where Q represents the quantity remaining after tyears and kis the decay
constant 0.00043. How long will take for 500g of radium to decay to 5g?

9514 1404 393

Answer:

  23)  x = ±3i, ±√2

  26)  x = 4/3, (-2/3)(1 ± i√3)

Step-by-step explanation:

23) Put in standard form to make factoring easier.

  x^4 +7x^2 -18 = 0

  (x^2 +9)(x^2 -2) = 0 . . . . factors in integers

Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:

  (x -3i)(x +3i)(x -√2)(x +√2) = 0

  x = ±3i, ±√2

___

26) This will be the difference of cubes after you remove the common factor.

  81x^3 -192 = 0

  3(27x^3 -64) = 0

  (3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes

The complex roots of the quadratic can be found using the quadratic formula.

  x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)

Then the three solutions to the equation are ...

  x = 4/3, (-2/3)(1 ± i√3)

A right circular cone is a three-dimensional geometric shape that consists of a circular base and a curved surface. The volume of the right circular cone is approximately 24.045 cubic feet.

To find the volume of a right circular cone, we can use the formula

\(V = (1/3) * π * r^2 * h\),
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.

In this case, we are given that the height of the cone is 4.5 ft and the base has a circumference of 14.2 ft.

To find the radius of the base, we can use the formula

\(C = 2πr\),

where C is the circumference and r is the radius. Rearranging the formula, we have

\(r = C / (2π)\).

Plugging in the given circumference, we get

\(r = 14.2 ft / (2π) \\≈ 2.26 ft.\)

Now that we have the radius and the height, we can plug these values into the volume formula.

\(V = (1/3) * π * (2.26 ft)^2 * 4.5 ft \\(2.26 ft)^2 = 5.1076 ft^2\\V = (1/3) * π * 5.1076 ft^2 * 4.5 ft\\V = (1/3) * π * 22.983 ft^3\\ = 24.045 ft^3\)

Therefore, the volume of the right circular cone is approximately 24.045 cubic feet.

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Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

When comparing hash values, if the provided hash value matches the one you calculated, it means that the file you have received is identical to the original file used to calculate the hash. This implies that the file has not been modified or tampered with since the hash was generated.

However, it is important to note that a matching hash value does not guarantee that the file is completely safe or trustworthy. Hash functions are designed to generate a unique hash value for each unique input, but it is still theoretically possible for two different files to have the same hash value (known as a collision). Although the chances of a collision are extremely low with well-designed hash functions, it is not entirely impossible.

Therefore, while a matching hash value provides some level of confidence that the file has not been altered, it does not guarantee the integrity or security of the file. Other factors should be considered, such as the source and reputation of the file, the context in which it was obtained, and the presence of any additional security measures or verification methods.

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Answer:

x=30

Step-by-step explanation:

Angle sum in a triangle=180

x+3x+2x=180

6x=180

x=30

Answer:

x°+3x°+2x°=180°[by angle sum property]

6x°=180°

x°=180°/6

x°=30°

The appropriate p-value for the given test statistic and hypotheses is approximately 0.0253.

Tο determine the apprοpriate p-value fοr the given hypοthesis test, we need tο use the t-distributiοn and the t-statistic value οbtained.

Given:

Null hypοthesis (H0): μ = 130 (pοpulatiοn mean)

Alternative hypοthesis (HA): μ > 130 (pοpulatiοn mean)

T-statistic: t = 2.73

Degrees οf freedοm: df = 5

Tο calculate the p-value, we cοmpare the t-statistic tο the t-distributiοn.

Since the alternative hypοthesis is μ > 130, it is a οne-tailed test, and we are interested in the right tail οf the t-distributiοn.

Using a t-table οr a statistical sοftware, we can determine the p-value assοciated with the t-statistic and the degrees οf freedοm.

Fοr a t-statistic οf 2.73 with 5 degrees οf freedοm, the p-value is apprοximately 0.0257 (assuming a twο-tailed test).

Since we have a οne-tailed test, the apprοpriate p-value is half οf the twο-tailed p-value:

p-value = 0.0257 / 2 = 0.01285

Therefοre, the apprοpriate p-value fοr the given hypοthesis test is apprοximately 0.01285.

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Answer:

e=2

Step-by-step explanation:

14e-7-3=6+6e

14e-10=6+6e

14e-6e=6+10

8e=16

e=2

congrats man!!

good job!! you did great on it

Answer:

\(\frac{14}{25}\)

Step-by-step explanation:

We want to know what is \(\frac{2}{5}\) ÷ \(\frac{5}{7}\), and we want to write it as a fraction.

When dividing fractions, we actually multiply the first fraction by the reciprocal of the second.

In other words, we "flip" the second fraction and multiply it by the first.

To get the reciprocal / "flip" a fraction, we put the number that is the numerator on the denominator, and the number that is on the denominator onto the numerator.

So, for \(\frac{5}{7}\), its reciprocal is \(\frac{7}{5}\).

Now, we multiply \(\frac{2}{5}\) by \(\frac{7}{5}\).

\(\frac{2}{5}\) × \(\frac{7}{5}\) = \(\frac{14}{25}\)

The fraction cannot be reduced, so the answer is \(\frac{14}{25}\).

Answer:

1st part is 16.8

2nd part is 2.2

Step-by-step explanation:

Joanne needs to produce and sell at least 262 T-shirts to make a profit of $900.

a. The cost function can be found by taking the total cost and dividing it by the number of shirts produced.

   Total cost ÷ quantity = cost per unit.  

Given that Joanne’s total cost to produce 50 T-shirts is $275, the linear cost function can be found as:

                               Cost function = $275/50

                                             = $5.50 per T-shirt.

Hence the linear cost function for Joanne's T-shirt production is $5.50 per T-shirt.

b. The break-even point is when the total revenue is equal to total cost.  

In this case, the total cost is $275. We can calculate the revenue by multiplying the number of T-shirts sold by the selling price.

So the equation is: Total revenue = Number of T-shirts sold x Selling pricePer the question, the selling price per T-shirt is $9.

To find out the number of T-shirts sold, we need to divide the total cost by the marginal cost per T-shirt and then multiply the result by the selling price.

We get: Quantity = (Total cost ÷ Marginal cost per unit) = $275 ÷ $4.50 = 61.11 (rounded to the nearest whole number)

Therefore, Joanne needs to produce and sell at least 62 T-shirts to break even.

e. Let's denote the profit as P.

We can find the number of T-shirts Joanne needs to produce and sell to make a profit of $900 by setting up the equation: Revenue - Total Cost = Profit

Using the information from the question, we can fill in the variables as follows:9x - (275 + 4.5x) = 900

Simplifying the equation gives us:9x - 4.5x = 900 + 2754.5x = 1175x = 261.11rounded to the nearest whole number

So Joanne needs to produce and sell at least 262 T-shirts to make a profit of $900.

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The answer is  X= 3, -2

Answer:

5/8

Step-by-step explanation:

1/2=4/8

4/8+1/8=5/8

Answer:

110 minutes or 1 hour 50 minutes

Step-by-step explanation:

44 divided into 4 since we want to find out how much time it takes to run 1 mile, so 44 divided into 4 is 11

then simply multiply 11 with 10 and the answer is 110

: )

Answer:

  A.  The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.

The described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.

The appropriate description is that of choice A.

Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.

Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.

Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.

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In the equation y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

What is a constant?

A predetermined amount. In algebra, a constant is a number that stands alone or, occasionally, a letter like a, b, or c that denotes a fixed number. 5 and 9 are constants in the formula "x + 5 = 9," for instance.

Since the equation can be written in the form y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

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Answer:

what are the instructions

Step-by-step explanation:

please repost with instructions

The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers  .

Let us understand the Division with the help of example ;

let the number be 10 ;

first we divide the number 10 by 0.5 ;

this can be written mathematically as ⇒ \(\frac{10}{0.5}\)  ;

⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;

So , on dividing 10 by 0.5 , we get the answer as 20 .

Second , the number 10 is divided by 2 ;

this can be written mathematically as ⇒ \(\frac{10}{2}\) ;

⇒ \(\frac{10}{2 }\)  = 5  ;

So , on dividing 10 by 2 , we get the answer as 5  .

Therefore , dividing by 0.5 is not same as dividing by 2 .

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Answer:

Step-by-step explanation:

If the lengths of two sides of a triangle are given the third side must be less than the sum of those two sides, but more than the value of the difference between the given two sides.

So for #9, the answer is 4 (which is 12-8) <x<16 (which is 12+8)

#10. 10<x<16

#11. 19<x<61

#12. 6<x<16

Below are what would happen if the 3rd side was too big (left) or too small (right)

The probability of getting the first two questions correct by randomly guessing is option D: 0.0625.

Since each question has four choices and you are randomly guessing, the probability of guessing the correct answer for each question is 1 out of 4, or 1/4 = 0.25.

To find the probability of getting both questions correct, we multiply the probabilities of each event since they are independent. So, the probability of getting the first question correct is 0.25, and the probability of getting the second question correct is also 0.25.

To find the probability of both events occurring, we multiply the individual probabilities:

P(both questions correct) = P(first question correct) * P(second question correct) = 0.25 * 0.25 = 0.0625.

Therefore, the probability of getting the first two questions correct by randomly guessing is 0.0625, which corresponds to option D.

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Answer:

Step-by-step explanation:

given the expression, we are expected to solve for the value of x

\(-(9x-4)+12+18x>79\)

we begin by opening the bracket

\(-(9x-4)+12+18x>79\\\\-9x+4+12+18x>79\\\\\)

collect like terms

\(-9x+4+12+18x>79\\\\-9x+18x+4+12>79\\\\9x+16>79\\\\\)

subtract 16 from both sides

\(9x+16>79\\\\9x>79-16\\\\9x>63\)

divide both sides by 9 we have

\(x>\frac{63}{9}\\\\ x>7\)

the greatest value of x that is not a solution is 7 since x is not equal to 7

Expression as a fraction of 0.7 cm³ for 117 mm³ is given by the fraction 0.117 / 0.7.

To write 117 mm³ as a fraction of 0.7 cm³,

we need to convert the units so they match.

Since there are 10 millimeters in a centimeter

1 cm = 10 mm

This implies,

1 cm³ = (10 mm)³

         = 1000 mm³

Now we can express 117 mm³ as a fraction of 0.7 cm³:

117 mm³ / 0.7 cm³

To convert mm³ to cm³, we divide by 1000,

117 mm³ / 1000 = 0.117 cm³

Now we can express it as a fraction,

0.117 cm³ / 0.7 cm³

Simplifying the fraction, we divide the numerator and the denominator by 0.117,

= (0.117 cm³ / 0.117 cm³) / (0.7 cm³ / 0.117 cm³)

= 1 / (0.7 / 0.117)

To divide by a fraction, we multiply by its reciprocal:

= 1 × (0.117 / 0.7)

= 0.117 / 0.7

Therefore, 117 mm³ is equal to the fraction 0.117 / 0.7 when expressed as a fraction of 0.7 cm³.

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Answer:

Step-by-step explanation:

Right Triangle Similarity

Acute Angle Similarity

If one of the acute angles of a right triangle is congruent to an acute angle of another right triangle, then by Angle-Angle Similarity the triangles are similar.

In the figure, ∠M≅∠Y , since both are right angles, and ∠N≅∠Z .

So, ΔLMN∼ΔXYZ .

Leg-Leg Similarity

If the lengths of the corresponding legs of two right triangles are proportional, then by Side-Angle-Side Similarity the triangles are similar.

In the figure,  ABPQ=BCQR .

So, ΔABC∼ΔPQR .

Hypotenuse-Leg Similarity

If the lengths of the hypotenuse and a leg of a right triangle are proportional to the corresponding parts of another right triangle, then the triangles are similar. (You can prove this by using the Pythagorean Theorem to show that the third pair of sides is also proportional.)

In the figure, DFST=DESR .

So, ΔDEF∼ΔSRT .

Taking Leg-Leg Similarity and Hypotenus-Leg Similarity together, we can say that if any two sides of a right triangle are proportional to the corresponding sides of another right triangle, then the triangles are similar.

Answer:

-2 is 4

Step-by-step explanation:

Answer:

x is less than or equal to 1 can also be written as x ≤ 1. The ≤ sign represents "less than or equal to"

Let me know if this helps!

Answer: True

Step-by-step explanation: because bias can lead to personal errors

Answer:

8

Step-by-step explanation:

In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.

The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:

\(56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3\)·\(7\)

\(72=(24)(3)=8(3)(3)=2^3\)·\(3^2\)

Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the \(2^3\).

Thus, \(2^3=8\) is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.

Answer:

√29 =c

Step-by-step explanation:

a^2+b^2=c^2

5^2+2^2=c^2

25+4=c^2

29=c^2

√29=c