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Task #1 Creating A Table Task

Create a table of x and y values that represents a proportional relationship.



a) Explain how you know the relationship is proportional.

b) What equation models the values in the table?

2) Create a table of x and y values that represents a linear, non-proportional relationship.




a) Explain how you know the relationship is non-proportional.

b) What equation models the values in the table?

Answer:

[tex] \large{ \tt{❃ \: STEP-BY-STEP \: EXPLANATION}} : [/tex]

[tex] \large{ \tt{❁ \: ORIGINAL \: PROBLEM : 12x + 2 = 26}}[/tex]

[tex] \large{ \tt{↦ \: 12x + 2 - 2 = 26 - 2}}[/tex]

[tex] \large{ \tt{↦ \:12x = 24}}[/tex]

[tex] \large{ \tt{ ↦ \: \frac{12x}{12} = \frac{24}{12}}} [/tex]

[tex] \boxed{ \boxed{ \large{ \tt{↦x = 2}}}} \large✓[/tex]

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Answer:

Last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Step-by-step explanation:

Since a grocery store manager notices that this month her store sold a total of 521 gallons of ice cream, which represents a decrease of 10% from last month, and on the other hand, her store sold 791 pounds of broccoli this month, which It represents an increase of 25% from last month, to determine how much ice cream and broccoli did the store sell last month, the following calculation must be performed:

Ice cream = 100 - 10 = 90

90 = 521

100 = X

100 x 521/90 = X

52,100 / 90 = X

578.88 = X

Broccoli = 100 + 25 = 125

125 = 791

100 = X

100 x 791/125 = X

79,100 / 125 = X

632.8 = X

Therefore, last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Answer:

9 and 10

Step-by-step explanation:

the closest squares to 84 are 81 and 100 which those square roots are 9 and 10 respectively so the square root of 84 is between the consecutive whole numbers nine and ten

ps in a calculator the sqrt of 84 is 9.16515139...

Hope this helps! :)

9514 1404 393

Answer:

  1/4 mile

Step-by-step explanation:

The length and width of a square are the same.

The length is 1/4 mile, so the width of the park is 1/4 mile.

A square park has an area of 1/16 square miles and a length of 1/4 mile. What is the width of the park?

[tex]\quad \quad \quad \boxed{ \tt{width = \frac{area}{length}}}[/tex]

[tex]\quad \quad \quad{\tt{w = \frac{1}{16} \div \frac{1}{4} = \boxed{\tt{0.25}}}}[/tex]

[tex]\quad \quad \quad \boxed{ \tt{w = 0.25}} \: ➡ \boxed{ \tt{w = \frac{1}{4}}}[/tex]

[tex]\boxed{ \tt{w = \frac{1}{4}}}[/tex]

_________

#LetsStudy

Answer:

1.  1/3

2. 0

Step-by-step explanation:

Answer:

-60

hope it helps

Answer:

The answer is "Categorical and Ordinal scale"

Step-by-step explanation:

Categorical factors affect data types that can be grouped. This analysis is the examination of data in which the answer variables are grouped in a series of reciprocal classifications, like the age group or even the unordered groups of eye colors.

An ordinal chart is a form of the category with such a specific order or scale. It is the 2nd assessment level that provides the ordering and order of data, without really measure the extent of variability. The first of the four measuring scales is the ordinal scale of listening.

Answer:

okay the first questions answer is ,c,is true and rest of them are false

Answer:

proportion

Step-by-step explanation:

2----> 15

42--->x

x=(42*15)/2

x= 21 *15.

x= 315

therefore there are 315 students in the school

Answer:

D) 5

Step-by-step explanation:

Answer:

The sample space of answering a true or false question is  "sample set = true, false"

Step-by-step explanation:

Sample Space is defined as the set of all possible outcomes in a given probability experiment. For example, the sample space of tossing one coin is head, tail.

Source: study.com/academy/answer/identify-the-sample-space-of-the-probability-experiment-answering-a-true-or-false-question.html

Answer:

y-inter:(0,-44)

x inter:(-10,0)

Answer:

0.0597in/s

Step-by-step explanation:

The volume of the spherical balloon V= 4/3πr³

r is the radius of the balloon

The rate at which the volume is changing dV/dt is expressed as;\

dV/dt = dV/dr*dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

dV/dt = 3 in³/s

Substitute inti the formula

3 = 16πdr/dt

dr/dt = 3/16π

dr/dt = 3/50.24

dr/dt = 0.0597in/s

Hence the balloon is increasing at the rate of 0.0597in/s

Answer:

The magnitude of the resultant force is:

[tex]R=100.3 \:pound[/tex]

The direction is:

[tex]\theta=1.2^{\circ}[/tex]

Step-by-step explanation:

Let's find the components of each vector is x and y-directions first.

Sum of x-component vector forces.

[tex]F_{tot-x}=F_{1}cos(45)+F_{2}cos(30)[/tex]

[tex]F_{tot-x}=50cos(45)+75cos(30)[/tex]

[tex]F_{tot-x}=100.3 \: pound[/tex]

Sum of y-component vector forces.

[tex]F_{tot-y}=-F_{1}sin(45)+F_{2}sin(30)[/tex]

[tex]F_{tot-y}=-50sin(45)+75sin(30)[/tex]

[tex]F_{tot-y}=2.1 \: pound[/tex]  

The magnitude of the resultant force is:

[tex]R=\sqrt{100.3^{2}+2.1^{2}}[/tex]

[tex]R=100.3 \:pound[/tex]

The direction is:

[tex]tan(\theta)=\frac{2.1}{100.3}[/tex]

[tex]\theta=arctan(\frac{2.1}{100.3})[/tex]

[tex]\theta=1.2^{\circ}[/tex]

I hope it helps you!

Answer:

0.3

Step-by-step explanation:

Answer:

24 and 9

Step-by-step explanation:

Hi there!

Let x be equal to the larger integer.

Let y be equal to the smaller integer.

1) Construct equations

2) Solve for one of the integer

Isolate x in the first equation

[tex]x+y=33\\x=33-y[/tex]

Plug the first equation into the second

[tex]33-y=6+2y[/tex]

Combine like terms

[tex]33-6=2y+y\\27=3y\\9=y[/tex]

Therefore, the smaller integer is 9.

3) Solve for the other integer

[tex]x+y=33[/tex]

Plug in y (9)

[tex]x+9=33\\x=33-9\\x=24[/tex]

Therefore, the larger integer is 24.

I hope this helps!

9514 1404 393

Answer:

  x = 142

Step-by-step explanation:

You want to find x such that ...

  [tex]\sqrt{x+2} -15=-3\qquad\text{given}\\\\\sqrt{x+2} =12\qquad\text{add 15}\\\\x+2=144\qquad\text{square both sides}\\\\\boxed{x=142}\qquad\text{subtract 2 to get x by itself}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

Diameter(line going across the circle that you've given) = 6 in

Radius(half of diameter) = 3 in

Circumference(the perimeter of the circle) = 18.85 in

Area = 28.27^2

Step-by-step explanation:

In order to find the circumference, you will need to first find the radius(which is always half the size of the diameter which in this case is 3 in). You will then need to do this formula: 2 x 3.14 x 3 which equals to 18.85.

Answer:

The circumference of a circle is about 18.85 inches.

Step-by-step explanation:

The radius is always half of the diameter, and the diameter is 6 inches.

6 divided by 2 is 3, so the radius of this circle is 3 inches.

The formula for circumference of a circle is :

C = 2πr = 2 · π · 3 ≈ 18.84956

The circumference of a circle is about 18.85 inches.

Answer:   876

Step-by-step explanation:so all you need to do is go into  

Answer:

[tex]S(y)=36000*(1+0.03)^{y}[/tex]

Step-by-step explanation:

Answer:

y=36,000×1.03^x

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

To compute a value for the table put the given "input" into the formula and do the arithmetic. Repetitive arithmetic is often easily handled by a graphing calculator or spreadsheet.

Example:

  for n=2, C = 40·2 +210 = 80 +210 = 290

Answer:

4n+5=30

Step-by-step explanation:

Answer:

62 miles per hour

Step-by-step explanation:

620mile/10hrs

62miles/hr

62 miles per hour

Answer:

B: x≤5

Step-by-step explanation:

Hi there!

We're given two inequalities; 3x−8≤23  and −4x+26≥6

We need to find the values of x that make BOTH of the inequalities true (which is the intersection of the two inequality graphs)

First, let's solve for x in both of them

taking the first inequality:

3x−8≤23  

add 8 to both sides

3x≤31

divide by 3

x≤31/3

now solve for x in −4x+26≥6

subtract 26 from both sides

-4x≥-20

divide both sides by -4 and remember to FLIP the inequality sign since we have a negative number

x≤5

now let's graph these two inequalities to find the intersection, and that is below with the answer

Hope this helps! :)

Answer:

[tex]\frac{1}{324632}[/tex] probability of picking the winning combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Since the order is not important, the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

The correct five numbers from a set of 5. So

[tex]D = C_{5,5} = \frac{5!}{5!0!} = 1[/tex]

Total outcomes:

Five numbers from a set of 35. So

[tex]T = C_{35,5} = \frac{35!}{5!30!} = 324632[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{1}{324632}[/tex]

[tex]\frac{1}{324632}[/tex] probability of picking the winning combination

Answer:

A

Step-by-step explanation:

5 x 10^4/2.5 x 10^2

10^2 gets cancel out by 10^4

5 gets divided by 2.5 which equals 2

Leaving us with 2 x 10^2

Answer:

A

Step-by-step explanation:

2 x 10^2

Answer:

3/5 * 5/6

= 15/30

Step-by-step explanation:

So the answer is the third one in line

Answer:

15/30 (simplified).

Step-by-step explanation:

[tex]3/5*5/6[/tex]

To multiply the find the value of this problem, multiply the numerators and denominators.

Remember, numerators are the numbers above the fraction bar.

Denominators are the numbers below the fraction bar.

Numerators: 3, 5

Denominators: 5, 6

[tex]3*5=15[/tex]

[tex]5*6=30[/tex]

After finding the products, add the fraction bar.

[tex]15/30.[/tex]

In most cases, you will be asked to simplify. It does not seem like simplifying is required in this question.

But, I'll simplify anyway.

15/30 = 1/2 (simplified).

Answer:

The expected total amount of time in minutes the operator will spend on the calls each day is of 210 minutes.

Step-by-step explanation:

Normal Probability Distribution:

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

n-values of a normal variable:

For the sum of a sample of n values, the mean is of [tex]M = n\mu[/tex] and the standard deviation is of [tex]s = \sigma\sqrt{n}[/tex]

Average 2.8 minutes

This means that [tex]\mu = 2.8[/tex]

75 calls each day.

This means that [tex]n = 75[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day?

[tex]M = n\mu = 75(2.8) = 210[/tex]

The expected total amount of time in minutes the operator will spend on the calls each day is of 210 minutes.

Answer:

16.129

Step-by-step explanation:

11+15+5=31

5÷31=0.16129

0.16129x100

=16.129