The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 5.8% per day. Find the
half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer:

-235+84i

Step-by-step explanation:

I hope this is what you were looking for.

1. Using mathematical operations, the cost of three 5kg bags of rice at ¢2 per kg is ¢30.

2. From the 2km piece, you can cut 2,000 pieces with each one meter long.

3. The fraction of a liter that is 259 ml can be written as ²⁵⁹/₁₀₀₀.

4. 60ps expressed as a decimal of ¢240 is 0.25.

5. The groups of 4 marks in 20, based on a division operation, is 5.

6. If an orange costs ¢150, by multiplication, 9 oranges will cost ¢1,350.

7. The product of 35 and 12, which is a multiplication operation, is 420.

8. Using division operation, from 1 kg, one could obtain 5.55 units of 180g each.

The four basic mathematical operations are addition, subtraction, division, and multiplication.

In this situation, the mathematical operations involved are division and multiplication.

1) The cost of price per kg = ¢2

The number of bags bought = 3

The weight per bag = 5kg

The total weight of 3 bags = 15kg (5 x 3)

The total cost = ¢30 (¢2 x 15)

2) The total length of the piece = 2km

1 km = 1,000 meters

2km = 2,000 meters

The length of each string = 1 meter

The number of strings = 2,000 (2,000 ÷ 1)

3) 1 liter = 1,000 ml

259 ml/1,000 ml = 259/1,000

= ²⁵⁹/₁₀₀₀

4) 60p as a decimal of ¢240

= 0.25 (60 ÷ 240)

5) 20 ÷ 4 = 5

4 x 5 = 20

6) The cost per orange =  ¢150

The number of oranges bought = 9

The total cost of 9 oranges = ¢1,350 (¢150 x 9)

7) The product of 35 and 12 = 420 (35 x 12)

8) The quantity of each unit = 180g

The total quantity = 1 kg

1 kg = 1,000 g

5.55 (1,000 ÷ 180)

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Answer:

A''(3, 0); B''(3, 2); C''(1, 1); D''(1, -1)

Step-by-step explanation:

The combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.

To find the combined length of the pieces of wire, we need to add the lengths of the two pieces of wire together.

The first piece of wire is 7/8 of an inch long.

The second piece of wire is 5/8 of an inch long.

To add the two fractions, we need to find a common denominator. The smallest number that both 8 and 5 will divide into is 40.

7/8 can be rewritten as 35/40 (multiply the numerator and denominator by 5)

5/8 can be rewritten as 25/40 (multiply the numerator and denominator by 5)

Now we can add the two fractions:

35/40 + 25/40 = 60/40

Simplifying the fraction:

60/40 = 3/2

Therefore, the combined length of the two pieces of wire is 3/2 inches or 1 and 1/2 inches.

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Answer:

Step-by-step explanation:

We know that the cosine of an angle is the reciprocal of the secant of the same angle, and the cotangent of an angle is the reciprocal of the tangent of the same angle. Therefore, we can use these relationships to find the value of the secant of an angle when the cotangent of the same angle is given.We are given that cot(o) = 13/6. Using the definition of the cotangent function, we know that:cot(o) = adjacent side / opposite sideWe can use the Pythagorean theorem to find the hypotenuse of a right triangle with adjacent side 13 and opposite side 6:h^2 = 13^2 + 6^2

h^2 = 169 + 36

h^2 = 205

h = sqrt(205)Now we can use the definitions of the secant and cosine functions to find the value of sec(o):sec(o) = hypotenuse / adjacent side

sec(o) = sqrt(205) / 13Therefore, the value of sec(o) is:sec(o) = sqrt(205) / 13 ≈ 1.5276

The median score, considering the frequency distribution in this problem, is given as follows:

334.5.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The total number of observations in the data-set is given as follows:

189.

Hence the position in the cumulative frequency table of the median element is given as follows:

0.5 x (189 + 1) = 95.

Which is in the following interval:

330-339.

Hence the median is of 334.5, as it is the middle value of the interval.

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The calculated value of the missing side length of the triangle is 13.96 units

From the question, we have the following parameters that can be used in our computation:

The triangle

The missing side length of the triangle can be calculated using the law of sines

The law of sines states that

a/sin(A) = b/sin(B) = c/sin(C)

Using the above as a guide, we have the following equation

x/sin(61) = 15/sin(70)

Cross multiply

x = sin(61) * 15/sin(70)

Evaluate

x = 13.96 units

Hence, the missing side length of the triangle is 13.96 units

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The number of multiples of both 2 and 5 that are there between 34 and 417 is given as follows:

39.

The rules for the multiples of 2 and 5 are given as follows:

Hence the numbers that are multiples of both 2 and 5 finish in zero, which are the multiples of 10.

Then the divisions are given as follows:

Hence the number of multiples is given as follows:

41 - 3 + 1 = 39.

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Answer:

Step-by-step explanation:

D

Answer:

Perdón no te puedo ayudar no entiendo

Step-by-step explanation:

To find the average velocity of the particle over the interval [1, e], we need to calculate the net displacement divided by the time interval.

Given the position function x(t) = ln(t), let's find the displacement by evaluating x(e) and x(1):

x(e) = ln(e) = 1

x(1) = ln(1) = 0

So, the net displacement is 1 - 0 = 1.

The time interval is e - 1.

Therefore, the average velocity is:

average velocity = (net displacement) / (time interval)

average velocity = 1 / (e - 1)

The correct answer is B. 1/(e - 1).

Answer: 27[tex]\pi[/tex]

Step-by-step explanation:

Use the circle area formula: r²[tex]\pi[/tex]...

6²[tex]\pi[/tex] = 36[tex]\pi[/tex]

And since a quarter of the circle is removed(aka [tex]\frac{1}{4}[/tex]), divide 36 by [tex]\frac{3}{4}[/tex]...

= 27[tex]\pi[/tex]

According to the figure the required lengths are

BD = 7 units

BC = 9.9 units

The required lengths is solved knowing that in a right triangle having angle 45 degrees, the lengths of the legs of the right triangle are equal.

Also,  the perpendicular bisector creates another angle 45 degrees at angle B.

hence we another right triangle with a leg as 7 units hence BD is 7 units

solving for BC

BC = BA

BC² + BA² = CA²

BC² + BC² = 14²

2 x BC² = 196

BC² = 98

BC = √(98)

BC = 9.9 units

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The diameter of the basketball is 16 cm given the volume of 268 [tex]cm^{3}[/tex]

Sphere is a three-dimensional object that is round in shape. It  is an object that is completely round in shape like a ball.

How to determine this

When a basketball has a volume of 268[tex]cm^{3}[/tex]

The volume of a sphere = 4/3 * π * [tex]r^{3}[/tex]

Where π = 3.14

Radius, r = ?

Volume of basketball = 4/3 * 3.14 * [tex]r^{3}[/tex]

268[tex]cm^{3}[/tex] = 4/3 * 3.14 * [tex]r^{3}[/tex]

268[tex]cm^{3}[/tex] = 12.56/3 * [tex]r^{3}[/tex]

Cross multiply

268 * 3 = 12.56 * [tex]r^{3}[/tex]

804 = 12.56 * [tex]r^{3}[/tex]

divides through by 12.56

804/12.56 = 12.56[tex]r^{3}[/tex]/12.56

64.01 = [tex]r^{3}[/tex]

cube both sides

∛64.01 = r

r = 4 cm

So, the radius = 4 cm

To find the diameter of basketball

When the radius = 4 cm

And diameter = 2(r)

Diameter = 2 * 4 cm

Diameter = 8 cm

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Answer:

22 = 2 × 11

40 = 2 × 2 × 2 × 5

LCM of 22 and 40 = 2^3 × 5 × 11 = 440

Answer:

X=20

Step-by-step explanation:

khan academy :))

Inverse variation is a relationship between two variables where one variable increases as the other variable decreases, and vice versa.

This means that as one variable doubles, the other variable will decrease by half, or vice versa.

The following are situations that depict inverse variation:

1. When you are traveling at a constant speed, the time it takes to cover a given distance is inversely proportional to the distance. This is because the distance will decrease as the speed increases.

2. If you have a light source, the intensity of the light decreases as you move further away from the source. This is because the distance between the source and the object increases as the intensity of the light decreases.

3. The force of gravity between two objects is inversely proportional to the square of the distance between them. This is because the force of gravity will decrease as the distance between the objects increases.

4. When the temperature of a gas decreases, its pressure increases. This is because the volume of the gas remains constant as the temperature decreases, which causes the pressure to increase according to the gas laws.

5. The period of a pendulum is inversely proportional to the square root of its length. This is because the length of the pendulum will decrease as the period increases.

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Answer:

x=5,1

Step-by-step explanation:

have a great day and thx for your inquiry :)

Answer: x = 5, 1

Step-by-step explanation:

Take the root of both sides and solve

Answer: 3r

Step-by-step explanation: because 2r+1r=3r

The equation that represents the direct variation between a and b in the given problem is: b = -a. So, option is correct.

The statement "a number, b, is located the same distance from 0 as another number, a, but in the opposite direction" means that b = -a. The statement "The number b varies directly with the number a" means that b is proportional to a, or mathematically, b = k*a, where k is the constant of proportionality.

Substituting b = -a into the equation b = ka, we get -a = ka. Solving for k, we get k = -1. Therefore, the equation that represents the direct variation between a and b is b = -a which is option B, "-b = -a".

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Complete question - On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 22 when a =  -2 Which equation represents this direct variation between a and b?

A. a = -1

B. -b = -a

C. b-a = 0

D. b(-a) = 0.

The length FE is 6 units and the arc AE is 64 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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The test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an Even distribution.

To carry out the chi-squared goodness-of-fit test, we need to calculate the expected number of appointments for each day if there were an even distribution. Since there are 5 days of the week, each day would have an expected value of 100 (i.e., 500 appointments / 5 days = 100 appointments per day).

Day | Monday | Tuesday | Wednesday | Thursday | Friday

Observed | 115 | 100 | 115 | 100 | 70

Expected | 100 | 100 | 100 | 100 | 100

To calculate the chi-squared test statistic, we use the formula:

χ2= ∑ (observed − expected)^2 / expected

Plugging in the observed and expected values, we get:

χ2= [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(115 - 100)^2/100] + [(100 - 100)^2/100] + [(70 - 100)^2/100]

  = 2.75 + 0 + 2.75 + 0 + 9

  = 14.5

To find the P-value, we need to use the chi-squared distribution table with 4 degrees of freedom (5 days of the week minus 1 for the expected value). Using the table, we find that the P-value for a chi-squared statistic of 14.5 with 4 degrees of freedom is less than 0.05. Therefore, we reject the null hypothesis that the appointments have an even distribution from Monday through Friday.the test statistic is 14.5 and the P-value is less than 0.05. Therefore, we have evidence to suggest that the distribution of days of the week of the appointments disagrees with an even distribution.

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The expression with the greatest value when a = 5 is:

a + 9 × 8 ÷ 7, with 9 in the first box, 8 in the second box, and 7 in the third box.

To create the expression with the greatest value when a = 5, we want to choose the largest possible numbers to fill in the missing parts.

Since each whole number can only be used once, we should choose the three largest numbers from 1 to 9.

The three largest numbers from 1 to 9 are 9, 8, and 7. So we can fill in the expression as follows:

a + 9 × 8 ÷ 7

When a = 5, this expression evaluates to:

5 + 9 × 8 ÷ 7 = 5 + 72 ÷ 7 = 15.2857...

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Answer:

The polygons are similar. They are similar in the way that the larger polygon is 3 times the size of the smaller one.

Answer:

----------------

The line that is perpendicular to x = 8 has a form of:

Since it has a point (-3, - 2), the value of a is the y-coordinate of this point. Therefore the line is:

Approximately 99.4% of people have an IQ score between 55 and 145.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to data that is normally distributed. It states that:

- Approximately 68% of data falls within one standard deviation of the mean.

- Approximately 95% of data falls within two standard deviations of the mean.

- Approximately 99.7% of data falls within three standard deviations of the mean.

In this case, we are given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. To find the percentage of people with an IQ score between 55 and 145, we need to find the number of standard deviations away from the mean that these scores are.

For an IQ score of 55, we have:

z = (55 - 100) / 15 = -3

For an IQ score of 145, we have:

z = (145 - 100) / 15 = 3

So, we can see that an IQ score of 55 is 3 standard deviations below the mean, and an IQ score of 145 is 3 standard deviations above the mean.

According to the empirical rule, approximately 99.7% of data falls within three standard deviations of the mean. Therefore, the percentage of people with an IQ score between 55 and 145 is approximately:

99.7% - (0.15% + 0.15%) = 99.4%

(Note that we subtracted the percentage of data that falls more than 3 standard deviations away from the mean, which is approximately 0.15% on either side.)

So, approximately 99.4% of people have an IQ score between 55 and 145.

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Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

We cannot conclude that 95% of the population agrees that there is no difference in Taste between Coke and Pepsi.

To calculate the probability that 95% of the population agrees that there is no difference in taste between Coke and Pepsi, we can use the binomial distribution formula.

Let X be the number of students who say there is no difference in taste, and n be the total number of students in the sample. Then, X follows a binomial distribution with parameters n and p, where p is the true proportion of students who say there is no difference in taste.

The point estimate of p is 7/10 = 0.7. The standard error of the proportion can be calculated as the square root of p(1-p)/n = sqrt(0.7*0.3/10) = 0.23.

Using a normal approximation to the binomial distribution, the 95% confidence interval for p is given by:

0.7 +/- 1.96*0.23 = (0.24, 1.16)

Since the interval includes 0.5, which represents the point where the proportion of agreement and disagreement is equal, we cannot conclude that 95% of the population agrees that there is no difference in taste between Coke and Pepsi.

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Answer:

Final Expression:

3.095D + $10

Step-by-step explanation:

Let's represent the Monthly Rent by "D" dollars

The amount Dave is expected to pay before renting the apartment is the Sum of All the Fees he has been quoted:

Application Fee:

1.5% of 1 month's rent = 0.015D

Credit Application Fee:

$10.00

Security Deposit:

1 Month's rent =  D

Last Month's rent:

1 Month's Rent = D

Broker's Fee:

9%

Thus, The algebraic expression that represents the amount Dave is expected to pay before renting the apartment is:

0.015D + $10  +  D  +  D + 1.08D

Simplify Expression:

3.095D  + $10

Hence, The final expression is:

Answer:  3.095D + $10

Answer:

Step-by-step explanation:

You probably should check for silly mistakes.