A
lodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days.
hospital purchased 27 grams of the substance but had to wait seven days before it could be used. How much of the
substance was left after seven days?

The amount of substance left after seven days was __ g.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)

Answer:

Step-by-step explanation:

First, you need to find the least common denominator (LCD) of 6, 12 and 8. 6 factors to 2*3, 12 to 2*2*3 and 8 to 2*2*2. The LCD will be the number that incorporates the combination that includes all the unique factors, which would be 2*2*2*3 or 24. 5/6 = 20/24, 1/12 = 2/24 and 7/8 = 21/24 so altogether the team covers

(20+2+21)/24 = 43/24 = 1 19/24 miles

Answer:1/2

Step-by-step explanation:

because three is half of six and you can get numbers larger than three also

The correct option is- (F) US Department of Homeland Security, is the sources of authority for given security officers.

The Department of Homeland Security (DHS) of the United States is a federal organisation created to defend the country against dangers.

The DHS statement of purpose lists the following five primary objectives for homeland security:

Thus, security officers' sources of authority are US Department of Homeland Security.

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Step-by-step explanation:

Distance formula to find distance from O to Q is sqrt (306)

Distance from R to P = sqrt (34)

Diagonals ( found above) intersect at right triangles in a rhombus

  so you can break it into two right triangles of base = sqrt (306)

           and height sqrt (34)/2

    TWO triangles of area = 1/2 base * height

         TOTAL Area is then :     TWO * 1/2 ( sqrt(34)/2)* sqrt (306) = 51 units^2

The answer is:

minimum value = √121/11 = 2/11

maximum value = √17/11

Here's how to solve it:

The given function is c(z) = √z, and the domain interval is 121 ≤ z ≤ 17.

The minimum value of the function occurs at the endpoint of the domain interval where the function takes the smallest value. In this case, the smallest value of the function occurs at z = 17, so the minimum value of the function is:

c(17) = √17

The maximum value of the function occurs at the endpoint of the domain interval where the function takes the largest value. In this case, the largest value of the function occurs at z = 121, so the maximum value of the function is:

c(121) = √121 = 11

Therefore, the minimum value of the function is √17 and the maximum value of the function is 11/√121, which simplifies to 1/11.

Answer: lol 3500 minus 4000 equals 500

Step-by-step explanation:

:) there

There are many banks but nowadays SBI is the one of popular bank of World.So I choose SBI bank for explanation.

Details about SBI bank:

State Bank of India (SBI) is one of the largest and oldest banks in India. It was founded in 1806 as the Bank of Calcutta and later became the Imperial Bank of India in 1921. In 1955, the bank was nationalized and became the State Bank of India.

SBI is headquartered in Mumbai and has a widespread network of branches across India as well as in other countries. The bank offers a wide range of financial products and services such as savings and current accounts, loans, credit cards, investment options, insurance, and many more.

SBI is known for its advanced technology and customer-centric approach. The bank has implemented various digital initiatives to make banking easy and convenient for its customers. SBI's mobile app and internet banking portal are among the most popular digital channels used by customers.

Apart from traditional banking services, SBI has also been actively involved in various social initiatives such as promoting financial literacy, supporting education, healthcare, and environment conservation. The bank has also launched many welfare schemes for the benefit of its customers and society at large.

SBI is recognized as a global banking leader and has received many prestigious awards and accolades over the years. The bank has also been ranked among the top banks in the world by leading international publications.

Overall, SBI is a reliable and trustworthy bank that has played a significant role in shaping the Indian banking industry.

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Correct question is " Choose a name of a perticular bank and write about the bank."

Answer:

The median is 6.

If you need the mean, mode, range, minimum, maximum, count n, or sum they are

Mean- 6.6666666666667

Mode- 1,3,4,5,6,7,8,12,14

Min- 1

Max- 14

Count n- 9

Sum- 60

Answer:

5.5

Step-by-step explanation:

The median is the middle number in a sorted list of numbers.

Therefore, the first step to solving this problem is sorting this list of numbers from least to greatest:

1, 2, 3, 4, 5, 6, 7, 8, 12, 14

To find the middle number, start by crossing out a number from each side. In this case, the first two numbers to cross out are 1 and 14. 1 is the smallest number in the list and 14 is the greatest. Our list should then look like this:

2, 3, 4, 5, 6, 7, 8, 12

Now, cross out the next smallest and largest numbers of the list (2, 12):

3, 4, 5, 6, 7, 8

The next (3, 8):

4, 5, 6, 7

The next (4, 7):

5, 6

Now we are left with two numbers. When this happens, to figure out the middle number, we have to find the average of these last two remaining digits. The average can be found by adding these two digits and dividing that by the total number of digits you used to add.

In this case, we have 2 numbers left: 5 and 6

1. Add 5 and 6: 5+6=11

2. We used 2 numbers for the addition which means we have to divide 11 by 2: 11/2

= 5.5

[tex]A-x=\cfrac{xr}{t}\implies At-xt=xr\implies At=xt+xr \\\\\\ At=x(t+r)\implies \cfrac{At}{t+r}=x[/tex]

make x the subject means write all terms in terms of x

look at attachment.

A circle is a two-dimensional geometric figure that consists of all points that are at an equal distance, called the radius, from a single given point, called the center. The radius is exactly twice as long as the distance across the circle, as measured by the diameter, which passes through its centre.

The tangent of a circle is a straight line that intersects the circle at exactly one point, known as the point of tangency.

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Answer:

Step-by-step explanation:

P(international | on time)< P(delayed | domestic) <P(on time and domestic)

correct in plato

Answer:

Step-by-step explanation:

To add numbers in base 5, we need to follow the same process as adding numbers in base 10. We will start by aligning the digits based on their place value and then add them up, carrying any remainders as necessary.

4023 base 5

3102 base 5

11325 base 5

Therefore, the sum of 4023 base 5 and 3102 in base 5 is 11325 base 5.

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

Value of variable x in the proportion is 6.

A fraction is used to express a portion of a whole or a ratio of two values. It is a mathematical statement known as a fraction bar or vinculum that has a numerator and a denominator separated by a horizontal line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of parts that are being taken into account.

Given proportion;

10/10+x=35/56

Cross multiplying the proportion, we get

10×56=35×(10+x)

Multiplying the values on both side, we get

560=350+35x

Taking 350 on left hand side,

560-350=35x

35x=210

Dividing the equation by 35, we get

x=210/35

x=6

Hence, value of x in the proportion is 6.

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Answer:

[tex]x = 5 \sqrt{3} [/tex]

Step-by-step explanation:

The base of a triangle, located in front of an angle of 30 degrees, is equal to half the hypotenuse:

y = 2 × 5 = 10

Now, we can find x by using the Pythagorean theorem:

[tex] {x}^{2} = {10}^{2} - {5}^{2} = 100 - 25 = 75[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{75} = 5 \sqrt{3} [/tex]

1) The permutation that is the next one in lexicographic order after (4, 6, 2, 7, 3, 1, 5) is (4, 6, 2, 7, 3, 5, 1). Therefore answer is a. (4, 6, 2, 7, 3, 5, 1).

2) The 5-subset from {1, 2, 3, 4, 5, 6, 7, 8, 9} that is the next one in lexicographic order after {2, 3, 7, 8, 9} is {2, 4, 7, 8, 9}. Therefore the answer is d. {2, 4, 7, 8, 9}.

The next permutation in lexicographic order is the one that comes immediately after the given permutation when the permutations are listed in numerical order. To find the next permutation, we need to find the rightmost pair of elements that are in decreasing order. In this case, that pair is (5, 1). We then need to find the smallest element to the right of 1 that is larger than 1, which is 3. We swap 1 and 3 to get (4, 6, 2, 7, 3, 5, 1).

To find the next 5-subset in lexicographic order, we need to find the rightmost element that can be increased. In this case, that element is 9. We then replace 9 with the smallest element to its right that is larger than 9, which is 4. We then need to rearrange the remaining elements in increasing order to get {2, 4, 7, 8, 9}.

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With 90% cοnfidence, we can say that the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre is between 0.601 and 0.685. In οther wοrds, we can be 90% cοnfident that the pοpulatiοn prοpοrtiοn οf custοmers whο prefer this market is within this range.

Percentage is a way οf expressing a number οr prοpοrtiοn as a fractiοn οf 100. It is represented by the symbοl "%".

Tο calculate the cοnfidence interval tο estimate the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre with 90% cοnfidence, we need tο check the fοllοwing cοnditiοns:

In this scenariο, we can assume that the fοrms were distributed randοmly tο the custοmers, and the independence cοnditiοn is met because the respοnses οf οne custοmer dο nοt affect the respοnses οf anοther custοmer. Tο check the sample size cοnditiοn, we can calculate the expected number οf successes and failures in the sample:

Expected number of successes: n * p = 429 * (276/429) ≈ 277

Expected number of failures: n * (1 - p) = 429 * (1 - 276/429) ≈ 152

Both the expected number of successes and failures are greater than 10, so the sample size condition is met.

Now, we can calculate the confidence interval using the formula:

CI = p ± sqrt(p(1-p)/n)

where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level.

In this case, p = 276/429 ≈ 0.643, n = 429, and z = 1.645 (from a standard normal table for 90% confidence level).

Plugging in these values, we get:

CI = 0.643 ± 1.645sqrt(0.643(1-0.643)/429) ≈ (0.601, 0.685)

Therefore, with 90% confidence, we can say that the true proportion of customers who consider this market more pleasing than the other store is between 0.601 and 0.685. In other words, we can be 90% confident that the population proportion of customers who prefer this market is within this range.

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Answer:

Step-by-step explanation:

35 is the answer because where it says frequency you have to add it all together.

Therefore , the solution of the given problem of percentage comes out to be  the account's yearly percentage yield (APY) is 2.24%.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

The following equation can be used to determine the worth of an account after t years, compounded quarterly:

=>  A = P * (1 + r/4)⁴ⁿ

When we enter the numbers, we obtain:

=>  A = 240 * (1 + 0.022/4⁴ⁿ

By condensing the solution, we obtain:

=>  A = 240 * 1.0055⁴ⁿ

Consequently, the following is the function displaying the account's worth after t years:

=>  f(t) = 240 * 1.0055⁴ⁿ

We can use the following formula to determine the yearly percentage yield (APY):

=> APY = (1 + r/n)ⁿ - 1

where r equals the 2.2% yearly interest rate.

n is the quantity of times interest is added annually. (4, since interest is compounded quarterly)

When we enter the numbers, we obtain:

=> APY = (1 + 0.022/4)⁴ - 1

APY = 0.02237 or 2.24% (rounded to the nearest hundredth of a percent)

As a result, the account's yearly percentage yield (APY) is 2.24%.

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1. A table in a book showed binomial probabilities with a tiny value for n (let's say 20, for example). The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation.

2. In a table in a book, binomial probabilities with a low value for n (let's say, 20) were shown. The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation. Take a basic random sample from the population to calculate the normal approximation to the binomial distribution.

There are n independent trials, where n is a number.

Any trial has two possible outcomes: success or failure.

The likelihood of each trial being successful is p.

3. It is necessary for the normal distribution's shape and the binomial distribution to be identical. The values np and nq must both be greater than five in order to guarantee this (np>5 and nq>5; the approximation is better if they are both greater than or equal to 10).

Just utilising a line to approximate the value of the function at a given position is what is meant by a function's linear approximation. We recall the idea of the tangent line as soon as we come across a curve (of a function) and a point on it. The value of the function at any point that is extremely close to the provided point can be estimated using the equation of the tangent line if we are able to identify the equation of the tangent line at the given point. Because it uses the tangent line, this idea is sometimes referred to as the tangent line approximation. It is also known as the linear approximation.

A table in a book showed binomial probabilities with a tiny value for n (let's say 20, for example). The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation.

In a table in a book, binomial probabilities with a low value for n (let's say, 20) were shown. The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation. Take a basic random sample from the population to calculate the normal approximation to the binomial distribution.

There are n independent trials, where n is a number.

Any trial has two possible outcomes: success or failure.

The likelihood of each trial being successful is p.

It is necessary for the normal distribution's shape and the binomial distribution to be identical. The values np and nq must both be greater than five in order to guarantee this (np>5 and nq>5; the approximation is better if they are both greater than or equal to 10).

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The probability that the subject tested negative or did not use marijuana is approximately 0.57.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is a way of quantifying the uncertainty or randomness associated with an event or an experiment.

In the given question,

To solve this problem, we can construct a table that summarizes the given information:

We are given the following information:

There are 143 subjects with positive test results, of which 20 are false positives.

There are 153 subjects with negative test results, of which 4 are false negatives.

Using this information, we can fill in the table as follows:

The numbers in parentheses are the counts of subjects in each category.

To find the probability that the subject tested negative or did not use marijuana, we need to add the probabilities of the two mutually exclusive events:

Tested negative and did not use marijuana (True Negative): P(True Negative) = 149/296

Tested positive but did not use marijuana (False Positive): P(False Positive) = 20/296

Therefore, the probability that the subject tested negative or did not use marijuana is:

P(Tested Negative or Did not use marijuana) = P(True Negative) + P(False Positive)

= 149/296 + 20/296

= 169/296

≈ 0.57

So, the probability that the subject tested negative or did not use marijuana is approximately 0.57.

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These are the transformed functions for each of the four transformations mentioned.

Vertical translation (shift) by k units: f(x) + k

Horizontal translation (shift) by h units: f(x - h)

Vertical stretch/compression by a factor of c: c * f(x)

Reflection across the x-axis: -f(x)

Replace k, h, and c with the desired values to obtain the specific transformed functions.
Here are four common types of transformations:
Vertical translation (shift) by k units: f(x) + k
Horizontal translation (shift) by h units: f(x - h)
Vertical stretch/compression by a factor of c: c * f(x)
Reflection across the x-axis: -f(x)
For the function f(x) = 2x + 3,

let's apply these transformations:
Vertical translation (shift) by k units: f(x) + k -> 2x + 3 + k (where k is the number of units shifted vertically)

Horizontal translation (shift) by h units: f(x - h) -> 2(x - h) + 3 (where h is the number of units shifted horizontally)
Vertical stretch/compression by a factor of c: c * f(x) -> c(2x + 3) (where c is the stretch/compression factor)
Reflection across the x-axis: -f(x) -> -(2x + 3).

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A translation of the sentence "Product of 3 and the cube of h increased by one-ninth is 1​" is

In order to translate a word sentence into an algebraic equation, we would have to assign a variable to the unknown number:

Let the variable n represent the unknown number.

By translating the word sentence into an algebraic expression, we have the following;

The product of 3 and the cube of h should be represented by the following algebraic expression;

3 × h³

Next, we would increase the above algebraic expression by one-ninth (1/9) and then equate to 1 as follows;

(3 × h³) + 1/9 = 1

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Complete Question:

Write an equation to represent the following word sentence;

Product of 3 and the cube of h increased by one-ninth is 1​.

Answer:

A.

Step-by-step explanation:

No, Manu's conclusion is not correct. He should look at the greatest data value on the number line that has any dots above it to find the greatest number of books read. The most dots represent the most frequent number of books read, but not necessarily the greatest number of books read.

Fiinding and interpreting the zero of a rational function involves solving for x when the function equals zero and understanding its significance within the context.

Hello! I understand you want to find and interpret the zero of a rational function, and I'd be happy to help.

The zero of a rational function occurs when the function's value is equal to zero. In other words, a zero is a value of x that makes the function f(x) = 0. To find the zero, you must set the numerator of the rational function equal to zero and solve for x.

It's important to note that the denominator should never equal zero, as this would make the function undefined.

Interpreting the zero helps us understand the behavior of the function and can be useful in various applications.

For instance, the zero might represent a break-even point in a business context or an equilibrium in a physical system. Whether the result makes sense within the context of a specific problem depends on the given scenario and the mathematical relationship between the variables.

To summarize,  Always ensure the denominator is never zero to maintain the function's validity.

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Therefore, the outer perimeter is approximately 73.20 ft.

Perimeter is the total distance around the outside of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape. The units for perimeter are the same as the units used for the length of the sides. For example, if the sides are measured in feet, the perimeter will be measured in feet as well.

Here,

We need to find the outer perimeter, which means we need to find the perimeter of the shape that includes all the sides of JROP. To do this, we need to find the length of side JO.

Using the Pythagorean Theorem on right triangle JOR, we have:

JO² = JR² + OR²

JO² = 10² + 14²

JO² = 296

JO ≈ 17.20 ft

Now we can find the outer perimeter:

Outer perimeter = JP + PO + OR + RJ + JO

Outer perimeter = 18 + 10 + 14 + 14 + 17.20

Outer perimeter ≈ 73.20 ft

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The straight sections each have a length of 100. So, the total distance around the inner lane of the track is 200 + 40pi units

The area of one of the blue half circles can be found using the formula:

Area = pi x radius squared.

The diameter of the circle is given as 40, so the radius is half of that, which is 20.

Therefore, the area of one blue half circle is:
Area = pi x [tex]\frac{20^{2} }{2}[/tex]

Area = 200pi square units
To cover the entire circle, we need both blue half circles. So the total area needed to be covered with grass is:
Total area = 2 x 200pi = 400pi square units
The distance around one of the semicircles at either end of the soccer field can be found using the formula: Circumference = pi x diameter.

Since the diameter is given as 40.

The circumference is:
Circumference = pi x [tex]\frac{40}{2}[/tex]

Circumference = 20pi units

To find the distance around the inner lane of the track, we need to add the lengths of the straight distances (which are 100 each) to the circumference of the two blue half circles.

The circumference of one blue half circle is 20pi, so the total distance around the inner lane of the track is:
Distance = 2 x 100 + 2 x 20pi

Distance = 200 + 40pi units

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The amount of feed that can the container hold is two hundred ninety-two and one-eighth in³.

The volume of a rectangular prism can be calculated using the formula:

                    V = l × w × h

where V is the volume, l is the length, w is the width, and h is the height of the rectangular prism.

Here we have

A student is building a squirrel feeder for a family member. The figure is a model of the feeder.

A rectangular prism with dimensions are

4 3/4 inches × 20 1/2 inches × 3 inches.

The amount of feed in a rectangular prism = Volume of rectangular  

Volume of container = 4 3/4 inches × 20 1/2 inches × 3 inches

= 19/4 × 41/2 × 3  = 2337/8 = 292 1/2 in³

Therefore,

The amount of feed that can the container hold is two hundred ninety-two and one-eighth in³.

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Step-by-step explanation:

blue box is x^2

orange box is 5x

yellow box is 3x

green box is 15