Find one solution for the equation, (2x-3)(3x+5)=0.

The artifact was made about 3102.5 years ago.

An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?

Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.

Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.

We'll have to solve the following equation to find the age of the artifact.

C1 = (70/100) * C0

Substitute the value of C0 into the equation and solve for t,

t = ln(0.7) / ln(1/2) = 3102.5 years

The artifact was made about 3102.5 years ago.

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Answer: 1.26 × 10 to the 10th power

Step-by-step explanation:

The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given data:

ratio of ounces to pounds = 16:1

16 ounce / 1 pound

Let the weight of dog in ounce be 'x'.

weight of dog in pounds = 46 pounds.

ratio : x ounce /  46 pounds

Equating both ratios:

16 ounce / 1 pound = x ounce /  46 pounds

Cross multiplying:

x = 16*46  ounce

x = 736 ounce

The correct option is c: 46lb x (16 oz / 1lb)

Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

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Complete question is-

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight

ounces. Which ratio shows the conversion to ounces?

The full question is attached.

Answer: 27.50

Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50

The theoretical probability of not picking the silver coin will be 0.38 .

Given,

200 silver coins and 123 gold coins are filled in a bag .

Now,

Total number of coins in a bag = gold + silver coins

Total number of coins in a bag  = 200 + 123

Total number of coins in a bag  = 323

Further ,

Probability of taking silver coin = 200/323

Probability of taking silver coin = 0.619.

probability of taking gold coin = 123/323

probability of taking gold coin  = 0.38

Hence the probability of not selecting silver coin is 0.38 .

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The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran

Step-by-step explanation:

Answer:

AB=8.1 and B=29.6

Step-by-step explanation:

1) To find the measure of AB, use the law of cosines

[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]

[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]

2) Use law of sines to find the measure of B

[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]

B=29.6

Step-by-step explanation:

p-grams have equal opposite side lengths

soooo  

 5x+7   =  27  

               x = 4

then 22x = 22(4) = 88  units      ( this is also AB length)

The equation |a + 5| = −5 − a is not true for any value of a, while the equation |a + 5| = a + 5 is true for values of a greater than or equal to -5.

The absolute value of a number is defined as the distance of the number from zero on a number line. Thus, |a + 5| is equal to the distance of (a + 5) from zero on a number line. Since distance is always non-negative, |a + 5| is always non-negative.

On the other hand, the expression −5 − a is always negative, since the sum of a negative number (-5) and any number (a) is always negative.

Therefore, for the equation |a + 5| = −5 − a to be true, the absolute value of (a + 5) would have to be negative, which is impossible since absolute value is always non-negative.

For the equation |a + 5| = a + 5 to be true, a must be greater than or equal to -5, because when a is greater than or equal to -5, (a + 5) is already non-negative, so the absolute value of (a + 5) is equal to (a + 5).

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Answer:

To solve the problem, we need to first determine the value of the quarters Anna has. Since there are 5 quarters, we have:

5 quarters = 5 x $0.25 = $1.25

Thus, Anna has $2.00 - $1.25 = $0.75 left. We can find the maximum number of dimes she can have by dividing this amount by the value of a dime, which is $0.10. Therefore:

$0.75 ÷ $0.10 = 7.5

Since Anna cannot have a fraction of a dime, we round down to the nearest whole number to get a maximum of 7 dimes. Therefore, the answer is option B, 5.

Answer:

16 represents the hours available to sew gloves.

2 represents the cost of producing gloves for a small pair.

Step-by-step explanation:

The probability using the demand distribution of a stockout is given as 0.6293.

Out-of-stock situations, commonly referred to as stockouts, occur when a company runs out of a product that a client is prepared to purchase. Stockouts have a direct influence on customer satisfaction and are a major reason for bad reviews, additional expenses, and lost revenue or, worse, customers.

Let X = no of demand for the toy

μ =20,000

P(10000 < X < 30000) = 0.90

X follows  normal distribution

z=x−μ​/σ

P(10000 < X < 30000)=0.90

P((10000−20000​)/σ) < (x−20000​)/σ < (30000−20000​)/σ )=0.90

as probability is 0.90, the z-score =1.645.

(30000−20000)​/σ =1.645

10000​/σ=1.645

σ=10000​/1.645

σ=6079

1.P(X>15,000)

=P(Z> (15000−20000​)/6079)

=P(Z> −0.82)

=P(Z< 0.82)

=0.5+0.1293

=0.6293

2. P(X> 24000)

=P(Z> (24000−20000​)/6079)

=P(Z> 0.66)

=0.5−0.2454

=0.2546

3.Expected profit = (profit per unit )*(no of sold units) + (loss per unit )*(of units unsold)

profit = $8

loss = -$11

a. profit if 15000 units are sold =(8)(15000) + (-11)(0) = $120,000

b. if there is demand for 15,000 units but orders only 18000 units profit is (8)(15000) + (-11)(3000) = $87,000

c. if there is demand for 18,000 units but orders only 24000 units profit is (8)(18000)+(-11)(6000)= $78,000.

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Complete question:

(a) What is the expected profit if all 15,000 units are sold? type your answer...

(b) Suppose there is demand for 15,000 units, but Specialty Toys orders 18,000 units? What is the expected profit? type your answer...

(c) Suppose there is demand for 18,000 units, but Specialty Toys orders 24,000 units? What is the expected profit? type your answer... 15 3 points Based on what you know about the distribution of demand, the probability of stock-outs, and the expected profit, how many units of Weather Teddy do you recommend that Specialty Toys purchase?

The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:

P(x=0) = (p^5)*(q^0) = p^5

In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.

For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.

To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

The correct question is:

A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective

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Answer:

The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.

The sum of the first 10 terms of the geometric progression that is given in the question is 1023.

What is geometric progression ?

Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.

The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.

The sum of the first n terms of a geometric progression is given by the formula:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Using this formula, we can find the sum of the first 10 terms of the given series as:

[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]

[tex]= 1(1 - 1024) / (-1)[/tex]

[tex]= 1023[/tex]

Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.

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Answer: 60%

Step-by-step explanation:

As mentioned earlier, we need to know the number of senior nutrition majors and sophomore non-nutrition majors to calculate the exact probability. Without this information, we cannot provide a specific answer to the question.

However, we can provide a general formula for computing the probability, assuming that the selections are made without replacement and the population of students is large enough to assume independence:

Probability of selecting a senior nutrition major and then a sophomore non-nutrition major = (Number of senior nutrition majors / Total number of students) × (Number of sophomore non-nutrition majors / (Total number of students - 1))

Once we have the values for the number of senior nutrition majors and sophomore non-nutrition majors, we can substitute them into this formula to obtain the probability, which will be a decimal number rounded to four decimal places.

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The MCAT scores variable can predict some of the variation in the response variable.

The logistic regression model is a type of regression analysis that is widely used in various fields. A logistic model can be fitted using the glm() function in R. Now fit a logistic model with a single explanatory variable, MCAT scores.In logistic regression, the null deviance is the deviance for a model that has only the intercept. The null deviance will always be equal to the residual deviance if the model has only the intercept.The null deviance is calculated based on the difference between the saturated and null models' likelihoods. It is the amount of variation in the response variable that cannot be explained by the model when no predictor variables are used. When the single predictor variable MCAT scores is added to the null model, it reduces the null deviance by 11.59. This is significant because it indicates that the MCAT scores variable can predict some of the variation in the response variable.

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Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.

We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.

A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.

The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.

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Answer: 3/2

Step-by-step explanation:

To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:

m = (y2 - y1) / (x2 - x1)

where:

m = slope of the line

(x1, y1) = coordinates of the first point

(x2, y2) = coordinates of the second point

Plugging in the values we have, we get:

m = (-2 - 1) / (0 - 2)

m = -3 / -2

m = 3/2

Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.

The width of the rectangular garden is 9.5 feet.

Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.

Let's assume the width of the rectangular garden be "w".

Now we need to find the width of the garden.

Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)

where l = length and w = width.

Substituting the given values in the above formula,

we get43.8 = 2(12.4 + w)

We can solve for "w" by simplifying the above equation.

43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w

Dividing both sides by 2,we get

w = 9.5 feet.

Therefore, the width of the rectangular garden is 9.5 feet.

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Answer:

G (-3,-1)

H (-2,-3)

I (1,1)

Step-by-step explanation:

After a reflection across y=2, the y-coordinates of the vertices will change sign while the x-coordinates remain the same. Thus, the new coordinates of the vertices will be:

G (-3,-1)

H (-2,-3)

I (1,1)

Answer:

G (3,3) , H (2,5), I (-1,1)

Step-by-step explanation:

Since it’s flipped over the Y-Axis, the X-Axis numbers remain the same.

WRONG!!

didnt read the question correctly, so the vertices are incorrect lol.

Answer:

  5240 kg/m³

Step-by-step explanation:

You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.

The mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.

The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)

The units of density tell you it is computed by dividing the mass by the volume:

  ρ = mass/volume

The volume of the sphere is found using the given formula, so the density is ...

  ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)

  ρ ≈ 5240 kg/m³

The average density of the planet is about 5240 kg/m³.

__

Additional comment

This is comparable to the average density of Earth, which is about 5520 kg/m³.

The standard deviation for a chi square distribution for given degree of freedom is 7.0711.

The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.

The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:

σ = sqrt(2k)

Therefore, for a chi-square distribution with 25 degrees of freedom:

σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711

Rounding this to four decimal places gives a standard deviation of approximately 7.0711.

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In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.

Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.

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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.

A state's license plates consist of 4 letters followed by 5 digits.

How many possible license plates can be issued using this condition?

When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.

Therefore, we can count the total number of license plates in two phases.

The number of choices for each segment must be taken into account separately for the letters and the numbers.

When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.

For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.

Similarly, for the last 5 positions,

there are 10 options for each position since there are 10 digits.

There are $10^5$ = 100,000 possibilities for the last 5 positions.

The entire plate's total number of combinations is obtained by multiplying these numbers.

There are a total of $26^4 × 10^5$ possibilities

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Based solely on statistical probability from demographic studies, the individual who has the greatest likelihood of being a smoker is a male aged between 18 to 24 years old.

According to demographic studies, men are more likely to smoke than women. Besides, the smoking rate increases with age, which means individuals aged between 18 to 24 have a higher likelihood of being a smoker than people of other ages.

Therefore, based solely on statistical probability from demographic studies, a male aged between 18 to 24 years old has the greatest likelihood of being a smoker.

It is important to note that statistical probability from demographic studies only shows what is likely or probable to happen but does not guarantee the actual occurrence of the event.

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After dividing and simplifying we get (x-3)/(x+3)

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are addition, subtraction, and multiplication.

At a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. There is no requirement that this quantity be an integer. For instance, if there are 20 apples and they are divided equally among four people, each person will get 5 apples (see picture).

The integer quotient, which is the quantity of times the second number is entirely contained in the first number, and the remainder are both produced by the division with remainder or Euclidean division of two natural numbers.

1/(x+4) divide by  [tex](x-3)/(x^2 + 7x +12)[/tex]

Simplify : [tex]x^2 +7x +12[/tex]

[tex]x^2 + (3+4)x + 12[/tex]

[tex]x^2 + 3x +4x + 12[/tex]

[tex]x(x + 3) + 4(x + 3)[/tex]

[tex](x+3)(x+4)[/tex]

[tex]1/(x + 4) x (x-3)/(x+3)(x-4)[/tex]

After dividing and simplifying we get the following answer;

[tex]= (x-3)/(x+3)[/tex]

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If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.

To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.

We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:

total = swim suits + sunglasses - both

Substituting in the given values, we get:

75 = 63 + 43 - x

Simplifying, we get:

x = 31

Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:

63 - 31 = 32

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Answer:

................

Step-by-step explanation:

.................