XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24$

So, the ratio for the sine is

$\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}$

6 0

3 years ago

Daily high temperatures in St. Louis for the last week were as follows: 95, 92, 93, 92, 95, 90, 90 (yesterday). a) The

hichkok12 [17]

Answer:

a) T = 91.7 degrees

b) T = 90 degrees

c) MAD = 1.9

d) MSE = 5.05

Step-by-step explanation:

Given:

- Daily high temperatures in St. Louis for the last week were as follows:

95, 92, 93, 92, 95, 90, 90

Find:

a) Forecast the high temperature today, using a 3-day moving average.

b) Forecast the high temperature today, using a 2-day moving average.

c) Calculate the mean absolute deviation based on a 2-day moving average, covering all days in which you can have a forecast and an actual temperature.

d) The mean squared error for the 2-day moving average

Solution:

a)

- The set of 3 day moving average is as follows:

4. (95 + 92 + 93) ÷ 3 = 93.33⁰C

5. (92 + 93 + 92) ÷ 3 = 92.33⁰C

6. (93 + 92 + 95) ÷ 3 = 93.33⁰C

7. (92 + 95 + 90) ÷ 3 = 92.33⁰C

8. (95 + 90 + 90) ÷ 3 = 91.667⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 91.7 degrees

b)

- The set of 2 day moving average is as follows:

3. (95 + 92) ÷ 2 = 93.5⁰C

4. (95 + 93) ÷ 2 = 92.5⁰C

5. (93 + 92) ÷ 2 = 92.5⁰C

6. (92 + 95) ÷ 2 = 93.5⁰C

7. (95 + 90) ÷ 2 = 92.5⁰C

8. (90 + 90) ÷ 2 = 90⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 90 degrees

c)

Error Error^2

3. 93.5⁰C 0.5 0.25

4. 92.5⁰C 0.5 0.25

5. 92.5⁰C 2.5 6.25

6. 93.5⁰C 3.5 12.25

7. 92.5⁰C 2.5 6.25

8. 90⁰C

- The mean absolute deviation as follows:

MAD = Sum of all errors / 5

MAD = (0.5+0.5+2.5+3.5+2.5) / 5

MAD = 1.9

d)

- The mean squared error deviation as follows:

MSE = Sum of all error^2 / 5

MSE = (0.25+0.25+6.25+12.25+6.25) / 5

MSE = 5.05

4 0

3 years ago

AAAAAAAAAAAAAAAAAAAAAAA wdjewkhfewhjfuhegkufygqe ANSWER

nikklg [1K]

Answer:

(8+t)^2-6 when t=2

Step-by-step explanation:

1: (8+2)^2-6

2: (10)^2-6

3: 100-6

4: 94

6 0

3 years ago