Find the least common multiple
(LCM) of 7, 9, and 21.

Answer:

621200 mg

1.36664 Lb

Step-by-step explanation:

Given;

Cullinan diamond weighed 3106 carats.

1 Carat - 0.2 grams

Question to Answer;

How much does the diamond weigh in milligrams/pounds?

Solve;

Since 1 carat = 0.2 grams

1g = 1000 mg

1g = 0.0022 lb

Thus,

3106 ct = 0.2 * 3106g = 6212g

621.2g = 621.2 * 1000 mg = 621200 mg

621.2g = 621.2 * 0.0022 lb = 1.36664 lb

[RevyBreeze]

Answer:

see explanation

Step-by-step explanation:

To determine if (3, 1 ) is a solution to the system

Substitute x = 3 into both equations and evaluate. If the result is y = 1 for both then the point is a solution.

y = \(\frac{4}{3}\) × 3 - 3 = 4 - 3 = 1

y = - 2(3) + 7 = - 6 + 7 = 1

Since both equations equal 1 then

(3, 1 ) is a solution to the system

Answer:Angle 4 and 1 are comp, angle 3 and 6 are comp

Step-by-step explanation:

Same degrees given that each sector is right angle

Answer:

Complementary angles are any two angles that add up to get 90°

hope this helps

Answer:

choice 1) 312 cm²

Step-by-step explanation:

area = (16 x 12) + (10 x 12) = 312 cm²

Answer:

312

Step-by-step explanation:

triangle：

10x12/2=60

two triangle：

60x2=120

rectangle：

16x12=192

add up：

120+192=312

Answer:

1cm³

Step-by-step explanation:

You do not need a calculator for this.

The formula for the volume of a rectangular prism is:

Length × Width × Height = Volume

If we substitute our numbers in:

5/4 × 4/3 × 3/5 = 1cm³

All you need to do is multiply across.

5 × 4 × 3 = 60

4 × 3 × 5 = 60

The numerator and denominator both equal 60. So the fraction would look like this if you were to keep it as a fraction.

60/60

Answer:

2 19/24 feet

Step-by-step explanation:

14 5/8 = 14 15/24

17 5/12 = 17 10/24 ==> 16 34/24

16 - 14 = 2

34/24 - 15/24 = 19/24

Answer = 2 19/24 feet

Hope this helps!

-The Business Man

Answer:

G-$3000, L- $1200, M- $1800

Step-by-step explanation:

Georgia= 5/10 * 6000= $3000

Leanee= 2/10 * 6000= $1200

Maya= 3/10 * 6000= $1800

If a prize of $6000 was divided among Georgia, Leanne and Maya to the ratio of 5:2:3 Georgia received $3000, Leanne received $1200, and Maya received $1800.

To find out how much each girl received, we can divide the prize of $6000 according to the given ratio of 5:2:3.

First, let's calculate the total parts in the ratio:

Total parts = 5 + 2 + 3 = 10

Now, we can determine the share of each girl by dividing the total prize by the total parts and multiplying it by the respective ratio:

Georgia's share = (5/10) * $6000 = $3000

Leanne's share = (2/10) * $6000 = $1200

Maya's share = (3/10) * $6000 = $1800

Therefore, Georgia received $3000, Leanne received $1200, and Maya received $1800.

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Given, equation in the question which we have to solve is

\(2x - 5 = 7\)

Here, we need to find x. So, Let's isolate x on one side of the equation. It is present in the left hand side. Add 5 to both sides,

\(2x - 5 + 5 = 7 + 5\)

\(2x = 12\)

Divide 2 from both sides,

\( \frac{2x}{2} = \frac{12}{2} \)

\(x = 6\)

So, the correct option is A.

━━━━━━━━━━━━━━━━━━━━

Answer:

d is correct

Step-by-step explanation:

Answer:

-0.28

Step-by-step explanation:

(-6)-(-8)=2.

7-14=-7

2/-7=-0.28

Answer:

30 kids

Step-by-step explanation:

A. I and II only true if we use a large sample rather than a small one

sampling model

A sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.

When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.

Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.

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Answer:

It’s the last one

Step-by-step explanation:

Did this before on a test

From the given mass spectrum, the base peak of the mass spectrum is 93. The parent peak is not visible in this mass spectrum.

Relative Intensity 100 80- 60 40 20 0
T 10 20 30 40 50 60
m/z 70 80 90 100 ㅠㅠㅠㅠㅠㅠㅠ 110

From the mass spectrum table given, the base peak of the mass spectrum is 93.

Thus, the answer is 93.

The parent peak is the peak that corresponds to the complete molecular ion or the molecular weight of the compound.

The parent peak is not visible in the given mass spectrum. There is no peak corresponding to the mass of the molecule itself or molecular ion in this mass spectrum table.

Hence, there is no parent peak in this mass spectrum.

Conclusion: From the given mass spectrum, the base peak of the mass spectrum is 93. The parent peak is not visible in this mass spectrum.

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The base peak is 20, which is the peak with the lowest intensity.

From the given spectrum, we have:

m/z:   70      80      90       100   110

Relative Intensity:   20      80      60       100    40

The highest peak is at

m/z = 100 and the intensity is 100.

Therefore, the base peak is 20, which is the peak with the lowest intensity.

Relative intensity refers to the intensity or strength of a particular signal or measurement relative to another reference intensity. It is often used in fields such as physics, chemistry, and spectroscopy to compare the strength of signals or data points.

In the context of spectroscopy, relative intensity typically refers to the intensity of a specific peak or line in a spectrum compared to a reference peak or line. It allows for the comparison of different spectral features or the identification of specific components in a spectrum.

The relative intensity is usually represented as a ratio or percentage, indicating the strength of the signal relative to the reference. It provides information about the relative abundance or concentration of certain components or phenomena being measured.

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Answer:

X=-1/2,6

Step-by-step explanation:

Answer:

(2x+1) (x-6)

Step-by-step explanation:

I think this is right

Answer:4,2

Step-by-step explanation: is u divide both side with 2 that will be your answer

Answer:

Your answer is: Midpoint =  (0.5, -0.5)

Step-by-step explanation:

(xa+xb/2 , ya+yb/2)

Plug the points ---> (5,2)(-4,-3)

= (1/2 , -1/2)

In decimal form it would be: (0.5,-0.5)

Hope this helped : )

Answer:

\(VW = 33\)

Step-by-step explanation:

See attachment for complete question

Given

\(VY = 4x - 1\)

\(VW = 5x + 3\)

\(Perimeter = 112\)

Required

Determine the length of VW

Perimeter is calculated as:

\(Perimeter = 2 * (Width + Length)\)

This gives:

\(Perimeter = 2 * (VW + VY)\)

Substitute values for VW, VY and Perimeter

\(112 = 2 * (4x - 1 + 5x + 3)\)

Collect Like Terms

\(112 = 2 * (4x + 5x -1 +3)\)

\(112 = 2 * (9x +2)\)

Divide through by 2

\(56 = 9x + 2\)

Collect Like Terms

\(9x = 56 - 2\)

\(9x = 54\)

\(x = 54/9\)

\(x = 6\)

Substitute 6 for x in \(VW = 5x + 3\)

\(VW = 5 * 6 + 3\)

\(VW = 30 + 3\)

\(VW = 33\)

Answer: 23

Step-by-step explanation:

A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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Answer:

\(Angle = 54\)

Step-by-step explanation:

Given

Kano = 45;

Kwara  = 410;

Ogun = 105;

Ondo = 126;

Oyo = 154

Total Distribution = 840

Required

Determine the angle subtended by Ondo (in a pie chart)

The general formula to calculate subtended angle in a Pie chart is;

\(Angle = 360 * \frac{Frequency}{Total\ Frequency}\)

In this case of Ondo

Frequency = 126

Total Frequency = Total Distribution = 840

Substitute these values in the given formula;

\(Angle = 360 * \frac{126}{840}\)

\(Angle = \frac{360 *126}{840}\)

\(Angle = \frac{45360}{840}\)

\(Angle = 54\)

Hence, the angle subtended by Ondo is 54

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Answer:

No

Step-by-step explanation:

The perpendicular bisector theorem wouldn't really work with it not being a clear right angle or perpendicular. But with HG being congruent with GJ, it would be easy to find the answer

Step-by-step explanation:

99 is the answer........

The sum of the first 9 terms of the given GP series will be 1533 thus option (c ) is correct.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

Let's say the first term of the given GP is a and the common ratio is r.

a = 3 and r = 2

The Sum of n term is given as,

S = a(\(r^{n}\) - 1) / (r - 1)

S₉ = [3(2⁹ - 1)/(2 - 1)]

S₉ = 1533

Hence "The sum of the first 9 terms of the given GP series will be 1533".

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===============================================

Explanation:

Add the equations by adding the terms straight down.

The x terms add to x+x = 2x.

The y terms add to y+(-y) = y-y = 0y = 0, so the y terms go away

The constants add to 5+7 = 12

The z terms add to -z+z = 0z = 0 and those go away as well

After all that adding, we have 2x = 12 which solves to x = 6 after dividing both sides by 2.

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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Answer:

5/9

Step-by-step explanation:

Number of accountants = 20

Number of economists = 12

Number of secretaries = 4

Total number of Staffs = 20 + 12 + 4 = 36 staffs

Probability = required outcome / Total possible outcomes

Required outcome = number of accountants

Total possible outcomes = total number of staffs

P(selecting an economist) = 20 / 36 = 5 / 9

The probability that the staff is an accountant is 5/9.

Given

A company staff consists of 20 accountants, 12 economists and 4 secretaries. a staff is chosen at random.

Probability is defined as the number of observations and total number of observation.

Total number of Staffs = 20 + 12 + 4 = 36 staffs.

The following formula is used to determine the probability;

\(\rm Probability=\dfrac{Accountant \ staff}{Total \ number \ of \ staff}\)

Substitute all the values in the formula;

\(\rm Probability=\dfrac{Accountant \ staff}{Total \ number \ of \ staff}\\\\\rm Probability=\dfrac{20}{36}\\\\\rm Probability=\dfrac{5}{9}\)

Hence, the probability that the staff is an accountant is 5/9.

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Answer:

Square root of 3 = 1.7321

Answer:

1.73

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

In the new design, the width at which the reflector (CD) would be at its widest point is "18".

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Hence,

In the given graph by concluding we observe that  on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit

Therefore,

CD = distance from -(8+1) to (8+1)

= distance between -9 to 9 which is 18.

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Answer:

Step-by-step explanation:

56.1,12.1,23.6