A sample of a radioactive substance has an initial mass of 58.7 . This substance follows a continuous exponential decay model and has a half-life of 5 hours. (a)Let t be the time (in hours) since the start of the experiment, and let y be the amount of the substance at time t . Write a formula relating y to t. y=__ e^__(t) . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. b)How much will be present in 8 hours? Do not round any intermediate computations, and round your answer to the nearest tenth.

Step-by-step explanation:

The given sequences are;

2,7,12,17......

difference =5

by using formula,

we get,

tn=a+(n-1)d

tn= 2+(n-1)5

Therefore, tn is 5n-3 is required formula for this arithmetic sequences.

Hope it helps....

Answer:

x=½

y=5

Step-by-step explanation:

(8x+7y=39)2

16x+14y=78

4x-14y=-68 add the two equations

20x=10.

divide both sides by 20

x=½

8x+7y=39

4+7y=39

7y=39-4

7y=35

y=5

The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.

8x + 7y = 39

4x – 14y = –68

Multiply by 2

16x + 14y = 78

-14y + 14y = 0

4x + 16x = 20x

-68 + 78 = 10

20x = 10

x = 1 / 2

8(1 / 2) + 7y = 39

4 + 7y = 39

7y  = 35

y = 35 / 7

y = 5

learn more on system of equation here: https://brainly.com/question/3861421?referrer=searchResults

Answer:

21564 ÷ 2 = 10782

40565 ÷ 5 = 8113

6365 ÷ 8 = 795.625

1436 ÷ 7 = 205.142857143

Answer:

The height and the radius of the cylinder are 3.67 centimeters and 5.19 centimeters, respectively.

Step-by-step explanation:

The volume ([tex]V[/tex]) and the surface area ([tex]A_{s}[/tex]) of the cone, measured in cubic centimeters and square centimeters, respectively, are modelled after these formulas:

Volume

[tex]V = \frac{h\cdot r^{2}}{3}[/tex]

Surface area

[tex]A_{s} = \pi\cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]

Where:

[tex]h[/tex] - Height of the cylinder, measured in centimeters.

[tex]r[/tex] - Radius of the base of the cylinder, measured in centimeters.

The volume of the paper drinking cup is known and first and second derivatives of the surface area functions must be found to determine the critical values such that surface area is an absolute minimum. The height as a function of volume and radius of the cylinder is:

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

Now, the surface area function is expanded and simplified:

[tex]A_{s} = \pi\cdot \sqrt{\frac{3\cdot V}{h} }\cdot \sqrt{\frac{3\cdot V}{h}+ h^{2}}[/tex]

[tex]A_{s} = \pi\cdot \sqrt{\frac{9\cdot V^{2}}{h^{2}} + 3\cdot V\cdot h }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V} \cdot\sqrt{\frac{3\cdot V+ h^{3}}{h^{2}} }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V}\cdot \left(\frac{\sqrt{3\cdot V + h^{3}}}{h}\right)[/tex]

If [tex]V = 33\,cm^{3}[/tex], then:

[tex]A_{s} = 31.258\cdot \left(\frac{\sqrt{99+h^{3}}}{h} \right)[/tex]

The first and second derivatives of this function are require to determine the critical values that follow to a minimum amount of paper:

First derivative

[tex]A'_{s} = 31.258\cdot \left[\frac{\left(\frac{3\cdot h^{2}}{\sqrt{99+h^{2}}}\right)\cdot h - \sqrt{99+h^{3}} }{h^{2}}\right][/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{3\cdot h^{3}-99-h^{3}}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{2\cdot h^{3}-99}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left[2\cdot h\cdot (99+h^{2}})^{-0.5} -99\cdot h^{-2}\cdot (99+h^{2})^{-0.5}\right][/tex]

[tex]A'_{s} = 31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5}[/tex]

Second derivative

[tex]A''_{s} = 31.258\cdot \left[(2+198\cdot h^{-3})\cdot (99+h)^{-0.5}-0.5\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-1.5}\right][/tex]

Let equalize the first derivative to zero and solve the resultant expression:

[tex]31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5} = 0[/tex]

[tex]2\cdot h - 99 \cdot h^{-2} = 0[/tex]

[tex]2\cdot h^{3} - 99 = 0[/tex]

[tex]h= \sqrt[3]{\frac{99}{2} }[/tex]

[tex]h \approx 3.672\,cm[/tex]

Now, the second derivative is evaluated at the critical point:

[tex]A''_{s} = 31.258\cdot \{[2+198\cdot (3.672)^{-3}]\cdot (99+3.672)^{-0.5}-0.5\cdot [2\cdot (3.672) - 99\cdot (3.672)^{-2}]\cdot (99+3.672)^{-1.5}\}[/tex]

[tex]A''_{s} = 18.506[/tex]

According to the Second Derivative Test, this critical value leads to an absolute since its second derivative is positive.

The radius of the cylinder is: ([tex]V = 33\,cm^{3}[/tex] and [tex]h \approx 3.672\,cm[/tex])

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

[tex]r = \sqrt{\frac{3\cdot (33\,cm^{3})}{3.672\,cm} }[/tex]

[tex]r \approx 5.192\,cm[/tex]

The height and the radius of the cylinder are 3.672 centimeters and 5.192 centimeters, respectively.

Answer:

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

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference , thus

a₇ = a₁ + 6d

a₄ = a₁ + 3d

Given a₇ - 2a₄ = 1 , then

a₁ + 6d - 2(a₁ + 3d) = 1, that is

a₁ + 6d - 2a₁ - 6d = 1

- a₁ = 1 ( multiply both sides by - 1 )

a₁ = - 1

Given a₃ = 0 , then

a₁ + 2d = 0 , thus

- 1 + 2d = 0 ( add 1 to both sides )

2d = 1 ( divide both sides by 2 )

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

Answer:

2400

Step-by-step explanation:

You have to follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction).  Based off of this, you have to do the multiplication first, and then add.

263 × 24 - 164 × 24 + 24

6312 - 3936 + 24

2376 + 24

2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expression is given below.

⇒ 263 · 24 − 164 · 24 + 24

Simplify the expression, then the value of the expression is given as,

⇒ 263 · 24 − 164 · 24 + 24

⇒ 6312 − 3936 + 24

⇒ 6336 − 3936

⇒ 2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

More about the value of the expression link is given below.

https://brainly.com/question/23671908

#SPJ2

Answer:

Step-by-step explanation:

First you need to find the slope of the line that contains those 2 points.

[tex]m=\frac{0-8}{0-(-4)}=\frac{-8}{4}=-2[/tex]

So the slope is -2. Now we can pick one of those points and sub it into the point-slope formula to find the equation:

y - 0 = -2(x - 0) gives us an equation of

y = -2x

Answer:

[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]

Answer:

6 Inches

Step-by-step explanation:

First Photograph

Length:Width = 24:18

Second Photograph

Let the unknown width =x

Length:Width = 8:x

Since the proportions of the two photographs are the same

[tex]8:x=24:18\\\\\dfrac{8}{x}= \dfrac{24}{18}\\\\24x=8 \times 18\\\\x=(8 \times 18) \div 24\\\\x=6$ inches[/tex]

The width of the photograph is 6 inches.

Answer:

a. 0.48

b. 0.14

c. 0.47

Step-by-step explanation:

Data provided in the question

0 - 2        0.48

3 - 5        0.26

6 - 8        0.12

9- 11        0.09

12- 14       0.05

Based on the above information

a. The probability for fewer than three phobias is

= P( x < 3)

= 0.48

b.  The probability for more than eight phobias is

= P( x >8)

= 0.09 + 0.05  

= 0.14

c. Probability between 3 and 11 phobias is  

= P(3 < x < 11)

= 0.26 + 0.12  + 0.09

= 0.47

Answer:

The time spent studying is the response variable.

Step-by-step explanation:

The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable.  In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.

The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.

Answer:

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Step-by-step explanation:

We assume your function definition is ...

  [tex]g(x)=\left\{\begin{array}{ccc}-\dfrac{1}{2}x+5&\text{for}&x<6\\x-6&\text{for}&x\ge 6\end{array}\right.[/tex]

For each given value of x, determine which segment applies, then evaluate.

For x = -6 and for x = 0, the first segment applies:

  g(-6) = (-1/2)(-6) +5 = 3 +5 = 8

  g(0) = (-1/2)(0) +5 = 5

For x = 6 and x = 12, the second segment applies:

  g(6) = (6) -6 = 0

  g(12) = (12) -6 = 6

In summary, ...

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Answer:

  m less-than-or-equal-to 28

Step-by-step explanation:

Xander's charge for m miles will be (3 +1.50m). He wants this to be no more than $45, so ...

  3 +1.50m ≤ 45

  1.50m ≤ 42 . . . . . . subtract 3

  m ≤ 28 . . . . . . . . . .divide by 1.5

Answer: M is less than or equal to 28 or C

Step-by-step explanation:

GOT RIGHT ON E D G

Answer:

Option (1)

Step-by-step explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle = [tex]\frac{360}{3}[/tex] = 120°

From the formula of arc length,

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 = [tex]\frac{120}{360}(2\pi r)[/tex]

12 = [tex]\frac{2}{3}\pi r[/tex]

[tex]18=\pi r[/tex]

r = [tex]\frac{18}{\pi }[/tex]

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.

Answer:pete

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

I'm not sure what the 0s are all about, but I can help with the equation;

To do this, we can do substitution. By equaling x-4 to 3x+2, we get

x-4=3x+2

By isolating the x, we get

-2x=6

x=-3

Hope this helped!

Answer:

1.79% probability that the number of times that the coin lands tails will be less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

100 times

[tex]n = 100[/tex]

Then

[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]

What is the probability that the number of times that the coin lands tails will be less than 40

Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{39.5 - 50}{5}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

1.79% probability that the number of times that the coin lands tails will be less than 40

Answer:

75%

Step-by-step explanation:

There are 3 numbers that fit this rule, 3, 5, and 6. There is a 3/4 chance spinning one or a 75% chance.

Answer:

75%

Step-by-step explanation:

The numbers 6 or odd are 3, 5, and 6.

3 numbers out of a total of 4 numbers.

3/4 = 0.75

Convert to percentage.

0.75 × 100 = 75

P(6 or odd) = 75%

-2

0

2

Answered on edge

Answer:

-2, 0, 2

Step-by-step explanation:

edge 2020

Answer:

4.9 hours = 4 hours 54 minutes

Step-by-step explanation:

speed = distance/time

time * speed = distance

time = distance/speed

time = (284 miles)/(58 mph) = 4.9 hours

4.9 hours - 4 hours = 0.9 hours

0.9 hours * (60 minutes)/(1 hour) = 54 minutes

4.9 hours = 4 hours 54 minutes

Answer:

-2

Step-by-step explanation:

The slope of a line is

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

   = (-2 -4)/(-1 - -4)

   = -6/ ( -1 +4)

   = -6 /3

    =-2

Answer:

[tex]= - 2 \\ [/tex]

Step-by-step explanation:

[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]

Now let's find the slope

[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

Answer:

C.) 60°

Step-by-step explanation:

The triangle is an equilateral triangle. So that means that all the angles measure the same. And we have to remember that a triangle always equals 180°

So, to find out the measure of an angle. We must divide 180 by 3. Which is 60

=60°

Hope this helps you out! : )

Answer:

b. not all the children can be above average

d. half the children must be below average

Step-by-step explanation:

In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.

Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.

Therefore, the correct answers are:

b. not all the children can be above average

d. half the children must be below average

Answer:

Second and last options are correct choices.

Step-by-step explanation:

If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.

Best Regards!

Answer:

(-1, 6)

(0, 7)

Step-by-step explanation:

Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.

Answer:

Use a graphing calc or desmos

Step-by-step explanation:

Answer:

solution,

Volume of cylinder=304 cm^3

height=10 cm

Radius=?

Now,

[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

The sample mean is 6.1

Step-by-step explanation:

Margin of Error (E) = (upper limit - lower limit)/2 = (6.8 - 5.4)/2 = 1.4/2 = 0.7

Sample mean = lower limit + E = 5.4 + 0.7 = 6.1

Answer:

$15

Step-by-step explanation:

Each cup is 50 cents which is basically $0.50

Multiply $0.50 by 120= $60

Because you and your three friends equal 4 total people,

divide 60 by 4 to get your own profit:

60/4=15

Answer:

The solution to this expression is 61,224.74

Step-by-step explanation:

To solve we initially have to convert the percentage to a decimal:

[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]

So

56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74

The solution to this expression is 61,224.74

Answer:

-5°C < 5°C

The temperature was higher on Wednesday than on Tuesday.