Find the distance between these two lines: 4x+3y=7 and 4x+3y=27

Please HELP!!! I'll make you Brainliest!!!!

erica [24]

Answer: 1. d. $7x\geq 350; x\geq 50$

2. a. (5, 28)

3. a: C(n) = 0.90 n - 0.40

Step-by-step explanation:

1. Here x represents the saving of one day.

Thus, the total saving for 7 day = 7 x

And, my goal is to save at least $350.00 ( According to the question)

⇒ $7x\geq 350$

⇒ $x\geq 50$ ( by dividing both sides by 7 )

Therefore, Option d is correct.

2. since, if a point satisfies an equation then we can say that it is the solution of the equation.

(5,28) satisfies y= 5x + 3

Because at x = 5, 5×5 + 3 = 25 + 3 = 28

except this point other points (28, 5), (4, 20) and (3, 19) are not satisfying given equation of line.

Therefore, only (5,28) is the solution of line.

⇒ Option a is correct.

3. Here n represents the number of tunas.

And, according to question the cost of one tuna = $0.90

⇒ Cost of n tunas = $ 0.90n

But again according to the question,

I have a coupon for $0.40 off your total purchase.

Thus, $ 0.40 will be less from my total purchasing cost.

⇒ The cost of n tunas = $ (0.90 n - 0.4)

Option a is correct.

7 0

2 years ago

A grading scale is set up for 1000 students' test scores. It assumes the

astra-53 [7]

Answer:

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.

This means that $\mu = 75, \sigma = 15$

How many students will score between 48 and 75?

First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So

X = 75

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

$Z = \frac{75 - 75}{15}$

$Z = 0$

$Z = 0$ has a p-value of 0.5

X = 48

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

$Z = \frac{48 - 75}{15}$

$Z = -1.8$

$Z = -1.8$ has a p-value of 0.0359

1 - 0.0359 = 0.4641

Out of 1000:

0.4641*1000 = 464

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

7 0

2 years ago

A package states that there are 60 calories in 12 crackers

kvv77 [185]

Answer: 5 calories = 1 cracker

Step-by-step explanation:

60:12 = 5:1

60 calories and 12 crackers = 5 calories and 1 cracker

7 0

2 years ago

*Translate into an algebraic expression: How much 50% sugar syrup can you make if you have x grams of sugar?

Irina-Kira [14]

Answer:

w = x/50% = x/50/100

Step-by-step explanation:

We would turn the above question into an algebraic expression using variables.

To make a sugar syrup, we need sugar and water to form the solution.

Amount of sugar = x gram

Let amount of water = w gram

Sugar syrup solution = 50%

Sugar syrup solution = (amount of sugar)/(amount of water) × 100

50% = x/w × 100%

50% = x/w

Making w subject formula

w = x/50%

w = x/50/100

5 0

2 years ago

Which choice is appropriate simplified form and restriction for the variable (x+3)(x+7)/3x+21

bekas [8.4K]

C. I used the app math way. it has been a lifesaver.

4 0

3 years ago