(8th grade. 4.4 Practice A.)PLEASE HELP!! what's the answer to all the CIRCLED questions. 85 points!!!
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The first and last expressions are identified as a limit that exists.

'In Mathematics, a limit is defined as a value that a function approaches the output for the given input values.'

According to the given problem,

For expression 1,

     [tex]\lim_{n \to4}\frac{x^{2}-x-12 }{2-x}[/tex]

⇒ [tex]\lim_{n \to4} \frac{x^{2}-4x+3x-12 }{4-x}[/tex]

⇒ [tex]\lim_{n \to4}\frac{-x(4-x)-3(4-x)}{4-x}[/tex]

⇒ [tex]\lim_{n \to4}\frac{(4-x)(-x-3)}{4-x}[/tex]

⇒ [tex]\lim_{n \to4 }(-x-3)[/tex]

Now, we put the value of x as 4

⇒ - 4 - 3

= -7

Therefore, the limit exists.

For the last expression,

    [tex]\lim_{x \to 2} \frac{x^{2}+3x-10 }{x^{2} -4}[/tex]

⇒ [tex]\lim_{x \to 2} \frac{x^{2}+5x - 2x-10 }{(x+4)(x-4)}[/tex]

⇒ [tex]\lim_{x \to2} \frac{x(x+5) -2(x+5)}{(x+4)(x-4)}[/tex]

⇒ [tex]\lim_{n \to 2} \frac{(x+5)(x-2)}{(x+4)(x-4)}[/tex]

Now, putting the value of x = 2 in the expression,

⇒ (2+5)(2-2) / (2+4)(2-4)

⇒ 7*0 / 6*(-2)

= 0

Therefore, the limit exists.

For the other expressions, we cannot factorize the numerator or the denominator to cancel out the denominator because of which if we put the values of x directly into the denominator without cancelling it out, the denominator would be zero, which means infinity because zero in the denominator of a fraction means infinity or undefined or does not exist.

Hence, we can conclude that expressions 1 and 6 are limits that exist.

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Answer:

B i think it is

Step-by-step explanation:

Answer:

Its is B

Step-by-step explanation:

There are 24 snake. the ratio is 3 frogs fro every 4 snakes. 24 divided by 4 is 6. 3 x 6 is 18. 18 + 24 is 42.

Answer:

[tex]963.34\ \text{years}[/tex]

Step-by-step explanation:

[tex]t_{1/2}[/tex] = Half life of carbon = 5730 years

[tex]\dfrac{N}{N_0}[/tex] = Decay rate = [tex]89\%=\dfrac{89}{100}[/tex]

Duration of time passed is given by

[tex]t=t_{1/2}\dfrac{\ln\dfrac{N}{N_0}}{\ln\dfrac{1}{2}}\\\Rightarrow t=5730\times\dfrac{\ln\dfrac{89}{100}}{\ln\dfrac{1}{2}}\\\Rightarrow t=963.34\ \text{years}[/tex]

The scroll is [tex]963.34\ \text{years}[/tex] old.

Answer:

f⁻¹(x) = (x + 10)/2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 2x - 10

Step 2: Rewrite

Step 3: Find Inverse

Solve for the new y.

Answer:

[tex]let \: the \: {f}^{ - 1}(x) \: be \: m \\ m = \frac{1}{2x - 10} \\ m(2x - 10) = 1 \\ 2x - 10 = \frac{1}{m} \\ x = \frac{1}{2m} + 5 \\ therefore \\ {f}^{ - 1} (x) = \frac{1}{2x} + 5[/tex]

Answer:

0.7 inches/day

Step-by-step explanation:

There are 3 counties, but the only one we care about is Broward County (because it only asks for the rainfall there), so we can disregard the other two. Next, we need to find the average over 5 days, and we can find that by doing (3.5)/5 = 0.7

=======================================================

Explanation:

First we need to find the slope of this given line.

The two points on here are (0,-3) and (3,0)

Apply the slope formula

m = (y2-y1)/(x2 - x1)

m = (0-(-3))/(3-0)

m = (0+3)/(3-0)

m = 3/3

m = 1

The slope of the given line is 1. The negative reciprocal of this is -1, which is the perpendicular slope.

Side Note: Any two perpendicular lines always have their slope multiply to -1, as long as neither line is vertical.

Answer:

perpendicular lines have an inverse slope and place a negative sign on it too so our give line is as below  

Step-by-step explanation:

P1 = (0, -3)  in the form ( x1, y1)

P2 = (3 , 0 )  in the form (x2, y2)

m= slope  

m = y2-y1 / x2 - x1

m = 0-(-3) / 3 - 0

m = 3 / 3

m = 1

since our slope of the given line is 1 then a perpendicular line will have -1

every line perpendicular to the given line has a slope of -1

Answer:

Form W-4

Step-by-step explanation:

Got a 100 on the test :)

The correct form which does an employee fill out to establish tax withholding from a paycheck is,

⇒ Form W - 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

To find for beginning a new job, which form does an employee fill out to establish tax withholding from a paycheck.

We know that;

Form W-4, Employee's Withholding Certificate, is generally completed at the start of any new job.

This form tells your employer how much federal income tax withholding to keep from each paycheck.

Hence, The correct form which does an employee fill out to establish tax withholding from a paycheck is,

⇒ Form W - 4

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Answer:

2.5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

ab - 0.5b

a = 1

b = 5

Step 2: Evaluate

Answer:

Answer: B San Francisco

Step-by-step explanation:

It can be read that Geneva is 12°C colder than Nikki's hometown. It can be seen in the table that Geneva is at -3°C.

This means that Nikki's hometown is 12°C hotter than Geneva, thus:

Temperature of Nikki's hometown = -3°C + 12°C = 9°C.

The only city with a temperature of 9°C is San Francisco.

Answer: B San Francisco

Answer:

69.04

Step-by-step explanation:

Given that:

Mean (m) = 69.0

Standard deviation (s) = 2.8

Zscore = 0.2

Find the corresponding height (x) ;

Using the relation :

Zscore = (x - m) / s

0.2 = (x - 69.0) / 0.2

0.04 = x - 69.0

0.04 + 69.0 = x

69.04 = x

Hence, the height of a man with a Zscore of 0.2 is 69.04

The price of sunglasses is greater original price and 0.45 is tax amount.

A tax is a mandatory fee or financial charge that a government imposes on a person or a business in order to raise money for public projects like building the greatest infrastructure and services.

Taxes are required financial contributions imposed by a government body, whether local, regional, or federal, on people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

Given:

Original price of sunglasses = $10.

Price according to cashier= $10.45

So, the price of sunglasses is greater original price.

and, the difference both price

= 10.45 - 10

= 0.45 is tax amount.

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Answer:

200mg is in 5 ml. So how much is in 1 ml? 200÷5=40mg per ml. 300÷40=7.5ml

Answer:

The sum does not exist, but if you are in a senior math class, it could be - infinity.

Step-by-step explanation:

If the sum does not have an endpoint (and it looks like it does not), then the sum really does not exist.

Consider this question.

Does the sum stop at 0 as in

50 + 40 + 32  + 24 + 16  + 8 + 0

But why not - 8 or - 16 or ...

So it is not that the sum does not exit. It is that we do not know where that stop is. Depending on your grade level, you could answer - infinity, but I doubt that is the expected answer.

Answer:

150π in^2/min.

Step-by-step explanation:

Area of circle A = πD^2/4

where D is the diameter of the circle.

now, taking differentiation w.r.t. to time t we get

dA/dt = π/4 ×2D×dD/dt

given dD/dt = 5in/min

therefore, dA/dt =  π/4×2×5×(20×12)

=π/4×600

=150π in^2/min.

Answer:

600π in^2/min

To make 100 ml of 25% saline solution, Riley will need 50 ml = 12% saline mixture and 50 ml= 38% saline mixture.

Given,

We have 12% and 38% of saline mixtures.

We need to find the amount in ml from each saline mixture which would give us 100 ml of 25%.

What are the methods to solve a system of linear equations?

There are a number of methods but the most and easiest used method is the substitution method and the elimination method.

We can make two linear equations from the given statements.

Let x = amount from 12% saline mixture and y = amount from 38% saline mixture.

Now we need to make 100 ml of 25% saline.

so,

x + y = 100.

So we have two equations.

x + y = 100..............(1)

12% of x + 38% of y = 100 x 25%

0.12x + 0.38 = 25 ...............(2)

Using the substitution method we have,

x = 100 - y

Putting x = 100 - y in {2}

0.12 ( 100 - y ) + 0.38y

= 2512 - 0.12y + 0.38y

= 250.38y - 0.12y

= 25 - 120.26y = 13y

= 13 / 0.26y = 50.

Putting y = 50 in (1)

x + y = 100x

100 -50x = 50.

So Riley will need 50 ml = 12% saline mixture and 50ml = 38% saline mixture to make 100 ml of 25% saline solution.

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Answer:

yea its C

Step-by-step explanation:

he is right.

Answer:

c

Step-by-step explanation:

Answer:

58.25n+30p-2

Step-by-step explanation:

Answer: I got 233n + 120p - 8

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        4    

Step-by-step explanation:

Answer:

Think of a =1 and b=3

All three choices are false

Step-by-step explanation:

Answer:

Step-by-step explanation:

a is less than b in all the cases... if a or b were below zero... it might make a difference.. but b/c they are both positive.. the abs signs make no difference

all the answers are false

Answer: 63 cupcakes

Step-by-step explanation:

1. Find the amount it took to bake 3 cakes:

3*30=90 minutes

2. Subtract 90 minutes from total minutes(12 hours):

720 mins-90 mins=630 mins

3. Find how many cupcakes you can make in 630 mins:

630/10=63

Solved

Have a nice day :D  

Answer:

So, a + b = 3 + 3 = 6

Hence,

There will be 6 marbles in the bag, 3 red and 3 blue.

Step-by-step explanation:

In this question probabilities are not given which should be given in order to calculate the number of marbles in the bag.

So, let's assume the probability that both marbles are red = 0.5

And probability that both marbles are blue = 0.5

Total Probability = 1

Furthermore, Let's suppose the bag contains

a number of red marbles and b number of blue marbles.

This problem includes the concepts of combination.

So,

[tex]\frac{_{2} C^{a} }{_{2} C^{a+b} }[/tex] = 0.5      Equation 1

[tex]\frac{_{2} C^{b} }{_{2} C^{a+b} }[/tex] = 0.5      Equation 2

Dividing Equation 1 and equation 2  we will get

[tex]\frac{_{2} C^{a} }{_{2} C^{b} }[/tex] = 1

It means, we can write:

[tex]_{2} C^{a} = _{2}C^{b}[/tex]

Hence, we can conclude that:

a = b

Now, from equation 1, we can write:

[tex]\frac{_{2} C^{a} }{_{2} C^{2a} }[/tex] = 0.5

Breaking down the combinations, we will get:

[tex]\frac{\frac{a!}{2! (a-2)!} }{\frac{2a!}{2! (2a - 2)!} }[/tex] = 0.5

[tex]\frac{a ( a-1)}{2a (2a-1)} = \frac{1}{5}[/tex]

(a-1)5 = 4a - 2

5a - 5 = 4a - 2

5a -4a = 5-2

a = 3

As, we know, a = b

So, a + b = 3 + 3 = 6

Hence,

There will be 6 marbles in the bag, 3 red and 3 blue.

Answer: 9/11

Step-by-step explanation:

Answer:

9/11

Step-by-step explanation:

3/22 * 6/1= 18/22

18/22 divided by 2 = 9/11

Answer:

The equations are x=a and y=b.

The graph of x=a is a line parallel to y-axis and y=b is a line parallel to x-axis.

∴ the angle between them is 90o, i.e. they intersect.

So, the equations are consistent.

Now solving simultaneously, the solution is (a,b).

So, the point of intersection is (a,b).

Hence, option D is correct.

Answer:

The correct answer is 0.15

Step-by-step explanation:

According to the given scenario, the probability is as follows:

X[tex]\sim[/tex] Bin (n,p)

Here

n = 8

p = 0.20 or 20%

Now this is a binomial probability distribution

[tex]P(X) = ^nC_x \times p^x \tmes (1 - p)^{n-x}\\\\P(3) = ^8C_3 \tims 0.20^3 \times (1 - 0.20)^5[/tex]

= 0.15

Hence, the correct answer is 0.15

Answer: c. [tex]P(I \text{ or }\overline{H})[/tex]

Step-by-step explanation:

Notation to show "not an event E" : [tex]\overline{E}[/tex]

Given:  I = the event that a player in an infielder.

H = the event that a player is a great hitter.

= the event that a player is not a great hitter.

The correct symbol for the probability that a player is an infielder or is not a great hitter : [tex]P(I \text{ or }\overline{H})[/tex]

hence, the correct option is  c. [tex]P(I \text{ or }\overline{H})[/tex]

Answer:

In triangle ABC and triangle CDA

AB=CD(given)

BC=DA(given)

AC=AC(common)

Thus triangle ABC and triangle CDA are congruent by SSS rule

Answer:

Step-by-step explanation:

Given:

Three congruent sides, two given and one shared

Side-side-side postulate SSS

Answer:

A. 20

Step-by-step explanation:

The two functions are equal at the point where the line of both function intercept. At this point, equilibrium is achieved.

The number chairs demanded and the number of chairs supplied are equal at this point.

Both lines intersect at x = 20. This means 20 (in hundreds) chairs must be sold for equilibrium to be achieved.

Answer:

5.1

Step-by-step explanation: