determine whether the system of linear equations has one solution, infinitely many solutions, or no solutions. Explain your reasoning. y=4x+6, 2y=8x+12

Answers

Answer 1

Answer:

Infinitely many solutions

Step-by-step explanation:

Since you already have y isolated in one equation, you can plug it in and use it in the other equation

2y = 8x + 12

2(4x + 6) = 8x + 12

8x + 12 = 8x + 12

Get the x's to one side

12 = 12

Meaning you have infinitely many solutions.

Try plugging in any x value you can think of and the left side will always equal the right side. so

x = 0 --> 8(0) + 12 = 8(0) + 12

12 =12

x = 1 --> 8(1) + 12 = 8(1) + 12

20 = 20

and so on.

I graphed it here for you and the 2 functions are on top of each other which means at every x value y = 4x + 6 is equal to 2y = 8x + 12

Determine Whether The System Of Linear Equations Has One Solution, Infinitely Many Solutions, Or No Solutions.

Related Questions

as an estimation 5 miles is 8km. convert 16km to miles

Answers

Answer:

if its 8 to 5 then 16 is 10

answer: 10 miles

Answer:

10 miles

Step-by-step explanation:

8 km = 5 miles

So, Let's use the unitary method

1 km = [tex]\frac{5}{8}[/tex] miles

Multiplying both sides by 16, we get

16 km = [tex]\frac{5}{8} * 16[/tex] miles

16 km = 5 × 2 miles

16 km = 10 miles

Find the y-intercept of the following equation. Simplify your answer.


y
=
–6
7
x
+
5
9


y-intercept =

Answers

Answer:

Y-intercept: 59

Step-by-step explanation:

Y=mx+b, in which b stands for y intercept

Answer:

59

Step-by-step explanation:

Question - Find the y-intercept of the following equation. Simplify your answer.

We write graphical equation as:

y = mx + b

where:

y: point on y axis

m: gradient/ slope (RISE/RUN)

x: point on x axis

b: y intercept (point where the line touches the y axis)

Now in:

y  =  –6 7  x  +  5 9

y-intercept = 59

Find the value of. (3° + 4 -¹) × 2²

Answers

Answer:

[tex]5[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

It is known that 60% of the students at a large university have a job and 40% do not have a job. If three of these students are randomly selected, what is the probability at least one does not have a job? (Hint: the compliment of this event is all three have jobs.)

Answers

Answer:

78.4% probability at least one does not have a job

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they have a job, or they do not have a job. The probability of a student having a job is independent of other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

60% of the students at a large university have a job

This means that [tex]p = 0.6[/tex]

Three of these students are randomly selected

This means that [tex]n = 3[/tex]

What is the probability at least one does not have a job?

Either all of them have a job, or at least one does not. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 3) + P(X = 3) = 1[/tex]

We want P(X < 3). Then

[tex]P(X < 3) = 1 - P(X = 3)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.6)^{3}.(0.4)^{0} = 0.216[/tex]

[tex]P(X < 3) = 1 - P(X = 3) = 1 - 0.216 = 0.784[/tex]

78.4% probability at least one does not have a job

Math question plz try your best

Answers

Answer:

[tex]\frac{13}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} +\bigg(\frac{1}{3}\div\frac{1}{6}\bigg)-\bigg(-\frac{1}{2}\bigg)\\=\frac{3}{4} + \bigg(\frac{1}{3}\times\frac{6}{1}\bigg)+\frac{1}{2}\\=\frac{3}{4} +2 + \frac{1}{2}\\=\frac{3}{4} +\frac{8}{4} + \frac{2}{4}\\=\frac{3+8+2}{4} \\=\frac{13}{4} \\= 3.25[/tex]

Calculate the exact value of

70/15 × 14/5

Answers

Answer:

14^2/15

Step-by-step explanation:

70/15 simplifies to 14/3

14/3 X 14/5

= 14^2/15

Direct Variation: If y = 9, when x = -3, find x when y = -27. a.9 b.27 c.-27 d,-9

Answers

Answer:

a. 9

Step-by-step explanation:

[tex]k = \frac{9}{-3} = -3\\y = -3x\\-27 = -3x\\\frac{-27}{-3} = \frac{-3x}{-3} \\9 = x[/tex]

Answer:

a. 9

Step-by-step explanation:

because the orginal number was 9 and the newer one is -27 we can determine that y was multiplied by -3 so you would apply the same rule to -3 or x and you would get a product of 9 because two negatives equals a postive

Given the translation T(-2, 5), translate the given ordered pairs: (2, 5) and (-1, 7)

Answers

Answer:

When we have a translation T(a, b) and we apply it to a ordered pair (x, y), the translated pair will be (x + a, y + b)

Here whe have the translation T(-2, 5)

a) if our pair is (2, 5) then:

T(-2, 5) applied to (2, 5) = (2 + (-2), 5 + 5) = (0, 10)

b) if our pair is (-1, 7)

T(-2, 5) applied to (-1, 7) = (-1 + (-2), 7 + 5) = (-3, 12)

The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?

Answers

You didn’t attach a picture with this

It should be B children

Bye giggity giggity gamers! nyah :3

find the lowest common multiple of 8 and 6

Answers

Answer:

24

Step-by-step explanation:

8x3

6x4

Answer:

24

Step-by-step explanation:

LCM is the Lowest Common Multiple

To find the LCM of 2 numbers, first list a few of the first multiples of each number:

8 = 8,16,24,32,40

6 = 6,12,18,24,30

Here, we notice that 24 is the first multiple that is common in both times tables. Thus, 24 is the LCM

hope this helps

Find the measure of the arc.

146°E

mFD =

Answers

Answer:

124

Step-by-step explanation:

A circle is a curve sketched out by a point moving in a plane. The measure of the arc mFD is 124°.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As we know that the angle made at the center of the circle is 360°. And it is mentioned that the measure of mFE is 146°, while mED is 90°. Therefore, the sum of all angles can be written as,

[tex]\angle FOE + \angle EOD + \angle FOD = 360^o\\\\146^o + 90^o + \angle FOD = 360^o\\\\236^o +\angle FOD =360^o\\\\\angle FOD = 124^o[/tex]

Thus, the measure of the arc mFD is 124°.

Learn more about Circle:

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XYZ is an isosceles triangle inscribed I a circle, center O. XY=XZ= 20 and YZ=18. Calculate to 3.s.f.
a) the altitude of ∆XYZ
b) the diameter of the circle

Answers

Answer: 17.9

Step-by-step explanation:

Using Heron's formula:

Area of a triangle is given by:

√s(s-a)(s-b)(s-c)

Where a, b and c ara sides of the triangle and

S = (a+b+c) / 2

In the question above sides are :

XY=XZ= 20 and YZ=18

S = (20 + 20 + 18) / 2 = 58/2 = 29

Area = √29(29-20)(29-20)(29-18)

Area = √29(9)(9)(11)

Area = √25839

Area = 160.74513

Altitude = height(h)

Area = 0.5 × base × height

Base = yz = 18

160.74513 = 0.5 × 18 × h

160.74513 = 9 × h

h = 160.74513 / 9

h = 17.9 (3 s.f)

The equation of the graphed line is..... x+......y=4 ANSWER FAST PLZZXZZ FILL IN THE BLANKS (DOTED LINE)

Answers

Answer:

x+2y=4

Hope this helped

The base of this solid crate has an area of 6 square meters. The height of the crate is 4 meters. What is the volume of the crate?

Answers

Answer: 24 m^3

Step-by-step explanation:

Given that you have a base with an area of 6 square meters, it has already calculated the product of length and width. In the Volume Formula Length x Width x Height, you're pretty much multiplying that given area by a height of 4, since you already have that length and width in the form of 6 square meters. The result you'll have is 24 Meters Cubed.

A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.

A. Find the original perimeter and area of the garden

B. Find the perimeter and area of the garden with a 20% increase in each dimension.

C. By what percent will the perimeter increase? By what percent will the area increase?

D. Explain why the area and perimeter will not increase by the same percentage.

Answers

Answer:

w=12 ft

l= 20 ft

A.

P= 2(12+20)= 64 ft

A= 12*20= 240 ft²

B.

P=2(12*1.2+20*1.2)= 76.8 ft

A= 12*1.2*20*1.2= 345.6 ft²

C.

(76.8-64)/64*100%= 20%

(345.6- 240)/240*100%= 44%

D.

perimeter increase is linear function of one dimension increase

area increase is function of 2 dimensions increase

The function f(x) = x + is used to complete this table.

A 2-column table with 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f of x with entries 1, three-halves, 2, five-halves.

Which statements are true of the given function? Check all that apply.

fStartFraction negative 1 Over 2 EndFraction = –2
f(0) = three-halves
f(1) = –1
f(2) = 1
f(4) = seven-halves

Answers

Answer:

b & e

Step-by-step explanation:

The statements that are true of the given function are f(0)=3/2 and f(4)=7/2. This can be obtained by finding the function and checking the values of given in the question.

Check which statements are true :

Given, f(-1/2)= -2

f(0)= 3/2

f(1)= -1

f(2)= 1

f(4)= 7/2

The function is of the form, f(x)= mx +b

where m is the slope of the line and b is the cutting point with the y axis.

For x=0, the value of the function is f(0)=3/2

b=3/2   and m=1/2

∴ The function is f(x) = (1/2)x + 3/2

f(-1/2) = (1/2)(-1/2) + 3/2 =5/4

f(0) = (1/2)(0) + 3/2 = 3/2

f(1) = (1/2)(1) + 3/2 = 2

f(2) = (1/2)(2) + 3/2 = 5/2

f(4) = (1/2)(4) + 3/2 = 7/2

Hence the statements that are true of the given function are f(0)=3/2 and f(4)=7/2.

Learn more about functions here:

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HELPPPPP PLZZZ
2) Tom can paint a fence in 12 hours. Huck can paint the same fence in 10 hours. How long would it take to put two coats of paint on the fence if Tom and Huck work together? Answer as an improper fraction, then round to 1 decimal place.

3) Kim and Josh can clean a house together in 3 hours. If it takes Kim 7 hours to clean the house by herself, how long would it take Josh to clean the house alone? Leave your answer in improper fraction form, then convert to a decimal.




4) Jack can mow the baseball grounds in 2 hours; Mike can mow the same grounds in 3 hours; and Chris can mow the grounds in 4 hours. How long will it take to mow the baseball grounds if Jack, Mike, and Chris work together?
Leave your answer in proper fraction form, then round to 1 decimal place.
Using your rounded answer, how many minutes would that be?


Answers

Answer:

1st answer

Step-by-step explanation:

Another way to say 2 coats is

to paint the fence twice

Also, that is the same as painting

2 identical fences

---------------

Tom's rate is:

+1%2F8+ = ( 1 fence ) / ( 8 hrs )

Huck's rate is:

+1%2F5+ = ( 1 fence ) / ( 5 hrs )

---------------------------

Let +t+ = the time in hrs for them

to paint 2 fences

+2%2Ft+ = ( 2 fences ) / ( t hrs )

---------------------------

+1%2F8+%2B+1%2F5+=+2%2Ft+

Multiply both sides by +40t+

+5t+%2B+8t+=+80+

+13t+=+80+

+t+=+6.154+

It will take them 6.154 hrs

2) They together will take 10.9 hrs or 120/11

3) josh will take 21/11 hrs or 1.9 hrs

4) Together they will take 36/13 or 2.8 hrs

Solutions to the above problem

2) Tom takes = 12 hrs

    Huck takes= 10hrs

We can aaply unitary method

together they will take= 1/12+1/10=2/t

11t=120;

t=120/11 or 10.9 hrs

3) Together kim and josh can clean the house together in = 3 hrs

   Kim takes = 7hrs

   Josh will take= 1/7+1/x=2/3

3x+21=14x

21=11x

x=21/11 or 1.9 hrs

4)  Jack makes baseball grounds in= 2 hrs

     Mike takes= 3 hrs

    Chris takes= 4 hrs

 Together they will take= 1/2+1/3+1/4=3/x

13x=36

x=36/13 or 2.8 hrs

To learn more about Unitary method refer to:

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Ariele is hiking down into the canyon. She starts at the rim and hikes down 55 feet in 234 minutes. If she continues at this rate, where will Ariel be in relation to the rim after 15 minutes?

Answers

Answer:

This means that she will be 16.35 ft away from the rim in 15 minutes at this current rate.

Step-by-step explanation:

What we are asked here is imply to state how long in terms of distance would be Arielle position after 15 minutes

Now, 55 ft will take her 234 minutes

x ft will take her 15 minutes

x * 234 = 55 * 15

234x = 3825

x = 3825/234

x = 16.35 ft

This means that she will be 16.35 ft away from the rim in 15 minutes at this current rate.

After 15 minutes, Ariele would be 3.5 feet away from the rim.

What is speed?

Speed is the ratio of distance travelled to total time taken. It is given by:

Speed = distance / time

Ariele is hiking down into the canyon. She starts at the rim and hikes down 55 feet in 234 minutes. Hence;

Ariele speed = 55 feet / 234 minutes

In 15 minutes, the distance covered is:

Distance = (55 feet / 234 minutes) * 15 minutes = 3.5 feet

After 15 minutes, Ariele would be 3.5 feet away from the rim.

Find out more on speed at: https://brainly.com/question/4931057

Nishchal was listening to a song. Shown above are the views of his player showing 'Time elapsed' and 'Time remaining' for the song in minutes and seconds. What is the total duration of the song?

Answers

Answer: T = time remaining + time elapsed.

Step-by-step explanation:

Time elapsed means the time that he has been listening to the song (the minutes passed since he hits the play button)

Time remaining is the time left to finish the song.

Then the total duration of the song will be:

T = time remaining + time elapsed.

"Time Elapsed" simply refers to the time which has been spent listening to the music track. The "time remaining" on the other hand is the time left on for the song to come to an end. Song duration is the addition of both.

How to calculate the total duration of the song

Please note that the information from the question required to give a well-rounded answer is incomplete. Hence the general answer.

To calculate the time duration of the song (which is the total length of the song in terms of time) the Time Elapsed must be added to the Time Remaining.

That is:

Total Duration = Time Elapsed + Time Remaining.

See the link below for more about Song Duration:

https://brainly.com/question/14701526


What is the measure of the angle formed by a side of the given angle and the given angle's bisector? 30° 52° 172° 171°30'

Answers

Answer:

30°=15° 52°=26° 172°=86° 171'30°=85.75°

Step-by-step explanation:

okay so re-reading over the question, and analyzing what the question wants us to answer, you will then realize that the way to get the answer is to divide x by 2.

our x examples, in this case, would be 30°,52°,172°, and 171'30°.

and that's how you find the answer to this type of question. :)))

Keep it 1000 someone who knows that they doing 20 points

Answers

Answer:

Box 1 is F and Box 2 is -62.1

Answer:

5/9( F -32) = -62.1

Step-by-step explanation:

5/9( F -32) = C

We have the Celsius temperature and want to find the Fahrenheit temperature

5/9( F -32) = -62.1

12e^5 divided 3e^3 simplified

Answers

Answer:

[tex]4 {e}^{2} [/tex]

Step-by-step explanation:

[tex] \frac{12 {e}^{5} }{3 {e}^{3} } \\ 12 \div 3 \times {e}^{5 - 3} \\ = 4 {e}^{2} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

find the value of trig function indicated, use Pythagorean theorem to find the third side if you need it. Part 4​

Answers

Answer:

[tex]\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}[/tex]

Step-by-step explanation:

A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)

According to the trigonometric properties:

[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]

[tex]cos(theta) = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan(theta) = \frac{opposite}{adjacent}[/tex]

[tex](adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}[/tex]

[tex](adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}[/tex]

[tex](opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}[/tex]

Use the above formulas with corresponding sides:

[tex]13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83[/tex]

[tex]14) sin(theta) = \frac{\sqrt{5^{2}-3^{2} } }{5} = \frac{4}{5} = 0.8[/tex]

[tex]15) sin(theta) = \frac{9}{\sqrt{(8\sqrt{7}) ^{2} + 9^{2} } } = 0.391[/tex]

[tex]16) tan(theta) = \frac{3}{4} = 0.75[/tex]

Hope this helps!

:)

How many combinations of 3 balloons can be chosen from 4 balloons?

Answers

Answer:  24

Step-by-step explanation:

You have 4 balloons to choose from.  

Once you have chosen a balloon, there are 3 remaining to choose from.  When you choose another balloon, there are only 2 remaining.

First pick   and    Second pick    and   Third pick

     4           x        3 remaining      x       2 remaining      =  24

Please help! Correct answer only!


Cooper and Alice made a list of 7 psychology experiments they want to try at home. Each experiment tackles one specific psychology topic. 5 of the experiments involve cats.


If Cooper and Alice randomly choose 4 experiments to try over the summer, what is the probability that all of them involve cats?


Write your answer as a decimal rounded to four decimal places.

Answers

Answer:

Probability = 0.2603

Step-by-step explanation:

Consider the steps below;

[tex]Probability of Experiment Involving Cats - 5 / 7,\\Probability That 4 Chosen Experiments Are All Involving Cats - ( 5 / 7 )^4,\\\\5 / 7 * 5 / 7 * 5 / 7 * 5 / 7 =\\\\Conclusion; Probability - 625 / 2401[/tex]

Solution; Probability = ( About ) 0.2603

PLEASE HELP!! QUICK. MULTIPLE CHOICE

Answers

Question 3 answer is C

Answer:

4 is a

Step-by-step explanation:

Let f(x) = -3x^2 + 6x. Find f(2).

Answers

Answer:

0

Step-by-step explanation:

Substitute x for 2

-3(2)^2 + 6(2)

Order of operations says that exponents are next, so square the 2

-3(4) + 6(2)

multiply

-12 + 12

add

0

Answer:

The correct answer is 0

Hope it helps

Step-by-step explanation:

F(x) is given

So to find f2 we substitute all the variables (x) with the number 2 so it becomes..

f(2)=

-3(2)^2 + 6(2)

= -3(4)+ 6(2)

= -12+12

= 0

Use the table of reciprocals to find the reciprocal of these numbers:
0.000 080 25
0.9596

Answers

Answer:

1000000/8025 = 40000/321 (simplified)

1000/9596

Step-by-step explanation:

Hi there,

There is an alternative way to do this....

First it is important to understand what a reciprocal is. The reciprocal of any number x is the number 1/x. The reciprocal of a number is also its multiplicative inverse, which means that the number times its reciprocal must equal 1. For a number such as 2, the reciprocal would be 1/2. For a fraction such as 2/5, the reciprocal would be 5/2.

Finding the reciprocal of a decimal can be done in a number of ways.

Change the decimal to a fraction first.

Ex. 0.25 is 25/100 and is equivalent to the fraction 1/4. Therefore Its reciprocal would be 4/1 or 4.

Keep the decimal and form the fraction 1/?? which can then be or converted to a decimal.

Ex. 0.75 The reciprocal is 1/0.75. Using a calculator, the decimal form can be found by performing the operation: 1 divided by 0.75. The decimal reciprocal in this case is a repeating decimal, 1.33333....

After finding a reciprocal of a number, perform a quick check by multiplying your original number and the reciprocal to determine that the product is 1:

(0.25)(4) = 1.00

(0.75)(1.33....) = 1 but it is easier to see for sure with repeating decimals if you use the fractions instead of the decimals.

(3/4)(4/3) = 12/12 = 1

Hope this helps, Mark as brainliest if liked it! thanks!

Reid's Hardware discounts all riding lawnmowers 6% to customers paying in cash. If Trey paid $1,278.75 in cash for a riding lawnmower, then what was the original price of the lawnmower?

Answers

Answer:

$ 1360.37

Step-by-step explanation:

Suppose we call the original price of the lawnmower x.

That means, to get a discount, the equation would be,

x * 1 -  x * 6% = 1278.75

= (94/100) * x = 1278.75

= (47/50) * x = 1278.75

x = 1278.75 * 47 / 50

= 1360.37

I need help ASAP I shall give brainlyist (idk how to spell)

Answers

Answer:

Step-by-step explanation:

Part A

[tex]V=\pi r^2h=\pi *2.5^2*7.5=147.26\\=147in^3\\[/tex]

Part B

[tex]r=\sqrt{\frac{V}{\pi h} } \\=\sqrt{\frac{75}{\pi *6} } \\=1.99\\=2in[/tex]

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12 + 3b 1 = 5 b Which thermodynamic process takes place at a constant temperature so that the internal energy of a system remains unchanged?A. the isovolumetric processB. the isobaric processC. the adiabatic processD. the isothermal process Let f(x) = ................. Find b+c. WILL GIVE BRAINLIEST TO GOOD EXPLANATION 2 PointsWhat was a major difference between social reformers and socialists in the18th and 19th centuries?O A. Socialists were more interested in drastic political and socialreorganizationO B. Social reformers were more interested in urging people to leaveurban centersC. Socialists were more influenced by wealthy and middle classcitizens' valuesD. Social reformers were more willing to engage in violence toachieve their goals. A number c minus 3.4 is less than 14. Write this word sentence as an inequality.An inequality is _____ Can you help me ? 70 points Any help would be great how many chromosomes does an elephant's egg cell have ? 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Qualitative, because numerical values, found by either measuring or counting, are used to describe the data. D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data. 2. What is the data set's level of measurement?A. Ratio, because the differences in the data can be meaningfully measured, and the data have a true zero point. B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zoro point. C. Nominal, because the data are categories or labels that cannot be ranked.D. Ordinal, because the data are categories or labels that can be ranked. 3. What is the probability of randomly selecting a diamond from a standard 52-card deck?The probability of selecting a diamond is 0.25. 4. Use the contingency table to complete parts a) through d) below. Event A Event B Event C 10 11Event D 3 4Event E 14 8A) Determine the probability of P(AIC). B) Determine the probability of P(CIA). C) Determine the probability of P(BE). 5. Use the contingency table to complete parts a) through d) below. Event A Event B Event C 10 11Event D 3 4Event E 14 8A) Determine the probability of P(CIA). B) Determine the probability of P(BE).C( Determine the probability of P(EB). Question 10 of 102 PointsWhich sentence is the best example of foreshadowing?A. The pharmacy called to let Jack know that his prescription wasready to be picked up.B. Jack saw the empty bottle of medicine and told himself toremember to refill his prescriptionC. Jack stopped at the pharmacy on his way home from work to pickup his prescriptionD. The pharmacy had Jack's prescription ready for him when he wentto pick it up Can someone please help me with this one?? 81. Find the pH of each mixture of acids. a. 0.115 M in HBr and 0.125 M in HCHO2 b. 0.150 M in HNO2 and 0.085 M in HNO3 c. 0.185 M in HCHO2 and 0.225 M in HC2H3O2 d. 0.050 M in acetic acid and 0.050 M in hydrocyanic acid Discuss any two of the socio-political changes that have taken place since 1945. When 106 g of water at a temperature of 21.4 C is mixed with 64.3 g of water at an unknown temperature, the final temperature of the resulting mixture is 46.8 C. What was the initial temperature of the second sample of water? (The specific heat capacity of liquid water is 4.184 J/g K.) A random sample of 48 was taken from a shipment of 10,080 light bulbs from Light Bulbs Express. Out of the 48 light bulbs, 5 were red. How many red bulbs would you expect in the entire shipment? ______________red bulbs (Round answer to the nearest whole number).A random sample of 62 was taken from another shipment of 15,500 from Light Bulbs R Us. There were 6 red bulbs in the sample. How many red bulbs would you expect in the entire shipment?_____________red bulbs (Round answer to the nearest whole number)Which company has the highest ratio of red bulbs in their shipment? Company ______ (Type either A or B)Company A = Light Bulbs ExpressCompany B = Light Bulbs R Us in each diagram the line BD bisects angle ABC. Find the measure of angle ABC What is the slope of a line perpendicular to the line whose equation is12x + 9y = 162. Fully reduce your answer.