Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.

Answer:

[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]

Step-by-step explanation:

Given equation:

[tex]t^2-10t+6=7[/tex]

When completing the square for a quadratic equation, the first step is to move the constant to the right side of the equation:

[tex]\implies t^2-10t+6-6=7-6[/tex]

[tex]\implies t^2-10t=1[/tex]

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies t^2-10t+\left(\dfrac{-10}{2}\right)^2=1+\left(\dfrac{-10}{2}\right)^2[/tex]

Simplify:

[tex]\implies t^2-10t+\left(-5\right)^2=1+\left(-5\right)^2[/tex]

[tex]\implies t^2-10t+25=1+25[/tex]

[tex]\implies t^2-10t+25=26[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (t-5)^2=26[/tex]

Square root both sides:

[tex]\implies \sqrt{(t-5)^2}=\sqrt{26}[/tex]

[tex]\implies t-5=\pm \sqrt{26}[/tex]

Add 5 to both sides:

[tex]\implies t-5+5=\pm \sqrt{26}+5[/tex]

[tex]\implies t=5 \pm \sqrt{26}[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]t=5 +\sqrt{26}, \quad t=5-\sqrt{26}[/tex]

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Answer:

(1, 1)

Step-by-step explanation:

x+y=2

y=5x-4

x + 5x - 4 = 2

6x - 4 = 2

6x = 6

x = 1

x + y = 2

1 + y = 2

y = 1

(1, 1)

The likelihood that the number is 3 or 5 is 0.47.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

There are 15 identical spaces. Once the spinner has been spun,

Probability is determined by dividing the number of potential outcomes by the number of possible positive outcomes.

5 times: 5, 10, and 15

3 times, 6, 9, 12, and 15.

Different results (3, 5, 6, 9, 10, 12, and 15) (stop doing them).

a variety of successful results 7

3) There are 15 possible outcomes.

4) Probability is equal to 7/15, or 0.47

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The number of students who passed only physics is 6, the number of students who passed only geography is 2, and the number of students who passed only history is 5.

First, let's represent the number of students who passed each subject with the variables P, G, and H. Then, we can represent the number of students who passed multiple subjects with the variables PG, PH, and GH.

We are given the following information:

39 students passed physics (P)

36 students passed geography (G)

40 students passed history (H)

22 students passed both physics and history (PH)

21 students passed both physics and geography (PG)

23 students passed both geography and history (GH)

10 students passed all three subjects (PHG)

We can set up the following equations to represent these relationships:

P = 39

G = 36

H = 40

PH = 22

PG = 21

GH = 23

PHG = 10

We can use these equations to solve for the number of students who passed only physics (P - PH - PG + PHG), only geography (G - GH - PG + PHG), and only history (H - PH - GH + PHG).

So, the number of students who passed only physics is:

P - PH - PG + PHG = 39 - 22 - 21 + 10 = 6

The number of students who passed only geography is:

G - GH - PG + PHG = 36 - 23 - 21 + 10 = 2

The number of students who passed only history is:

H - PH - GH + PHG = 40 - 22 - 23 + 10 = 5

Thus, there are 6 students who passed only physics, 2 students who passed only geography, and 5 students who passed only history.

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Step-by-step explanation:

find the equation of a line with slope 2 and 6 unit away from the origin​

slope intercept form: y = mx + b where m = slope and b = y-intercept.

You are given:

slope = 2

b = 6

answer:

y = 2x + 6

The five-number summary required to construct a box plot of this data does not include 11.

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful.

The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

So, sort the numbers in the row {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} from least to largest:

{1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27}

The range starts at 1 and ends at -27.

The middle value in this row—9—is the median.

18 is the median of the right part {12, 15, 18, 19, 27} and 5 is the median of the left part {1, 2, 5, 6, 7}.

The only option missing from A through D is number 11. (numbers 1, 5, and 9 are part of the five-number summary).

Therefore, the five-number summary required to construct a box plot of this data does not include 11.

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Complete question:
Which value is not part of the five-number summary needed for a box plot of this data?

{ 5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19}

A. 1

B. 5

C. 9

D. 11

The equation of the transformed function is g(x) = x + 4

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

f(x) = x

g(x) = translation 4 units up of f(x) = x

The above equations implies that, we have the transformation to be:

Translation 4 units up of f(x)

Mathematically, this can be represented as

g(x) = f(x) + 4

Substitute the known values in the above equation, so, we have the following representation

g(x) = x + 4

Hence, the transformed function si g(x) = x + 4

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Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex] \frac{12}{x} = \frac{8}{6} \\ 12 = \frac{8x}{6} \\ 12 \times 6 = 8x \\ \frac{72}{8} = x \\ 9 = x[/tex]

Check

[tex] \frac{12}{x} = \frac{8}{6} \\ \\ \frac{12}{9} = \frac{8}{6} \\ \\ 1.333 = 1.333[/tex]

Hello,

I hope you and your family are doing well!

To find the value of x, we can use the fact that TL is the perpendicular bisector of BE. This means that TL splits BE into two segments of equal length. Therefore, we have:

EL + BF = BE

Substituting the values for EL, BF, and BE gives:

[tex](8x - 17) + (7x - 5) = (3x + 6)[/tex]

Combining like terms gives:

[tex]15x - 22 = 3x + 6[/tex]

Subtracting 3x from both sides gives:

[tex]12x - 22 = 6[/tex]

Adding 22 to both sides gives:

[tex]12x = 28[/tex]

Dividing both sides by 12 gives:

[tex]x = 28/12 = 7[/tex]

Now that we know the value of x, we can use this value to find the value of y. We can use the equation TE = 2x - 10 to find the value of TE:

TE = 2x - 10 = 2 * 7 - 10 = 14 - 10 = 4

Now we can use the equation EL = 8x - 17 to find the value of EL:

EL = 8x - 17 = 8 * 7 - 17 = 56 - 17 = 39

Since TL is the perpendicular bisector of BE, the length of TL is the average of the lengths of EL and TE. The average of EL and TE is:

(EL + TE)/2 = (39 + 4)/2 = 43/2 = 21.5

So the length of TL is 21.5, and the value of y is 21.5 and x is 7

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Answer:

a = 84°

b = 21°

c = 48°

Step-by-step explanation:

Step 1.)

The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°

180°-75° = 105 = a° + b°

Step 2.)

We also know that the line RS is 180°. Therefore, it must be true that

75° + 4b° + b° = 180°

or simply

5b + 75 = 180°

Now solve for b. Subtract both sides by 75 and divide the right side by 5

5b = 105°

b = 21°

4b° = 4 x b = 4 x 21° = 84° = 4b°

Step 3)

Since we know that a + b = 105°, we use substitution to get:

a + 21° = 105

Now subtract both sides by 21

a = 84°

Now let's double check if a + b + 75 = 180

84 + 21 + 75 = 180 [check]

Step 4.)

Since we know that PQ is a straight-line that is 180°, we can say:

180° = 4b° + 2c°

Now substitute 4b with 84°

180° = 84° + 2c

Now solve by subtracting 84 from 180 and divide by 2, if needed.

96° = 2c°

48° = c°

Now double check

96° + 84° = 180° [check]

Therefore:

a = 84°

b = 21°

c = 48°

Hope that helps.

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The second-period interest and amount after two months, if The principal amount is $400, The rate of interest is 6% per annum, are $4.02 and $406.02 respectively.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The principal amount, P = 400,

The rate of interest, r = 6% per annum,

The time period, t = monthly = 1 / 12 year,

Calculate the simple interest for the first month as shown below,

Simple interest = [tex]p\times r\times t/100[/tex]

Simple interest = 400 × 6 × 1 / (12 × 100)

Simple interest = 2

Thus, the amount of the first month is the principle for the second month,

Amount of the first month =  Principal of the second month = 400 + 2 = 402,

Calculate the simple interest for the second month as shown below,

Simple interest = [tex]p\times r\times t/100[/tex]

Simple interest = 402 × 6 × 2 / (12 × 100)

Simple interest = 4.02

Amount after two months = 402 + 4.02 = 406.02.

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Answer:

48% discount

Step-by-step explanation:

39/75 = 0.52

39 is 52% of 75 but to find the percent discount you have to

1 - 0.52 = .48 *100 = 48%

Answer:

You can get the answer of 1,2,3,4,5 or 6. Each are 1/6 likely to be rolled.

Step-by-step explanation:

The die has 6 sides. If you were to roll the die 6 times you have the chance to roll the side with 1. The chances of rolling a 1 are 1/6.

Answer:

b

Step-by-step explanation:

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

Inequality is the unequal distribution of resources, opportunities, or rewards among individuals or groups in society. It can occur in many forms, such as unequal access to healthcare, education, employment, or other resources, or unequal treatment based on race, gender, ethnicity, and other factors. Inequality can also manifest as unequal income and wealth distribution, as well as unequal access to political power and decision-making. Inequality can be caused by a variety of factors, including structural factors and personal or individual-level factors, such as discrimination. Inequality can have a negative effect on both individuals and societies, leading to social and economic inequities that can be difficult to overcome.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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The correct option is B in the given Temperature problem by Calculation T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius,

T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius

According to the given information:

For the first question, we need to compare the rate of change of temperature with respect to rotation speed for both engines. We can do this by calculating the difference in temperature for a change in rotation speed of 111 cycles per second for both engines.

For the first engine, the temperature increased by:

31.2 - 28.8 = 2.4 degrees Celsius

For the second engine, the temperature increased by:

60 - 50 = 10 degrees Celsius

Since the temperature increase for the second engine is greater, we can conclude that the second engine's temperature increased more for each increase of 111 cycles per second. Therefore, the answer is (B) The second engine.

For the second question, we can use linear interpolation to estimate the temperature of each engine at 20 cycles per second.

For the first engine, we can use the two closest data points (8.8 and 11.1 cycles per second) to estimate the temperature at 20 cycles per second:

T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius

For the second engine, we can use the same method with the two closest data points (10 and 20 cycles per second):

T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius

Therefore, we can conclude that the second engine was hotter when it rotated at 20 cycles per second. The answer is (B) The second engine.

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Answer:

5/ Slope is 0

6/ Slope is 4/1

7/ Slope is -4/2 = -2

8/ Slope is undefined

Step-by-step explanation:

5/ Slope is 0 when it goes straight to the right

6/ We see that the y goes up 4, x over 1, so the slope is 4/1

7/ We see that the y goes down by 4, and x over by 2, so the slope is -2

8/ Slope is undefined when it goes straight up!

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Answer:

A) The equation y = 2x represents a proportional relationship. This is because the values of y are directly proportional to the values of x. In other words, as x increases, y also increases by the same factor. This is the definition of a proportional relationship.

B) The unit rate of change for this situation is 2 hot dogs per minute. This is because the equation y = 2x represents a linear relationship, where the rate of change (the slope) is constant. The unit rate of change is the slope of the line, which in this case is 2. This means that for every 1 minute that passes, Peter eats 2 hot dogs.

1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²

The circle is a 2D geometrical figure, with no side or angle, and is made a collection of points.

Given that, 1) a circle with circumferences = 2πr and radius = r, 2) a circle having circumferences = 76 cm and 3) Jada is painting a table having diameter 37 in.

1) Assume the figure as a rectangle, (refer to attached figure)

We get, the length of it is πr and width is r.

And the area of a rectangle is = the Product of length and width.

So, we can conclude that the area of this rectangle is = πr×r = πr²

Therefore, by assuming the figure as a rectangle, we can explain why the area of a circle is πr²

2) circumferences = 2πr

2πr = 76

πr = 38

r = 38/3.14  (π ≈ 3.14)

r = 12.01 cm

Diameter = 2r

D = 2x12.01 = 24.20 cm

Area = πr²

= 3.14x12.01²

= 452.91 cm²

3) Diameter = 37 in

r = 37/2 = 18.5 in

Area = πr²

= 3.14x18.5²

= 1074.66 in²

Therefore, the area of the table is 1074.66 in²

Hence, the answers are 1) We can explain why the area is πr² by assuming the figure as a rectangle, 2) Diameter = 24.20 cm, Area = 452.91 cm² and 3) the area of the table is 1074.66 in²

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Answer: 356 mil

Step-by-step explanation:

Answer:

Each tube will contain 15.7 millimeters

Step-by-step explanation:

Since  235.5 milliliters of water is to be shared among 15 test tubes then the amount of water in each test tube is:

[tex]\frac{235.5}{15} \\\\= 15.7[/tex]

Thus each tube will contain 15.7 millimeters

The ratio of the numbers of bananas to the number of oranges is 2:3, thus Ms Rehka bought 48 bananas.

A ratio is a fraction which shows the way of dividing two quantities.

Since the ratio of the numbers of bananas to the number of oranges is 2:3 furthermore there are 24 more oranges to bananas.

Let

Since the ratio of the numbers of bananas to the number of oranges is 2:3, we have that

x:y = 2:3

x/y = 2/3

Also, there are 24 more oranges to bananas. We have that

y = x +24

Substituting y into the ratio, we have

x/y = 2/3

x/(x + 24) = 2/3

Cross-multiplying, we have

3x = 2(x + 24)

Expanding the brackets, we have

3x = 2x + 48

3x - 2x = 48

x = 48

So, Ms Rehka bought 48 bananas.

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[tex]-2.5(4x-4)= -6[/tex]

Distribute:

[tex](-2.5)(4x)+(-2.5)(-4)=-6[/tex]

[tex]-10x+10=-6[/tex]

Subtract 10 from both sides:

[tex]-10x+10-10=-6-10[/tex]

[tex]-10x=-16[/tex]

Divide both sides by -10:

[tex]\dfrac{-10x}{-10} =\dfrac{-16}{-10}[/tex]

[tex]\fbox{x = $\dfrac{8}{5} $}[/tex]

Answer:

-2.5. or - 2.5= they are the same

Answer:

9

Step-by-step explanation:

Equation

[tex]3n + 11 = 38[/tex]

3n=38-11

n=27/3

n=9

therefore triplets are 9 years old

Check

[tex]3n + 11 = 38[/tex]

[tex]3 \times 9 + 11 = 38 \\ 27 + 11 = 38 \\ 38 = 38[/tex]

Answer:

equation: 3n+11=38

The triplets are 9 years old.

Step-by-step explanation:

3n : triplets x their age

11 : the sum

38 : the sum of the ages

We must isolate n to know their age so,

<=> 3n+11=38

<=> 3n=38-11

<=> n=(38-11)/3

<=> n=9

Answer:

[tex]1 {p}^{2} + 3p - 3.5[/tex]

Step-by-step explanation:

Look at the picture attached. Hope this helps!

There are 325 ways we can write two different letters so that they are in alphabetical order.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).

A k-combination of a set S is officially defined as a subset of S's k unique elements.

We have 25 ways to have the combo A_

Then 24 ways to have the combo  B_

The number of combos = 25 * (26/ 2)  

                                       = 25 * 13  

                                       = 325  ways

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Answer:

Picture 1:

Step 1- Given

Step 2- Addition Property of Equality

Step 3- Division Property of Equality

Picture 2:

Step 1- Given

Step 2- Combine Like Terms

Step 3- Subtraction Property of Equality

Picture 3:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Division Property of Equality

Picture 4:

Step 1- Given

Step 2- Distributive Property

Step 3- Combine Like Terms

Step 4- Addition Property of Order

Step 5- Division Property of Order

Picture 5:

Step 1- Given

Step 2- Distributive Property

Step 3- Subtraction Property of Order

Step 4- Addition Property of Order

Step 5- Combine Like Terms

Step 6- Division Property of Order

Hope this helps :)

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Because it is multiplication, the parenthesis are not important. It is the equivalent of 3*9*8 = 8*3*n. From here, you can tell that the 9 is missing.

Answer:

The two numbers are 44 as the smaller number and 89 as the larger number.

Step-by-step explanation:

Hope it helps!

Let's call the larger number x, and the smaller number y. We know that y is one more than half of x, so we can write y = x/2 + 1. We also know that the sum of the two numbers is 133, so we can write x + y = 133. We can use these two equations to solve for the values of x and y. Substituting the first equation into the second, we get:

x + (x/2 + 1) = 133

Combining like terms, we get:

1.5x + 1 = 133

Subtracting 1 from both sides, we get:

1.5x = 132

Dividing both sides by 1.5, we get:

x = 88

Substituting this value for x in the first equation, we get:

y = 88/2 + 1 = 44 + 1 = 45

Therefore, the two numbers are 88 and 45, and we can check our solution by verifying that the sum of these numbers is indeed 133.

x + y = 88 + 45 = 133

This confirms that our solution is correct.