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2 years ago

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Lyle works at a bakery. He needs to mix 1 cup of brown sugar and 12 cup of granulated sugar to make each tray of 60 cookies. Eac

h week, Lyle uses a total of 75 cups of his sugar mixture. How many trays of cookies does Lyle make each week? What is the total number of cookies he makes in a week?

1 answer:

andriy [413]2 years ago

8 0

Answer:

50 trays

3000 cookies

Step-by-step explanation:

We are given the following in the question:

1 cup of brown sugar and $\frac{1}{2}$ cup of granulated sugar makes a tray of 60 cookies.

Total cups of sugar used(brown and granulated) = 1.5 cups

Number of sugar cups used by Lyle each week = 75

We have to find the number of trays made each week.

$\text{Ratio} = \dfrac{\text{Cups of sugar mixture}}{\text{Number of trays}}\\\\\dfrac{1.5}{1} = \dfrac{75}{\text{Number of trays}}\\\\\Rightarrow \text{Number of trays} = \dfrac{75}{1.5} = 50$

Thus, 50 trays of cookies are made each week.

Total number of cookies made each week =

$=\text{Number of trays}\times \text{Number of cookies in 1 tray}\\=50\times 60\\=3000$

Thus, 3000 cookies are made each week.

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) If the pattern shown continues, how many black keys appear on a portable keyboard with 49 white keys? Suggestion: use equivale

andriy [413]

Answer:

35

Step-by-step explanation:

Here we see 5 black keys for every 7 white keys.

So the ratio is 5:7

If we need 49 white keys, find the amount we scale the original ratio by:

49/7 = 7

So we are scaling by a factor of 7.

The number of black keys would be 5 * the scale of 7. = 35

So there should be 35 black keys.

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1 year ago

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The picture shows the footprints of a man walking. The pace length P is the distance between the rear of two consecutive footpri

Rina8888 [55]

Bernard’s walking speed is 140 meters per minute

Bernard’s walking speed is 8.4 kilometers per hour

Step-by-step explanation:

The pace length P is the distance between the rear of two consecutive footprints

The formula, n P = 140, gives an approximate relationship between n and P where,

n = number of steps per minute
P = pace length in meters
Bernard knows his pace length is 0.80 meters
The formula applies to Bernard’s walking

We need to calculate Bernard’s walking speed in meters per minute and in kilometers per hour

∵ n = number of steps per minute

∴ n unit is number / minute

∵ P = pace length in meters

∴ P unit is meter

- That means n P unit is meters/minute

∴ n P represents the speed in meters per second

∵ The formula applies to Bernard’s walking

∵ His pace length is 0.80 meters

∵ n P = 140

∴ n(0.8) = 140

- Divide both sides by 0.8

∴ n = 175

- That means he moves 175 steps per minute

∵ The distance he walks in minute = 175 × 0.8 = 140 meters/minute

∴ His speed is 140 meters per minute

Bernard’s walking speed is 140 meters per minute

∵ 1 km = 1000 m

∵ 1 hour = 60 minutes

- Divide the meters by 1000 and the minute by 60 to change

from meters per minute to kilometers per hour

∴ His walking speed = $\frac{140}{1000}$ ÷ $\frac{1}{60}$

- Change ÷ to × and reciprocal the fraction after the division sign

∴ His walking speed = $\frac{140}{1000}$ × $\frac{60}{1}$ = 8.4 km/h

Bernard’s walking speed is 8.4 kilometers per hour

Learn more:

You can learn more about the speed in brainly.com/question/5461619

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2 years ago

PLS HELP ASAP I WILL IVE BRAINLIST ANSWER!!!!!Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using thi

Juliette [100K]

Answer:

Leon is correct. (Option 1)

Step-by-step explanation:

Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.

Step 1: Find the greatest common factor of the given lengths: 7

Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5

Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.

we have to explain whether or not Leon is correct.

As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem

$Hypotenuse^2=Base^2+Perpendicular^2$

⇒ $5^2=3^2+4^2$

Let a, b, c forms a Pythagorean triplet

$a^2+b^2=c^2$

Multiplied by 4 on both sides

⇒ $4a^2+4b^2=4c^2$

⇒ ${2a}^2+{2b}^2={2c}^2$

Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.

∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.

Hence, Leon is correct.

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2 years ago

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A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

1 year ago

Linda commutes a total of 54 miles to and from work every day. She needs a new car, and good gas mileage is important to her. Sh

Alchen [17]

The answer is 1 gallon.

Miles per gallon(mpg) is computed by dividing the distance traveled by the how many gallons used. So you can derive a formula for how many gallons you would use given the mpg. You will end up with:

$gallon = \frac{miles travelled}{miles per gallon}$

The problem asks for how many gallons of gas she will safe in a five-day work work week. So first you need to compute how many miles that would be.

54 miles/day x 5days = 270 miles

So in a five day work week, she will travel 270 miles.

Now to see how much gas she will save, compute how many gallons she will use up for each car, given the mpg of each and find the difference.

First model:30 mpg

$gallons = \frac{270miles}{30mpg}$
$gallons = 9g$

This means that with the first model, she will have used up 9 gallons in a 5-day work week.

Second model: 27 mpg
$g = \frac{270mi}{27mi/g}$
$g = 10g$

This means that with the second model, she will have used up 10g in a 5-day work week.

Now for the last bit. How much will she save? You can get that by getting the difference of how many gallons each car would have used up.

10gallons - 9gallons = 1g

So she would have saved 1 gallon of gas if she buys the first car instead of the second.

8 0

1 year ago

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