A particle moves along the x-axis so that at any time t >= 0 its position is given by x(t)= 1/2(a - t)^2, where a is a positive constant. For what values of t is the particle moving to the right?

In linear equation, Balanced diet is of utmost importance for proper functinality and growth of our body.

What is a linear equation in mathematics?

An algebraic equation of the form y=mx b, where m is the slope and b is the y-intercept, and only a constant and first-order (linear) term is referred to as a linear equation.

                               The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are the variables. There might be more than one variable in a linear equation. It is known as a bivariate linear equation, for example, if a linear equation has two variables.

he recommended daily requirement of Calories is Men: 2400 , Women: 1900 , Children: 1800 Also daily requirement for protein is Men: 55 gm , Women:45 gm and Children:33 gm Calculate the total requirement of calories and proteins for each of the two families.

Given the details of two families A and B.

A : 4 men, 6 women and 2 children  

B : 2 men, 2 women and 4 children

Hence, the number of people in both the families A and B can be represented in matrix form with rows denoting the family and columns denoting the number of people of each type as

X = [ 4 6 2 2 2 4 ]

The calorie and protein requirements for different types of people are also given.

Men: 2400 calories, 45gm proteins

Women: 1900 calories, 55gm proteins

Children: 1800 calories, 33gm proteins

Hence, the required calories and proteins can be represented in matrix form with each row corresponding to different type of people as

Y = ⎡ ⎢ ⎢ ⎣ 2400 45 1900 55 1800 33 ⎤ ⎥ ⎥ ⎦ [240045190055180033]

Now,  

The required number of calories and proteins for each of the two families can be obtained by taking the product of the matrices X and Y.

Thus,

The requirement of calories and protein is as follows

Family A : 24600 calories and 576 grams protein

Family B : 15800 calories and 332 grams protein

It can be said that a balanced diet with proper amounts of calories and protein must be consumed by the people of all ages in order to lead a healthy life.

So 24600 calories and 576 grams of proteins are needed for Family A and 15800 calories and 332 grams of proteins are needed for Family B.

Balanced diet is of utmost importance for proper functinality and growth of our body. So people must be aware to take food which provides all the necessary nutrients.

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(a)The probability is approximately 0.4441 or 44.41%.

(d) The probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.

Probability is defined as the ratio of favourable outcome to the total number of outcome.

A number is a mathematical concept that represents a quantity or a value. It is an abstract idea used to count, measure, or compare quantities of objects, events, or abstract entities. Numbers can be classified into various types, such as natural numbers (e.g., 1, 2, 3), whole numbers (e.g., 0, 1, 2, 3), integers (e.g., -3, -2, -1, 0, 1, 2, 3), rational numbers (e.g., fractions like 1/2, 3/4, etc.), irrational numbers (e.g., π or square root of 2), and real numbers (which include both rational and irrational numbers). Numbers are fundamental to mathematics and play a crucial role in many areas of science, engineering, economics, and everyday life.

The probability that at least one of the selected adults says they were too young is equal to 1 minus the probability that none of them say they were too young.

Let p = probability that an adult says they were too young to get tattoos

p = 13% = 0.13

The probability that none of the selected adults say they were too young is given by:

P(none say they were too young) = (1 - p)^10

Putting the values of p, we get:

P(none say they were too young) = (1 - 0.13)^10 ≈ 0.4441

Let p = probability that an adult says they were too young to get tattoos

p = 13% = 0.13

Let X = number of adults out of 10 who say they were too young

Using the binomial probability formula, we have:

P(X = 1) = (10 choose 1)×(0.13)¹ ×(1 - 0.13)⁹

where "10 choose 1" is the binomial coefficient, representing the number of ways to choose 1 out of 10.

Plugging in the value for p, we get:

P(X = 1) = (10 choose 1) × (0.13)¹× (1 - 0.13)⁹≈ 0.3513

So, the probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.

Since 1 is not significantly low compared to the probability of getting exactly 1 adult who says they were too young (which is 0.3513), we cannot conclude that 1 is a significantly low number of adults who say they were too young to get tattoos based on the given information. Additional statistical analysis and comparison with appropriate thresholds would be necessary to make a conclusive determination.

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[tex]\dfrac{5}{6}.[/tex]

[tex]\dfrac{\dfrac{2}{3} }{\dfrac{4}{5} }[/tex]

[tex]\dfrac{2}{3} *\dfrac{5}{4}[/tex]

[tex]\dfrac{2}{3} *\dfrac{5}{4}=\dfrac{2*5}{3*4}=\dfrac{10}{12}=\dfrac{5}{6}.[/tex]

Step-by-step explanation:

this question is marked as "college".

that cannot be. this is elementary school stuff, so, I hope you are an elementary school student.

remember what you learned about divisions of fractions :

a/b / c/d = (a×d) / (b×c)

so, "outer / inner".

you can also say

a/b / c/d = a/b × d/c = (a×d) / (b×c)

as dividing by a fraction is the same as the multiplication with the upside-down version of that fraction.

the result of a multiplication of fractions is then "upper / lower".

so, your problem here is

2/3 / 4/5 = (2×5) / (3×4) = 10/12 = 5/6

Answer:

tan D = 4.9/9.1 = 7/13

tan F = 9.1/4.9 = 13/7

The probability that less than 75% of the sample students have iPhones is approximately 0.2478.

What is probability?

This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.

Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)

Using the binomial probability formula, we have:

P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37

However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.

Using the normal approximation, we can standardize the random variable X:

Z = (X - μ) / σ

where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.

Then, we have:

P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)

Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.

Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.

Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.

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So the probability of a random person having no credit cards is 1/3, or approximately 0.3333.

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one.

The likelihood that a person chosen at random did not have any credit cards is the ratio of those who did not have any credit cards to the total number of people:

P(No credit cards)  = (Number of persons without credit cards) /(Total number of people)

According to the table, the number of people who did not have credit cards is the sum of the values in the "Zero" column, which is 27. The sum of all the values in the table, which is 81, is the total number of persons. Therefore:

P(Credit Cards Not Accepted) = 27/81

simplified term:

P(Without credit cards) = 1/3

So the probability of a random person having no credit cards is 1/3, or approximately 0.3333.

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Complete question:

In the image form.

The person must leave the money in the bank for approximately 10.6 years (rounded to the nearest tenth of a year) for it to reach 8700 dollars.

To solve this problem,  the compound interest formula:

[tex]A = P(1 + r/n)^{nt}[/tex]

where:

A = the future worth of the speculation

P = the underlying speculation (present worth)

r = the yearly loan cost (as a decimal)

n = the times the interest is accumulated each year

t = the quantity of years

We need to find the worth of t that will make An equivalent to 8700 bucks. We are aware that P is $3,500 and that r is 6.25 percent, or 0.0625 in decimal form. The value of n is unknown, but the fact that the interest is compounded annually indicates that n is 1.

Substituting these values into the formula, we get:

[tex]8700 = 3500(1 + 0.0625/1)^{1t}[/tex]

Simplifying the right side, we get:

[tex]8700 = 3500(1.0625)^t[/tex]

Dividing both sides by 3500, we get:

[tex]2.485714286 = 1.0625^t[/tex]

Taking the logarithm of both sides (with any base), we get:

[tex]log(2.485714286) = log(1.0625^t)[/tex]

Using the power rule of logarithms, we can bring the exponent t down:

[tex]log(2.485714286) = t log(1.0625)[/tex]

Dividing both sides by log(1.0625), we get:

[tex]t = log(2.485714286) / log(1.0625)[/tex]

Using a calculator, we get:

t ≈ 10.6

Therefore, to reach $8700, the individual must keep the money in the bank for approximately 10.6 years (rounded to the nearest tenth of an year).

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1. The probabilities of Poison distribution are: [tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]. [tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]. [tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex].

The Poisson distribution is a discrete probability distribution that defines the number of events that take place during a specific period of time or space, provided that they do so independently of one another and at a certain average rate. Siméon Denis Poisson, a French mathematician, invented it in the early 19th century to simulate the occurrence of uncommon events, such as horse kick fatalities in the Prussian army. He gave it his name.

The mean or expected value of the number of occurrences in the interval is represented by the Poisson distribution's single parameter, indicated by the Greek letter lambda.

The Poisson distribution is given as:

[tex]P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x![/tex]

Now,

a. For P(0) we have:

λ = (total number of homicides) / (total number of city-years)

= 193 / 280 = 0.689

Substituting the values of  λ = 0.689 and x = 0 we have:

[tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]

b. For P(1), we can plug in λ = 0.689 and x = 1 :

[tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]

c. For P(2), we can plug in λ = 0.689 and x = 2:

[tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex]

d. For P(3), we can plug in λ = 0.689 and x = 3:

[tex]P(3) = (e^{(-0.689)} * 0.689^3) / 3! = 0.0272[/tex]

e. P(4), we can plug in λ = 0.689 and x = 4:

[tex]P(4) = (e^{(-0.689)} * 0.689^4) / 4! = 0.0047[/tex]

2 ) The comparison for the actual and distributed values is:

Expected 0 homicides: 0.5012 * 280 ≈ 140.35

Expected 1 homicide: 0.3447 * 280 ≈ 96.72

Expected 2 homicides: 0.1189 * 280 ≈ 33.32

Expected 3 homicides: 0.0272 * 280 ≈ 7.62

Expected 4 homicides: 0.0047 * 280 ≈ 1.31

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Answer:

We did this by substituting the slope and point values into the equation

y

=

m

x

+

b

and then solving the equation for b.

We will now show you how you can use either use the slope and a point or just two points to define the equation of the line using point-slope form:

y

−

y

1

=

m

(

x

−

x

1

)

This is an important formula, as it will be used in other algebra courses and often in calculus to find the equation of a tangent line. We need only one point and the slope of the line to use the formula. After substituting the slope and the coordinates of one point into the formula, we can simplify it and then write the equation in slope-intercept form.

POINT-SLOPE FORM

Given a point

(

x

1

,

y

1

)

and slope m, point-slope form will give the following equation of a line:

y

−

y

1

=

m

(

x

−

x

1

)

Now that we know both the slope-intercept form and the point-slope for linear equations, when we are asked to find an equation for a linear function, we can choose which method to use based on the information we are given and our personal preferences. The information provided may be in the form of a graph, a point and a slope, two points, and so on. Let’s look at the graph of the function f below and determine its equation.

$480 worth of fuses can power 240 motors. This is calculated by dividing $480 by $2 to get the total amount of policies that can be purchased. Then the total number of fuses is divided by 3, which is the number of fuses per motor.

This calculation results in 240 motors that can be supplied with $480 worth of fuses. In more detail, the calculation is as follows:

(480/2) / 3 = 240

This means that 240 engines can be supplied with $480 worth of fuses. This calculation is based on the assumption that each motor requires 3 fuses and that each fuse costs $2

Hopes this helps with your question. :)

Answer:

23 motors

Step-by-step explanation:

fuses = $4

motor uses 3 fuses = $4 × 3 = $12

$284 ÷ 12 = 23.6 = 23 motors

Answer: No, she will not be audited

Step-by-step explanation: 40 - 26 =16 which is the increase. the increase is 16/40 which is equal to 2/5 which can be expressed as a percent such as 40% far away from 62.5

Answer:4.9987

Step-by-step explanation:

Formula for the volume of a cylinder: (π)(r^2)(h)  which is pi x radius squared x height

The final product is 314 therefore you make that number equal to the formula and plug in the known variables to the formula which becomes

314 = (π)(r^2)(4)

Since you know both the value for pi and the height, by following the reverse order of PEMDAS (because we are trying to solve for an unknown variable), you can divide the values of height and pi from both sides since they are being multiplied to radius squared. We are doing this in order to isolate the radius on one side which will give us the value for the radius.

This leaves you with 24.9873 = r^2

The final step is to squareroot both sides as squareroot eliminates a square.

This leaves us with  

r = 4.9987

The value of the denominator in the expression is 0.205.

The value of the denominator in the expression is calculated as follows;

The given expression is;

x = 0 + √1.16 / ?

when x = 5.252, the value of the Uknown is calculated as follows;

5.252 = 0 + √1.16 / ?

5.252 = √1.16 / ?

make the unknown "?" the subject of the formula;

? = √1.16 /5.252

? = 0.205

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A) Expansion of the given fraction expression gives: ⁵/₆x - 1

B) The given fraction expression is not the same as that of part A

A) We are given the expression:

¹/₂x + 3 + ¹/₃x - 4

Regrouping this to get like terms together gives:

(¹/₂x + ¹/₃x) + (3 - 4)

x(¹/₂ + ¹/₃) - 1

= ⁵/₆x - 1

B) We are given the expression:

¹/₂(x + 3) + ¹/₃(x - 4)

Expanding the bracket gives:

¹/₂x + ³/₂ + ¹/₃x - ⁴/₃

= ¹/₂x + ¹/₃x + ³/₂ - ⁴/₃
= ⁵/₆x + ¹/₉

This is not the same as the answer in Part A.

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Answer: b= 90

Step-by-step explanation:

Solve to find b. I multiplied both sides by 6 to get my answer.

[tex]\frac{b}{6} = 15\\b= 15(6)\\b= 90[/tex]

Answer:

B/6= 15

B=15×6

B=90

Step-by-step explanation:

When you change the position you change the sign in to opposite divide will be change into multiply.

(1)The break - even sales for last year is $600000.

(2)(a) The operating income for last year is $300000.

(b) The maximum operating income that could have been realized during the year is $337500.

In mathematics, a range refers to the set of all possible values or outputs that a function or relation can produce. It is the collection or set of all values that a function can take on as its output when given various inputs from its domain.

The term "volume" typically refers to the measure of the amount of space occupied by a three-dimensional object. It is a quantitative measure of the capacity or size of a solid shape in three-dimensional space. Volume is often used to describe the amount of space enclosed by an object or the amount of material it can hold.

Cost-Volume-Profit (CVP) Chart for Last Year:

To construct a CVP chart, we need to plot the sales, variable costs, fixed costs, and profit (or operating income) on the y-axis and the number of units sold on the x-axis.

Based on the given information:

Sales = $900,000

Unit selling price = $200

Variable cost per unit = $125

Fixed costs = $225,000

Maximum sales within relevant range = 7,500 units

Using the formula for calculating the break-even point:

Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)

Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units

Now we can construct the CVP chart:

Sales:

The sales line will start from the origin (0,0) and have a slope of $200 per unit, as the unit selling price is $200.

Variable Costs:

The variable costs line will also start from the origin (0,0) and have a slope of $125 per unit, as the variable cost per unit is $125.

Fixed Costs:

The fixed costs line will be a horizontal line parallel to the x-axis, at a height of $225,000, as the fixed costs are constant and do not change with the number of units sold.

Profit (Operating Income):

The profit line can be calculated by subtracting the total variable costs and fixed costs from the total sales. So, the profit line will start from the origin (0,0) and have a slope of ($200 - $125) per unit, which is the difference between the unit selling price and variable cost per unit.

The break-even point will be the point where the profit line intersects the x-axis, which is at 3,000 units. So, the break-even sales for last year is 3,000 units x $200 per unit = $600,000.

Verification using the break-even equation:

Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)

Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units

Operating Income for Last Year and Maximum Operating Income:

Operating Income for Last Year:

Operating Income = Sales - Variable Costs - Fixed Costs

Operating Income = $900,000 - ($125 x Number of Units Sold) - $225,000

Substituting the break-even point of 3,000 units, we get:

Operating Income = $900,000 - ($125 x 3,000) - $225,000

Operating Income = $900,000 - $375,000 - $225,000

Operating Income = $300,000

Maximum Operating Income:

The maximum operating income can be achieved at the maximum sales within the relevant range, which is 7,500 units.

Operating Income = Sales - Variable Costs - Fixed Costs

Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000

Operating Income = $1,500,000 - $937,500 - $225,000

Operating Income = $337,500

Verification using the mathematical approach to CVP analysis:

Plugging in the values for last year's sales of 7,500 units:

Let's calculate the maximum operating income using the mathematical approach to CVP analysis:

Operating Income = (Unit Selling Price x Number of Units Sold) - (Variable Cost per Unit x Number of Units Sold) - Fixed Costs

Given:

Unit Selling Price = $200

Variable Cost per Unit = $125

Fixed Costs = $225,000

Number of Units Sold = 7,500

Putting  the values:

Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000

Operating Income = $1,500,000 - $937,500 - $225,000

Operating Income = $337,500

So, the maximum operating income that could have been realized during the year is $337,500.

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There is sufficient evidence at 0.10 because Yes, because 0.001 < 0.10

Alana is running a test to analyze if the amount of messages transmitted between them surpasses an average of 100 daily.

The given α, or significance level, is 0.10, which requires proof strong enough to affirm the alternative hypothesis (H: μ > 100) while negating the null hypothesis (H0: μ = 100), supposing P < 0.10.

As the P-value is approximately 0.001 and hence lower than 0.10, it is sufficient evidence prohibitting acceptance of the null hypothesis and proposing that they usually dispatch more than 100 communications each day.

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Alana and her friends have been using a group messaging app for over a year to chat with each other. She suspected that, on average, they sent each other more than 100 messages per day. She took a random sample of 30 days from their chat history and recorded how many messages were sent on those days. The sample data had a mean of 127 messages and a standard deviation of 44 messages.

Alana used those results to test Hoμ= 100 messages versus H: > 100 messages, where is the average number of messages sent per day. She calculated a test statistic of t≈ 3.36 and a P-value of approximately 0.001. Assume that the conditions for inference were met.

Is there sufficient evidence at the a = 0.10 level to conclude that, on average, they sent each other more than 100 messages per day?

Choose 1 answer:

No, because 0.001 < 0.10.

Yes, because 0.001 < 0.10.

No, because 0.001 < 3.36.

Yes, because 0.001 < 3.36.

The activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.

Given the activity cost and activity base data, we can calculate the allocated costs for each activity as follows:

Procurement:

Allocated cost for tape drives = (Activity cost for procurement * Number of purchase orders for tape drives) / Total number of purchase orders

= ($370,000 * 4,000) / (4,000 + 300 + 1,400 + 10 + 2,000)

= $1,480,000 / 7,710 ≈ $192.11

Scheduling:

Allocated cost for tape drives = (Activity cost for scheduling * Number of production orders for tape drives) / Total number of production orders

= ($250,000 * 150) / (4,000 + 150 + 800 + 10 + 8,000)

= $37,500 / 12,960 ≈ $2.89

Materials handling:

Allocated cost for tape drives = (Activity cost for materials handling * Number of moves for tape drives) / Total number of moves

= ($500,000 * 800) / (4,000 + 300 + 1,400 + 10 + 2,000)

= $400,000 / 7,710 ≈ $51.83

Product development:

Allocated cost for tape drives = (Activity cost for product development * Number of engineering changes for tape drives) / Total number of engineering changes

= ($730,000 * 10) / (4,000 + 150 + 800 + 10 + 8,000)

= $7,300,000 / 12,960 ≈ $562.73

Production:

Allocated cost for tape drives = (Activity cost for production * Machine hours for tape drives) / Total machine hours

= ($1,500,000 * 8,000) / (4,000 + 150 + 800 + 10 + 8,000)

= $12,000,000 / 12,960 ≈ $925.93

Now, we can calculate the total allocated cost for tape drives by summing up the allocated costs for each activity:

Total allocated cost for tape drives = Allocated cost for procurement + Allocated cost for scheduling + Allocated cost for materials handling + Allocated cost for product development + Allocated cost for production

= $192.11 + $2.89 + $51.83 + $562.73 + $925.93

= $1,735.49

Finally, we can calculate the activity-based cost per unit for tape drives by dividing the total allocated cost by the number of tape drive units:

Activity-based cost per unit for tape drives = Total allocated cost for tape drives / Number of tape drive units

= $1,735.49 / 4,000

≈ $0.434

Therefore, the activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.

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The number line where we plotting -2 1/6 and 11/6 is attached

From the question, we have the following parameters that can be used in our computation:

-2 1/6 and 11/6

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-13/6 and 11/6

This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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Answer:

Step-by-step explanation:

The graphs can be sketched without using any software.

Answer:

The sin B got canceled and the one left same as on the other parenthesis inside the parenthesis I canceled the cos so one left now 1*1=1 and 1 over tan b plus 1 over tan b- we extract the tan to opp/adj then opp and adjacent got canceled and the one too so just only one left so 1=1

We need to multiply the equation x = 3 by a factor of 5 to find the equilibrium of the scale.

According to the statement, we find the following mathematical equation that describes the initial situation of the scale:

x = 3

Then, if we multipliy the equation by a factor of 5 on both sides (by property of compatibility with multiplication), then we find the following expression:

5 · x = 15

A factor of 5 must be added to the mathematic equation.

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The ordered pair that is potted in quadrant II is (-4, 6)

The domain of the second quadrant in a Cartesian coordinate system, also identified as a Cartesian plane, is located above the x-axis and to the left of the y-axis.

This area forms one of four quadrants that comprise the entirety of said system, frequently leveraged for graphing functions or equations and illustrating various data points.

Examining the graph, the point plotted in the second quadrant is (-4, 6)

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The radius are already given and hidden in the images. For example:

7) Radius = 4.1

8) Radius = 8.7

9)  Radius = 3

10) Radius = 7

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more recent use, it is also their length. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.

The diameter is the distance across a circle via its center. The radius is the distance from the center of a circle to any point on its edge. 2r=d; the radius is half the diameter. 2 r = d .

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We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:

[tex]t = -2 h + 32[/tex]

The temperature, t, in Burrtown starts at 32°F at midnight, when [tex]h = 0[/tex]. This represents the y-interception of the right line, when [tex]h=0[/tex] hours, [tex]t=32^\circ\text{F}[/tex]:

[tex]\text{Point}=(h,t)\longrightarrow Point=(0,32)=(0,b)\longrightarrow b=32[/tex]

For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): [tex]m=-2[/tex], negative because the temperature drops.

Slope-Intercept form:

[tex]y=mx+b: y=t, m=-2, x=h, b=32[/tex]

Replacing the values:

[tex]\boxed{\bold{t=-2h+32}}[/tex]

Complete Question-

The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour. Which equation represents the temperature, t, at hour h?

The value of the quadratic expression  ax² + bx when x = 5 is 10.

A quadratic expression is an expression in which the highest power of the unknown is 2.

Since we have the expression ax² + bx takes the value 6 when x = 1 and 10 when x = 2. We need to find its values when x = 5.

We proceed as follows.

Let y = ax² + bx.

When x = 1, y = 6. So, substituting these into the equation, we have that

y = ax² + bx

a(1)² + b(1) = 6

a + b = 6    (1)

Also, when x = 2, y = 10. So, substituting these into the equation, we have that

y = ax² + bx

a(2)² + b(2) = 10

4a + 2b = 10    (2)

From (1) a = 6 - b  (3).

So, substituting equation (3) into (2), we have that

4a + 2b = 10

4(6 - b) + 2b = 10

24 - 4b + 2b = 10

24 - 2b = 10

-2b = 10 - 24

-2b = -14

b = -14/-2

b = 7

Substituting b into (3). we have that

a = 6 - b

= 6 - 7

= - 1

So, substituting a = - 1 and b = 7 into the quadratic expression, we have that

y =  ax² + bx

= -1x² + 7x

= -x² + 7x

So, the value of the expression when x = 5 is

= -x² + 7x

= -(5)² + 7(5)

= -25 + 35

= 10

So, the value is 10

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The possible number of minutes Pablo has used his phone in a month is given by the inequality m ≥ 1009 minutes

Given data ,

Let's assume that the number of minutes Pablo has used his phone in a month is denoted by "m". Given that he pays a monthly fee of $24 and an additional $0.06 per minute, the total cost of his phone service in a month can be expressed as:

Total cost = Monthly fee + (Per minute charge x Number of minutes used)

Total cost = $24 + ($0.06 x m)

On simplifying , we get

$ 84.54 = $24 + ($0.06 x m)

Subtracting 24 on both sides , we get

m = $60.54 / $0.06

m = 1009 minutes

Hence , the inequality is m ≥ 1009 minutes

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