Two professors in the mathematics building have offices that are consecutive odd numbers with a sum of 14,600. What are the official numbers of these two professors?

Answer:

h(g(x)) = x²+4x+4

Domain restriction = [tex][-\infty, \infty][/tex]

Step-by-step explanation:

Given the functions  h(x)=x^2 and g(x)=x+2, we are to find h(g(x)). To get the indicated operation we need to follow the steps;

Since the function in parenthesis g(x) = x+2

h(g(x)) can be written as h(x+2). Hence we are to look for the equivalent expression of  h(x+2).

Since h(x) = x², h(x+2) can simply be gotten by simply replacing the variable x in h(x) as x+2 as shown;

h(x+2) = (g(x))²

h(x+2) = (x+2)²

We can open the bracket

h(x+2) = x²+4x+4

The domain restriction is the point where the function cannot exist for the value of x. The function can therefore exist on any real value R. The only domain restriction is at the interval [tex][-\infty, \infty][/tex]

Hence h(g(x))  is equivalent to x²+4x+4.

Answer:

73

Step-by-step explanation:

Since DA is the diameter, this means that you can divide the circle into two half-circles.  You will solve with the right half-circle.  A half-circle has a 180 total degrees.  Add up the values given and solve for x.

(2x) + (7x - 4) + (85) = 180

2x + 7x - 4 + 85 = 180

9x - 4 + 85 = 180

9x + 81 = 180

9x = 99

x = 11

Now that you have the value of x, solve for m∠CZB.

m∠CZB = 7x - 4

m∠CZB = 7(11) - 4

m∠CZB = 77 - 4

m∠CZB = 73

Answer:

Step-by-step explanation:

Let larger number be x

Let smaller number be y

[tex]x = 5 + y[/tex]---> equation (i)

[tex]y = \frac{1}{2} x[/tex]

[tex]x = 2y[/tex]-----> equation (ii)

Equate equation (i) and (ii),

[tex]5 + y = 2y[/tex]

Move variable to L.H.S and change its sign:

Similarly, Move constant to R.H.S and change its sign

[tex]y - 2y = - 5[/tex]

[tex] - y = - 5[/tex]

The difference sign (-) will be cancelled on both sides

[tex]y = 5[/tex]

Putting the value of y in equation (ii) in order to find the value of X ( larger number)

[tex]x = 2y[/tex]

Plug the value of y

[tex] = 2 \times 5[/tex]

Calculate the product

[tex] = 10[/tex]

Hence,

Smaller number = 5

Larger number = 10

Hope this helps..

Best regards!!

Answer:

10 and 5

Step-by-step explanation:

Let the first number be x.

Let the second number be y.

x = 5 + y

y = 1/2x

Plug y as 1/2x in the first equation.

x = 5 + (1/2x)

Solve for x.

Subtract 1/2x on both sides.

x - 1/2x = 5 + 1/2x - 1/2x

1/2x = 5

Multiply both sides by 2.

2(1/2x) = 2(5)

x = 10

Plug x as 10 in the second equation.

y = 1/2(10)

Solve for y.

y = 5

x = 10

y = 5

The two numbers are 10 and 5.

10 is the larger number.

5 is the smaller number.

Answer:

800 artículos.

Step-by-step explanation:

Sea x = la cantidad de artículos vendidos

De la pregunta,

Precio de costo = 60 x + 4000

Venta (precio de venta) = 80x

También nos dieron ganancias como S12000

Para determinar la ganancia

Precio de venta: precio de costo = beneficio (cuando el precio de venta es más alto que el precio de costo)

Por lo tanto,

12,000 = 80x - (60x + 4000)

12,000 = 80x - 60x - 4000

Recolectando términos similares

12,000 + 4,000 = 80x - 60x

16,000 = 20x

x = 16,000 / 20

x = 800

Por lo tanto, la cantidad de artículos que se venderán si desea obtener una ganancia de S12,000 es de 800 artículos.

Answer:

The correct answer is:

Double-blind (b)

Step-by-step explanation:

A blind/blinded experiment is one in which information which may influence the participant or experimenter is withheld throughout the process of the experiment either by masking (giving false identity) or completely blinded, to avoid biases that may arise from such knowledge by the participant or experimenter.

Blinding is of three types: single-blind, double-blind and triple-blind experiements and this is named with respect to three categories involved in the experiment; participant, researcher or a third party, which may include: analysts, monitoring committees stakeholders etc. The blinding type is explained as follows

Blinding Type              participant       researcher           Third-party

single-blind                   blinded               unblinded           unblinded

double-blind                  blinded               blinded               unblinded

triple-blind                     blinded               blinded                blinded

In this example, the 200 headache sufferers (participants) and the Migrane testing service (researchers) do not know the contents of the bottles being administered, whereas the pharmaceutical company (third-party knows), hence it is a double-blinded experiment.

Complete Question

The options for the above question is  

a There is not sufficient evidence to warrant rejection of the claim.    

b  There is sufficient evidence to warrant rejection of the claim.

c There is sufficient evidence to support the claim.    

d There is not sufficient evidence to support the claim.

Answer:

Option A is correct

Step-by-step explanation:

From the question we are told that

     The  population mean is  [tex]\mu =[/tex]$47,500

     The sample size is [tex]n = 86[/tex]

      The sample  mean is  [tex]\= x =[/tex]$48,061

      The standard deviation is [tex]\sigma =[/tex]$2,351

       The  level of significance is  [tex]\alpha = 0.02[/tex]

The null hypothesis  is  

     [tex]H_o : \mu =[/tex]$47,500

 The  alternative hypothesis is

      [tex]H_a : \mu \ne[/tex] $47,500

The critical value of  [tex]\alpha[/tex] from the t-Distribution table is  [tex]Z_{\frac{\alpha }{2} } = 2.326[/tex]

Now the test statistics is mathematically evaluated as

       [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }[/tex]

      [tex]t = 2.21[/tex]

Now from the values  obtained we can see that

        [tex]Z_{\frac{\alpha }{2} } > t[/tex]

hence we fail to reject the null hypothesis

Hence there is not sufficient evidence to warrant rejection of the claim

Answer:

[tex]\boxed{Option \ A}[/tex]

Step-by-step explanation:

[tex]f(x) = 2*3^x[/tex]

y intercept is when x = 0

So, Putting x = 0 in the above function

=> f(0) = [tex]2*3^0[/tex]

=> f(0) = 2*1

=> f(0) = 2

So, y-intercept is (0,2)

Answer:

A

Step-by-step explanation:

f(x) = 2 × 3^x

Plug x as 0 to find y-intercept.

2 × 3⁰

2 × 1

= 2

Answer:

C ( 1,-2)

Step-by-step explanation:

We can plot the points and see what point is not in the shaded section

Answer:

Step-by-step explanation:

The class interval is simply the difference between the lower or upper class boundary or limit  of a class and the lower or upper class boundary or limit of the next class.

In this case for the class

$4 up to $7 18 and

$7 up to $10 36

The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7

Answer:

pay the 11 AM ticket

Step-by-step explanation:

Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).

However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.

Therefore, the best choice is to pay the 11 AM ticket.

Answer:

X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]

Step-by-step explanation:

4B = -2X - 2A

Dividing both sides by -2

=> -2B = X + A

Subtracting A to both sides

=> X = -2B-A

Now, Let's Solve:

=> X = [tex]-2\left[\begin{array}{ccc}0&2&-2\\5&0&3\end{array}\right] -\left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}-2*0&-2*2&-2*-2\\-2*5&-2*0&-2*3\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}0&-4&4\\10&0&6\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}0-(-2)&-4-3&4-1\\10-(-3)&0-0&6-4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]

Answer: The first number is 4 and the second is 5

Step-by-step explanation:

Let's say the first number is x and the second is y:

x+2y=14

2x+y=13

I'll use the linear combination method to solve this.

  2x+4y=28

-  2x+y=13

3y=15

y = 5

x = 4

Hope it helps <3

Answer:

y=1

x=12

Step-by-step explanation:

Let the first number be x

Let the first number be y

Given:

x+2y=14

2x+y=13

Substitution:

x=14-2y

Solution:

2x+y=13

14-2y+y=13

-2y+y=13-14

-y=-1

y=1

x=14-2y

x=14-2(1)

x=14-2

x=12

Proof:

1) x+2y=14

12+2(1)=14

12+2=14

14=14

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer

Answer:

B

Step-by-step explanation:

To solve this you do 80/100=.8

You than do .8×60= 48

Answer:

x ≥ 4

Step-by-step explanation:

Well to find the inequality we need to single out x,

4x - 1 ≥ 15

+1 to both sides

4x ≥ 16

Divide 4 by both sides

x ≥ 4

Thus,

x is greater than or equal to 4.

Hope this helps :)

Answer:

1. true - dilating figures does not change their angle measure

2. true - dilating figures does not change the orientation, so AD would still be on a horizontal line parallel to its current position

Answer:

adult=18$ and children=13$

Step-by-step explanation:

a= adult. and. c= children

first change the statement into linear equation

3a+4c=106

2a+3c=75

then it just solving for a and y

3a+4c=106. a= 75-3c.

2

3(75-3c)+ 4c=106. solve for c

2

c=13

then find c by substituting the value you got into a . you can you either 3a+4c=106

or 2a+3c=75 to find the answer but the value of a is the same.

2a+3c=75. c=13

2a+3(13)=75

2a=75 -39

2a= 36

a=18

Answer:

Adults Ticket = $18

Child's Ticket = $13

Step-by-step explanation:

Let A denote the price of an adult's ticket

Let C denote the price of a child's ticket

It is given that the three adults and four children must pay $106.

Mathematically,

[tex]3A + 4C = 106 \:\:\:\:\:\:\:\:\:\:\: eq. 1[/tex]

It is also given that the two adults and three children must pay $75.

Mathematically,

[tex]2A + 3C = 75 \\\\2A = 75 - 3C[/tex]

[tex]$ A = \frac{(75 - 3C)}{2} \:\:\:\:\:\:\: eq\:. 2 $[/tex]

Substitute eq. 2 into eq. 1

[tex]3A + 4C = 106[/tex]

[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]

Simplify,

[tex]$ \frac{3(75 - 3C)}{2} + 4C = 106 $[/tex]

[tex]$ \frac{225 - 9C}{2} + 4C = 106 $[/tex]

[tex]$ \frac{225 - 9C + 2(4C)}{2} = 106 $[/tex]

[tex]$ \frac{225 - 9C + 8C}{2} = 106 $[/tex]

[tex]$ 225 - 9C + 8C = 2(106) $[/tex]

[tex]$ 225 - C = 212 $[/tex]

[tex]C = 225 - 212[/tex]

[tex]C = \$13[/tex]

Substitute the value of C into eq. 2

[tex]$ A = \frac{75 - 3(13)}{2} $[/tex]

[tex]$ A = \frac{75 - 39}{2} $[/tex]

[tex]A = \$18[/tex]

Therefore, the price of the​ adult's ticket is $18 and the price of a​ child's ticket is $13

Answer:

(A) [tex]\text{The slope of OA is }\dfrac{4}{3}[/tex]

(C) It’s equation is 4x-3y=0.

Step-by-step explanation:

Point O is at (0,0)

Point A is at (3,4)

[tex]\text{Slope of OA}=\dfrac{4-0}{3-0} \\m=\dfrac{4}{3}[/tex]

The equation of a straight line is in the form: y=mx+b

The y-intercept of the line OA=0

Therefore, we have:

[tex]y=\dfrac{4}{3}x+0\\3y=4x+0\\$Subtract 3y from both sides$\\4x-3y=0[/tex]

The equation of the line is: 4x-3y=0

Answer:

19/70 of NASA shuttle missions were carried out by Discovery.

9/140 of NASA shuttle missions were carried out by Challenger.

17/70 of NASA shuttle missions were carried out by Endeavour.

Step-by-step explanation:

Adding the number of missions carried out by NASA gives us 140 in total.

Discovery's total amount of missions simplified is 19/70.

Challenger's total amount of missions is already in the simplest form.

Endeavour's total amount of missions simplified is 17/70.

Answer:

81/140

Step-by-step explanation:

Well to find the fraction we first need to total amount of NASA missions.

38 + 32 = 70

70 + 34 = 104

104 + 27 = 131

131 + 9 = 140

Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.

38 + 9 + 34 = 81

Now we can make the following fraction,

81/140

This is already in simplest form.

Thus,

the answer is 81/140.

Hope this helps :)

Answer: 6 hours

Step-by-step explanation:

Given, Tim and Jim are working on a school project together.

Tim takes 10 hours to complete the school project.

If Jim worked alone, it would take him 15 hours

Let t be the time they both take if they work together.

Then, [tex]\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}[/tex]

[tex]\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6[/tex]

So, it will take 6 hours to complete the school project together .

Answer:

The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.

Step-by-step explanation:

Vectorially speaking, let assume that ship A is located at the origin and the relative distance of ship B with regard to ship A at noon is:

[tex]\vec r_{B/A} = \vec r_{B} - \vec r_{A}[/tex]

Where [tex]\vec r_{A}[/tex] and [tex]\vec r_{B}[/tex] are the distances of ships A and B with respect to origin.

By supposing that both ships are travelling at constant speed. The equations of absolute position are described below:

[tex]\vec r_{A} = \left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]

[tex]\vec r_{B} = \left(170\,km\right)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]

Then,

[tex]\vec r_{B/A} = (170\,km)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j-\left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]

[tex]\vec r_{B/A} = \left[170\,km-\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]

The rate of change of the distance between the ship is constructed by deriving the previous expression:

[tex]\vec v_{B/A} = -\left(40\,\frac{km}{h} \right)\cdot i + \left(15\,\frac{km}{h} \right)\cdot j[/tex]

Its magnitude is determined by means of the Pythagorean Theorem:

[tex]\|\vec v_{B/A}\| = \sqrt{\left(-40\,\frac{km}{h} \right)^{2}+\left(15\,\frac{km}{h} \right)^{2}}[/tex]

[tex]\|\vec r_{B/A}\| \approx 42.720\,\frac{km}{h}[/tex]

The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.

Answer:

6 pads

Step-by-step explanation:

Take the amount of money and divide by the cost per pad

26/4 = 6 with 1 dollar left over

He can buy 6 pads

Answer:

(70-55)/4.5=y rounded down to the nearest whole number

Step-by-step explanation:

The first step is to take away the $55 from $70

70-55=15

Simba has $15 to spend on the yoga classes, to find the number of yoga classes she can attend, you divide 15 by the amount a yoga class costs, $4.50

15/4.50=3 1/3

Because she can not have 1/3 of a yoga class, she can attend 3 yoga classes in her budget.

Hope this helps, if you have any questions feel free to ask

Have a good day! :)

Answer:

The answer is

Step-by-step explanation:

(6)(-1)(-3)(10)(-2)

Multiply the terms in the bracket

That's

(6)(-1) = - 6

(-3)(10) = - 30

So we have

(-6)(-30)(-2)

= 180( - 2)

= - 360

Hope this helps you

Answer:

Sydney's age is 28

Step-by-step explanation:

Let Devaughn be D

And Sydney be S

D=S+8..... equation 1

D+S=64...... equation 2

Substitute equation 1 to equation 2

S+8+S=64

2S+8=64

2S=64-8

2S=56

S=56/2

S=28

Hope it helps

Good luck

Step-by-step explanation:

just substitute the value of g(X) and f(X)

Answer: what is the question to this?

Step-by-step explanation: thanks let me know okay

Answer:

(11/5) (a ratio)

Step-by-step explanation:

11 ounces to 5 ounces could be rewritten as

 11 oz.

---------- = (11/5) (a ratio)

 5 oz

Answer:

Step-by-step explanation:

According to SOH in SOH, CAH TOA;

SOH means  sin theta = opposite/hypotenuse = 2/3

This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.

According to Pythagoras theorem; hyp² = opp²+adj²

adj² = hyp² - opp²

adj² = 3² - 2²

adj² = 9 - 4

adj² = 5

adj = √5

Hence the adjacent side is √5.

From the trigonometry identity above;

cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5

Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)

sec theta = hyp/adj = 3/√5

From the above calculation, the following are possible:

cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5

The correct options are C and D

Answer:8

Step-by-step explanation:

You find the average which is adding them all together then dividing by how many numbers you added.

Answer:

the linear system has two valid solution.

Answer:one solution

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

Since 1/3x = 6,

x = 6 x 3

Thus, x = 18