You roll a 6-sided die two times.What is the probability of rolling a 6 and then rolling a number less than 2?Simplify your answer and write it as a fraction or whole numb

You Roll A 6-sided Die Two Times.What Is The Probability Of Rolling A 6 And Then Rolling A Number Less

Answers

Answer 1

We are asked to determine the probability of rolling a 6 and then rolling a number less than 2. To do that we will use the product rule probabilities since we want to find the probability of two independent events happening:

[tex]P(AandB)=P(A)P(B)[/tex]

Where:

[tex]\begin{gathered} A=\text{ rolling a 6} \\ B=\text{ rolling a number less than 2} \end{gathered}[/tex]

To determine the probability of rolling a 6 we need to have into account that there are 6 possible outcomes out of which only one is a 6. Therefore, the probability is:

[tex]P(A)=\frac{1}{6}[/tex]

To determine the probability of B we need to have into account that in a 6-sided die the numbers that are less than 2 are (1), this means that there is only one number less than 2 out of 6 possible numbers. Therefore, the probability is:

[tex]P(B)=\frac{1}{6}[/tex]

Now, we substitute in the product rule:

[tex]P(AandB)=(\frac{1}{6})(\frac{1}{6})[/tex]

Solving the product:

[tex]P(AandB)=\frac{1}{36}[/tex]

Therefore, the probability is 1/36.


Related Questions

Gourmet in Italy has a policy of automatically adding an 18% tip to a restaurant bill. How much would a restaurant bill be if it had a tip of $3.20 added to it?

Answers

The restaurant charger a tip of the 18% of the bill

So the total amount charged is the money spent + 18%

The bill had a tip of $3.20 this is the 18% of the amount spent.

Using cross multiplication you can calculate the amount of the bill as:

Bill without tip: 100%

Tip: 18%

Total amount (bill + tip): 118%

If 18% ____ $3.20

Then 118%___$x

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How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have

Answers

The number of solutions that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.

How to illustrate the information?

It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation given is illustrated as:

-14 + 6b + 7 - 2b = 1 + 5b

Collect like terms

-8 + 6b - 2b = 5b

b = -8

Therefore, it has only one solution.

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How could you correctly rewrite the equation 6(11-3) = 4(7 + 5) using the distributive property?
66-3 = 28 +35

Answers

Answer:

The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c );

Step-by-step explanation:

6(11-3) = 4(7 + 5)

(6×11)-(6×3)=(4×7)+(4×5)

66 - 18 = 28 + 20

A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.

Answers

[tex]\begin{gathered} P(A)=Probability\text{ that the student got a B} \\ P(B)=\text{Probability that the student are male} \\ P(A|B)=\text{Probability that the student got a B given they are male} \\ P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(A\cap B)=Probability\text{ that the student got a B and be male} \\ \text{From the table} \\ P(A\cap B)=\frac{19}{75} \\ P(B)=\frac{43}{75} \\ \\ P(A|B)=\frac{\frac{19}{75}}{\frac{43}{75}} \\ P(A|B)=\frac{19}{43}=0.442=44.2\text{ \%} \\ \text{The probability is }\frac{19}{43}=0.442=44.2\text{ \%} \end{gathered}[/tex]

The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°

Answers

Answer:

x=13

Step-by-step explanation:

We add all the numbers together, and all the variables

6x-78

We move all terms containing x to the left, and all other terms to the right

6x=78

x=78/6

which should equal 13

please quick I need this

Answers

Answer:

The remainder is [tex]4[/tex].

The quotient is [tex]3x^{2}+6x+1[/tex]

Step-by-step explanation:

Step 1: Do long division

To divide these expressions, we will have to make use of long division, which is shown in the picture.

Step 2: Identifying the remainder and quotient

The remainder is [tex]4[/tex].

The quotient is [tex]3x^{2}+6x+1[/tex]

A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)

Answers

The cost of DVD = $16.99

The list price of this DVD was $18.75

So, the discount =

[tex]18.75-16.99=1.76[/tex]

And the percent discount =

[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]

Rounding the answer to the nearest tenth

So, the answer will be : the percent discount = 9.4%

write an equivalent expression for (925x to the 3rd times y to the negative 4th times z to the second) 0

Answers

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1.

Ex:

[tex]x^{0} =1\\3643737737^{0} =1\\[/tex]

A baker has a bag with 20 cups of flour. The baker plans to use the flour to make 4 loaves of bread. Each loaf of
bread uses 3 cups of flour.
How many cups of flour will remain in the bag when the baker has finished making the bread?
Enter your answer in the space provided.

Answers

Answer: 8

Explanation:
4 x 3 is = 12
20 - 12 = 8

8 cups of flour will remain in the bag.

help
fast 20 point
please

Answers

Answer is 2

x * 2 = y

Answer:

A. 2

Step-by-step explanation:

Hope this helps

Find 98.6% of 343.7. Round to the nearest thousandth.

Answers

Percentage, a relative value indicating hundredth parts of any quantity.

98.6% of 343.7 is  in nearest thousandth 338.888

What is Percentage?

Percentage, a relative value indicating hundredth parts of any quantity.

We need to find 98.6% of 343.7.

Ninty eight point six percentage of three hundred forty three point seven.

Ninty eight point six percentage we need to convert into decimal number this can be achieved by dividing with 100.

98.6% =98.6/100

When ninty eight point six is divided by hundred we get zero point nine eight six.

=0.986

We need to find what is  98.6% of 343.7.

To find ninty eight point six percentage of three hundred forty three point seven. we are required to multiply the converted value of 98.6% with  three hundred forty three point seven.

Simply we need to multiply 0.986 with 343.7.

=0.986×343.7

=338.888

Hence 98.6% of 343.7 is 338.888

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Mr. Connor's physics class has 105 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work
Academic Year male female
Junior 8 11
senior 19 19
freshman 9 12
sophomore 19 8

Answers

The probability that he selects a Mel given that he chooses randomly from only the Juniors is 0.076.

How to calculate the probability?

It should be noted that the probability is the likelihood that something will happen. The table shows that Connor's physics class has 105 students, classified by academic year and gender.

The probability will be:

Fraction of males that are junior / Fraction if Junior

= 8/105 / 19/105

= 0.076

The probability is 0.076.

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What is the probability that he selects a Mel given that he chooses randomly from only the Juniors.

The circumference of a circle is 12.56 miles. What is the circle's diameter?

Answers

Answer:

d= 4 miles

Step-by-step explanation:

C=2πr

d=2r

d=C

π=12.56

π≈3.99797mi

Help with this problem

Answers

I₃ indifference curve represents the highest utility

What is an indifference curve?

An indifference curve is a graph that illustrates numerous pairings of two goods or commodities that leave the customer equally well off or satisfied—hence indifferent—when it comes to owning any pairing of the two items that is represented along the curve.

A consumer must give up more of one good in order to buy more of another, hence an indifference curve will always have a negative slope.

The given indifference map is a fast food meals per week vs movie tickets per week graph .

In which I₃ yields more than I₂ .

And I₂ yields more than I₁.

Thus,  I₃ curve represents the highest utility.

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the phone sells Jan a bicycle for $175 and a helmet for $17. The total cost for Jin is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin

Answers

Jin

The bicycle selling price was : $175

The helmet was for : $17

Jin total cost was 160% of what Stefan spent originally to buy the two items

This means ; 160/100 * x = { 175+17} -----where x is the original amount stefan spent to buy the two items

1.6 x = 192

x = 192 /1.6

x=120

Stefan originally spent $120

The money he made after the sell is: $192-$120 =$72

Answer

a) $120

b) $72

3. Compute the derivatives of the following functions. Do not simplify.
a) f(x)=tanx/e^3
b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)

Answers

Answer:

A im sure

Example

hope itz helpppp

f(x)=x^2+6x+7
f(x+h)=?
f(x+h)-f(x)=?
f(x+h)-f(x)/h=?

Answers

The values are;

f (x + h) = x² + 2xh + h² + 6x + 6h + 7

f (x + h) - f (x) = h² + 2xh + 6h

f (x + h) - f (x) / h = h + 2x + 6

What is substitution method?

Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The value of the function is;

f (x) = x² + 6x + 7

Now, Find the given values of f (x + h) , f (x + h) - f (x) and f (x + h) - f (x) / h by substitution method.

The value of the function is;

f (x) = x² + 6x + 7

Substitute x = x + h;

The value of the function is;

f (x + h) = (x + h)² + 6(x + h) + 7

           = x² + 2xh + h² + 6x + 6h + 7

           

Thus, The value of f (x + h) =  x² + 2xh + h² + 6x + 6h + 7.

Now,

f (x + h) - f (x) = (x² + 2xh + h² + 6x + 6h + 7) - (x² + 6x + 7)

                   = x² + 2xh + h² + 6x + 6h + 7 - x² - 6x - 7

                   = h² + 2xh + 6h

Thus, The value of f (x + h) - f (x) = h² + 2xh + 6h.

Now,

f (x + h) - f (x) / h =  h² + 2xh + 6h / h

                         = h (h + 2x + 6) / h

                         = h + 2x + 6

Thus, The value of f (x + h) - f (x) / h =  h + 2x + 6.

Therefore, The values are;

f (x + h) = x² + 2xh + h² + 6x + 6h + 7

f (x + h) - f (x) = h² + 2xh + 6h

f (x + h) - f (x) / h = h + 2x + 6

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The measures of the angles of a triangle are shown in the figure below. Solve
for x.
62⁰
82⁰
(x+12)

Answers

Answer: 24

Step-by-step explanation:

The angles of a triangle add to 180 degrees, so:

[tex]62+82+x+12=180\\\\156+x=180\\\\x=24[/tex]

What can be concluded from the statement ∠1+∠2m∠1+m∠2 = 90°?

Answers

When two angles add to 90º they are called complementary angles.

Then, if in the given statement the sum of angles 1 and 2 is equal to 90º, angles 1 angle 2 are complementary.

Answer: <1 and <2 and <1and <2 are complementary

Evaluate : limx→ tan2-sin2x x3

Answers

Given:

[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]

Solve:

[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]

Use l'hopital's rule:

[tex]\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}[/tex]

Simplify:

[tex]\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}[/tex]

Apply the constant multiple rule:

[tex]\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}[/tex][tex]\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}[/tex]

Similary :

[tex]\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}[/tex]

Sue used 4 ounces of dark chocolate chips for every 3 ounces of white chocolate chips if she uses 21 ounces of chips altogether how many ounces of dark chocolate chips did she use

Answers

Answer: 12 oz

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

If a 1/3 cup serving of cheese provides your fully daily value of calcium, then what percentage of your daily value of calcium is provided by 3/4 cup of the cheese?

Answers

If a 1/3 cup serving of cheese provides your full daily value of calcium, then 225% of your daily value of calcium is provided by ¾ cup of the cheese.

What are the ratios rules?

Between amounts of the same sort, the ratio should exist. The units used to compare two items should be comparable.

Terms should be in a meaningful sequence. If two ratios are comparable to one another like fractions,  they may be compared.

An easy ratio Is what?

When both sides are whole numbers and cannot be split by another

whole number, a ratio is considered to be in its simplest form.

Think about full number ratios, such as 6:4. The fraction 64 can be used to represent it.

What proportion of your daily intake of calcium is delivered by 3/4 cup of the food if a serving of cheese that is 1/3 cup in size delivers your whole daily value of calcium?

Daily value of calcium= (3/4)/(1/3) = 9/4

3/4 cup gives you 9/4 of your daily value of calcium.

We can convert fractions to percentages, we will get

9/4= 2.25

2.25*100=225%

Then the percentage of your daily value of calcium is 225%.

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I need help
There are 3 consecutive even integers with a sum of 72. Which equation can be used to find such integers?
x + 2 = 24
x + 2 = 12
x + 1 = 12
x + 1 = 24

Answers

The equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.

What is defined as the even integers?An even integer is one that is divisible by two, i.e. a multiple of two.For eg:- 2,4,6,... and −2,−4,−6,.... are divided by twoAs a result, the integers 2,4,6,... and −2,−4,−6,.... are all even integersThus, the integer of a form 2k is a even integer, in which k is an integer.

For the given data in question.

Let the first even integer be 'x'.

Second even integer will be 'x + 2'.

Thirst even integer will be 'x + 4'.

The sum is 72

x + x + 2 + x + 4 = 72

Simplifying;

3x + 6 = 72

Divide whole equation by 3.

x + 2 = 24

Thus, the equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.

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Use the point-slope formula to write an equation of the line that passes through (0,6) and (-2,0) write answer in slope intercept form

Answers

Equation using slope intercept form is 3y = x + 18

What is slope intercept form?

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.

Given Data

Points(0,6) and (-2,0)

The slope formula = [tex]\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }[/tex]

y₂= 0

y₁=6

x₂=-2

x₁=0

Slope = (-2-0)/(0-6)

Slope = -2/ -6

Slope = 1/3

Slope intercept form

y = mx + b

y = (1/3)x + 6

y = (x+18)/3

3y = x + 18

Equation using slope intercept form is 3y = x + 18

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Mary sold 192 worth of greeting cards if she received 25% Commission on all sales how much commission did she receive

Answers

25% of 192 = 192 * 25/100 = 192 * 0.25 = 48

Answer:

Mary received $48

Show all work for full credit.

Sketch the following curves, indicating all relative extreme points and inflection points. (10 pts)
a. y= x^3-6x^2+9x+3

Answers

For the given function, it is found that:

The extreme points are given by: (3,3) and (1,7).The inflection point is: (1,7).

What are the extreme points of a function?

The extreme points of a function happen at the values for x for which the first derivative is zero, that is:

y' = 0.

In this problem, the function is:

y = x³ - 6x² + 9x.

Hence the first derivative is:

3x² - 12x + 9.

The extreme values of x are:

3x² - 12x + 9 = 0.

3(x² - 4x + 3) = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0.

Then:

x - 3 = 0 -> x = 3.x - 1 = 0 -> x = 1.

The numeric value of the function at these points is:

x = 3: y = 3³ - 6(3)² + 9(3) + 3 = 3.x = 1: y = 1³ - 6(1)² + 9(1) + 3 = 7.

Hence the points are:

(3,3) and (1,7).

What are the inflection points of a function?

The extreme points of a function happen at the values for x for which the second derivative is zero, that is:

y'' = 0.

For this problem, the second derivative is given by:

y'' = 6x - 12.

Hence the x-coordinate of the inflection point is:

6x - 12 = 0

6x = 12

x = 2.

The numeric value at x = 2 is:

2³ - 6(2)² + 9(2) + 3 = 5.

Then the inflection point is:

(2,5).

The graph with these points labeled is given at the end of the answer.

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Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 28 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90​% confidence interval with a margin of error equal to ​2% to estimate this proportion.

Part 1
The additional number of patients that need to be sampled is
​(Round up to the nearest​ integer.)

Answers

174 more patients need to have their samples taken than were originally anticipated. This is further explained below.

What is a Marginal error?

Generally, the equation for the margin of error is mathematically given as

[tex]{Margin\ of \ error } & \ amp;=Z_{o \text { it }} \text { at } 5 \% \text { lo.s } \times S E(p)[/tex]

Where

Z is the distributionSE is the standard deviation

Given that the margin of error should be 7%, or 0.07, the total number of extra patients is denoted by n.

sample proportion  = 11/20 = 0.55

q =0.45

Margin of error = Zo at 5% lo.s * S E(p)

To solve for the 0.07amp

[tex]\\\\0.07 =1.96 \times \sqrt{\frac{p q}{n}}[/tex]

[tex]\\\\&0.07=1.96 \sqrt{\frac{0.55 \times 0.45}{20+n}} \\\\0.07 =\frac{0.97508}{\sqrt{20+n}} \\\\\sqrt{20+n} =\frac{0.97508}{0.07} \\\\\end{aligned}[/tex]

20+n =194.04

n =174.04

n=174

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What is the answer to m

Answers

the sum of the internal angles of a quadrilateral is 360, therefore:

[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \text{and} \\ m\angle A+m\angle C=180 \\ m\angle B+m\angle D=180 \end{gathered}[/tex]

so

[tex]\begin{gathered} a+5+a-25=180 \\ 2a-20=180 \\ 2a-20+20=180+20 \\ 2a=200 \\ \frac{2a}{2}=\frac{200}{2} \\ a=100 \end{gathered}[/tex]

mm

mm


There are 500 fish in a pond, to 1sf. What is the least possible number of fish that could be taken from
the pond so that there are 400 fish in the pond to 1sf

Answers

Answer:

one

Step-by-step explanation:

The least number of fish COULD be 450  ....this would be 500 to 1 S.F.

    if you take ONE fish away there are then 449 which would be 400 to 1 S.F

Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2

Answers

The formula in getting the area of the circle is:

[tex]A=\pi r^2[/tex]

where r = the radius of the circle and the value of π = 3.14

In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14

[tex]A=(3.14)(4mm)^2[/tex]

Then, simplify.

[tex]\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}[/tex]

Therefore, the area of the circle is 50.24 mm². (Option D)

Circle area

We have π = 3.14 and the radius is 4 mm. Therefore we apply the following formula:

A = π * r²

Replacing values in the equation.

A = 3.14 * (4 mm)²

We calculate potentiation.

A = 3.14 * 16 mm²

We multiply

A = 50.24 mm²

Answer: The circle area is 50.24 mm^2 (option D)✅ .

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A rocket toy moves straight upward, starting from rest with an acceleration of 4 m/s2. It runs out of fuel at the end of 10 s and continues to coast upward, reaching a maximum height before falling back to eartha. Find the rockets velocity and position at the end 10 sB. Find the velocity before the rocket crashes on the groundC. Find the time flight of rocke what are the advantages and disadvantages of the medicine bag? HELPPPPPPPPPP URGENTWhich of the following methods would NOT be used to prove that two triangles are congruent?A. Prove that the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle.B. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle.C. Prove all three sets of corresponding angles congruent.D. Prove all three sets of corresponding sides congruent. Mr. Darcy said in chapter 36 that some of Elizabeth's relatives were, "questionable." What does he mean by this? Is there any truth in what he says? Which tribe lived in multi-floor buildings made of clay? a.Cheyenne b.Hopi c.Chinookd.Creek parkway void co. issued 14-year bonds two years ago at a coupon rate of 8.7 percent. the bonds make semiannual payments. if these bonds currently sell for 111 percent of par value, what is the ytm? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) solve the equation of 3/4 - 1/5 Solve for f(-2).f(x) = 2x - 4f(-2) = [?] Hi, I was absent today in class and I really need help with question 8 I will be much appreciated if you show work and the step so I can be more understanding thank you! Can a revolution be a good thing The two points on the graph are given by the linear function f use the two points to find the equation that represents the linear function f. What is f(6)? In Common Sense, Paine claims that Great Britain has lost the authority and the ability to fairly and effectively govern America.What reasoning does Paine use to support this point? Question 3 options:A. "I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain, that the same connection is necessary towards her future happiness, and will always have the same effect."B. "This new world hath been the asylum for the persecuted lovers of civil and religious liberty from every part of Europe."C. "To be always running three or four thousand miles with a tale or a petition, waiting four or five months for an answer, which when obtained requires five or six more to explain it in, will in a few years be looked upon as folly and childishnessthere was a time when it was proper, and there is a proper time for it to cease."D. "Her trade will always be a protection, and her barrenness of gold and silver secure her from invaders." Carlita had -$15 in her checking account. She earned $87.99 from her job and decided to pay her phone bill for $47.82. After paying her phone bill, how much money is left in her account? Responses how would i find acceleration? im really confused rn. i can solve it, i just cant remember the right equation. help write an equation of the line in slope intercept format (-3,3) (0,-1) what are the types of social welfare services What is the impulse of a car hitting another car if it's initial velocity was 50m/sand it's velocity after hitting it is 4.4m/s? The car weighs 2168kg.J=A PAP=mvf-mvi shirt sold at buyer for $7.00 each.buyer sells shirt for $10.50, what ishis gain? suppose marcy's medical machines operates in a perfectly competitive market and is producing its profit-maximizing level of output. suppose further that at this level of production its average total cost is $1500, average variable cost is $800, and its price is $1300. at this point in time, marcy should english is the unofficial language of business and the internet, as the number of people learning this language worldwide over the past few decades has increased dramatically. how is this different than other major languages in the world, such as arabic, spanish, or japanese?