0.571428
is or is not the decimal equivalent of
4
7
. Write your answer in the space provided.

The half-life of radium-230 is approximately 5 hours and 24 minutes, or equivalently, 324 minutes.

The half-life of a radioactive substance is the time it takes for half of the initial quantity of the substance to decay. In this case, the initial quantity of radium-230 is 2.00 mg, and it decays to 0.25 mg over a time period of 1 hour and 21 minutes.

To determine the half-life, we need to find the time it takes for the quantity of radium-230 to decrease to half of the initial amount. In this case, the initial quantity is 2.00 mg, so half of that is 1.00 mg.

Since it takes 1 hour and 21 minutes for the sample to decay to 0.25 mg, we can determine the time it takes for the sample to decay to 1.00 mg by multiplying the given time by (1.00 mg / 0.25 mg).

(1 hour and 21 minutes) * (1.00 mg / 0.25 mg) = 5 hours and 24 minutes

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Answer:

C

Step-by-step explanation:

The expression uses the associative property to make it easier to evaluate 14(3/2 . 1/4) would be equal to (3/2 . 1/4)14

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; can  be used to indicate the logical syntax's order of operations and other features.

Now we have given an expression as;

14(3/2 . 1/4)

Using associative property to make it easier to evaluate;

14(3/2 . 1/4)

= (3/2 . 1/4)14

The correct answer is D.

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Frank cannot recover the reward because he was unaware of the reward being offered by Emma.

In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.

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The surface area of the rectangular pyramid is 72 m^2. Answer: (B) 72 m^2.

The rectangular pyramid has a rectangular base of dimensions 4 meters by 4 meters, so the area of the base is:

A_base = length * width = 4 m * 4 m = 16 m^2

The triangular faces are isosceles triangles with base 4 meters and height 7 meters, so the area of each triangular face is:

A_tri = 0.5 * base * height = 0.5 * 4 m * 7 m = 14 m^2

There are four triangular faces, so the total area of the triangular faces is:

4 * A_tri = 4 * 14 m^2 = 56 m^2

The surface area of the pyramid is the sum of the areas of the base and the triangular faces, so:

SA = A_base + 4 * A_tri = 16 m^2 + 56 m^2 = 72 m^2

Therefore, the surface area of the pyramid is 72 m^2. Answer: (B) 72 m^2.

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Step-by-step explanation:

A chord is a segment with endpoints on the circle.

A tangent line is a line that touches a circle at only one point.

A diameter is a chord that passes through the center of the circle.

A secant line is a line that touches a circle at two points.

Therefore, AB is a secant line.

The statement related to the diagram is true is that AB is the secant line.

A chord should be treated as the segment that contains the endpoints on the circle. A tangent line refers to the line that touches a circle at only one point. A diameter refer to a chord that passes via the center of the circle. A secant line should be a line that touches a circle at two points.

Hence, The statement related to the diagram is true is that AB is the secant line.

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The probability that a student will have at least 3 similar personality traits in common with their friends is 0.8802 or 87.98%.

The probability of having at least 3 similar personality traits in common is calculated by taking into account the probability of having 3, 4 or all 4 traits in common.

To do this, Susan uses the formula for finding the probability of a complement event, which is 1 minus the probability of not having at least 3 traits in common.

The probability of not having at least 3 traits in common is found by adding up the probabilities of having 0, 1, or 2 traits in common. This gives us a total probability of

=> 0.4009 + 0.316 + 0.3538 + 0.0472 = 0.1198.

The probability of having at least 3 traits in common is then found by subtracting this value from 1, which gives us a probability of

=> 1 - 0.1198 = 0.8802.

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Answer:

it is 2 1/10 i took the test from K12

Step-by-step explanation:

Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Answer:

The  equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

Step-by-step explanation:

Given the equation

y + 5 = 3(x - 1)

Writing in the slope-intercept form

y=mx+b

where m is the slope and b is the y-intercept

y = 3(x-1) -5

y  = 3x-3-5

y = 3x - 8

Thus, the slope = m = 3

We know that the parallel lines have equal slopes.

So, the slope of a parallel line is also 3

Using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = 3 and the point (3, -4)

y-(-4)=3(x-3)

y+4 = 3x-9

y = 3x-9-4

y = 3x-13

Thus, the  equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

Answer:

51

Step-by-step explanation:

Well we first need to find the volume of the soup in the pot using the following formula,

πr^2h

15*15 = 225

225 * 25 = 5625

5625 * pi = 17671.46

Now we need to find the volume of the ice cube using the formula,

l*w*h

7*7*7 = 343

Now we do 17671.46 ÷ 343 = 51.5202915452

You can have half an ice cube,

thus, Sharon can make 51 whole cubes.

Hope this helps :)

Answer:

130 cubes  ( if the cylindrical height is 25 in )

51 cubes ( if the cylindrical height is 25 cm)

Step-by-step explanation:

cube edges = 7 cm long

volume of the soup = pi * r² * h

where h = 25in convert it to cm = 25 in * 2.54 cm/1 in = 63.5 cm

cylindrical pot diameter d = 30 cm

Volume of cylindrical pot = 3.14 * 15² * 63.5 = 44,885.5 cm³

Volume of ice cube = 7 * 7 * 7 = 343 cm³

to get the number of cubes = 44,885.5 / 343 = 130 cubes

therefore, Sharon can make 130 whole cubes

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

if the cylindrical height is 25cm then

Volume of cylindrical pot = 3.14 * 15² * 25 = 17,671.5 cm³

Volume of ice cube = 7 * 7 * 7 = 343 cm³

to get the number of cubes = 17,671.5 / 343 = 51 cubes

Answer:

3/5=w

Step-by-step explanation:

the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.

Answer:

16/5

Step-by-step explanation:

10x3/5=10x w-2/2

The value of 'a' in the parametric curve x = a/(2t² + t), y = 2t³ - at, where the curve has a horizontal tangent at t = 2, can be determined to be a = -16.

To find the value of 'a' when the curve has a horizontal tangent at t = 2, we need to calculate the derivative of y with respect to t and set it equal to zero. Differentiating y = 2t³ - at, we get dy/dt = 6t² - a. Setting this derivative equal to zero gives 6t² - a = 0. Plugging in t = 2, we have 6(2)² - a = 0, which simplifies to 24 - a = 0. Solving for 'a', we find a = 24. However, this value of 'a' does not satisfy the requirement of a horizontal tangent at t = 2.

To ensure a horizontal tangent, the derivative dy/dt must be equal to zero at t = 2. Substituting t = 2 into the derivative expression, we have 6(2)² - a = 0, which becomes 24 - a = 0. Solving for 'a' gives a = 24. However, this value does not satisfy the requirement. Therefore, we must continue searching for a different value of 'a'.

Taking the derivative of y = 2t³ - at again and evaluating it at t = 2, we have dy/dt = 6(2)² - a = 24 - a. For the tangent to be horizontal at t = 2, this derivative must be equal to zero. Setting 24 - a = 0 and solving for 'a', we find a = 24. However, this value does not satisfy the condition. We need to search for another value of 'a'. Substituting a = -16 into the equation, we have 24 - (-16) = 0. Therefore, the value of 'a' that gives a horizontal tangent at t = 2 is a = -16.

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Answer:

(x - 3)(x - 2)(x + 2)

Step-by-step explanation:

Given

x³ - 3x² - 4x + 12 ( factor the first/second and third/fourth terms )

= x²(x - 3) - 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(x² - 4) ← x² - 4 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4

= x² - 2²

= (x - 2)(x + 2)

Thus

x³ - 3x² - 4x + 12 = (x - 3)(x - 2)(x + 2) ← in factored form

Answer:

(x - 2)(x - 3)(x + 2).

Step-by-step explanation:

The Factor Theorem states that if x - a is a factor of f(x) the f(a) = 0.

f(x) = x^3 - 3x^2 - 4x + 12​

We try the factors of 12:

f(2) =  2^3 - 3*4 - 8 +12

= 8 - 12 - 8 + 12  = 0

- so (x - 2) is a factor of f(x)

Dividing:

        x^2  -  x -  6            <-----------Quotient

       -----------------------------

x - 2 )x^3 - 3x^2 - 4x + 12​

        x^3 - 2x^2

                  -x^2 - 4x

                  -x^2 + 2x

                          -6x + 12

                          -6x + 12

So we factor x^2 - x - 6:

= (x - 3)(x + 2)

Answer:

the ratio is 12:5

Step-by-step explanation:

48:20 divided in half 24:10 divided in half 12:5

Answer:

? anything else or..

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

is the median

give email id

The number of Hopper's steps that is equivalent to one of Skipper's jumps is given as follows:

2.45.

The situation can be modeled by a system of equations.

The variables for the system of equations are given as follows:

Hopper takes three jumps, he lands in the same place as Skipper does when she takes 4 jumps, hence:

3x = 4y.

x = 4/3y.

When Hopper takes six jumps and nine steps, he lands in the same place as Skipper does when she takes nine jumps, hence:

6x + 9z = 9y.

Replacing x = 4/3y on the second equation, we have that:

4(4/3y) + 9z = 9y.

9z = 9y - 16/3y

9z = 27/3y - 16/3y

9z = 11/3y

y = 27/11z

y = 2.45.

Meaning that 2.45 of Hopper's steps are equivalent to one of Skipper's jumps.

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The constant of proportionality that relates the number of cups of cereal, y, to the number of cups of pretzel sticks, x is y= 5/2x.

We have,

A snack mix recipe calls for 10 cups of cereal and 4 cups of pretzel sticks.

Using constant of proportionality

y = kx

where k is the constant

So, put y= 10 and x= 4 then

10 = k (4)

k = 10/4

k= 5/2

Thus, the constant of proportionality is 5/2.

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Answer:

8 - 4x^2y - 6y^6

Step-by-step explanation:

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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Answer:

16a^21

Step-by-step explanation:

Answer:

16 a^21

Step-by-step explanation:

= (2a^3)^4 (a^3)^3

= (2^4 a^3*4) (a^3*3)

= (16a^12) (a^9)

= 16 a^21

The addition symbol (+) can be used in between the two parentheses to show that you will be using the distributive property.

Distributive property:

The distributive property states that multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

It can be written as,

a x (b + c) = (a x b) + (a x c)

Where a, b and c are the values of the variables.

Given,

Here we have the expression:

8 x 57 = (8 x 50) _____(8x7)

Here we need to find the symbol that can be used in between the two parentheses to show that it will be using the distributive property.

Based on the definition of the distributive property we have know that the symbol (+) can be used to make this one as distributive property used equation.

Therefore, the expression is written as,

8 x 57 = (8 x 50) + (8x7)

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

\( \sf \large \: x = -1\)

Step-by-step explanation:

4x + 7 = 3

Substract 7 from both sides

4x + 7 - 7 = 3 - 7

4x = -4

Divide both sides by the coefficient of x

4x/4 = -4/4

calculate

x = -1

As the number of replicates in a simulation increases the width of a confidence interval computed from the simulation results will decrease.

As the number of replicates in a simulation increases the width of a confidence interval computed from the simulation results will decrease. The width of the confidence interval depends on the sample size, the variability in the data (measured by the standard deviation), and the level of confidence required.

When more replicates are taken, the sample size is larger, and the variability in the data is reduced, which results in a narrower confidence interval.

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Answer:

equilateral

Step-by-step explanation:

The hash marks on the sides mean that all four sides are congruent.

Answer:

first one I think hope this help