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3 years ago

13

Madeline and Isaac are baking cakes for a fundraiser. Madeline has already made 9 cakes and is making cakes at a rate of 1 cake

per hour. Isaac has already made 1 cake and is making cakes at a rate of 2 cakes per hour.

1 answer:

Nadya [2.5K]3 years ago

5 0

Answer:

17

Step-by-step explanation:

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Analyze the situation(s).

allochka39001 [22]

Answer:

is there a graph so I can show you?

3 0

3 years ago

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Which expression could help you find the distance

Fynjy0 [20]

Answer:

2.5 Finding the Distance Between Two Numbers - Math 7 CCSS

FlexBooks® 2.0 > CK-12 Interactive Middle School Math 7 - Teacher's Edition > Finding the Distance Between Two Numbers - Math 7 CCSS

Last Modified: Sep 04, 2020

Common Core Standards

Focus Standards: 7.NS.A.1.c

Learning Objectives

Show that the distance between two rational numbers on the number line is the absolute values of their difference.

Solve problems involving finding the difference between two rational numbers in a real-world context.

Agenda

Warm-Up: Diving Deeper 10 min

Activity 1: Along the Street 20 min

Activity 2: Getting Around Washington DC 15 min

Review Questions 5 min

(Students do not see text in purple)

Now that subtraction has been introduced, it is applied to finding the distance between two points in this lesson. The distance between two points will first be introduced as counting units on a number line, but then formalized into a definition with subtraction and absolute value. Review with students that distance is always positive and the definition of absolute value before beginning.

Warm-Up: Diving Deeper

The distance between two points can be defined as the number of units between them. Typically, this means we subtract the values, but what if one point is negative and the other is positive?

Example

Fatima’s friend, Tyler, is more daring than she and when he jumps into the water to scuba dive, he starts from 4 feet above the water, at the back of the boat. After his first jump, he went 7 feet below the water. How many feet did he actually travel?

This interactive shows an application of how negative values are used; in this case, it is how deep a diver dives. Students will see a body of water, a diver on a cliff, boat and some fish. There are also two number lines; the horizontal line ranges from -20 to 5 and the vertical line ranges 5 feet to -20 feet. The horizontal line has a red point that students can click and drag to make the diver dive. While the student moves the point in the negative direction the father down the diver will go. The arrow on the vertical line will travel down with the diver showing the student how many feet down the diver is.

TRY IT

Inline Questions: Students see inline questions here. The questions are formative and have detailed instructional feedback. The questions and correct answers are printed below for your convenience as an instructor.

Which expression tells us the total distance Tyler travels to return to 5 feet above the water from a depth of 15 feet?

|-15 - 5|

|5 -15|

|5 - (-15)|

|-15 - (-5)|

Which expression can we use to find the total distance Tyler traveled?

|4 - (-7)|

4 - 7

|4 - 7|

-7 - 4

If Tyler started 5 feet above the water, jumped, then went 8 feet below the water, which of the following represent the total distance traveled?

|5 - (-8)|

|-8 - (-5)|

|5 - 8|

|-8 - 5|

Tyler is 7 feet below the water's surface and dives another 8 feet down. How can we determine how far below the water's surface he is now?

|-7 - (-8)|

|7 - 8|

|-7 - 8|

|8 - 7|

It is important to remember that when finding the total distance between two points on a number line, you may need to find the absolute value of those distances separately, depending on what the question is asking for.

Emphasize to students that when finding the total distance between two points on a number line, they need to use absolute value. As is the case with #3, you may need to draw a picture showing them that he starts at -7 feet down and goes down another -8 feet. His total distance from the surface is |-7| + |-8| or |-7 - 8|.

Activity 1: Along the Street

Jason lives on the same street as his school, the movie theater, his friend's house and the store. They are all different distances away from his house. Treat Jason's house as the origin, and determine the distance he needs to travel.

This interactive is another application of how negative numbers may be used to show distance traveled. On the number lines there are five places Jason can travel: Jason’s house is the starting point and located at zero. The school is located at -8, the movies are at -5, his friend’s house is at 4 and the store is at 7. Students can move the red point along the number line to the different locations. Above the number line students can see the distance the location is from the starting point (Jason’s house).

TRY IT

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Solve the system of linear equations.<br><br> y = x + 3<br><br> y = 2x - 2

AlekseyPX

Answer:

x=5, y=8

Step-by-step explanation:

Since both equations equal y, we can set them equal

y = x + 3

y = 2x - 2

x+3 = 2x-2

Subtract x from each side

x-x+3 = 2x-x-2

3 = x-2

Add 2 to each side

3+2= x-2+2

5 =x

Now we need to find y

y =x+3

y=5+3

y=8

5 0

3 years ago

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The level of nitrogen oxides (NOX) in a exhaust of cars of a particular model varies normally with mean 0.25 grams per miles and

antoniya [11.8K]

Answer:

a) 15.87% probability that a single car of this model fails to meet the NOX requirement.

b) 2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

Step-by-step explanation:

We use the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 0.25, \sigma = 0.05$

a. What is the probability that a single car of this model fails to meet the NOX requirement?

Emissions higher than 0.3, which is 1 subtracted by the pvalue of Z when X = 0.3. So

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

$Z = \frac{0.3 - 0.25}{0.05}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8417.

1 - 0.8413 = 0.1587.

15.87% probability that a single car of this model fails to meet the NOX requirement.

b. A company has 4 cars of this model in its fleet. What is the probability that the average NOX level of these cars are above 0.3 g/mi limit?

Now we have $n = 4, s = \frac{0.05}{\sqrt{4}} = 0.025$

The probability is 1 subtracted by the pvalue of Z when X = 0.3. So

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

By the Central Limit Theorem

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

$Z = \frac{0.3 - 0.25}{0.025}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the average NOX level of these cars are above 0.3 g/mi limit

4 0

3 years ago

Decide whether the two events are disjoint and tell why or why not:

Agata [3.3K]

Answer:

Disjoint, because the events cannot occur at the same time.

Step-by-step explanation:

disjoint events are mutually exclusive events.

if a and b are two events then a intersection b will be 0 . they cannot occur at the same time.

here in the given problem let the event A be randomly drawing a jack from a standard deckn of card and evnt B be randomly drawing an ace from a standard deck of card.

since in a same card jack and ace cannot occur they are disjoint events.

therefore randomly drawing a jack from a standard deck of cards and randomly drawing an ace from a standard deck of cards are disjoint events because the events cannot occur at the same time.

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3 years ago