I need help with this practice problem from my ACT prep guideIt is trigonometry It asks to graph the function yourself, on paper, or on desmos

The equation of a linear model to describe the data is 14x - y = 26904

To find a linear equation of the provided data,

Let us put the number of legislature on the y axis and the year corresponding at the x axis,

According to provided information,

In year 2003, the number of legislature is 1138.

In year 2009, the number of legislature is 1222.

So here we have two points,

A(2003,1138) and B(2009,1222).

As we have two points now,

We can use the two point form of the line to find the equation of line,

It says if we have two point (a,b) and (c,d), then the equation of line is,

(y-b)/(x-a) = (d-b)/(c-a)

So, our equation of line is with points A and B is,

(y - 1138)/(x-2003) = (1222-1138)/(2009-2003)

(y-1138)/(x-2003) = 14

y - 1138 = 14x - 28042

14x - y = 26904

When,

x = 2000, y = n,

14(2000) - n = 26904

n = 1096.

The Linear Equation is 14x - y = 26904

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Given the equation : 2x + 3y = 12?

We will find the slope of the equation by re-arranging the equation into the standard form of slope intercept formula:

Re-arranging the equation will be :

Step 1:

Concept:

Use the rate of change formula below.

Step 2

Find k(a) and k(b)

Step 3:

Answer:    Uhm hold on

Step-by-step explanation:

The greatest number of bouquets that the florist can make is 12.

The greatest number of bouquets that the florist can make can be determined by calculating the highest common factor of 60 and 72. The factor of a number is the number that divides another number without any remainder. The highest common factor of two or more numbers is the highest factor that is common to two or more numbers.

Factors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Highest common factor = 12

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Let's begin by listing out the information given to us:

Jaylen's beta volume = 4 1/2 gallons = 4.5 gal

Time taken = 1 7/8 minutes = 1.785 min

Flow rate = volume / Time taken = 4.5 / 1.875 = 2.4 gal/min

A change in temperature of 6°C is equivalent to a

change in temperature of 10.8°F

From the table drawn:

A change in temperature of 1°C is equivalent to 1.8°F

A change in temperature of 2°C is equivalent to 3.6°F

Following the relationships above, we can conclude that the relationship between °C and °F is:

°F = 1.8 °C

Therefore, a change in temperature of 6°C will be equivalent to:

°F = 1.8 °C

°F = 1.8 x 6

°F = 10.8°F

The procedure describe a completely randomized design for this research as B. Yes, the subjects are randomly assigned to each treatment.

In a randomized block design, the experimental units are divided into groups that we refer to as blocks. The experimental units inside each of the blocks will then be randomly assigned treatments.

As we can see from the question, they were divided into Blocks based on how much sun exposure they received while engaging in outdoor activities. After that, random treatments are assigned to each group.

Here, the participants are divided into groups based on their sun exposure, and then both treatments are distributed at random among the groups.

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Equivalent linear expressions are expressions that have the same value. That is, if you have two linear expressions that are equivalent to one another, and you plug the same value in for the variable in each of them, you will get the same result in each of them.

In the case of this question, the equaivalent expression can be gotten by factorizing the expression

By using products and percentages, the grandson had the amount of $ 225 before to buy foods and beverages.

In accordance with the statement, the grandson spent 80 % of all his amount to buy some food, later 40 % of the remaining money to buy some beverages and there was $ 27 remaining. We need to determine the amount that the grandson had initially. Then, the situation can be described by the following mathematical expression:

(1 - 80 / 100) · (1 - 40 / 100) · x = 27

(20 / 100) · (60 / 100) · x = 27

(1200 / 10000) · x = 27

(12 / 100) · x = 27

12 · x = 2700

x = 2700 / 12

x = 225

By means of percentages, the grandson had an amount of $ 225 before buying foods and beverages.

The name of the grandson cannot be added due to profanity detector.

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Answer:

f(2) = 4

Step-by-step explanation:

Hello!

We can find f(2) by substituting 2 for x in the equation.

The value of f(2) is 4.

Since in this group of ordered pairs shown above, the x-values are inputs and the y-values are outputs, all the statements that are true include the following:

A. There is only one input for every output.

B. There is only one output for every input.

An ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Generally speaking, the values on the x-coordinate or x-axis (abscissa) of any graph represents all of the input values while the values on the y-coordinate or y-axis (ordinate) of any graph represents all of the output values.

In this context, we can reasonably and logically deduce that there is a unique input for every output and a unique output for every input.

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We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:

Where "k" is a constant to be determined. To determine "k" we will use the given values:

Now, we plug in the values:

Now, we solve for "k" by multiplying both sides by 3:

Therefore, the value of "k" is 18. Now, we substitute in the relationship:

And thus we get the equation.

The frequency means how many times specific data shows up in a set of values.

Score Frequency

1-6 2

7-12 4

13-18 5

...

And so on.

[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]

Answer:

70

Step-by-step explanation:

[tex]\frac{(700)(0.1)(0.3)}{0.3}=70[/tex]

Starting from the given formula:

Multiply both sides of the equation by 2:

Divide both sides by h:

Substract a from both sides of the equation:

Therefore:

If Greg has 1 1/2 servings of cereal for breakfast each day, he can consume 8 breakfasts from a box of cereal.

The price of one breakfast from a regular-sized box of cereal is $0.54 if the box costs $4.29.

Greg could consume 4 additional breakfast portions from a single family-sized box.

A regular-sized box of cereal = 12 servings

If Greg eats 1 1/2 servings for breakfast every day

Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday

= [tex]\frac{12}{\frac{11}{2} }[/tex]

=[tex]\frac{12}{\frac{3}{2} }[/tex]

multiply by the reciprocal of [tex]\frac{3}{2}[/tex]

= 12 × [tex]\frac{2}{3}[/tex]

= [tex]\frac{24}{3}[/tex]

= 8 breakfast

Cost of regular-sized box of cereal = $4.29.

Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box

= [tex]\frac{4.29}{8}[/tex]

= 0.53625

Approximately,

$0.54 per breakfast

If Greg purchased the family-sized box of cereal that contains 18 servings

Family-sized box of cereal divided by the daily serves of breakfast is the number of breakfasts Greg can consume.

= 18 servings / [tex]\frac{11}{2}[/tex]

= 18 ÷[tex]\frac{3}{2}[/tex]

= 18 × [tex]\frac{2}{3}[/tex]

= [tex]\frac{36}{3}[/tex]

= 12 servings

Consequently, the number of additional breakfasts Greg may consume from a single family-sized package

= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box

= 12 servings - 8 servings

= 4 servings

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The probablity that first one selected is a criminal justice major is,

Now, the probablity that second one is a criminal justice major is when selected without replacement,

Simirally,

Thus, using the multiplication theorem,

Thus, the above equation gives the requried probablity.

1st term

Given:

With the formula of the sequence:

________

Second term:

____________

Third term:

_________

Fourth term:

-________________

Fifth term:

[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]

ATTACHED IS THE SOLUTION

BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is twenty one lesser or equal to minus four z minus twenty one.

21 ≤ −4z − 21.

We need to solve for z

Let us add twenty one on both sides

21+21≤ −4z − 21+21

42≤ −4z

Divide both sides by 4

10.5≤ -Z

-10.5≥Z

Z≤ -10.5

Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

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Mrs. long bought 4 types of fruits at the market:

- 2 cantaloupes that weighed 2.3 pounds each:

that is, a total of 2.3x2 = 4.6

- 6 peaches that weighed a total of 1.7 pounds.

- 4 apples that weighed a total of 1.25 pounds.

- and 3 pounds of grapes.

The total weight of the four fruits is:

4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.

ANSWER and EXPLANATION

We want to draw a quadilateral that has 2 pairs of congruent parallel sides and 4 right angles.

There are 2 quadilaterals that fit this description:

A square and a rectangle

The given expression : y-1=2/3(x-3)

Simplify the equation :

for the graph we need atleast two coordinates

Let at x=0 then

y=2/3(0)-1

y=-1

Cooridnate = (0,-1)

Now, let x=9 then

y=2/3(9)-1

y=2(3)-1

y=5

Coordinate =(9,5)

Plot these point (0,-1) & (9,5)on the graph and join them by staright line

The graph will be ;

We know that the ratio of pink markers to total markers is 1:3.

This means that for every 3 markers, one of them is pink. The other 2 will be yellow markers.

We can write that the ratio of pink markers to yellow markers is 1:2, based on the last sentence. This means that if we have N yellow markers, we will have N/2 pink markers.

Then, if we have 16 yellow markers, then we will have 16/2=8 pink markers.

Answer:

Step-by-step explanation:

You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.

We like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...

  (minutes, population) = (110, 60000)

We can put these numbers in the form ...

  p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))

where the growth factor (2) is applicable over the growth period (15 minutes).

This makes our equation ...

  p(t) = 60000(2^((t-110)/15))

We want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.

The population at t=0 was about 372.

The population after 4 hours will be 24,382,480.

__

Additional comment

A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...

  p(t) = 372·e^(0.0452098t)

where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15

These rounded numbers don't give the problem statement values exactly:

  p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).

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The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for this graph:

k = y/x

k = 0.8/2

k = 0.4.

In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:

c = 0.4w

where:

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Answer:

Step-by-step explanation:

The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.

How to determine the equation of a proportional relationship?

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

y and x are the variables.

k represents the constant of proportionality.

Next, we would determine the constant of proportionality (k) for this graph:

k = y/x

k = 0.8/2

k = 0.4.

In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:

c = 0.4w

where:

c is the total cost.

w is weight in ounces.

The number of people who ride the bus is 70 students.

From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.

Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.

This will be illustrated as:

4/7 = 40/x

Cross multiply

4x = 40 × 7

4x = 280

Divide

x = 280/4

x = 70

Therefore there are 70 students.

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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?