A teacher aide can use modeling to

Joanna is making a recipe that uses 1 1/2 teaspoon of salt for every 2 cups of sugar. If Joanna increases the recipe to use 5 of

GrogVix [38]

Answer: B. 3 3/4

Step-by-step explanation:

From the question, we are told that Joanna is making a recipe that uses 1 1/2 teaspoon of salt for every 2 cups of sugar. Since, uses 1 1/2 teaspoon of salt for every 2 cups of sugar, 1 cup of sugar will use 1/2 of 1 1/2 teaspoon of salt. This will be:

= 1/2 × 1 1/2

= 1/2 × 3/2

= 3/4 teaspoon of salt.

We then multiply the value used for a cup of sugar by 5 since Joanna increases the recipe to use 5 cups of sugar. This will be:

= 3/4 × 5

= 15/4

= 3 3/4

8 0

3 years ago

Complete the sentence.

igomit [66]

Answer: 3|x| = 3x when x $\geq$ 0 and 3|x| = -3x when x < 0

Step-by-step explanation: Absolute value basically refers to the distance of a point from the origin (zero), regardless of the direction. The absolute value of a number is represented by two vertical lines enclosing the number. For example, |6| = 6, or in this case, 3|x| = 3x. Here, the value is replaced by the term "x". "x" is used as a term for an unknown value/variable. so basically, we're solving for x kinda. Multiplying "x" (the unknown variable) by 3 gives us = 3x. We know from the sign $\geq$ that x can't be below zero, only above or equal to. So, 3lxl = 3x when x is above or equal to the origin (zero). We know from the second problem that x can't be above zero because of the sign <, only below zero. Because we can only go below zero, that positive 3 turns negative. Multiplying x by -3 gives us = -3x. So, 3|x| = -3x when x is blow the origin (zero).

Note: the absolute value of a number is always positive, but in this scenario this rule doesn't apply because "x" is not a number, only a unknown value.

Sorry in advance if my explanation still doesn't make sense. Math isn't my thing really.

3 0

3 years ago

g A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with

rodikova [14]

Answer:

a) 85.31%

b) 56 minutes

c) 17 days

d) 0.1721

Step-by-step explanation:

In order to make the calculations easier, let's standardize the curve by doing the change

$Z=\frac{X-\mu}{\sigma}$

where $\mu$ is the average trip-time and $\sigma$ the standard deviation and

P(X≤ t) is the probability that the trip takes less than t minutes.

a)

Here we are looking for the value of P(X>20).

For X=20 we have Z = (20-24)/3.8 = -1.05

So, we want the area under the standard normal curve for Z > -1.05

that we can compute either using a table or a computer and we find this area equals 0.8531

So, he arrives late to work 85.31% of the times.

(See picture 1 attached)

b)

In this case we are looking for a value t of time such that

P(X≥ t) = 20% = 0.2

So, we are seeking a value Z such that the area under the normal curve to the left of Z equals 0.2

By using a table or a computer we find Z = 0.842

(See picture 2 attached)

By inserting this value in the equation on standardization

$0.842=\frac{X-24}{38}\Rightarrow X=38*0.842+24=55.996$

So 20% of the longest trips takes 55.996 ≅ 56 minutes

c)

Since the average of days he arrives late is 85.31%, it is expected that in 20 work days he arrives late 85.31% of 20, which equals 17 days.

d)

Since the probability that he does not arrive late is 1-0.8531 = 0.1469 and the probability of arriving early is independent of the previous trip,

the probability of arriving early n days in a row is

0.1496*0.1496*...*0.1496 n times and

the probability of being early most than 10 trips in 20 days is

$(0.1469)+(0.1469)^2+(0.1469)^3+...+(0.1469)^10=0.1721$

3 0

3 years ago

PLEASE HURRY!!! AB = 20 cm, m∠A = 30° , and $m∠C = 45° . Express the number of centimeters in the length of BC in simplest radic

MrRissso [65]

Using the Sine Rule:-

20 /sin 45 = BC / sin 30

BC = 20 sin 30 / sin45

= 20 * 1/2 / 1 / sqrt2
= 20 * 1/2 * sqrt2
= 10 sqrt2 answer

3 0

3 years ago

a. Harry started a new job where he earns the same amount every hour. Last week, he worked 9 hours and earned $108. Write the li

qaws [65]

Answer:

I=12

Step-by-step explanation:

y=108

I=108/9

I=12

5 0

3 years ago

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