Over twenty years, it was found that the number of doctors of medicine, MD (in thousands), in the United States can be approximated by MD=(28,390+693t)/(85-t) where t=0 represents 1980. The number of doctors of osteopathy, DO (in thousands), can be approximated by DO=(776-12t)/(65-2t) .

Write an expression for the total number I of doctors of medicine (MD) and doctors of osteopathy (DO). Simplify the result.

How many MDs did the United States have in 2010? How many MDs did the United States have in 2010?

Answer:

The inverse is g(x)=-x+5.

Both f and g have domain and range all real numbers.

In interval notation that is [tex](-\infty,\infty)[/tex]

Step-by-step explanation:

f(x)=-x+5 is a linear function.

Since isn't f(x)=constant then it is diagonal so this means the range is all real numbers.

For any linear function, the domain will be all real numbers.  

So to find the inverse of y=-x+5, you interchange x and y and resolve for y.

y=-x+5

(interchange)

x=-y+5

(solve for y)

Subtract 5 on both sides:

x-5=-y

Multiplying both sides by -1:

-x+5=y

So the inverse is g(x)=-x+5. To find find the domain and range of the inverse function given you already did it for the original function, the sets are swapped.  The sets were the same here because they were both all real numbers.

Answer:

Domain of this function become R

Step-by-step explanation:

Answer:

  C.  0.006 g/cm³

Step-by-step explanation:

As the units tell you, density is the ratio of mass to volume. The volume of the container is found from ...

  V = πr²h = π(10 cm)²(25 cm) = 2500π cm³

Then the density is ...

  ρ = (50 g)/(2500π cm³) = 1/(50π) g/cm³

  ρ ≈ 0.006 g/cm³

_____

Comment on the problem

The "liquid" has about the same density as air pressurized to 75 psi.

Can someone confirm is this answer is right?

Step-by-step explanation:

[tex]\text{A conjugate of}\ a+b\ \text{is}\ a-b.\\\\1)\ \sqrt8-\sqrt9\to\sqrt8+\sqrt9\\\\2)\ 2x^2+\sqrt3\to2x^2-\sqrt3\\\\3)\ a-\sqrt{a-1}\to a+\sqrt{a-1}\\\\4)\ \sqrt{x}+2\sqrt{b}\to\sqrt{x}-2\sqrt{b}[/tex]

Answer:

y<-3x+8

Step-by-step explanation:

We are given 3x+y<8. There is exactly one step to put this in slope-intercept form, y=mx+b form where the equal sign can be an inequality sign. Our goal is to isolate y.

To do in 3x+y<8, we will just need to subtract 3x on both sides giving us y<-3x+8.

Answer:

y<-3x + 8

Step-by-step explanation:

y=mx+b form

Answer:

Factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Step-by-step explanation:

Given:

A= 125

B = 27p^12

To find: A-B

A-B = 125 - 27p^12

A-B=(5)^3-(3p^4)^3

We know that, a^3 - b^3 = (a-b)(a^2+ab+b^2)

Using this formula and finding factored form of A-B:

=(5-3p^4)((5)^2+(5)(3p^4)+(3p^4)^2)

=(5-3p^4)(25+15p^4+9p^8)

So, factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Answer:

D. y[9]=15.5410

Step-by-step explanation:

Let's find the answer by using the following observation:

Notice that the y-value differences between consecutives obstacles are:

(y-value from obstacule 2) - (y-value from obstacule 1)= 7.975 - 7.25 = 0.725

which is equal to:

(y-value from obstacule 1) / 10 = 7.25 / 10 = 0.725

So, an equation can be written as follows:

y[i+1]=y[i]+y[i]/10 let's find the other values:

y[2]=7.25+(7.25/10)= 7.975

y[3]=7.975+(7.975/10)= 8.7725

y[4]=8.7725+(8.7725/10)= 9.64975

Notice that we obtained the same y-values using the formula as the ones reported. So using the same formulas we can calculate:

y[9]=15.5410

In conclusion, the general equation is y[i+1]=y[i]+y[i]/10 with a starting point (1, 7.25) and y[9]=15.5410. So the answer is D.

Answer:

D.) f(9) = 7.25(1.1)8; f(9) = 15.541

Step-by-step explanation:

Answer: its the third one try that

Step-by-step explanation:

Answer:

It's C

Step-by-step explanation:

Answer:

> 1

Step-by-step explanation:

A scale factor greater than 1 will produce an enlargement

A scale factor less than 1 will produce a reduction

Since the image is larger than the pre- image the scale factor > 1

Answer:

Fixed cost is the weekly cost of the rent payment for the factory i.e. $2,250

Variable cost can be computed as :

Variable cost = Total wages paid + Cost of raw material

Variable cost = (20 workers × 40hrs/week × $15) + ($10/unit × $500 units)

Variable cost = $17,000

∴ The Total Cost is given as:

Total Cost = Fixed Cost + Variable Cost

Total Cost = $2,250 + $17,000 = $19,250

∴ Total variable cost is $17,000; total fixed cost is $2,250; total cost is $19,250

Option (a.) is correct

Answer:

-10.5 deg

Step-by-step explanation:

Yesterday's temp = 7-1/2 deg (or 7.5 deg)

Today's temp = -3 deg

net change = today's temp - yesterday's temp

= -3 - 7.5 = -10.5 deg

Answer:

-10.5

Step-by-step explanation:

I listened to the other person and they helped me get it right. I'm just here to confirm it. Stay safe!! <3

Ari will think that there is not enough ice cream for the amount of caramel.

3:5 and 6:8 are not equivalent

But let's prove that;

We know that 3 x 2 is 6, so let's multiply 3 x 2 and 5 x 2, when we do so, we get 6:10.

6:10 is greater than 6:8, so there is obviously less ice cream for the amount of caramel.

Answer:

[tex]f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

Step-by-step explanation:

The zeros of the polynomial are: -3, -1, 1, 2

According to the factor theorem, the factors of the polynomial will be:

(x - (-3)) = x + 3

(x - (-1)) = x + 1

(x - 1)

(x - 2)

Since we have the factors, we can multiply them to obtain the equation of the polynomial.

So,

[tex]f(x)=(x+3)(x+1)(x-1)(x-2)\\\\ f(x)=(x+3)(x^{2}-1)(x-2)\\\\ f(x)=(x^{2}-1)(x^{2}-2x+3x-6)\\\\ f(x)=(x^{2}-1)(x^{2}+x-6)\\\\ f(x)=x^{4}+x^{3}-6x^{2}-x^{2}-x+6\\\\ f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

The above equation give the polynomial with integer coefficients and a leading coefficient of 1

The polynomial of degree 4 that has -3, -1, 1, and 2 as its real zeros and integer coefficients with a leading coefficient of 1 can be expressed in its factored form as f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

To form a polynomial with the given real zeros and degree, we must first understand that each real zero corresponds to a factor of the form (x - a), where a is the zero.

Therefore, given the zeros -3, -1, 1, and 2,

the corresponding factors of the polynomial are (x + 3), (x + 1), (x - 1), and (x - 2).

The polynomial of degree 4 with these zeros can then be written as the product of these factors,

obtaining f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

Since it's required that polynomial has integer coefficients and a leading coefficient of 1,

we leave it in this factored form.

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Answer:

A = 13.5 cm²

Step-by-step explanation:

* Lets explain how to find the area of the parallelogram

- In any parallelogram each two opposite sides are parallel

- In any parallelogram each two opposite sides are equal in length

- Each two opposite sides have height perpendicular on them

- So the parallelogram has 2 different bases and 2 different heights

- The area of the parallelogram = base × the height of this base

* Lets solve the problem

- The lengths of the two bases of the parallelogram are 4.5 cm , 5 cm

- The height of the base which length is 4.5 is 3 cm

- We will calculate the area of the parallelogram from this base

∵ The base of the parallelogram = 4.5 cm

∵ The height of this base = 3 cm

∵ Area of parallelogram = base × its height

∴ Area of parallelogram = 4.5 × 3 = 13.5 cm²

* The area of the following parallelogram is 13.5 cm²

Answer:

13.5 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 = 4.5 and h = 3, so

A = 4.5 × 3 = 13.5 cm²

Answer:

The confidence interval shows a range of values that includes this parameter of the population with an ascribed degree of confidence: (1) Mean; (2) Standard deviation; (3) Variance; (4) None of the above

Step-by-step explanation:

In statistics, a pair or several pairs of numbers between which it is estimated that there will be a certain unknown value with a certain probability of success is called a confidence interval.

The standard deviation, is a measure used to quantify the variation or dispersion of a set of numerical data.

The answer is: (2) standard deviation.

Answer:

  ABCDEADBEC

Step-by-step explanation:

A path that traverses all streets exactly once is called an Euler path. It is only possible for a graph that has an even number of streets coming together at each vertex, or one that has an odd number of streets at only two vertices.

This map has an odd number of streets at vertices A and C, so those are suitable starting and ending points for the path. I find it convenient to travel the outside ring first, then fill in the inner paths that weren't previously traveled. The list of vertices for one possible path is shown above.

Answer:

c

Step-by-step explanation:

5/12, 1, 1/3, 5/6. 1/3 is the smallest.

Answer with Step-by-step explanation:

Mixture A-

Blue Paint - 5 cups

White Paint - 12 cups

Ratio of blue paint to white paint=5:12

Mixture B-

Blue Paint- 6 cups

White Paint- 6 cups

 Ratio of blue paint to white paint=6:6=12:12  

(on multiplying numerator and denominator by 12 i.e.6/6=12/12)

Mixture C-

Blue Paint - 4 cups

White Paint - 12 cups

 Ratio of blue paint to white paint=4:12

Mixture D-

Blue Paint - 5 cups

White Paint - 6 cups

Ratio of blue paint to white paint=5:6=10:12

(on multiplying numerator and denominator by 12 i.e.5/6=10/12)

The denominator of the ratios are same in each mixture now,to determine the lowest ratio we have to see the numerator with smallest value which is 4

Hence, Mixture C has the lowest ratio of blue paint to white paint

Answer:

y= 12

Step-by-step explanation:

2/3 y + 7 = 15

Subtract 7 from each side

2/3 y + 7-7 = 15-7

2/3 y = 8

Multiply each side by 3/2 to isolate y

3/2 * 2/3 y = 3/2 * 8

3/2 * 2/3 y = 3 * 4

y = 12

Answer:

b/x=y/b

Step-by-step explanation:

Switch it over and get the y.

Answer:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

Step-by-step explanation:

In statistics we have to deal with populations and samples to carry out our studies. A population is a large group under consideration and the elements or members of the population have some common features or attributes. For example, all the school going kids in a certain town will be considered a population. Sample on the other hand is a subset(a part) of the population. For example, all school going kids in the town aged 5-6 years will be considered a sample.

The term Parameter and Statistic are very similar as they represent some numeric description. Parameter represents the data of the entire population, while statistic represents that data of a sample. An easy way to remember this is to match the initials i.e. Parameter for Population and Statistic for Sample.

Considering this, we can say the correct answer is:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

A parameter is a numerical value describing a characteristic of a population whilst a statistic is a numerical value describing a characteristic of a sample. A population is any whole set, while a sample is a subset of the population.

The primary difference between a parameter and a statistic lies in the data they refer to. A parameter is a numerical measurement that describes a characteristic of a population. A population is the whole set of items or individuals that we are interested in. On the other hand, a statistic is a numerical measurement that describes a characteristic of a sample, where a sample is a subset of the population.

For example, if we were to measure the average height of all adult men in a certain city (the population), the resulting value would be a parameter. If we were to take a sample group of 100 men from that city and measure their average height, the resulting value would be a statistic.

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Answer:

GCF of 36x^3 and 48x^4 is 12x³....

Step-by-step explanation:

To find the GCF of 36x3 and 48x4 we have to perform prime factorization of both the terms:

Prime Factorization of 36x³ = 2*2*3*3*3*x*x*x

Prime factorization of 48x^4 = 2*2*2*2*3*x*x*x*x

Thus the common factors are 2*2*3*x*x*x

Therefore GCF of 36x^3 and 48x^4 is 12x³....

Answer:

it is 12x^3

Step-by-step explanation:

Answer:

164 legs all together

Step-by-step explanation:

There are 144 legs out of all the numbered creatures together.

Spiders = 8 legs

8 x 8 = 64

Cockroaches = 6 legs

6 x 5 = 30

Bees = 6 legs

7 x 6 = 42

Deer = 4 legs

3 x 4 = 12

Cows = 4 legs

4 x 4 = 16

Since the graph above shows a proportional relationship between x and y, an equation of the line is y = -1/4(x).

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = -1/4 = -2/8 = -12/3

Constant of proportionality, k = -1/4.

Therefore, the required linear equation for y(x) is given by;

y = kx

y = -1/4(x)

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Answer:

C. The system has no solution.

C. The system has no solution.

A system of linear equations has no answer whilst the graphs are parallel. A coordinate plane. The x- and y-axes both scale by way of one-1/2. A graph of a line is going through the factors 0, one and a half of and three, two.

No solution would suggest that there's no answer to the equation. it's miles not possible for the equation to be proper regardless of what price we assign to the variable. infinite answers would suggest that any value for the variable would make the equation authentic.

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Answer:

(a) Five

(b) Thirteenth

Step-by-step explanation:

We have the mean is 12.6 and

that 11 occurs 4 times, 12 occurs 7 times, 13 occurs 9 times, and 14 occurs f times.

How many children are there in all (that is the sum of the frequencies).

4+7+9+f

20+f

Alright so the mean could be found by doing:

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}[/tex]

But we are given this is also equal to: 12.6.

So we have

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}=12.6[/tex]

I'm going to simplify what I can on top.

[tex]\frac{245+14f}{20+f}=12.6[/tex]

I'm going to write 12.6 as [tex]\frac{12.6}{1}[/tex] because I want to cross multiply:

[tex]\frac{245+14f}{20+f}=\frac{12.6}{1}[/tex]

[tex](245+14f)(1)=12.6(20+f)[/tex]

Distribute:

[tex]245+14f=252+12.6f[/tex]

Subtract 12.6f on both sides:

[tex]245+1.4f=252[/tex]

Subtract 245 on both sides:

[tex]1.4f=7[/tex]

Divide both sides by 1.4:

[tex]f=5[/tex]

There are five 14 years old.

(b) I would say 13 is good age to represent this bunch.

The means was 12.6 which when rounded is 13.

The mode is 13 because it is the most occurring

The median is also 13. Why? If you list out the data 13 will be the middle number. Or you could say there are 25 kids and if I divide it by 2, I get 12.5.  This means you only need to count to the 13th kid with the ages in order to tell with the median is.

There are 4 eleven yr olds.

There are 7 twelve yr olds.  That is 11 kids so far.

So the median has to be included in the 9 thirteenth yr olds.

Answer:

The correct option is C.

Step-by-step explanation:

Using the given box plots:

The data set for Asian elephant is

6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10

Divide the data set in 4 equal parts.

(6, 6, 7), 7, (7, 8, 8), 8, (8, 8, 8), 9, (9, 9, 10)

[tex]Q_1=7, Median=8, Q_3=9[/tex]

IQR of the Asian elephant is

[tex]IQR=Q_3-Q_1=9-7=2[/tex]

IQR of the Asian elephant is 2.

If the data set lies in interval [tex][Q_1-1.5(IQR),Q_3+1.5(IQR)][/tex], then the data set has no outliers.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[7-1.5(2),9+1.5(2)]=[4,12][/tex]

All the data lie in [4,12], therefore Asian elephant  has no outliers.

The data set for African elephant is

4, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14

Divide the data set in 4 equal parts.

(4, 6, 7, 7, 8, 8, 8), 9,( 9, 9, 10, 10, 10, 10, 11), (11, 11, 11, 11, 11, 12, 12), 12, (12, 12, 12, 13, 13, 14, 14)

[tex]Q_1=9, Median=11, Q_3=12[/tex]

IQR of the African elephant is

[tex]IQR=Q_3-Q_1=12-9=3[/tex]

IQR of the African elephant is 3.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[9-1.5(3),12+1.5(3)]=[4.5,16.5][/tex]

All the data lie in [4.5,16.5] except 4, therefore African elephant has lower outliers.

African have a greater IQR because there were some very short elephants.

Therefore the correct option is C.

Answer:

African Elephants have a greater IQR because there were some very short elephants (low outliers).

Step-by-step explanation:

Apex

Answer:

D. 66.

Step-by-step explanation:

There has to be 3 even multiples in the 5 numbers so we try:

22+33+44+55+66

= 220.

Answer:

Option D. 66

Step-by-step explanation:

A multiple is an exact number of times to another number.

The five consecutive multiples of 11 are:

22 -> 11/22 = 2 times, no remainder

33 -> 33/11 = 3 times, without remainder

44 -> 44/11 = 4 times, without remainder

55 -> 55/11 = 5 times, without remainder

66 -> 66/11 = 6 times, without remainder

Of those five multiples of 11 (22, 33, 44, 55, 66), the greatest is 66.

f(x)=(x-5)(x-4)(x-2)

x-5=0

x-5+5=0+5

x=5

x-4=0

x-4+4=0+4

x=4

x-2=0

x-2+2=0+2

x=2

Answer: 5,4,2 -C

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

Option C is correct

Note that:

The zeros of a function f(x) are the values of x that makes f(x) to be equal to zero

If f(x)  =  (x - a)(x - b)(x - c), then the zeros of the function f(x) are:

x  = a,  x  =  b,  x  =  c

Therefore, the zeros of f(x)=(x-5)(x-4)(x-2) are found by equating f(x) to zero

(x - 5)(x - 4)(x - 2)  =  0

Equate each of the terms to zero

x  -  5  =  0

x  =   5

x  -  4  =  0

x   =  4

x  -  2  =  0

x   =  2

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

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Answer:

2y

Step-by-step explanation:

-2y + 3y x 2  – 3y + y

= -4y + 3 x 2y

= 4y + 6y

= 2y

Answer: I hope it's right :3

Step-by-step explanation:

Answer:

The minimum number of lenses that Mira must purchase is= 12 packs=600 lenses

Step-by-step explanation:

You know that one Telescope is made for:

2 lenses (they are purchased by packs of 50 (only 25 works for Telescopes)

1 tube (they are purchased by packs of 10)

1 eyepiece (they are purchased by packs of 30)

Then the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses, should be a whole number that is divisible by 30 and 10.

You can calculate how many packs Mira Needs to purchased in order to find that number.

You Know that 2 lenses are needed for 1 Telescope and that they are purchased by packs of 50 where only 25 works for Telescopes

Then you can express that how:

Number of telescopes Mira can make from Lenses= (50/4)* Number of packages of lenses

Then If Mira purchases:

1 pack of lenses, she can make 12.5 telescopes (it's no divisible by 30 and 10)

2 packs of lenses, she can make 25 telescopes(it's no divisible by 30 and 10)

3 packs of lenses, she can make 37,5 telescopes(it's no divisible by 30 and 10)

4 packs of lenses, she can make 50 telescopes(it's no divisible by 30 and 10)

5 packs of lenses, she can make 62,5 telescopes(it's no divisible by 30 and 10)

6 packs of lenses, she can make 75 telescopes(it's no divisible by 30 and 10)

7 packs of lenses, she can make 87,5 telescopes(it's no divisible by 30 and 10)

8 packs of lenses, she can make 100 telescopes(it's no divisible by 30 and 10)

9 packs of lenses, she can make 112,5 telescopes(it's no divisible by 30 and 10)

10 packs of lenses, she can make 125 telescopes(it's no divisible by 30 and 10)

11 packs of lenses, she can make 137,5 telescopes(it's no divisible by 30 and 10)

12 packs of lenses, she can make 150 telescopes(it's a whole number and is divisible by 30 and 10)

Then she needs to purchase 600 lenses, 5 packs of eyepieces and 15 packs of tubes in order to make 150 Telescopes.

Answer: it's only refracting

E2020