Evaluating Expressions I
Slumbertec is a sleep medication designed for patients with severe insomnia. The follow function is a
pretty good measure of the dosage a patient needs depending on their weight:
where w represents the patient's weight in pounds, and
d represents the dosage required in milligrams (mg).
a. Under the function equation above, label the meaning of the variables d and w.
b. Evaluate 2w-60 when w-140.
d=2w-60
C.
17
When w 175, the value of 2w-60 is 290. Explain what this means in the context of this
function. In other words, what does this tell you about the patient and this medicine?
d. Evaluate 2w-60 when w-25. Explain what this means in the context of this function.
e. Your patient was prescribed 260 mg of Slumbertec by another doctor. What would you guess was
the patient's weight at the time when the prescription was written?

1. Joshua's raise stated as a percentage is 6.1%.

2. When inflation is factored in, Joshua's raise reduces to 3.7%

A percentage is the ratio of a variable when compared to the whole.

Percentages are expressed over 100, like ratios, probabilities, and proportions.

Initial salary on the job = $42,800

New salary after the raise = $45,400

The salary increase in dollars = $2,600 ($45,400 - $42,800)

The salary increase in percentage = 6.1% ($2,600/$42,800 x 100)

Inflation rate = 2.4%

The real increase in salary = 3.7% (6.1 - 2.4%).

Thus, Joshua’s raise stated as a percentage is 6.1%.

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Answer:6-lane, 200-meter rubberized track (8 laps = 1 mile)

Step-by-step explanation:

The required coordinate of b is given as (6, 7 ).

To find out the coordinate of b  if M is the midpoint of AB. A(1, -4) and M(-3 ,0).

The midpoint is that point the line whose length from both the ends of the line is equal.

Here,

We have coordinates of two points i.e. A(1, -4) and M(-3, 0).

Definition of midpoint says,

x = [x₁ +  x₂] / 2 ; y = [y₁ + y₂] / 2

x₁ = 2, x = 4 , y₁ = -1, y = 4

now,

4 = [2 + x₂] / 2 ; 4 = [1 + y₂] / 2

x₂ = 8 - 2         ; y₂ = 8 - 1

x₂ = 6               : y₂ = 7

Thus, the coordinate of b is given as (8, 7 ).

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Answer:  A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given below.

f(x) = –3x – 5

The value of the function at x = –5, 0, 2 will be

f(–5) = –3(–5) – 5

f(–5) = 15 – 5

f(–5) = 10

f(0) = –3(0) – 5

f(0) = 0 – 5

f(0) = –5

f(2) = –3(2) – 5

f(2) = –6 – 5

f(2) = –11

Step-by-step explanation:

In maths, Conjugates are defined as a pair of binomials with identical terms but parting opposite arithmetic operators in the middle of these similar terms. For example, p – q is the conjugate of p + q.

complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, the complex conjugate of {\displaystyle a+bi} is equal to {\displaystyle a-bi.}

The math conjugate of a number is a number that when multiplied or added to the given number results in a rational number. For example,

The conjugate of a surd 6 + √2 is 6 - √2.

The conjugate of a complex number 5 - 3i is 5 + 3i.

Answer:

If to create a CD 9 songs are needed and user have 19 songs then he can create 33522128640 such CD's if solving through permutations.

What is permutations?

It is basically an arrangement of objects in a certain order.It is expressed as n and it is equal to n!/(n-r)!.

How to calculate ways?

We have been given that user have 19 songs and 1 CD is made from 9 songs so the number of CD's which can be made is basically the number of ways these 9 songs are arranged from 19 songs in CD's. So, the number of CD's will be 19=19!/(19-9)!

=19!/10!

=19*18*17*16*15*14*13*12*11*10!/10!

=19*18*17*16*15*14*13*12*11

=335322128640 CD's

Hence 335322128640 CD's can be made from 19 songs by the user.

Answer:

Just multiply 6x8x5

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

[tex]f(x_1)=4 \\ \\ f(x_2)=9 \\ \\ \frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{1}{13}[/tex]

Answer:

bases....................

Answer:

I think it should be 1 pm

Step-by-step explanation:

The Smiths left at 11 am and traveled 180 miles. If they drive at 60 miles per hour, that means that they traveled for 2 hours because 180 divided by 60 is two. That means they traveled for 2 hours and arrived at 1 pm.

Answer:

Step-by-step explanation:

The Red circles have a probability of 1/2 of getting chosen, The red and blue circles together have an 100% chance of getting chosen because they are the total of circles. Np

Answer:

Step-by-step explanation:

substitute the value for x and y

-6 + 6(-4)

= -6 -24

= -30

Answer:

-30

Step-by-step explanation:

plug in variables

-6 + 6(-4)

-6+ -24

= -30

Answer:

-$90 + $130= $40

Step-by-step explanation:

Im not sure if this is what you were looking for

The length of the missing side is √69

The triangle is a right triangle with the following parameters

Hypotenuse = 13

Leg = 10

Represent the missing side with x

By the Pythagoras theorem, we have

x = √Hypotenuse² - Leg²

This gives

x = √13² - 10²

Evaluate

x = √69

Hence, the length of the missing side is √69

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Answer:

d = -8

Step-by-step explanation:

4(-3d+14) = -17d + 16

-12d + 56 = -17d + 16

+17d            +17d

5d + 56 = 16

      -56    -56

5d = -40

÷5      ÷5

d= -8

I hope this helps!

Using Chebyshev's Theorem, it is found that:

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

For the first item, we first have to find k when P = 56, hence:

[tex]56 = 100\left(1 - \frac{1}{k^{2}}\right)[/tex]

[tex]1 - \frac{1}{k^{2}} = 0.56[/tex]

[tex]\frac{1}{k^2} = 0.44[/tex]

k² = 1/0.44

k = sqrt(1/0.44)

k = 1.5.

Within 1.5 standard deviations, hence the bounds are:

Hence:

According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between 30 years and 60 years.

25 and 65 years are both 2 standard deviations from the mean, hence:

At least 75% of the home buyers' age lie between 25 years and 65 years.

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There are 6,435 different selections of 7 bonsais that William Smith can choose.

If we have a set of N elements, the number of different combinations of K elements (such that K is equal to or smaller than N) of those N elements is given by:

C(N, K) = N!/( (N - K)!*K!)

In this case, we know that she has 15 different variants of bonsai and she wants to use 7, then:

N = 15

K = 7

Replacing these values in the above formula we will get the possible combinations of bonsais.

C(15, 7) = 15!/( (15 - 7)!*7!) = 15!/( 8!*7!) = (15*14*13*12*11*10*9)/(7*6*5*4*3*2*1) =  6,435

There are 6,435 different selections of 7 bonsais.

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Answer:

$1,945.91

Step-by-step explanation:

To find the amount a family would have spent to be at the 80th percentile, we can use the normal distribution.

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given that the average spending on a summer vacation is $1,600 and the standard deviation is $411:

We need to convert the problem to the standard normal distribution by calculating the z-score.

The z-score represents the number of standard deviations a data point is away from the mean. To find the z-score corresponding to the 80th percentile, we need to find the critical value or z-score that corresponds to an area of 0.80 under the standard normal curve.

Using a standard normal distribution table or a calculator, the z-score corresponding to an area of 0.80 is 0.84162084...

Next, we use the formula for the z-score:

[tex]\boxed{z = \dfrac{x - \mu}{\sigma}}[/tex]

where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.

Substitute z = 0.84162084..., μ = 1600, σ = 411 into the z-score formula:

[tex]0.84162084... = \dfrac{x - 1600}{411}[/tex]

Solving for x:

[tex]x=1945.90616...[/tex]

Therefore, a family would have spent approximately $1,945.91 to be at the 80th percentile of spending on a summer vacation.

Answer:

$1,945.03

Step-by-step explanation:

To find the amount a family would have spent to be at the 80th percentile, we need to find the z-score that corresponds to the 80th percentile and then use that z-score to calculate the corresponding amount.

First, we find the z-score using the standard normal distribution table or a calculator:

z = InvNorm(0.8) ≈ 0.8416

Next, we use the formula for transforming a z-score to a raw score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values and solving for x, we get:

0.8416 = (x - 1600) / 411

x - 1600 = 0.8416 * 411

x - 1600 = 345.0256

x = 1945.0256

Therefore, a family would have spent about $1,945.03 to be at the 80th percentile.

Answer:

i could only work out (A)

Step-by-step explanation:

Given: P(MOTHER) = 0.10 P(FATHER) = 0.10 P(MOTHER AND FATHER)= 0.02 P(FIRST CHILD) = 0.20 P(SECOND CHILD) = 0.20 P(FIRST CHILD AND SECOND CHILD) = 0.10 So, we get: P(MOTHER) X P(FATHER) = 0.10X 0.10 = 0.01 Since P(MOTHER) X P(FATHER) = 0.01 P(MO

The required measures of the corresponding parts in the reflection of figure a = 3.2 and b = 46 degrees. Option C is correct.

As given in the question, the figure on the left is reflected using a line to form the image on the right.

Here,
Since the reflection of a figure never changes its dimension so,
in the figure,
b + 143 + 108 + 63 = 360
b = 46
And also in reflection, the measure of the site will not change so the measure of a = 3.2

Thus,  the required measures of the corresponding parts in the reflection of figure a = 3.2 and b = 46 degrees. Option C is correct.

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The total cash due at signing if the dealership requires down payment, security deposit, first month's payment and the acquisition fee at signing  is 2400 + 375 + 500 = 3275

When you buy a car, you don't make monthly payments at the beginning. Plus, you don't care how much the buyout costs when you close the lease, that's after you've had it for two years.

You must take care of the deposit, this is your good faith commitment to the rental car. In addition, you may have to pay a deposit based on your credit, and the acquisition fee is what you would pay a broker or dealer to get the car to you if you wanted it from somewhere else.

Therefore,

2400 + 375 + 500 = 3275

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Answer:

Step-by-step explanation:

For each one you would take the Q1 and the Q3 value of the box and whisker plot and subtract them

Q3 - Q1 = IQR(interquartile range)

45 - 20 = 25

40 - 10 = 30

10 - 6 = 4

20 - 8 = 12

Based on the revenue, total equity, and the ending liabilities, the total assets at the end of the year is $362,000.

First, find the ending equity:

= Opening equity + Revenue - expenses

= 185,000 + 250,000 - 185,000

= $250,000

The total assets by the accounting equation is:

Assets = Liabilities +  Equity

= 112,000 + 250,000

= $362,000

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Answer:

18. in imge

19. is D

20. 10/3 (just divided by 5)

21. 8/7 bc negtive reciprocal

22. (0,8) y-int

Step-by-step explanation:

Answer:

n=8/3

Step-by-step explanation:

3n-5=13

3n=8

n=8/3

Probability of event E is = a/c

In the given statement is:

If the odds in favor of an event E are a : b,

To find  the probability of event E is

Formula for Probability

The Probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favourable outcomes / total number of outcomes

Now, According to the question:

Here, Number of outcomes in favor of the event = a

Number of outcomes in against the event = b

Total Outcomes => a + b = c

Therefore, Probability of event E is = a/c

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Answer:

Step-by-step explanation:

it means the rate is 8% and the time is 5 years

Answer:

  A.  The only solution is (-2, 1).

Step-by-step explanation:

Given a graph of two lines, you want the number of solutions to the system of equations the lines represent.

The graph of an equation represents all of the points that satisfy that equation. When a system of equations has more than one equation, the set of points that satisfies all of the equations is the set of points where the graphs intersect (overlap) each other.

Here, the two straight lines intersect at exactly one point: (-2, 1). That one point represents the only solution to the system of equations.

The only solution is (-2, 1).

By using permutation, the college can fill the position in 7 ways.

Permutation shows the no. of ways to arrange the objects or elements.

The Formula for the permutation is P(n, r) = [tex]\frac{n!}{(n-r)!}[/tex]

Given data:

The college needs two additional faculty members a chemist and a statistician. There are five applications for the chemistry position and seven applications for the statistics position.

No. of ways the college can fill the position = no. of ways the college can select Statistics + no. of ways the college can select chemist

By using, the permutation method we can find the no. of ways of selection of both chemist and statistician.

No. of ways the college can fill the position =[tex]5p_{1} +7p_{1}[/tex]

= 5 + 7

= 12 ways

The college can fill the position in 12 ways.

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Answer:

18

Step-by-step explanation:

f(-2) = 3(4-x)

=3(4+2)

=3*6=

=18