As drug A gets absorbed into the body, less and less of it remains. A scatterplot of data showed a curved relationship between hours since drug A was administered (x) and the number of milligrams of drug A remaining in the body (y). Taking the logarithm of the milligrams of drug A remaining obtains a linear pattern on a scatterplot, and creates the following printout from a statistical software package:


Predictor Coef SE Coef t-ratio P

Constant 3. 00 0. 401 7. 481 0. 000

Time -0. 0737 0. 005 -14. 74 0. 000


s= 0. 014 R-sq= 98. 5% R-Sq(Adj)= 99. 0%


Required:

Write down the correct equation that follows from this output?

A statement which best describes the solution set of the given inequality 5n + 1.5 ≥ 4 is: C. all rational number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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Complete Question:

Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers, n, of hours he could read on each of the 5 weekdays this week. The graph is shown.

Which describes the solution set of the inequality?

A. all whole number values of n that are at least 1

B. all whole number values of n that are greater than 1

C. all rational number values of n that are at least 0.5

D. all rational number values of n that are greater than 0.5

NP, PM, and MN are all midsegments and bisect each side.

value of x = 5 unit

NP = 12

MP=2x

RQ = 5x-1

SQ=6x

Using Midsegments of a Triangle

A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle

Triangle Midsegment Theorem

Using Midsegments of a Triangle

Theorem 5-1 Triangle Midsegment Theorem

The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

Triangle Midsegment Theorem A segment whose endpoints are the

midpoints of two sides of the triangle

Midsegment

Base

Midsegment = ½ of Base

M = ½ b

NP =1/2(RQ)

12 =1/2(5x-1)

12* 2 = 5x-1

24 =5x-1

24+1 =5x

25 =5x

x=25/5

x = 5 unit

NP, PM, and MN are all midsegments and bisect each side.

value of x = 5 unit

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The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.

Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.

Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.

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The solution of the pair of equations y = 0 and y = -3 is y = -3/2.

The given pair of equations is:

y = 0

y = -3

We can solve this pair of equations using elimination. To do this, we first add the two equations together, which gives us:

y + y = 0 + (-3)

2y = -3

We then divide both sides by 2 to get the solution for y:

2y/2 = -3/2

y = -3/2

Therefore, the solution of the pair of equations y = 0 and y = -3 is y = -3/2.

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178 students taking a music class and 82 students taking an art class

There was no clear question, but I'm assuming you want to know how many students are enrolled in music and painting classes.

Let x= the number of children enrolled in art classes.

number of children enrolled in music classes: 2x + 14

The overall number of children will be 260, including all of these children.

x+2x+14 = 260

3x=246 x=82 pupils attend an art lesson.

To find people taking music classes, enter x to 2x+14.

2(82)+14 = 178

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The complete question would be;

There are 260 eighth-grade students at South Whitemarsh Middle School. All eighth-grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes.

According to the following graph, the for the expression y = 5 is horizontal.

The term graph in math is known as the set of vertices and a binary relation between vertices, adjacency.

Here we have given the expression y = 5.

Now, we have to plot these expression on the graph, then we get the following graph.

Through the given graph, we have identified that the expression makes the horizontal line on the graph.

Here we also know that if the equation of a line is y = 5, then it is a horizontal line.

Here we know that the line is parallel to the x-axis and passes through the point y = 5 at the y-axis.

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Answer:

-33

Step-by-step explanation:

Plug 9 in for c, then simplify the resulting expression.

5c - 9c + 3

5(9) - 9(9) + 3

↓ execute multiplication

45 - 81 + 3

↓ simplify by adding 81 and 3

45 - 84

↓ execute subtraction

-33

Answer:

[tex] \sf \: - 33 \: (if \: c = 9)[/tex]

Step-by-step explanation:

Given expression,

→ 5c - 9c + 3

Now we have to use,

→ c = 9

Simplifying the given expression,

→ 5c - 9c + 3

→ 5(9) - 9(9) + 3

→ 45 - 81 + 3

→ -36 + 3

→ -33 => (answer)

Hence, required answer is -33.

After solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.

What is algebra?

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x

$3.00 when converted to cents is 300 cents.

The value of nickels is 5 x 4x=20x.

The value of dimes is 10 x 3x=30x.

The value of quarters is 25x.

As the total value of money Miguel has is 300 cents, then the algebraic equation will be -

20x + 30x + 25x = 300

Solve to get the value of x -

75x = 300

x = 4

Therefore, the amount of quarters is x = 4 quarters.

The amount of dimes is x = 3x = 3 x 4 = 12 dimes.

The amount of nickels is 4x = 4 x 4 = 16 nickels.

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No, isosceles triangles do not always have to have 90-degree angles.

An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.

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Diana's savings will be 280 dollars after four weeks.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

300 - 5x

Where x represents the number of the week.

We have to determine Diana's savings after four weeks

As per the question, we have

⇒ 300 - 5x

Substitute the value of x = 4 in the above expression

⇒ 300 - 5(4)

⇒ 300 - 20

⇒ 280

This means her savings will be 280 dollars after four weeks.

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The question seems to be incomplete the correct question would be:

Diana's savings at the end of each week can be described by the expression 300-5x where x represents the number of the week.

What is her savings after four weeks?

On solving the provided question we can say that - in fractions 2/3 and 2 we can do 2/3X2 = 4/3

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here,

in the given fractions 2/3 and 2/1,

we can do that -

2/3 X 2/1 = 4/3

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Answer:

x - intercept = (15, 0)

y - intercept = (0, 6)

Step-by-step explanation:

x-int. is when y = 0

y-int. is when x=0

Plug in y = 0 and x = 0 to get intercepts.

FOR X-INT.:

12x + 30(0) = 180

12x = 180

x = 15

x-int. is (15, 0)

FOR Y-INT. :

12(0) + 30y = 180

30y = 180

y = 6

y-int. is (0, 6)

Answer:

First, you need to calculate your grade in percentages. The total answers count 70 - it's 100%, so we to get a 1% value, divide 70 by 100 to get 0.70. Next, calculate the percentage of 15: divide 15 by 1% value (0.70), and you get 21.43% - it's your percentage grade.

Step-by-step explanation:

Some polynomials have specific names indicated by their prefix like monomial is a polynomial with exactly one term (“mono”—means one) binomial is a polynomial with exactly two terms (“bi”—means two) trinomial is a polynomial with exactly three terms (“tri”—means three).

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three). A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

Here,

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three).

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Step-by-step explanation:

Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°

Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360

Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.

If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.

Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.

X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0,  If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0

The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.

If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).

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Answer:Bilquis finds some nickels and quarters in her piggy bank. How much money (in

cents) does she have if she has 7 nickels and 5 quarters? How much money

does she have if she has n nickels and q quarters?

Step-by-step explanation:

Answer: 157 cents ($1.57)

Step-by-step explanation: Nickels are worth 5 cents each, so 5 cents times 7 nickels equals a total of 35 cents. After that, we have 5 quarters which cost 25 cents each, so 25 cents times 5 quarters equals a total of 125 cents. Combine these two products, and you get 157 cents. Or, if you want it in dollars, you can divide 157 by 100 cents (there are 100 cents in a dollar) and end up with $1,57.

The system X² y² 25 and ay 10 has no real solutions.

To solve this system, we need to solve each equation for y.

For the first equation, X² y² 25, we can divide both sides by X² to get:

y² = 25/X²

Then, take the square root of both sides to get:

y = ± √(25/X²)

For the second equation, ay = 10, we can divide both sides by a to get:

y = 10/a

To find out if the system has real solutions, we need to compare the two equations. Since the two equations are not equal, the system has no real solutions.

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Step-by-step explanation:

x^4-9x^2-8x^2+72

x^2(x^2-9)-8(x^2-9)

(x^2-8)(x^2-9)

(x^2-8)(x+3)(x-3)

Answer:

y > 14/3

Step-by-step explanation:

-3y<-14

Divided both sides by -3. Because divided by a negative number, the < will switch to the >

y > 14/3

Answer:

A = 80 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 4 and h = 2 , then

A = 4 × 2 = 8 cm²

there are a total of 10 tiles required ( 5 black and 5 white ) , then total area is

A = 10 × 8 cm² = 80 cm²

The unit price of the portion of the chicken will be $0.50.

To find the portion cost of the chicken, we need to know how much it costs per ounce, and then multiply that by the number of ounces in a serving.

We can begin by calculating the cost per ounce of chicken by dividing the cost per pound by the number of ounces in a pound:

$2 (cost per pound) ÷ 16 (ounces per pound) = $0.125 (cost per ounce)

Now that we know the cost per ounce, we can find the portion cost of the chicken by multiplying it by the number of ounces in a serving:

$0.125 (cost per ounce) × 4 (ounces per serving) = $0.50

So the portion cost of the chicken is $0.50 . So the answer is

C. $0.50.

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The complete question is-

The cost per pound of chicken is $2. Each serving of chicken is about 4 oz. What will be the portion cost of the chicken?

A. $0.75

B. $2

C. $0.50

D. $0.60

E. $1

Answer:

180-25-60=95

Step-by-step explanation:

The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number

1. Cost of a paperback = 25 cents = $0.25

Cost of a hardcover book = $1.25

There were 54 paperbacks and 163 hardcover books sold.

Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25

2. Cost for round trip airfare = $398.60

Cost of room per night = $115.70

Cost of room for two nights = 2 × $115.70 = $231.40

Cab fare from airport to hotel = $40.00

Total fare from airport to hotel and the return = 2 × $40.00 = $80.00

Total cost = $398.60 + $231.40 + $80.00 = $710

3. Total working hour of Paula = 48 hours

Earning for first 35 hours = $14.50/h × 35

                                          = $507.50

Remaining hours = 48 - 35 = 13 hours

Earning for next 13 hours = ($14.50/h × 1.5) × 13

                                          = $282.75

Total earnings =  $507.50 + $282.75 = $790.25

4. Number of cards Will has = 26

Number of cards Liam has = 19

When they combine, total cards = 26 + 19 = 45

When father also shared, total number of cards = 3 × 45 = 135

Number of cards Nestor has = 4 × 8 = 32

Total number of cards = 135 + 32 = 167

Hence all the questions are cleared using multiplication as one of the basic operations.

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The experimental probability is 30% higher than the predicted probability.

What is meant by experimental probability?

Experimental Probability: what actually occurs when the experiment is carried out. For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

The spinner has 10 sections and a 10% chance of landing on the section representing rain. Therefore, the probability of rain predicted by the spinner is 0.1 or 10%.

From the simulation, the results are 3, 6, 1, 8, and 3. Out of these 5 spins, 2 of them landed on the section representing rain (1, 3). Therefore, the experimental probability of rain from the simulation is 2/5 or 40%.

The difference between the experimental probability from the simulation and the prediction is the difference between the two percentages, which is:

(experimental probability) - (predicted probability) = 40% - 10% = 30%

Hence, the experimental probability is 30% higher than the predicted probability.

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Answer: -2(4*2+(1/2)2) = -18

Step-by-step explanation: In order to solve this problem, we just have to use the order of operations. This can be shortened to PEMDAS.

The first step is PARENTHESIS. There are two parenthesis within this problem, so we start from the smaller ones and then go to the bigger ones. So, 1/2. That's equal to 0.5, so now we have -2(4*2+(0.5)2).

There are no EXPONENTS within this problem, so we skip the E part of the order.

Next is MULTIPLICATION and DIVISION. There are two instances of multiplication within the parenthesis. 4*2 is equal to 8. Because 2 is right next to the parenthesis, its contents are being multiplied by it. So, 0.5*2 is equal to 1.

Next is ADDITION and SUBTRACTION. There's no subtraction, but we can add 1 and 8 to get 9. This was the final process within the parenthesis, so now we can focus on what's happening outside.

For the same reasons mentioned before, we know that 9 is being multiplied by -2. 9*-2 is equal to -18. This is because any positive number multiplied by a negative number will result in a negative product.

Thus, our final answer is -18.

Answer:

x= 1/4 - 1/4 x= 1/4 + 1/4

Step-by-step explanation:

Answer:

Type: (+ ve)

Number of solutions: 2

Step-by-step explanation:

We are given an equation (-8x² + 4x - 1 = 0)

Now, change the sign

-8x² + 4x - 1 = 0

8x² - 4x + 1 = 0

Here,

Now, discriminant

D = b² - 4ac

D = (8)² - (4)(8)(1)

D = 64 - 32

D = 32 > 0

Here, 32 is greater than 0 so, it has two solutions.