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chubhunter [2.5K]
3 years ago
10

1.) Is (0, 3) a solution to the equation y= x+3

Mathematics
2 answers:
Delvig [45]3 years ago
8 0
1. yes
2. no
3. (4,0) and (3,-1)
4. 8 crackers in 1 serving....so in 12 servings, there is (12 * 8) = 96 crackers
5. x + 5 = 10 (open equation)
6. ?
7. y = 1.5x....y being the cost of the pizza and x being the number of slices
abruzzese [7]3 years ago
6 0

1. The answer is Yes


The equation:

y=x+3

represents a <em>straight line </em>with slope m=1 and y-intercept b=3. To know if the point (0,3) is a solution to the equation, let's substitute the x and y coordinates into the equation, therefore:

(3)=(0)+3 \\ \\ \therefore 3=3 \ True!


Since our result is true, this point is a solution to the equation.


2. The answer is No


The equation:

y=-2x

represents a <em>straight line </em>with slope m=-2 and no y-intercept, that is, it passes through the origin. By substituting this point into the equation:

(-4)=-2(1) \\ \\ \therefore -4=-2 \ False!


Since our result is false, this point is not a solution to the equation.


3. In this problem, we have four points, so let's solve it step by step. Our equation is:

y=x-4

and represents a <em>straight line </em>with slope m=1 and y-intercept b=-4


3.1 <u>For the point</u> (4, 0)

<em>This point is a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (0)=(4)-4 \\ \\ \therefore 0=0 \ True!


Since our result is true, this point is a solution to the equation.


3.2 <u>For the point</u> (3, -1)

<em>This point is a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (-1)=(3)-4 \\ \\ \therefore -1=-1 \ True!


Since our result is true, this point is a solution to the equation.


3.3 <u>For the point</u> (6, 3)

<em>This point is not a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (3)=(6)-4 \\ \\ \therefore 3=2 \ False!


Since our result is false, this point is not a solution to the equation.


3.4 <u>For the point</u> (2, -4)

<em>This point is not a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (-4)=(2)-4 \\ \\ \therefore -4=-2 \ False!


Since our result is false, this point is not a solution to the equation.


4. In this problem we have:

  • There are 8 crackers in 1 serving.
  • There are 16 crackers in 2 servings.
  • There are 24 crackers in 3 servings, and so on.

So, there is a <em>linear relationship</em> between crackers and servings. Thus, it is easy to write a linear equation like this:

y=8x \\ \\ \\ where: \\ \\ y:Represents \ crackers \\ \\ x:Represents \ servings


Therefore, for x = 12 servings, we have:

y=8(12)=96


Finally:

<em>There are 96 crackers in 12 servings</em>


5. An open equation is an equation containing one or more <em>variables </em>such that the <em>truth or falsehood </em>of the equation depends on the values of the variables assumed in a specific instance. An example of an open equation is:

2x-16=-2


  • If x = 7

2(7)-16=-2 \\ \\ \therefore -2=-2 \ True!


For this particular x-value, the equation is true.


  • If x = 3

2(3)-16=-2 \\ \\ \therefore -10=-2 \ False!

For this particular x-value, the equation is false.


So, we can conclude that this equation is  only  true  when  x = 7


6. Equations can be used to model and solve  real-life problems. In this way, we can make predictions from an equation that models a real-life situation. For instance, a kitchen an <em>appliance manufacturing company </em>can determine the total cost in  dollars of producing units of a blender by using the equation:


C=20x+2500


Thus, the cost of producing zero units is $2500, found by the y-intercept, that is the fixed cost of production. It includes costs that must be paid regardless  of the number of units produced. The slope m=20 means that the cost of  producing each unit is $20, called by the Economists <em>the marginal cost </em>(cost per unit).


7. In this exercise, pizza costs $1.50 per slice. This can be modeled by the following equation:


C=1.50s \\ \\ \\ where: \\ \\ s:Represents \ the \ number \ of \ slices \\ \\ C:Represents \ the \ total \ cost


This can be represented by the following Table as well:

\begin{array}{cc}&#10;s(slices) & C(\$)\\&#10;1 & 1.50\\&#10;2 & 3.00\\&#10;3 & 4.50\\&#10;4 & 6.00\\&#10;5 & 7.50&#10;\end{array}


So, in this Table we have indicated the total cost up to 5 slices of pizza.

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Answer:

slope = 2

Step-by-step explanation:

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Find the slope of the line that passed through (5,8) and (1,13)​
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3 years ago
Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.7 grams an
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Answer:

<u>a. s.e. = 0.338</u>

<u>b. The  probability of finding a random slice of pizza with a mass of less than 67.2 grams is 0.5871 or 58.71%</u>

<u>c. The probability of finding a 20 random slices of pizza with a mean mass of less than 67.2 grams is 0.0694 or 6.94%</u>

d. <u>The sample mean of 62.75 would represent the 15th percentile</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question properly:

μ of the mass of slices of pizza for a certain brand = 67.7 grams

σ of the mass of slices of pizza for a certain brand = 2.28 grams

2. For samples of size 20 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

Let's recall that the standard deviation of the sampling distribution of the mean is called the standard error of the mean and its formula is:

μσs.e.= √σ/n, where n is the sample size.

s.e. = √2.28/20

<u>s.e. = 0.338</u>

3. What is the probability of finding a random slice of pizza with a mass of less than 67.2 grams?

Let's find the z-score for X = 67.2, this way:

z-score = (X - μ)/σ

z-score = (67.2 - 67.7)/2.28

z-score = 0.5/2.28

z-score = 0.22 (rounding to the next hundredth)

Now, using the z-table, let's find p, the probability:

p (z = 0.22) = 0.5871

<u>The  probability of finding a random slice of pizza with a mass of less than 67.2 grams is 58.71%</u>

4.  What is the probability of finding a 20 random slices of pizza with a mean mass of less than 67.2 grams?

Let's use the central limit theorem to find the z-score, this way:

z-score = X - μ/s.e

z-score = 67.2 - 67.7/0.338

z-score = -0.5/0.338

z-score = - 1.48

Now, using the z-table, let's find p, the probability:

<u>p (z = -1.48) = 0.0694</u>

5. What sample mean (for a sample of size 20) would represent the bottom 15% (the 15th percentile)?

For p = 0.150, let's find the z-score:

z-score = - 2.17

z-score = X - μ/s.e

- 2.17 = (X - 67.7)/2.28

- 4.95 = X - 67.7

X = 67.7 - 4.95

X = 62.75 (rounding to the next hundredth)

<u>The sample mean of 62.75 would represent the 15th percentile</u>

7 0
3 years ago
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