a radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=15e^(-0,02t) where m(t) is measured in kilograms.
a. Find the mass at time t=3
b. How much of the mass remains after 20 days?

1. 20 for $1.56 = A. 7.8 cents each

2. $3.78 for 6 =B. 63 cents each

3. For one dollar =C. 40 cents each

4. 5 at $3.90  = D. 78 cents each

5.  for $1.58  = E. $1.05 each

1.   20 for $1.56

Since cost of 20 items = $1.56

So, cost of 1 item =    1.56/20                          

                            =$0.078

1 dollar = 100 cents

So, $0.078= 0.078 × 100

                 =7.8 cents.

2. $3.78 for 6

Since cost of 6 items = $3.78

So, cost of 1 item = 3.78/ 6

                             =$0.63

1 dollar = 100 cents

So, $0.63 = 0.63 × 100 =63 cents.

3. 2 1/2 for one dollar

Cost of 2 1/2 = 5/2 = $1

So, cost of 1 item = 1/5/2

                            = 2/5

1 dollar = 100 cents

So, $2/5 =2/5 × 100

              =40 cents.

4. 5 at $3.90

Since cost of 5 items = $3.90

So, cost of 1 item = 3.90/5

                             =$0.78

1 dollar = 100 cents

So, $0.78 = 0.78 × 100

                =78 cents.

5. 1 1/2 for $1.58

Cost of  1 1/2 = $1.58

So, cost of 1 item =  1.58/3/2

                            = 1.05

Thus,

1. 20 for $1.56 =A. 7.8 cents each

2. $3.78 for 6=B. 63 cents each

3.   or one dollar =C. 40 cents each

4. 5 at $3.90 = D. 78 cents each

5.  for $1.58 = E. $1.05 each

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The decision rule is reject H(0) if t>1.714, test statistic t is 7.157 and Yes, we can conclude that the correlation in the population is greater than zero.

In the given question,

A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86.

n=20, r = 0.86

The decision rule for α=0.05 significance level:

H(0): P ≤ 0

H(1): P > 0

Degree of freedom(df) = n-2

Degree of freedom(df) = 20-2

Degree of freedom(df) = 18

This is the right tailed test using the t table.

Critical Value: [tex]t_{\alpha /2}[/tex], df = [tex]t_{\alpha /2}[/tex] = 1.714

(a) The decision rule is reject H(0) if t>1.714.

(b) Test statistic is t

t= r√(n−2)/√(1–r^2)

t= 0.86*√(20 -2)/√(1-(0.86)^2)

t= 0.86*√18/√(1-0.7396)

t= 0.86*4.243/√0.2604

t= 3.65/0.51

t= 7.157

Test statistic = 7.157

(c)  We have to conclude that the correlation in the population is greater than zero.

Yes, we can conclude that the correlation in the population is greater than zero.

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Answer: 23

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

The rate of the slower car is 152 km/hr.

Given:

two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours.

Let x be the rate of slower car.

We have two cars heading towards each other. They start 340 km apart and meet up 2 hours later. This means that they are traveling:

340 / 2 = 170 km/hr towards each other.

If the two cars were traveling the same speed, they'd both be going:

170 / 2 = 85 km/hr

We know that one car is traveling 18 km/hr faster than the other car. One way we can account for this is to  ± 9 km/hr to the average speed:

85 ± 9 = 94 , 76 km/hr

rate of slower car x = 84 - 9 * 2

x = 76 * 2 km/hr

= 152 km/hr

Therefore The rate of the slower car is 152 km/hr.

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Full question:

two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours, what is the rate of the slower car?

Answer:

(a-b+c+d)(a-b-c-d) answer of the following questoin

The statements are insufficient to answer the question.

What is measurement?

Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.

So we are given 2 lists, x and y and we are given the

1.  The total number of measurements is 30. x(n) + y(n) = 30.

2. Largest measurement - Smallest Measurement = 25

But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.

We need to find the largest measurement of x and the smallest measurement of x for our answer.

1)The range for the 12 measurements in list y is 20.

Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT

2) List x consists of 18 measurements.

We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA

Hence, the statements are insufficient to answer the question.

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Answer:12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  (d)  -(√2)/2

Step-by-step explanation:

You want the exact value of the sine of an angle when its terminal side intersects the unit circle at (√2/2, -√2/2).

The coordinates of the point where the terminal side of angle θ intersects the unit circle are ...

  (cos(θ), sin(θ))

Comparing this to the given point, we find that ...

  sin(θ) = -√2/2

Peter's number is 27

Step-by-step explanation:

You would need to multiply -6 with 11 to get -66. 11+16=27 this 27-16=11 so 11×(-6)=-66.

In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

The strength of the association is measured by the sample correlation coefficient, or r. The statistical significance of correlations is also examined.

For describing straightforward links between data, correlations are helpful. Consider a dataset of campgrounds in a park in the mountains as an illustration. You're interested in finding out if the height of the campsite—how high up the mountain it is—and the summer's typical high temperature are related.

Hence, In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.

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Answer: r=4

Step-by-step explanation:

12/3 = 4

48/3 = 4

192/48 = 4

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.

Here,

For figure 1 slope field=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}[/tex]

For figure 2 slope field=

[tex]\frac{dy}{dx} = xy-3\\[/tex]

For figure 1 a solution passing through the point (0,-1)

therefore,

slope=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2[/tex]

so slope comes out to be negative

For figure 1 a solution passing through the point (-2,2)

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30[/tex]

so slope comes out to be negative

For the slope field in figure 2. a solution passing through the point (1.-3)

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6[/tex]

so slope comes out to be negative

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3[/tex]

so slope comes out to be negative.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

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The system of equations is equivalent to this system is 2x = 3y - 10

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given the equation as;

5x + 10 = 3(x+y)

x+7=3x+y

Solving the equation as;

5x + 10 = 3(x+y)

5x + 10 = 3x+ 3y

combine the like terms;

2x = 3y - 10

The system of equations is equivalent to this system is 2x = 3y - 10

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Answer:

The answer is 941/1000.

Step-by-step explanation:

The simplified decimal is 0.941 and the 1 is in the thousandth place.

Hope this helped!

Answer:

It will take the plane 11 mph to travel 850 miles

Answer:

35%

Step-by-step explanation:

Xavier downloaded 40 songs last week,

14 of them were jazz songs.

Therefore, [tex]\frac{14}{40}[/tex] of Xavier's downloads were jazz songs.

In order to convert it into a percentage, we need to multiply 100 to the fraction.

We get [tex]\frac{1400}{40}[/tex], which is equal to 35%.

I would appreciate it if you mark my answer as brainliest.

Since an adult movie ticket costs $8 and a kid movie ticket costs $6, the equation for the given condition is 8x+6y=40.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The cost of movie ticket for adult= $8

The cost of movie ticket for adult= $6

Total amount to spend= $40

Let x be the number of adult and y be the number of children,

8x+6y=40

The equation for the given condition is 8x+6y=40 as the cost of movie ticket for adult is $8 and for children, it is $6.

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The traditional division of a day into 24 hours of 60 minutes each, with each minute made up of 60 seconds.

A tool used to measure and indicate time is a clock, often known as a timepiece.

One of the earliest human creations, the clock satisfies the requirement to measure time intervals less than those found in natural units like the day, lunar month, and year.

Over the centuries, various physical mechanisms have been utilized to power devices.

A few clocks that predate the contemporary model and are based on natural movement include:

A sundial displays the location of a shadow on a flat surface to indicate the time. There are various duration timers; the hourglass is one well-known type. The two time-telling devices that may be the oldest are water clocks and sundials.

The development of led to a significant advancement.

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The probability that he will miss is 25%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The odds in favor of Michael Jordan making a free throw were 21:4.

Total number of throw is 21+4 = 25

The number of time he will miss is 4

So the probability that he will miss is 4/25 = 0.25

Hence, the probability that he will miss is 25%.

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99.7% of the students scored between (44.67 , 56.33) i.e.

between 44 and 56.

On Subtracting 1 from your sample size, we get

100 – 1 = 99.

On Subtracting confidence level from 1, and then divide by two.

(1 – .997) / 2 = 0.0015

Now, df = 99 and α = 0.0015

from the table at df = 99 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(100) = 2.8

Now, 2.262 × 2.8 = 6.33

So, the confidence interval be,

(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)

Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.

between 44 and 56.

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A) The maximum revenue is 450000$

B) The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each

C) When each set is taxed at ​$55​, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.

A)p(x)=300−(x/20​),

revenue R(x)=p*x

revenue R(x)=300x -(x2/20)

for maximum revenue dR/dx =0 ,

=>300-(2x/20)=0

=>x/10=300

=>x=3000

maximum revenue = R(3000)=300*3000 -(30002/20)

maximum revenue = R(3000)=450000$

B) profit =revenue -cost

profit P(x)=300x -(x2/20)-72000-60x

profit P(x)=240x -(x2/20)-72000

for maximum cost dP/dx =0

240 -(2x/20)=0

x=240*10

x=2400

p(2400)=300−(2400/20​)=180

profit P(2400)=240*2400 -(24002/20)-72000 =216000

The maximum profit is 216000$ when 2400 sets are manufactured and sold for 180$ each

c)

profit =revenue -cost -tax

profit P(x)=300x -(x2/20)-72000-60x-55x

profit P(x)=185x -(x2/20)-72000

for maximum cost dP/dx =0

185-(2x/20)=0

x=185*10

x=1850

p(1850)=300−(1850/20​)=207.5

profit P(1850)=185*1850 -(18502/20)-72000

profit P(1850)=99125$

When each set is taxed at ​$55​, the maximum profit is 99125$ when 1850 sets are manufactured and sold for 207.5$ each.

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Answer:

$36

Step-by-step explanation:

Each of the 6 people in Mandy's family orders 2 tacos. Each taco costs $3. What is the total cost of the tacos?

$3 * 2 * 6 = $36

Answer: rate of change = 2

Step-by-step explanation:

The required length and width of the square garden is 5ft.

Given that,
Regan is making a square garden in her backyard with an area of 25ft² length and width of the garden is to be determined.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
According to the question, l = w
Area of the garden = 25
l × w = 25
l × l = 25
l = 5

Thus, the required length and width of the square garden is 5ft.

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The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

What is a function?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable

solution:

The linear function:

  C(x) =  1.25x + 500

For revenue function:

  R(x) = 3.50x

R(50) = 3.50(50)

         = $175

Using the C(x) and revenue function we can find the number of slushies and profit.

Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

Hence the linear and revenue functions are C(x) =  1.25x + 500 and  R(x) = 3.50x

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Answer:

6ft

Step-by-step explanation:

3 divided by 1/2 = 6

After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

Given that,

We have to find what is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

We know that,

1 feet is equal to 12 inches.

So,

We can write as

11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches.

11f 7in+ 14f 6in +35.5in+ 30in + 6f 10in

11(12)+7in+14(12)+6+35.5+30+6(12)+10

132+7+168+6+35.5+30+72+10

460.5

Therefore, After solving the given expression that is 11 feet 7 inches plus 14 feet 6 inches plus 35.5 inches plus 30 inches plus 6 feet 10 inches is 460.5.

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The student's conclusion is not appropriate or no, because there were not enough measurements to use standard deviation.

Given:

suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise.

standard deviation:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

To find standard deviation :

σ =  x - μ / z

But here sample mean and proportion , z score not given so there are not enough measurements to use standard deviation.

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