What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?

When standard deviation is estimated from data, the result is standard error of the statistics. the standard error estimates how far the sample statistic is likely to be from the true population parameter.

An estimate of corresponding population parameter is made when a statistic is computed using a sample of data. However, due to random sampling error and other sources of unpredictability, it is doubtful that the statistic's value would exactly correlate with an underlying population parameter. An indicator of how much the sample statistic is likely to deviate from actual population parameter is statistic's standard error, which is a total measure of this variability.

When the overall standard error is smaller, the sample statistic is more accurate and is likely to be closer to the genuine population parameter. Whereas, when the standard error is larger, there is more variability and uncertainty about the parameter's true value.

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The total cost of the metal which will be used to construct the metal tank would be = $82.5

To calculate the area of the metal tank, the formula for the area of the cylinder is used which would be;

= 2πr (h+r)

Where

R = 12/2 = 6 ft

h = 4ft

π = 3.14

area = 2×3.14×6(4+6)

= 37.68×10

= 3.75 ft²

But 1ft² = $22

3.75ft² = X

make X the subject of formula;

X = 22× 3.75 = $82.5

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Answer:

32 liters is the volume of the glass tank

Answer:

y = 19/14 and x = 25/42

Step-by-step explanation:

Answer:

(5/2, 4/3)

Step-by-step explanation:

the solution is the point (2.41,1.36)

x=5/2  

y=4/3

Answer:

123456789012345678901234567890123456678901234567890123445667890123456789012345678901234567890

Step-by-step explanation:

Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

Answer:

log = cylinder

board = rectangular prism

Step-by-step explanation:

The log has a radius of 5 in and a length of 30 in.  

This implies that the cross-section is a circle, and so it can be modeled as a cylinder.

The board has a width of 5.5 in, a height of 1.5 in and a length of 3ft.

Therefore, it can be modeled as a rectangular prism.

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

C) A geometric cumulative distribution function should be used because the question states that the probability for having a hand with three of a kind is about 6%.

Step-by-step explanation:

A geometric cumulative distribution function should be used because the question states that the probability for having a hand with three of a kind is about 6%.

A geometric cumulative distribution function should be used because the question asks for the probability of having a hand with five cards in the same suit in one of the first three hands

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The geometric cumulative distribution is a discrete likelihood conveyance where the random variable describes the quantity of the expected Bernoulli trial.

A Bernoulli trial is an experiment that can have just two results.

Success and failure.

Now,

We are interested in the first success in the three chances, which is a distribution function of a geometric distribution.

Now,

The probability of having a hand with five cards in the same suit in one of the first three hands.

This is a geometric distribution.

Thus,

A geometric cumulative distribution function should be used.

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Answer:

18.69

Step-by-step explanation:

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

The values of x, y, and z based on the system of equations will be (-2,4,7).

x + 3y + 5z = 45

6x - 3y + 2z = - 10

------------------------add

7x + 7z = 35

6x - 3y + 2z = -10

-2x + 3y + 8z = 72

----------------------add

4x + 10z = 62

7x + 7z = 35....multiply by 4

4x + 10z = 62...multiply by -7

---------------------

28x + 28z = 140 (result of multiplying by 4)

-28x - 70z = - 434 (result of multiplying by -7)

--------------------add

- 42z = - 294

z = -294/-42

z = 7

4x + 10z = 62

4x + 10(7) = 62

4x + 70 = 62

4x = 62 - 70

4x = - 8

x = -8/4

x = -2

x + 3y + 5z = 45

-2 + 3y + 5(7) = 45

-2 + 3y + 35 = 45

3y + 33 = 45

3y = 45 - 33

3y = 12

y = 12/3

y = 4

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Solve the following system of equations algebraically for all values of x,y and z

x+3y+5z=45

6x-3y+2z=-10

-2x+3y+8z=72

Given:

Find: the another equivalent value of

Explanation:

Final answer: The required answer is

Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

An outlier, to put it simply, is a data point in a data graph or dataset you're dealing with that is abnormally high or abnormally low in comparison to the nearest data point and the rest of the nearby coexisting values.

The vocabulary term is explained as,

1.Outlier - Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

2. Cluster - An identifiable cluster of values in a numerical variable's distribution that is close to one another and appears notably more frequently than values on either side of them.

3. Positive linear association - When the variable on the x-axis grows as the variable on the y-axis increases, a positive linear connection exists. An upward-sloping linear regression line demonstrates this.\

4. Negative linear association - A negative linear correlation exists when one variable rises while the other falls. An upwardly sloping straight regression line illustrates this.

5.No association - There is a "negative correlation" when one variable rises while the other one falls. The points in the scatterplot have no connection if there is no correlation between the variables.

6. Non-linear association - When two variables have a nonlinear relationship, the slope of the curve illustrating the relationship alters when the value of one of the variables varies. Any curve whose slope alters when one of the variables' values changes is said to be nonlinear.

Thus, extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

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Answer:

7X+7=2(X+1)

7X+7=2X+2

7x-2X =2-7

5X/5 =-5/5

. X =-1

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

the left is infinite hh

Answer: 8/3 and -9/4

Step-by-step explanation:

1. \(\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}\)

2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.

\(-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}\)

Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

Answer:

70 days

Step-by-step explanation:

Given that,

→ fresh fruit to last 10 days

→ fresh vegetables for 7 days

→ dried insects for 5 days

Then in how many days will they order all three items on the same day?

Then the LCM of 10, 7 & 5 is,

→ 2 × 5 × 7

→ 10 × 7 = 70

Hence, the answer is 70 days.

Answer:

Option (2)

Step-by-step explanation:

Given:

∠1 ≅ ∠3

To Prove:

∠AXD ≅ ∠CXB

Solution:

Given question is incomplete; find the complete question in the attachment.

            Statements                                                              Reasons

1). m∠1 ≅ m∠3 because m∠1 ≅ m∠3          1). Given

2). m∠1 + m∠2 = m∠CXB and                    

    m∠2 + m∠3 = m∠AXD                            2). Angle addition postulate

3). m∠1 + m∠2 = m∠AXD                             3). Because you can substitute

                                                                          m∠1 for m∠3

4). m∠CXB = m∠AXD                                   4).Transitive property of equality

5). ∠AXD ≅ ∠CXB

Therefore, Option (2) will be the correct option.