The half life of a radioactive kind of cadmium is 14 years. How much will be left after 28 years, if you start with 72 grams of it?

Alice will receive £80 and Brian will receive £320

When dividing an amount of money in a given ratio, we need to first determine the total number of parts that the ratio is divided into.

In this case, the ratio between Alice and Brian is 1:4. This means that for every 1 unit of money that Alice receives, Brian receives 4 units of money. Therefore, the total number of parts in this ratio is 1 + 4 = 5.

To divide £400 in the ratio of 1:4, we need to find out how much of the total amount each part represents. To do this, we divide the total amount by the total number of parts:

£400 ÷ 5 = £80

So each part in this ratio represents £80.

Now that we know the value of each part, we can calculate how much Alice and Brian will receive.

Alice's share is one part, which represents £80. Therefore, Alice will receive

1 part x £80 = £80

Brian's share is four parts, which represents 4 x £80 = £320. Therefore, Brian will receive:

4 parts x £80 = £320

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Answer:

x ≥ -30

Step-by-step explanation:

The equation is 3 - x / 2 ≤ 18.

First, subtract 3 on both sides:

- x / 2 ≤ 15.

Multiply by -2 on both sides and swap the less than or equal to sign:

x ≥ -30

Hope this helps!

The function f is an onto function but not a one-one function.

To determine whether f is an onto function or a one-one function, we need to look at the relationship between the elements in the domain and the elements in the range.

An onto function is a function where every element in the range is mapped to by at least one element in the domain. In other words, every element in the codomain has a corresponding element in the domain that maps to it. To determine if f is an onto function, we need to check if every element in the range {1,2,3} is mapped to by at least one element in the domain {a,b,c,d}.

Looking at the function f, we see that all three elements in the range are mapped to by elements in the domain. For example, 1 is mapped to by c, 2 is mapped to by b, and 3 is mapped to by a and d. Therefore, f is an onto function.

A one-one function (also called an injective function) is a function where each element in the domain maps to a unique element in the range. In other words, no two distinct elements in the domain map to the same element in the range. To determine if f is a one-one function, we need to check if there are any distinct elements in the domain that map to the same element in the range.

Looking at the function f, we see that both a and d in the domain map to 3 in the range. Therefore, f is not a one-one function.

In summary, the function f is an onto function but not a one-one function.

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p³q⁴

Step-by-step explanation:

given. 2p²q³ × 5pq ÷ 10p³q⁴

multiply. 10p³q⁴ ÷ 10 p³q⁴

Divide. p³q⁴

Answer: Hi. The height of the tree is 27 ft

Step-by-step explanation:

Answer link- https://socratic.org/answers/601885

Answer:

1.o5 I fell i I'm in heven

The  binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string is 2¹⁰ - 2⁹.

Binary number:

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".

Given,

Here we need to find How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string.

Here the length of the binary string is 10.

So, it can be written in the power form as 2¹⁰.

Now we need to find the number of 0's in the string is not equal to the number of 1's in the string.

For that, we have to consider,

There are 2⁹ number of binary strings are not have same number of 0's in the string is not equal to the number of 1's in the string.

So, it can be written as,

=> 2¹⁰ - 2⁹

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Answer:

no because Chance is likely to account the result.

Using the unitary method, we found that Mary used 11 1/2 cups of flour altogether in the two recipes.

Mary had 6 3/4 cups of flour, which can be written as 27/4 cups of flour. We can multiply the whole number 6 by the denominator 4, which gives us 24. Adding the numerator 3 to this product gives us a total of 27. Therefore, 6 3/4 cups of flour is equivalent to 27/4 cups of flour.

Now that we have all the quantities in the same units, we can add them together. To add fractions, we need a common denominator. In this case, the common denominator is 4.

27/4 cups of flour + 5/2 cups of flour + 9/4 cups of flour

To add fractions, we need the denominators to be the same. We can rewrite 5/2 as an equivalent fraction with a denominator of 4 by multiplying the numerator and denominator by 2:

27/4 cups of flour + (5 * 2)/(2 * 2) cups of flour + 9/4 cups of flour

27/4 cups of flour + 10/4 cups of flour + 9/4 cups of flour

Now that we have a common denominator, we can add the numerators together:

(27 + 10 + 9)/4 cups of flour

46/4 cups of flour

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

46 ÷ 2 / 4 ÷ 2 cups of flour

23/2 cups of flour

Since 23/2 can be simplified further, we can express it as a mixed number:

23 ÷ 2 = 11 with a remainder of 1

So, the total amount of flour Mary used altogether is 11 1/2 cups.

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Complete Question:

Mary had 6 3/4 cups of floor. She used 2 1/2 cups of flour in one recipe and 2 1/4 cups of flour in another.

How much flour did she use altogether?

The true statement is that no number in base 10 can be written in multiple ways in base 4

The base of the numbers are given as:

Base 10 and base 4

Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers

There is only one equivalent of each number in each base.

This means that (for instance)

357 in base 10 is 11211 in base 4

The above number does not have any other representation in base 4 and it can not be written in another way.

This is the same for other numbers in base 10

Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4

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Answer:

You have to multiply the denorminator to both sides in order to make x the subject :

\( \frac{x}{7 + 2y} = 6\)

\(x = 6(7 + 2y)\)

Answer:

Given

x/7 + 2y = 6

Multiply through by 7 to clear the fraction

x + 14y = 42 ( subtract 14y from both sides )

x = 42 - 14y

Step-by-step explanation:

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

\(\frac{7}{20}=\frac{7}{2*2*5}\)

The possible 4-digit numbers are 1,680.

Probability that 4-digit number ends up being an odd number greater than or equal to 6000 is 57.14%.

a) The number of possible 4-digit numbers that can be formed using the given digits without repetition is given by the permutation formula:

P(8,4) = 8! / (8 - 4)! = 8 x 7 x 6 x 5 = 1,680

Therefore, there are 1,680 possible 4-digit numbers using the given digits.

b) The total number of 4-digit numbers that can be formed from the given digits is 1,680, as calculated in part a).

To find the probability that the 4-digit number is odd and greater than or equal to 6000, we need to calculate the number of odd 4-digit numbers in the range [6000, 6999] and the number of odd 4-digit numbers greater than or equal to 7000, and divide each by the total number of 4-digit numbers.

Number of odd 4-digit numbers in [6000, 6999]:

The last digit must be 1, 3, 5, or 7 (4 choices). The first three digits can be any of the remaining 7 digits (7 choices for the first digit, 6 choices for the second digit, and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers in [6000, 6999] is:

4 x 7 x 6 x 5 = 840

Number of odd 4-digit numbers greater than or equal to 7000:

The first digit must be 7 (1 choice). The last digit must be 1, 3, 5, or 7 (4 choices). The second and third digits can be any of the remaining 6 digits (6 choices for the second digit and 5 choices for the third digit). Therefore, the number of odd 4-digit numbers greater than or equal to 7000 is:

1 x 4 x 6 x 5 = 120

The total number of odd 4-digit numbers is 840 + 120 = 960.

Therefore, the probability that the 4-digit number is odd and greater than or equal to 6000 is: 960 / 1,680 = 0.5714 or approximately 57.14%.

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A. (left-truncatable-prime? p) procedure:

(define (is-prime? n)

(define (divides? a b)

(= (remainder b a) 0))

(define (iter i)

(cond ((> i (sqrt n)) #t)

((divides? i n) #f)

(else (iter (+ i 1)))))

(iter 2))

(define (left-truncatable-prime? p)

(define (truncate n)

(if (< n 10)

n

(truncate (quotient n 10))))

(define (iter n)

(if (<= n 10)

(is-prime? p)

(and (is-prime? n) (iter (truncate n)))))

(iter p))

B. (nth-left-trunc-prime n) procedure:

(define (nth-left-trunc-prime n)

(define (find-trunc-prime i p)

(cond ((= i n) p)

((left-truncatable-prime? (+ p 1)) (find-trunc-prime (+ i 1) (+ p 1)))

(else (find-trunc-prime i (+ p 1)))))

(find-trunc-prime 1 7)) ; start at 7 because it is the first left-truncatable prime.

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a) The number of donations collected by Organization A and B  represents linear function and C has exponential growth function

b) Average rate of change of A and B is 4

   Average rate of change of C is 121.3333

c) The rate of change of a linear function is constant, while the rate of change of an exponential function is always increasing .

d) The numbers of donations collected by the three organizations increasing as the time increases

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

a) The number of donations collected by Organization A and B  represents  linear function and C has exponential growth function

b)   Average rate of change = ( f(x2) -f(x1) ) /( x2 - x1) ------(1)

    x1 = 0,  x2= 6

Organization  A and B:

f(6)= 24 ,  f(0) = 0

(1) =>  Average rate of change = (24-0)/(6-0) = 24/6 = 4

Organization  C:

f(6)= 729, ( y-coordinate  3 times the previous y-coordinate ),   f(0) = 1

(1) =>  Average rate of change = ( 729 -1)/(6-0) = 728/ 6 = 121.333

c) The rate of change of a linear function is constant, while the rate of change of an exponential function is always increasing .

d) The numbers of donations collected by the three organizations increasing as the time increases

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Answer:

Aubree can use 4.6 gigabytes of data while staying within her budget.

If the answer choices only use whole numbers, use 4 gigabytes, because it is the number of full gigabytes she can use.

Step-by-step explanation:

x= gigabyte

58.50 + 3x = 72.30

3x = 72.30-58.50

3x= 13.8

x= 4.6

The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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The probability that among those selected the second smallest in 2020 is 1/3

In this question, we have been given six distinct integers are selected at random from 2018, 2019, 2020, . . . , 2027

We need to find the probability that among those selected the second smallest in 2020.

Here, total integers are: 10

The total number of ways to choose six distinct integers :

10C6

= 10!/6!(10 - 6)!

= 210

Assume 2020 is the second-lowest number.

There are 5 numbers left to choose, 4 of which must be greater than 2020.

This is equivalent to choosing 4 numbers from the seven numbers larger than 2020, and 1 number from the two numbers less than 2020

using combination formula,

7C4 * 2C1

= 35 * 2

= 70

So, the probability would be,

P = 70/210

P = 1/3

Therefore, the required probability is 1/3  

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When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.

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Compare two similar sides:

24:32 this reduces to 3:4

Answer: D) 3:4

Based on the entries into the TVM solver, the expression that will return the same value for PV is \(\frac{(620) (( 1 + 0.066)^{108} - 1) }{(0.066) (1 + (0.066))^{108}}\).

The formula for present value for this series of cashflows is:

= \(\frac{(Payment) (( 1 + Interest rate)^{Number of years} - 1) }{(Periodic interest) (1 + (Periodic interest))^{Number of years}}\)

Based on the P/Y and the C/Y being 12, the number of periods given in the graphing calculator will be the same in the formula, which is 108 periods.

The interest rate of 6.6% will also be the same in the formula.

The best option is therefore option B which has all these figures and so will give the same present value.

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Answer: 0.0055 and 108

aka ($620) ((1+0.0055)^108 -1 / (0.0055) (1+0.0055)^108

Step-by-step explanation: Just did it, Good luck! :)

Answer:

A:1/3

Step-by-step explanation:

There are 6 possible outcomes when Sauli rolls the number cube, with each outcome having an equal probability of 1/6. To find the probability of rolling a number greater than 4, we need to count the number of favorable outcomes, which are the numbers 5 and 6.

Therefore, the probability of rolling a number greater than 4 is 2 favorable outcomes out of 6 possible outcomes, which simplifies to 1/3.

So the answer is A. 1/3.

Answer:

Center: 10, -6, Radius: 7

Step-by-step explanation:

This equation can be rewritten using the formula

(x-p)²+(y-q)²=r²

From this we get that p=10 and q=-6, because -(-6)=+6. This is how we get the center points.

And since the square root of 49 is 7, we see that the radius is 7.

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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Answer: Symbol max-min and answer 10-4

Step-by-step explanation:

Answer:

1.48 m

Step-by-step explanation:

mean is calculated as

mean = \(\frac{sum}{count}\)

Then the sum for the 14 boys is

\(\frac{sum}{14}\) = 1.56 ( multiply both sides by 14 )

sum = 21.84 m

The sum for the class of 32 is

\(\frac{sum}{32}\) = 1.515 ( multiply both sides by 32 )

sum = 48.48 m

Thus the sum for the 18 girls is

sum = 48.48 - 21.84 = 26.64 m

Then mean height of girls is

mean = \(\frac{26.64}{18}\) = 1.48 m

The exact behavior and consequences depend on the Operations system's process management mechanisms and the actions taken by process z or the system's process manager.

When process y dies, the Operations system handles the termination of the process and performs certain actions related to its termination. Here are the likely outcomes when process y, with process x as its child and process z as its parent, dies:

1. Process y's termination: When process y dies, the operating system marks it as terminated and frees up any system resources that were allocated to it. This includes releasing memory, closing file descriptors, and removing its entry from the process table.

2. Parent-child relationship: Since process x is the child of process y, the operating system updates the parent-child relationship. Typically, when a parent process dies, the child process is reassigned to another process called the init process or is terminated if no other process adopts it. The exact behavior depends on the operating system's process management policies.

3. Process z's status: Process z, being the parent of process y, may receive a notification or a signal indicating the termination of its child process. The operating system usually sends a SIGCHLD signal to the parent process, allowing it to handle the termination of its child process appropriately. Process z can choose to ignore the signal or perform actions such as cleaning up resources or spawning a new child process to replace the terminated one.

4. Orphaned process: If process z does not handle the termination of process y appropriately or if process z itself terminates before process y, process x becomes an orphaned process. Orphaned processes are typically adopted by the init process or the system's process manager, ensuring that they are handled and terminated properly.

In summary, when process y dies, the operating system marks it as terminated, updates the parent-child relationship, and may notify process z. The exact behavior and consequences depend on the operating system's process management mechanisms and the actions taken by process z or the system's process manager.

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A one-tailed test has a P-value of 0.01 and a two-tailed test has a P-value of 0.053.

We must utilize the F-distribution table or calculator to address this question. The F test follows an F-distribution since it is a ratio of two variances.

a. To calculate the P-value for a one-tailed test, we must first calculate the likelihood that the F-statistic is greater than or equal to 7.46.

Using a table, we can find the area under the F-distribution curve to the right of 7.46 with 5 degrees of freedom in the numerator and 7 degrees of freedom in the denominator.

Assuming an alpha level of 0.05, we reject the null hypothesis if the P-value is less than 0.05.

For the given F-statistic of 7.46, the P-value for a one-tailed F-test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator is approximately 0.01.

b. For a two-tailed test, we must calculate the likelihood of seeing an F-statistic that is 7.46 or more in either direction. This means we must calculate the area under the F-distribution curve in the distribution's two tails.

To find the p-value for a two-tailed F-test with 5 and 7 degrees of freedom and a test statistic of 7.46, we need to use an F-distribution table.

Using a table, we would look for the intersection of the row with 5 degrees of freedom and the column with 7 degrees of freedom, which gives us the critical F-value for a significance level of 0.05 (assuming equal variances in the two populations being compared). The critical F-value is 4.03.

Since the test statistic of 7.46 is greater than the critical F-value of 4.03, the p-value for the two-tailed test is less than 0.05. Specifically, the p-value is the probability of observing an F-statistic as extreme or more extreme than 7.46, which is the probability in the right tail of the F-distribution plus the probability in the left tail:

p-value = P(F > 7.46) + P(F < 1/7.46)

       = 0.052 + 0.001

       ≈ 0.053

Therefore, the p-value for the two-tailed test is approximately 0.053.

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Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height