Witch is a equation is equivalent to 3[x+3(4x - 5)]

Based on the information supplied, the estimated age of archaeological sample is = 0.183536  years.

The given half life is 5730.

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate of change,

k = 0.00012 year⁻¹

Given that 15 % of the 14C is still present,

|A1|/|A2| = e ⁻₍kt₎3

Consequently,

|A1|/|A2| = 0.18

As a result of solving the equation, we obtain,

ln(0.18)= -1.7147

t = -0.31471/ —1.7147

= 0.183536  years

The half-life is the amount of time required for a quantity (of material) to drop to half of its initial value (symbol t12). The phrase is widely used in nuclear physics to emphasise how quickly unstable atoms decay radioactively or how long stable atoms remain. The term is often used to denote any type of exponential decay (or, very infrequently, nonexponential decay).

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Answer:1, fractions come in different shapes,2, how to divide fractions and how to simplify mixed fractions. 3, we get to interact with electronics we get a better understanding of the work and more online work

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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In comparison with the addresses given, the address of the boutique is 538elm. Option B

From the information given, we have the grocery, cafe, boutique and dance studio addresses.

Given the addresses:

500 elm, 524 elm, 538 elm, and 544 elm

We have that :

Boutique is between cafe and studio

Studio has the highest address = 544 elm

Grocery is between cafe and boutique

CBS

S = 544elm

CGB

Thus, In comparison with the addresses given, the address of the boutique is 538elm. Option B

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Answer:

First Answer: 12.5 weeks

Third Answer: 16 minutes(I think it was a really long decimal so I rounded it up)

A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.

Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.

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Answer:

D. $24.75

Step-by-step explanation:

24.75 - 4.75 - 1.65 = 18.35

Given, log2(x−1) + log2(x+5) = 4. We need to find the value of x which satisfies this equation.

We know that loga m + loga n = loga(m*n).Using this formula, we can rewrite the given equation as,log2(x−1)(x+5) = 4We know that if loga p = q then p = aq Putting a = 2, p = (x−1)(x+5) and q = 4, we get,(x−1)(x+5) = 24x² + 4x − 21 = 0Solving this equation using factorization or quadratic formula, we get,x = (–4 ± √100)/8x = (–4 ± 10)/8x = –1 or 21/8Hence, the values of x that satisfy the given equation are x = –1 or x = 21/8. Answer more than 100 words:Given, log2(x−1) + log2(x+5) = 4.

We need to find the value of x which satisfies this equation.Logarithmic functions are inverse functions of exponential functions. If we have, y = ax then, loga y = x, where a is the base of the logarithmic function. For example, if a = 10, then the function is called a common logarithmic function.The base of the logarithmic function must be positive and not equal to 1.

The domain of the logarithmic function is (0, ∞) and the range of the logarithmic function is all real numbers.Let us solve the given equation,log2(x−1) + log2(x+5) = 4Taking antilogarithm of both sides,2log2(x−1) + 2log2(x+5) = 24(x−1)(x+5) = 16(x−1)(x+5) = 24(x²+4x−21) = 0On solving the quadratic equation, we get,x = –1 or x = 21/8

Hence, the values of x that satisfy the given equation are x = –1 or x = 21/8.

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Answer:

It should be red or green 125 times

Step-by-step explanation:

The first thing to do here is to calculate the probability of selecting a red or a green marble

Total number of marbles = 7 + 3 + 2 + 8 = 20

Probability of selecting a red marble is 7/20

Probability of selecting a green marble is 3/20

The probability of selecting a red or a green marble = Probability of selecting a red marble + Probability of selecting a green marble = 7/20 + 3/20 = 10/20 = 1/2

Now our selection spans 250 times, the number of times it should have been a green or a red marble = The probability of selecting a green or a red marble * number of selection times = 1/2 * 250 = 125 times

Notice that the intersecton of both inequality is located approximately at the point (150,50). This means that there are at least 100 more feet of quarter inch pipe than half inch pipe, and since the combined cost is represented by the inequality

then, it must not cost more than 800. Therefore, the correct option is a)

Chris has to pay $8.5 for all the fruit.

given:

Oranges are 2 pounds for $1.00. Apples are $2.00 per pound. Chris

bought 5 pounds of oranges and 3 pounds of apples.

       total apple purchase by Chris = 3 pounds

        the total cost of apples (3 * $2 )= $6

         total cost for 5 pounds of orange will be $2.5

   the total cost of fruits is the cost of apples plus the cost of orange

             = ($6+$2.5)= $8.5

therefore, the total amount to be paid by Chris is $8.5

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Answer:

Step-by-step explanation:

9a. Yes, because 10/12 = 5/6 (simplified)

9b. yes, because 20wins/24losses = 5/6 (simplified)

9c. no, because 12/13 does not simplify at all

9d. yes, because 15wins/18losses = 5/6

(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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To determine if the degree of the function is odd or even we need to look at the extrema of the graph. If both points to the same side, it is, if X goes to positive infinity or to negative infinity, to both direction Y of the graph is going to the same direction, it means that the degree os even. Otherwise, when the extrema are pointing in different directions, it means the degree is odd.

In the present graph, the degree is odd, because the graph has different directions for each extrema.

To determine the signal to the leading coeficient, we check the direction Y is going to increasing values of X. If Y goes positive, the leading coeficient is positive, if it is negative, the leading coeficiente is negative.

In the present graph, the leading coeficient is positive, because for increasing values of X we have increasi

y=x+4

slope intercept form is y=mx+b

mx= slope

b= y- intercept

the graph shows you the y-int (basically whatever y is when x=0)

you can find the slope by using the slope formula (y2 - y1/x2 - x1) or by counting rise/run

slope is 1, so its just x

In order to find the absolute maximum and minimum of the function \(\( g(x)=\cos x+\sin x \)\)where \(\( \pi \leq x \leq 2 \pi \).\)

Then, we will evaluate the function at these critical points, as well as the endpoints of the interval.  The highest value of these is the absolute maximum, and the smallest value is the absolute minimum.

\($$g(x)=\cos x+\sin x$$$$g'(x)=-\sin x+\cos x$$\)

The critical points of the function are given by the values of \( x \) that make the first derivative equal to zero:

\($$-\sin x+\cos x=0$$$$\sin x=\cos x$$$$\tan x=1$$$$x=\frac{\pi}{4}+k\pi\qquad k\in\mathbb{Z}$$\)

\($$g(\pi)=\cos\pi+\sin\pi=-1+0=-1$$$$g(2\pi)=\cos2\pi+\sin2\pi=1+0=1$$$$g\left(\frac{5\pi}{4}\right)=\cos\frac{5\pi}{4}+\sin\frac{5\pi}{4}=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}=-\sqrt{2}$$\)

Thus, the absolute maximum of the function is \(\( 1 \),\) which is attained at\(\( x=2\pi \)\), and the absolute minimum is

\(\( -\sqrt{2} \)\),

which is attained at\(\( x=\frac{5\pi}{4} \)\).

Hence, the absolute maximum and minimum of the function are \(\( 1 \) and \( -\sqrt{2} \)\), respectively, in the interval

\(\( \pi\leq x\leq 2\pi \)\).

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Answer:

x = -8

Step-by-step explanation:

3.2 - 1/2(x + 4) = 4.8x + 2 - 5.2x

3.2 - 0.5x - 2 = - 0.4x + 2

1.2 - 0.5x = -0.4x + 2

1.2 - 0.1x = 2

-0.1x = 0.8

x = -8

Answer: 6.8 = 1.6

Step-by-step explanation:

3.2-1/2 (+4)                         4.8+2-5.2

2.8+4                                   6.8-5.2

6.8                      =                    1.6

Answer: x=2.5, and x-1=1.5

Step-by-step explanation:

x + 3 = 3x - 1

(-x)= 3 = 2x - 1

(÷2) = 1.5 = x - 1

(+1)= 2.5 = x

Answer:

9 : 25

Step-by-step explanation:

Given the ratio of the sides of 2 similar equilateral triangles = a : b , then

the ratio of their areas = a² : b²

Given ratio of sides = 3 : 5 , then

ratio of areas = 3² : 5² = 9 : 25

Answer:

The new price is $25.30.

22x0.15= 3.3.

22+3.3= 25.30

Step-by-step explanation:

hope this helps :)

PQCB is a parallelogram. (A) To determine the length of the fence for the triangular region PQR, we need to calculate the lengths of the sides PQ, QR, and RP.

To find the length of the fence:

Identify the midpoints: P, Q, and R are the midpoints of sides AB, AC, and BC, respectively.

Calculate the lengths:

PQ: Since P is the midpoint of AB, PQ is half the length of AB. As AC = 30 meters, AB = 2 * AC = 2 * 30 = 60 meters. Therefore, PQ = 60 / 2 = 30 meters.

QR: Since Q is the midpoint of AC, QR is half the length of AC. Hence, QR = AC / 2 = 30 / 2 = 15 meters.

RP: As R is the midpoint of BC, RP is half the length of BC. Since BC = AC = 30 meters, RP = BC / 2 = 30 / 2 = 15 meters.

The total length of the fence is the sum of the lengths of the three sides: PQ + QR + RP = 30 + 15 + 15 = 60 meters.

(B) The quadrilateral PQCB is a parallelogram.

Justification:

Opposite sides are parallel: In triangle ABC, P and Q are midpoints of sides AB and AC, respectively. This implies that PQ is parallel to BC.

Opposite sides are congruent: As P and Q are midpoints, PQ is half the length of AB, which is equal to BC.

Diagonals bisect each other: The diagonals of a parallelogram bisect each other. In this case, the diagonal AC bisects PQ, and the diagonal BC bisects QR. Therefore, the diagonals of PQCB bisect each other.

Hence, based on these properties, we can conclude that PQCB is a parallelogram.

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Answer:

D. 23% decrease

Step-by-step explanation:

To find the percentage of increase or decrease, we can use the following formula:

Percentage change = ((New value - Old value) / Old value) * 100

Let's calculate the percentage change in the price of the television:

Old value = 398

New value = 306.46

Percentage change = ((306.46 - 398) / 398) * 100

Percentage change = (-91.54 / 398) * 100

Percentage change ≈ -22.98%

The percentage change is approximately -22.98%.

Since the value decreased, the correct answer is:

D. 23% decrease

91.54 decrease

91.54/398 ~ 0.23 ~ %23

the answer must have been D

The cost for each ton of sugar being transported increase by $1200.

The slope of the line is equal to 800.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (2800 - 1200)/(2 - 0)

Slope (m) = 1600/2

Slope (m) = 800.

Based on the y-intercept is the initial cost and it is located at data point (0 1200), which represent the increase in cost for each ton of sugar being transported.

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Answer:

3.15

Step-by-step explanation:

The solution is, the price of one cupcake is $3.15.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Jordan paid $390.60 for 124 cupcakes

that each cost the same amount.

so, the price of one cupcake = $390.60/ 124

                                                =$3.15

Hence, The solution is, the price of one cupcake is $3.15.

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The area of the teacher workroom is 64 feet squared

95% confidence that the true mean of the violent crime rate in Seattle's census tracts lies between 20.43 and 33.69 per 1,000.

In the given study, Rountree and Warner (1999) observed a mean official violent crime rate of 27.06 per 1,000 in 100 census tracts over a two-year period in Seattle, WA. The standard deviation was 33.81. To construct a 95% confidence interval around this mean, we can use the formula:

\(CI = mean ± (Z-score * (standard deviation / √sample size))\)

For a 95% confidence interval, the Z-score is 1.96. The sample size is 100 census tracts. So, we can calculate the interval as follows:

CI = 27.06 ± (1.96 * (33.81 / √100))

CI = 27.06 ± (1.96 * (33.81 / 10))

CI = 27.06 ± (1.96 * 3.381)

CI = 27.06 ± 6.63

The lower bound for this confidence interval is 27.06 - 6.63, which is approximately 20.43. Therefore, we can say with 95% confidence that the true mean of the violent crime rate in Seattle's census tracts lies between 20.43 and 33.69 per 1,000.

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Answer:

Fraction: 3/10

Decimal: 0.30

Step-by-step explanation:

Answer:

0.30 or 0.3
(three tenths)

3/10

(and also three tenths)

or

30/100

Step-by-step explanation:

Answer:

The correct option is

C. \(18x^2y^2\sqrt[3]{3xy^2}\\\)

Step-by-step explanation:

We have the expression,

\(3x\sqrt[3]{648x^4y^8}\)

Simplifying,

\(3x\sqrt[3]{648x^4y^8}\\3x\sqrt[3]{648x^3xy^6y^2}\\3x\sqrt[3]{648(x)^3x(y^2)^3y^2}\\\)

Taking out x and y^2,

\(3xxy^2\sqrt[3]{648xy^2}\\3x^2y^2\sqrt[3]{(2)(2)(2)(3)(3)(3)(3)xy^2}\\3x^2y^2\sqrt[3]{(2)^3(3)^3(3)xy^2}\\\\(3)(2)(3)x^2y^2\sqrt[3]{(3)xy^2}\\18x^2y^2\sqrt[3]{3xy^2}\\\)

Hence the correct option is C

The 95% confidence interval for the difference in population means of light marijuana users and heavy users when the populations are normally distributed is (3.777, 6.223). Hence, the correct option is (A).

Given that a study was conducted to test the effects of marijuana use on mental abilities of college students. Groups of light and heavy users of marijuana in college were tested for memory recall. The below table shows the results;Light UsersHeavy UsersSample Size(n1)40Sample Size(n2)30Sample Mean(X1) 28Sample Mean(X2)23Sample Standard Deviation(S1) 4.4Sample Standard Deviation(S2)

In order to find the 95% confidence interval for the difference in population means of light marijuana users and heavy users, the steps are as follows:Step 1:  The first step is to determine the degrees of freedom, which are (n1 - 1) + (n2 - 1) = 39 + 29 = 68.Step 2:  The second step is to calculate the pooled standard deviation using the formula;Sp = sqrt [((n1 - 1) * S12 + (n2 - 1) * S22) / (n1 + n2 - 2)]where S1 and S2 are the standard deviations of the two groups, and n1 and n2 are the sample sizes.

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Answer:

49 Dogs

Step-by-step explanation:

Cats : Dogs

     4 : 7

4C + 7D = 11 CD

CCCC DDDDDDD = 11 pets

77 / 11 = 7

CCCC * 7 = CCCCCCCCCCCCCCCCCCCCCCCCCCCCC = 28 cats

DDDDDDD * 7 = 49 dogs