What is the value of \dfrac{d}{dx}\left(\dfrac{2x+3}{3x^2-4}\right) dx d ​ ( 3x 2 −4 2x+3 ​ )start fraction, d, divided by, d, x, end fraction, (, start fraction, 2, x, plus, 3, divided by, 3, x, squared, minus, 4, end fraction, )at x=-1x=−1x, equals, minus, 1 ?

Answer:

The rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Step-by-step explanation:

In mathematical language, the slope m of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Plugging (x₁, y₁) ⇒ (-7, 5) and  (x₂, y₂) ⇒ (3, 9) into the slope equation

[tex]m=\frac{9-5}{3-(-7)}[/tex]

[tex]m=\frac{4}{10}[/tex]

[tex]m=\frac{2}{5}[/tex]

So, the rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Keywords: rate of change, slope, coordinates

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Answer:

six raised to the one twelfth power

Step-by-step explanation:

The cubed root of 6/the fourth root of 6 equals (6^1/3)/(6^1/4)

6^((1/3)-(1/4))

6^((4-3)/12)

6^1/12

The simplified form of the expression is six raised to the one twelfth power

Given the expression

According to indices, this expression can also be written as:

Using the law of indices;

[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]

Applying this expression will give:

[tex]=\dfrac{6^{1/3}}{6^{1/4}} \\= 6^{1/3-1/4}\\=6^{4-3/12}\\=6^{1/12}[/tex]

Hence the simplified form of the expression is six raised to the one twelfth power

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Answer:

Step-by-step explanation:

Annual interest rate is 2.75%. Hence, the monthly interest rate is [tex]\frac{2.75}{12}[/tex]

The amount will be compounded [tex](20\times12) = 240[/tex] times.

Every month they deposits $500.

In the first month that deposited $500 will be compounded 240 times.

It will be [tex]500\times [1 + \frac{2.75}{1200} ]^{240}[/tex]

In the second month $500 will be deposited again, this time it will be compounded 239 times.

It will give [tex]500\times [1 + \frac{2.75}{1200} ]^{239}[/tex]

Hence, the total after 20 years will be [tex]500\times [1 + \frac{2.75}{1200} ]^{240} + 500\times [1 + \frac{2.75}{1200} ]^{239} + ........+ 500\times [1 + \frac{2.75}{1200} ]^{1} = 160110.6741[/tex]

The account will have approximately $159,744.59 after 20 years.

To calculate the future value of the savings account after 20 years with a 2.75% annual interest rate compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Plugging in the values, we can calculate:

A = 500(1 + 0.0275/12)^(12*20)

A = 500(1.00229167)^(240)

A ≈ $159,744.59

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Answer: Here is the answer.

Step-by-step explanation:

The question is missing a tabular data. So, it is attached below.

Answer:

The total cost for the party is $74.50.

Step-by-step explanation:

Given:

Lanes rented at regular cost = 4

Cost of 1 lane rented  at regular cost = $9.75

Cost of 1 lane rented for members = $7.50

Cost of 1 shoe rental at regular cost(non members) = $3.95

Cost of 1 shoe rental for members = $2.95

Since, lanes are rented at regular cost, we use unit rate at regular cost

So, cost of 4 lanes rented = [tex]4\times 9.75= \$ 39[/tex]

Now, out of 10 people who rented shoes, 4 are members. So, the number of non-members is given as:

Non members who rented shoes = 10 - 4 = 6

So, 4 members and 6 nonmembers rented shoes.

So, cost of 6 non members renting shoes = [tex]6\times 3.95=\$ 23.70[/tex]

Cost of 4 members renting shoes = [tex]4\times 2.95=\$ 11.80[/tex]

Total cost for the party is the sum of all the costs. This gives,

= 39 + 11.80 + 23.70

= 50.80 + 23.70

= $74.50

Therefore, the total cost for the party is $74.50.

Answer:

Blend of Whole bean coffee used = 22.5 Ib

Blend of Half bean Coffee used = 2.5 lb

Correction in statement:

The problem statement is missing information. The proper statement is as follows:

Seattle Star blends whole bean coffee worth $3 per pound with half bean coffee worth $3.5 per pound to get 25 pounds of a coffee blend worth $3.05 per pound. How many pounds of each type of coffee does she use?

Step-by-step explanation:

Whole Bean Coffee = $3

Half Bean Coffee = $ 3.5

Amount of whole bean coffee in Pounds (lbs) = Y

Mixture amount of whole bean and half bean blend = 25 lbs

Amount of half bean coffee = 25-Y (lbs)

Total blended mixture = $3.05

Cost of mixture = Cost of whole bean coffee used + Cost of half bean coffee used

3.05 (25) = 3Y + 3.5 (25-Y)

76.25 = 3Y + 87.5 - 3.5 Y

76.25 - 87.5 = 3Y - 3.5Y

- 11.25 = - 0.5 Y

or

0.5 Y = 11.25

Y=[tex]\frac{11.25}{0.5}[/tex]

Y= 22.5 lb

Which is the amount of whole bean coffee.

Amount of half bean coffee = 25-Y = 25- 22.5 = 2.5 lb

So,

Blend of Whole bean coffee used = 22.5 lb

Blend of Half bean Coffee used = 2.5 lb

Answer:

C. $144,200

Step-by-step explanation:

We have been given that a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877.

To find the loan amount, we will use simple interest formula.

[tex]I=Prt[/tex], where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

One month will be equal to 1/12 year.

[tex]7.3\%=\frac{7.3}{100}=0.073[/tex]

Upon substituting our given values in simple interest formula, we will get:

[tex]877=P*0.073*\frac{1}{12}[/tex]

[tex]877*12=P*0.073*\frac{1}{12}*12[/tex]

[tex]10524=P*0.073[/tex]

[tex]P*0.073=10524[/tex]

[tex]\frac{P*0.073}{0.073}=\frac{10524}{0.073}[/tex]

[tex]P=144164.3835616438356[/tex]

Upon rounding to nearest hundred, we will get:

[tex]P\approx 144,200[/tex]

Therefore, the loan amount was $144,200 and option C is the correct choice.

Final answer:

To calculate the loan amount based on a monthly interest payment and an annual interest rate, convert the rate to monthly and divide the payment by this rate. For a monthly payment of $877 at 7.3% annual interest, the loan amount is approximately $144,200.

Explanation:

To determine the loan amount of an interest-only loan given a monthly interest payment and an annual interest rate, follow these steps:

In this case, the annual interest rate is 7.3%, so the monthly interest rate is 7.3% / 12 = 0.6083%. The monthly interest payment is $877. Therefore, the loan amount can be calculated as follows:

$877 / 0.6083% = $877 / 0.006083 = $144,200.46

When rounded to the nearest hundred, the loan amount is $144,200.

The correct answer is C. $144,200.

Given the total weight of the hot air balloon as 210 kg, the envelope weighting half of this, the weight of the basket, which is 3/5 of the envelope, is calculated to be 63 kg.

To determine the weight of the basket attached to a hot air balloon, we can use the information that the envelope weighs  [tex]\frac{1}{2}[/tex]  of the total weight of the balloon and that the basket weighs [tex]\frac{3}{5}[/tex] of the envelope's weight. If the total weight of the hot air balloon will be 210 kg, then the envelope weighs 105 kg (which is [tex]\frac{1}{2}[/tex] of 210 kg). The weight of the basket can then be calculated as:

Weight of the balloon = 210 kg

Weight of the envelope = 210 * (1/2) = 105 kg

Weight of the basket = 105 * (3/5) = 63 kg

Therefore, the weight of the basket is 63 kg.

Answer:

D

Step-by-step explanation:

Finding y int by substituting the points given (say y int is x)

(-9) = 4(-4) + x

(-9) = -16 + x

x = 7

With the y int, you can now write the equation

y = -4x + 7

The equation of the line will be y = –4x + 7 having a slope of –4 that passes through the point (4, –9). Option D is correct.

To find the equation of a line that has a slope of –4, and includes the point (4, –9), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plugging in our values, we get y - (-9) = -4(x - 4). Simplifying this, we have:

Subtract 9 from both sides to solve for y:

Thus, the correct equation is y = –4x + 7.

Hence, D. is the correct option.

Answer:

Dα/dt   = 0.079 degree/sec

Step-by-step explanation:

From problem statement, is easy to see, that if point A is ubicated at the top of the telescope,  the shoreline is directly below the woman ( point B), and the point where the boat is, which is at distance x from shoreline  is point C. These three point  shape a right triangle with angle α (the angle of the telescope).

So we have

tan α  =  x/250    

Differentiating both sides of the equation we get

D (tan α)/dt    =  ( 1/250)* Dx/dt

sec² α Dα/dt  =  ( 1/250)* Dx/dt  

we already know that    Dx/dt   = 20 feet/sec

sec² α Dα/dt  =  20/250   ⇒     sec² α Dα/dt  = 0.08  

Dα/dt   =  0.08 / sec² α

Then

tan α  =  20/250  = 0,08        α   = arctan 0.08      α  ≈ 5⁰

Dα/dt   =  0.08/ sec² α  

From tables we get    cos  5⁰  =  0.9961  then

1/ 0.9961  = 1.003

sec α  = 1.003      and     sec²  α   =   1.0078

Dα/dt   =  0.08/ sec² α    ⇒   Dα/dt   =  0.08/1.0078

Dα/dt   = 0.079 degree/sec

The change of position of the boat results in a change of the angle of the telescope, which can be calculated using related rates. With known factors such as the speed of the boat and its distance from shore, the rate of change of the telescope's angle can be found using the principles of trigonometry and calculus.

This question is about related rates in calculus.  Related rates describe the relationship between different rates of change that are connected to each other. In this case, the changing position of the boat creates a change in the angle of the telescope.

We know the woman is watching a boat that is approaching a shoreline directly below her at 20 feet per second, and we are asked to find the rate that the angle of the telescope is changing when the boat is 250 feet from shore. Here is a way of visualizing it:

Let D be the distance of the boat from the base of the cliff and θ the angle that the telescope makes with the horizontal. We are given that D(t) decreases at 20 feet per second and that when D(t) = 250, we want to know what is dθ/dt.

By using trigonometry, we can find a relationship between D and θ. Specifically, tan(θ) = 250/D, so by implicit differentiation, (sec^2(θ)) * dθ/dt = -250/D^2 * dD/dt. From the given data, dD/dt = -20 and D = 250, so substitute them into the equation and evaluate θ using the tan–1(1) to obtain dθ/dt.

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The price of each regular pizza is $8 and the price of each deluxe pizza is $10.

To find the price of each pizza, we need to set up a system of equations using the given information. Let's denote the price of a regular pizza as 'r' and the price of a deluxe pizza as 'd'. Using the first customer's order, we can write the equation: 7r + d = 74. Using the second customer's order, we can write the equation: 5r + d = 58. To solve this system of equations, we can subtract the second equation from the first equation to eliminate the 'd' variable: (7r + d) - (5r + d) = 74 - 58. Simplifying, we get 2r = 16, which gives us r = 8. Plugging this value back into the first equation, we find d = 10. Therefore, the price of each regular pizza is $8 and the price of each deluxe pizza is $10.

Answer:

[tex]p_v =2*P(Z>4.21) =2.55x10^{-5}[/tex]

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example[tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

D) Are statistically different.

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]  

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]  

Or equivalently:  

Null hypothesis: [tex]\mu_1 - \mu_2 = 0[/tex]  

Alternative hypothesis: [tex]\mu_1 -\mu_2\neq 0[/tex]  

Where [tex]\mu_1[/tex] and [tex]\mu_2[/tex] represent the percentages that we want to test on this case.

The statistic calculated is on this case was Z=4.21. Since we are conducting a two tailed test the p value can be founded on this way.

[tex]p_v =2*P(Z>4.21) =2.55x10^{-5}[/tex]

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example[tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

And the best option on this case would be:

 D) Are statistically different.

Answer:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

[tex]R=\frac{2n!}{m!*(2n-m)!}[/tex]

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of [tex]P_{case}=0.5^{2n}[/tex] so:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

For example, to toss 4 heads in 5 rounds:

[tex]P=\frac{10!}{4!*(10-4)!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205[/tex]

It is proportional because the relationship between gallons of gas and distance is constant and linear. The rate is 32 miles per gallon. You can also call 32 the slope of this linear relationship.

Answer:

The new crew and the experience crew working together can paint the apartment in 4 hours.

Step-by-step explanation:

Given:

Time taken by new crew of painters to paint an apartment = 12 hours

Time taken by experience crew of painters to paint an apartment = 6 hours

To find the time taken by them to  paint the apartment working together.

Solution:

Using unitary method to determine their 1 hour work.

In 12 hours the new crew can paint = 1 apartment

So,in 1 hours the new crew can paint = [tex]\frac{1}{12}[/tex] of the apartment

In 6 hours the experience crew can paint = 1 apartment

So,in 1 hour the experience crew can paint = [tex]\frac{1}{6}[/tex] of the apartment

Now, the new crew and the experience crew are working together.

So, in 1 hour, they can paint :

⇒ [tex]\frac{1}{12}+\frac{1}{6}[/tex]

Taking LCD = 12, we will add fraction.

⇒ [tex]\frac{1}{12}+\frac{2}{12}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Simplifying fraction we have:

⇒ [tex]\frac{1}{4}[/tex] of an apartment

Again using unitary method to determine the time taken by them working together to paint the whole apartment.

They can paint  [tex]\frac{1}{4}[/tex] of an apartment in 1 hour.

To paint 1 apartment they will take  = [tex]\frac{1}{\frac{1}{4}}=4[/tex] hours

Thus, the new crew and the experience crew working together can paint the apartment in 4 hours.

Answer:

15 students visited both museums.

Step-by-step explanation:

Operations With Sets

Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say

[tex]N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)[/tex]

where [tex]N(A\bigcup B)[/tex] is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and [tex]N(A\bigcap B)[/tex] is the number of elements in their intersection. If we wanted to know that last number, then we isolate it

[tex]N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)[/tex]

Let A= Students who visited the museum of natural history

B=Students who visited the natural air and space museum

We know [tex]N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so[/tex]

[tex]N(A\bigcap B)=18+22-25=15[/tex]

Answer: 15 students visited both museums.

Note: We are assuming no students didn't visit at least one museum

The set theory in Mathematics implies that 15 out of the 25 students must have visited both the Museum of Natural History and Natural Air and Space Museum, since these students are counted twice when you add the students who visited each museum separately.

The problem asked is: When 25 students went to Washington DC, 18 of them visited the Museum of Natural History and 22 visited the Natural Air and Space Museum. How many students visited both museums?

To answer this, we need to understand the concept of the set theory in Mathematics. It helps us know the total number of students who visited both museums: we subtract the total number of students from the sum of students who visited each museum separately.

So, if we add those who visited the Museum of Natural History (18 students) and those who went to the Natural Air and Space Museum (22 students), we get 40. But we know there were only 25 students in total, implying that 15 students must have visited both museums since these students are counted twice in our sum. Therefore, 15 students visited both museums.

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Tan(Angle) = Opposite leg / Adjacent leg

Tan(A) = 5/7

A = Arctan(5/7)

A = 35.54 degrees.

Answer:

A.  35.54

Step-by-step explanation:

To find the angle A in the diagram above, we will simply use angle formula, we will check and see which angle formula will be best fit to use.

The formulas are;

SOH CAH TOA

sin Ф  =  opposite /   hypotenuse

cos Ф  =  adjacent / hypotenuse

tan Ф   =  opposite / adjacent

Looking at the figure given, since we are to find angle A, then our adjacent is 7 and the opposite is 5.

since we are given both opposite and adjacent, then the best formula to use for this is  tan Ф

tan Ф  =  opposite / adjacent

opposite =  5  and adjacent =7

we will go ahead and insert our values

tan A   =   5/7

tan A    = 0.71429

To get the value of tan A, we will simply take the [tex]tan^{-1}[/tex]  of both-side

[tex]tan^{-1}[/tex]   tan A  =   [tex]tan^{-1}[/tex]  0.71429

                A    =  35.54

Therefore angle A is 35.54

Answer:

Remainder would be [tex]5x^2+21[/tex]

Step-by-step explanation:

Given,

Dividend = [tex]x^5+x^4+x^3+x^2+x[/tex]

Divisor = [tex]x^3-4x[/tex]

Using long division ( shown below ),

We get,

[tex]\frac{x^5+x^4+x^3+x^2+x}{x^3-4x}=x^2+x+5+\frac{5x^2+21}{x^3-4x}[/tex]

Therefore,

Remainder would be [tex]5x^2+21[/tex]

the answer of this question is 603.2yd2

Answer:Area of the shaded region is 603.2 yards^2

Step-by-step explanation:

The diagram contains two circles. The smaller circle has a radius of 8 yards.

The bigger circle has a radius of 16 yards.

The area of a circle is expressed as

Area of circle = πr^2

Where

r = radius of circle

π is a constant whose value is 3.142

The area of the smaller circle would be

3.142 × 8^2 = 201.088 yards^2

The area of the bigger circle would be

3.14 × 16^2 = 804.352 yards^2

Area of the shaded region would be area of the bigger circle - area of the smaller circle. It becomes

804.352 - 201.088 = 603.2 yards^2

Answer:

The answer to your question is

a) Poster             width = 3 in

                            lenght = 9 in

b) banner

                           width = 2 in

                           lenght = 10 in

Step-by-step explanation:

a) For the poster

   width = x

   lenght = 3x

Perimeter of a rectangle = 2base + 2 height

                                         = 2(x) + 2(3x) = 24

                                         2x + 6x = 24

                                         8x = 24

                                           x = 24/8

                                           x = 3

    width = 3 in

     lenght = 3(3) = 9 in

b) For the banner

    width = y

    lenght = 5y

Perimeter of a banner = 2 base + 2 height

                                        2 (y) + 2(5y) = 24

                                        2y + 10y = 24

                                        12y = 24

                                           y = 24/12

                                           y = 2

     width = 2 in

     lenght = 5(2) = 10 in

The problem can be solved by using a theorem from number theory stating that gcd(a, b) * lcm[a, b] = a * b. Applying this theorem with the given values leads us to solution where a = 210^2 and b = 210^2.

In this mathematics problem, we're given two positive integers, a and b, whose greatest common divisor (gcd) equals to 210, and the least common multiple (lcm) equals to 210^3.

It is a well-known theorem in number theory that for any two positive integers a and b, gcd(a, b) * lcm[a, b] = a * b. We can apply this theorem to our problem. Since we know the values for greatest common divisor and least common multiple, namely gcd = 210 and lcm = 210^3 = 210 * 210 * 210, we have:

210 * 210^3 = a * b

This can be simplified to a * b = 210^4. Since we're told that a < b, and both a and b must divide 210^4, the only possible values for a and b are a = 210^2 and b = 210^2, which respects the condition a < b.

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Answer:

  E.  1/2

Step-by-step explanation:

Divide by 2, then make use of the Pythagorean identity for sine and cosine.

  sin(x)^2 +cos(x)^2 = 2a

  1 = 2a . . . . . . . sin²+cos²=1

  1/2 = a

Answer:

Option E) is correct.

[tex]a=\frac{1}{2}[/tex]

Step-by-step explanation:

Given trignometric equation is [tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]

To find the value of "a" from the given equation:

[tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]

Taking common number "2" outside the equation of left hand side

[tex]2(sin^{2}x +cos^{2}x) = 4a[/tex]

[tex]sin^{2}x +cos^{2}x =\frac{4a}{2}[/tex]

[tex]sin^{2}x+cos^{2}x =2a[/tex]

( We know the trignometric formula  [tex]sin^{2}\theta +cos^{2}\theta=1[/tex] here

[tex]\theta=x[/tex]  )

Therefore  [tex](1) =2a[/tex]

[tex]\frac{1}{2} =a[/tex]

It can be written as

[tex]a=\frac{1}{2}[/tex]

Therefore  [tex]a=\frac{1}{2}[/tex]

Option E) is correct.

Answer:

B

Step-by-step explanation:

because, the closer the data points are to the x axis on a residual plot with no definite shape means that a linear model is appropriate for this data set

A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape. So, option B is correct.

A residual is a measure of how far away a point is vertically from the regression line.

It is the error between a predicted value and the observed actual value.

A residual plot is a graph that has data points that are all very close to the x-axis. It shows the residuals on the y axis and the independent variable on the x axis.

The goodness of fit of a linear model is depicted by the pattern of the graph of a residual plot. If each individual residual is independent of each other, they create a random pattern together.

When graphing the residual values you know if a linear model is an appropriate model for your data if the points in the residual plot are scattered.

A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape.

So, option B is correct.

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Answer:

(-2,-11)

Step-by-step explanation:

x = -2

y = -11

The cost of the bike for the given condition will be $230.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the cost of one bike is x while accessories for one bike is y.

As per the given,

x + y = 276

The cost of bike is 5 times more then accessories,

x = 5y

5y + y = 276

6y = 276

y = 46

Bike cost = 5(46) = $230

Hence "The bike will cost $230 in the specified condition".

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Answer:

Step-by-step explanation:

Here is an illustration of the problem:

             ----------------------------->|<------------------

            A                                  t                     J

Alex and Jo start from their separate homes and drive towards one another.  The t indicates the time at which they meet, which is the same time for both.  Filling in a d = rt table:

              d           =        r        x        t

Alex                              14                t

Jo                                   6                t

The formula for motion is d = rt, so that means that Alex's distance is 14t and Jo's distance is 6t.

                      14t                               6t

   ---------------------------------->|<------------------

   A                                       t                      J

The distance between them is 5 miles, so that means that Alex's distance plus Jo's distance equals 5 miles.  In equation form:

14t + 6t = 5 and

20t = 5 so

t = .25 hours or 15 minutes.

If they leave their homes at 3 and they meet 15 minutes later, then they meet at 3:15.

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

Answer:

Step-by-step explanation:

Total number of Pokemon cards that Tim has in his collection is 480

He arranges the cards in his album and each page of his album holds 12 cards.

The total number of pages in the album is 35. After he has filled his album completely, the total number of cards that the album would contain would be 35 × 12 = 420

Let x represent the number of Pokemon cards he has left. Therefore, the expression becomes

x + 420 = 480

x = 480 - 420 = 60

Answer:

The answer to your question is letter A

Step-by-step explanation:

Process

1.- Find two points of the line

 A ( -2, 0)

 B ( 0, 3)

2.- Find the slope

     [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

            [tex]m = \frac{3 - 0}{0 + 2}[/tex]

                   [tex]m = \frac{3}{2}[/tex]

3.- Find the equation of the line

            y - y1 = m(x - x1)

            y - 0 = [tex]\frac{3}{2} (x + 2)[/tex]

            y = [tex]\frac{3}{2} (x + 2)[/tex]

Simplify

            y = [tex]\frac{3}{2} x + 3[/tex]

Answer:

P(X1=1, X2=1) = 1/15

P(X1=1, X2=0) = 7/30

P(X1=0, X2=1) = 7/30

P(X1=0, X2=0) = 7/15

Step-by-step explanation:

Let Xi = 1 if the i-th white ball is selected. In this question the 3 white balls are marked 1,2 and 3.

We need to know the possible combination between X1 and X2 i.e. for the white ball 1 and 2 being chosen in the event.

We also need to note that the event is dependent which that after a ball is being chosen, it will not be put back hence affecting the probability of picking the next ball.

Consider all the possible combination between X1 and X2

a) both being chosen P(X1=1, X2=1)

= (3/10) x (2/9) = 1/15

Note that the first probability is the probability before any ball is being picked. The chances for ball white to be pick is 3/10 (3 white ball from the total 10 balls).

After 1 white ball being selected, that ball is not again out back into the urn making white ball 2 and total ball 9. Hence probability of picking another white ball is 2/9

b) only X1 chosen P(X1=1, X2=0)

= (3/10) x (7/9) = 7/30

After the white ball was picked, the probability of white not being pick again is the same as red being picked. Since there is still 7red balls and a total of 9 balls, the probability is 7/9

c) only X2 chosen P(X1=0, X2=1)

= (7/10) x (3/9) = 7/30

The white is not being picked first, making the probability of picking red is 7/10. Then the probability of white being picked is 3/9

d) both not chosen

P(X1=0, X2=0)

= (7/10) x (6/9) = 7/15

In other word only red being chosen. So the first probability is 7 red out of 10 balls (7/10), and the next red ball being picked next is 6/9