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KATRIN_1 [288]
2 years ago
13

Melanie is making lemonade and finds a recipe that calls for 1 part lemon juice, 2 parts sugar, and 8 parts water. She juices 2

lemons to obtain 6 tablespoons of lemon juice. How much sugar and water will she need to make lemonade with the same ratio of ingredients as the recipe? Express your answers as decimals if necessary. (1 cup equals 16 tablespoons) With
Mathematics
2 answers:
Brums [2.3K]2 years ago
7 0

Answer:

Amount of lemon juice, sugar and water required will be = 0.375 cups, 0.75 cups and 3 cups.

Step-by-step explanation:

Malanie is making lemonade and finds a recipe that requires lemon juice, sugar and water in the ratio of 1 : 2 : 8.

She juices 2 lemons to obtain 6 tablespoons of lemon juice.

∵ 16 tablespoons = 1 cup

∴ 1 tablespoon = \frac{1}{16} cup

∴ 6 tablespoon =  \frac{6}{16} cup =  0.375 cups

Since ratio between lemon and sugar is 1 : 2

So amount of sugar required = 0.375×2 = 0.75 cups

Ratio between lemon and water is 1 : 8

So amount of water required = 0.375×8 = 3 cups

Therefore, amount of lemon juice, sugar and water required = 0.375 cups, 0.75 cups sugar and 3 cups respectively.

MakcuM [25]2 years ago
3 0
12 tablespoons of sugar and 3 cups of water (48 tablespoons)
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A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into t
Svet_ta [14]

Answer:

F_w=9408\ N

Weight of the truck=9408 N

Step-by-step explanation:

Boat is experiencing the buoyant force as it is in the water and is sinking

According to the force balance in y direction. As both is floating, two forces balance each other:

F_b-F_w=0

where:

F_b is the buoyant force

F_w is the weight=mg

F_b=F_w        Eq (1)

Buoyant force is equal to the mass of water displaced * gravitational acceleration.

F_b=m_{water\ displaced}*g\\F_b=\rho Vg\\

Taking density of water to be 1000 Kg/m^3

F_b=1000*(6*4*4*10^{-2})*9.8\\F_b=9408 N

From Eq(1):

F_w=9408\ N

Weight of the truck=9408 N

6 0
2 years ago
Consider a single spin of the spinner.
alex41 [277]

Answer:

"landing on a shaded portion and landing on a 3"

"landing on an unshaded portion and landing on a number less than 2 "

Step-by-step explanation:

Mutually exclusive means the events will have no intersection.

Let's look at your first choice:

"landing on a shaded portion and landing on an even number"

Landing on a shaded portion would be 1 or 4.

Landing on an even number would be 2 or 4.

There is an intersection (they contain a common element), the 4.

These events are not mutually exclusive.

Let's look at your second choice:

"landing on a shaded portion and landing on a number greater than 3"

Landing on a shaded portion would be 1 or 4.

Landing on a number greater than 3 would be just 4.

There is an intersection; they both contain 4.

These events are not mutually exclusive.

Let's look at your third choice:

"landing on a shaded portion and landing on a 3"

Landing on a shaded portion would be 1 or 4.

Landing on 3 would just be 3.

There is no common elements in the lists listed.  These events have no intersection.

These events are mutually exclusive.

Let's look at your fourth choice:

"landing on an unshaded portion and landing on an odd number"

Landing on a unshaded portion would be 2 or 3.

Landing on an odd number would be 1 or 3.

There is an intersection; they both have 3 in common.

These events are not mutually exclusive.

Let's look at your fifth choice:

"landing on an unshaded portion and landing on a number less than 2 "

Landing on an unshaded portion would 2 or 3.

Landing on a number less than 2 would be 1.

There is no intersection.

These events are mutually exclusive.

6 0
2 years ago
Read 2 more answers
Sergio and Lizeth have a very tight vacation budget. They plan to rent a car from a company that charges $75 a week plus $0.25 a
nordsb [41]

Answer: 500 miles

Step-by-step explanation:

Given : Sergio and Lizeth have planned to rent a car from a company that charges $75 a week plus $0.25 a mile.

i.e. Fixed charge= $75

Rate per mile = $0.25

Let x denotes the number of miles.

Then, Total charges = Fixed charge+ Rate per mile x No. of miles traveled

=  $75+ $0.25x

To keep budget within $200, we have following equation.

75+0.25x=200\\\\\Rightarrow\ 0.25=200-75\\\\\Rightarrow\ 0.25=125\\\\\Rightarrow\ x=\dfrac{125}{0.25}=\dfrac{12500}{25}=500

Hence, they can travel 500 miles and still keep within their $200 budget.

4 0
2 years ago
The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A ran
Ganezh [65]

Answer:

a) Hypothesis mean differs from 0.5025. Rejected

b) P-value = 0

c) 0.50456 < u < 0.50464

Step-by-step explanation:

Given:

- The standard deviation s.d = 0.0001 in

- The mean of the sample x = 0.5046 in

- Sample size n = 25

Find:

a) Test the hypothesis that mean rod. Assume two-sided alternative and significance level of 0.05.

b) Find the p-value for test in part

c) Construct a 95% two-sided confidence interval on the mean rod diameter.

Solution:

- The random variable X: the measurements for rod diameter follows a normal distribution:  

                                       X~ N( 0.5025 , 0.0001 )

- Testing H_o: u_o = 0.5025  , H_1 : u_o not equal 0.5025

- Compute the corresponding Z-score:

                             Z_o = (0.5046 - 0.5025) / 0.0001/sqrt(25)

                             Z_o = 105

- The Z score value with respect to significance level is:

                            Z_a/2 = Z_0.025 = 1.96

Hence, Z_o > Z_a/n

- The hypothesis H_o is rejected the mean differs from 0.5025.

- The corresponding P-Value is:

                            P-value = 2*(1 - sig(Z_o)) = 2*(1 - sig(105))

                           P-value = 2*(1-1) = 0

- The confidence interval is:

                 ( x - Z_a/2(s.d/sqrt(n)) < u <  ( x + Z_a/2(s.d/sqrt(n))

  ( 0.5046 - 1.96(0.0001/sqrt(25)) < u <  ( 0.5046 + 1.96(0.0001/sqrt(25))  

                              0.50456 < u < 0.50464

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