A sample of radioactive isotope of an element contains 60 millions atoms and is found to have a decay rate of 5 hundred atoms per year. What is the half life of the isotope?

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

\(\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }\)

The distance between the points (−3,− 8), (6, – 8) is 9.

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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Answer:

33

Step-by-step explanation:

48 - 15 = 33

Answer:

33??

Step-by-step explanation:

Answer:

=

You is welcome

Answer:

less than or equal

Step-by-step explanation:

I can put the actual inequality sign but the inequality is less than or equal to... if the sentence say no more than, then it would have to be less than or equal to.

Answer:

13

Step-by-step explanation:

Answer:

7^2=49

3^2=9

49-9*4

49-36=13

Answer: \(\frac{5\pi}{3}\)

Step-by-step explanation:

\(A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}\)

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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\(s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} \)

The shaded region represents 1.5 grids

\(1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} \)

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

ok

P1 = (0, 3)

P2 = (1,6)

1.- Find the slope

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

m = (6 - 3) / (1 - 0)

m = 3/1

m = 3

2.- Find the equation of the function

y - y1 = m(x - x1)

y - 3 = 3(x - 0)

y - 3 = 3x

y = 3x + 3 This is the equation of the function

3.- This is a linear function. The domain of a linear function is all real numbers and the range of a linear function are also all real numbers.

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.

The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.

In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.

For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).

A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.

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Answer:

2.6 x 0.47 = 1.222

Step-by-step explanation:

Distance reading at the start of journey = 12468

Distance reading at the end of the journey = 12845

Distance traveled in the journey = 12845 - 12468 = 377 miles

Cost of petrol per mile = 13p

Cost of petrol for the journey = 13 × 377 = 4901p

Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds

Cost of petrol used in the journey is 49.01 pounds

Null hypothesis: The mean number of points scored by the taller team is not significantly different from the population mean of 72.

Alternative hypothesis: The mean number of points scored by the taller team is significantly greater than the population mean of 72.

Since the population variance is unknown, we will use a t-test. The degrees of freedom for this test will be 9 (n-1), where n is the sample size of the taller team (10).

Using an alpha level of 0.05 and 9 degrees of freedom, the critical t-value is 1.833.

To calculate the test statistic, we first need to find the sample mean and standard deviation of the taller team's scores. The sample mean is 82, and the sample standard deviation is 9.89. Using these values, we can calculate the t-value:

t = (82-72) / (9.89 / sqrt(10)) = 3.19

Since the calculated t-value (3.19) is greater than the critical t-value (1.833), we reject the null hypothesis and conclude that there is a significant difference between the mean number of points scored by the taller team and the population mean of 72. The coach can therefore conclude that having a taller team does result in a greater number of points scored.

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Answer:

-1/2

Step-by-step explanation:

\( m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

\(m = \dfrac{0 - 5}{10 - 0} = \dfrac{-5}{10} = -\dfrac{1}{2}\)

Answer: slope = -1/2

So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.

When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.

Given by the question.

To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:

40% of 337 tons = 0.4 x 337 = 134.8 tons

Adding this to last year's production gives:

337 + 134.8 = 471.8 tons

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Answer:

3c) x = 1/4, x = 6

3d) t = 0, t = 4

Step-by-step explanation:

3c).....................................

==============================

3d).....................................

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:

her down payment is her down payment.........

Step-by-step explanation:

B sus

Given

To find

we know that

Inserting the value of radius

The difference between the half-life of uranium-238 and uranium-234 is:

first we have to write these numbers so that they have the same exponent in 10:

and now we can take 10⁵ common factor and subtract the decimal numbers:

But this is not in scientific notation, we have to move the decimal point to there's just one integer on the left:

Half-life of uranium-238 is 4.49975 * 10⁹ times greater than uranium-234

Answer: equilateral triangle ANP inscribed in circle C, regular hexagon AMNBPQ inscribed in circle C

Step-by-step explanation:

By looking through our choices, we can eliminate which choices could be wrong and which choices could be right.

Δ MNQ does form a triangle, however, it DOES NOT form a equilateral triangle.

Δ ANP does form a triangle and it is ALSO an equilateral triangle.

Hexagon AMNBPQ does form a hexagon and it is ALSO a regular polygon as we can see all the sides and angles within the polygon are congruent to one another.

MNPQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

ANBQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

Answer:

55%

Step-by-step explanation:

100%-> 380

1%->3.8

209 ÷ 3.8 = 55%

Answer:

Answer is 55%

Step-by-step explanation:

Answer:

30 questions

Step-by-step explanation:

6 questions= 20%

6/20=x/100

6*100/20=x

6*5=x

x=30

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

12.87  12.1  12.07  12.07

Step-by-step explanation:

Answer:

Not a function

Step-by-step explanation:

This is not a function. It will fail the vertical line test.  For any value of x, there are two different y values.  This tells us that it is not a function

Answer:

0.026, 8.062, 8.26, 8.6

Step-by-step explanation:

Hope this helps!

Btw, pls give brainliest, thanks!

Answer:

0.026, 8.062, 8.26, 8.6