The diagram below shows a cylinder with diameter 6 cm and height 20 cm. The
Volume, in cm³, of the cylinder is
-6 cm
20 cm

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6/2=3

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer:

The exponential probability should be 33%.

Step-by-step explanation:

\(4 \div 12 = .33 \\ \)

\(.33 \times 100 = 33\%\)

The experimental probability of rolling a multiple of 3 will be 33%.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A pair of dice was rolled many times and the results appear below. Based upon these results.

Outcome      2     3     4     5     6     7     8     9     10     11     12

Frequency    3    6     8     11     14   16    15    12     9      5      1

Then the experimental probability of rolling a multiple of 3 will be

Favorable events = 6 + 14 + 12 + 1 = 33

Total events = 100

Then the probability will be

P = (33 / 100) x 100

P = 0.33 x 100

P = 33%

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Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

What are we supposed to answer? how fast it can swim in 1 second, its 819 meters a second if I divide that 363636 by 444 seconds.

Step-by-step explanation:

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Mr.West ate 23 ounces of grapes in 11 days by eating 2 1/11 ounces of grapes each day.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day.

Therefore, The total number of grapes Mr.West ate is,

= 11×(2 1/11) grapes.

= 11×(23/11) grapes.

= 23 grapes.
So, He ate 23 ounces of grapes in 11 days.

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The person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

To determine how high up the person was shot, we can use the principles of projectile motion and the dimensions of the blood drop. Since we have the horizontal distance and the dimensions of the blood drop, we can assume that the drop followed a parabolic trajectory.

First, let's convert the distance from feet to meters for consistency. 5.1 feet is approximately 1.554 meters. Now, we need to calculate the time of flight. Since there is no information about the drop's initial velocity or angle, we cannot calculate the exact time. However, we can estimate it by assuming a reasonable range of velocities.

Let's assume the drop was traveling between 5 and 20 meters per second. With a distance of 1.554 meters, the estimated time of flight would be between 0.0777 and 0.311 seconds.

Next, we need to calculate the vertical displacement. We have the dimensions of the blood drop, with a width of 0.8 mm and a length of 2.1 mm. Assuming the drop maintained a spherical shape while in motion, we can take the average of the width and length to find the diameter. So, the diameter is approximately 1.45 mm, which is 0.00145 meters.

Using the estimated time of flight, we can calculate the vertical displacement using the formula:

Vertical displacement = (1/2) * g * t^2

where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the estimated values, the vertical displacement ranges from 0.0038 to 0.0301 meters (3.8 to 30.1 mm).

Therefore, based on the given information, the person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

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Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer: Unit rates are the factor that takes you from one column to the other column in a table of equivalent ratios. Equivalent ratios have the same unit rates.

Hope this helps!

Answer:

q. point of intersection

Step-by-step explanation:

Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.

Answer:

\((\frac{5}{3} ;\frac{4}{3} ).\)

Step-by-step explanation:

\(\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.\)

The slope of the given line in  the image is -4 , Option A is the answer.

The equation of the straight line is given by

y =mx +c ,

Where m is the slope , C is the intercept

The line is passing through the point

(-1,8)  ,(2,-4)

The slope is given by

m = (y₂-y₁) /(x₂-x₁)

m  = (-4 - 8 )/(2 +1)

m = -12/3

m = -4

Therefore the slope of the given line in  the image is -4 , Option A is the answer.

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Answer:

Step-by-step explanation: 3x^2 + 300 = 0

is a monomial expresion.

For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.

To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.

First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:

Discount amount = Marked price × Discount percentage

= Rs. 26,600 × 10/100

= Rs. 2,660

So, the discount amount for the item is Rs. 2,660.

Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.

It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.

Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.

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Probable question:

What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?

Answer:

The answer is "The Sold quantity has decreasing by 270".

Step-by-step explanation:

The number of units selling was expected to shift by - 270.

As just a result, the number of goods sold would be reduced by 270.

Its equation of regression is provided by:

Y = Sold quantity

X1= Price of the Competitor

x2=Heller's Price

\(Y = 66520 + (413.9)X_1 + ( - 269.8)\) Hey, X2 (By Multiple Linear regression calculator)

If the price of Heller rose by $1, the price of fresh Heller is \(1 + X_2\)

From the above regression equation, we will substitute \(1+X_2 \ for \ X_2.\)

\(Y = 66520 + (413.9)X_1 + (-269.8)(1+X_2)\\\\\)

   \(= 66520 + 413.9X_1 - 269.8 - 269.8X2\\\\ = 66250.2 + 413.9X_1 - 269.8X2\)

Answer:

2.57 - 1.75 = 0.82

Step-by-step explanation:

Let us assume that we need to find the value of 2.57 - 1.75 i.e. we need to subtract 1.75 from 2.57. It can be done as follows :

The first number is 2.57 and other no is 1.75.

In 2.57, 2 is in ones place, 5 is in tenths place and 7 is in hundredths place.

In 1.75, 1 is in ones place, 7 is in tenths place and 5 is in hundredths place.

Subraction :

  2.57

-  1.75

= 0.82

Hence, the value of 2.57 - 1.75 is 0.82

Answer:

It would be D, 1/4.

Step-by-step explanation:

I hope this helps you!

The transformation of f(x) to g(x) is (a) f(x) is shifted right π/3 units to g(x).

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the above functions, we have the equations of the functions to be

f(x) = sin(x)

g(x) = sin(x - π/3)

Next, we calculate the horizontal difference of the functions as follows

Horizontal difference = π/3 - 0

Evaluate

Horizontal difference = π/3

This means that the transformation of f(x) to g(x) is (a) f(x) is shifted right π/3 unit to g(x).

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Answer:

The vector of magnitude 3 in the direction of \(\vec v = 12\,\hat{i}-5\,\hat{k}\).

Step-by-step explanation:

Let be \(\|\vec u\| = 3\) and \(\vec v = 12\,\hat{i}-5\,\hat{k}\), the resultant in the direction of \(\vec v\) can be obtained by using the following expression:

\(\vec u = \frac{\|\vec u\|}{\|\vec v\|} \cdot \vec v\)

Where:

\(\|\vec v\|\), \(\|\vec u\|\) - Norms of \(\vec v\) and \(\vec u\), respectively.

Now, we get the norm of \(\vec v\) by Pythagorean Theorem:

\(\|\vec v\| = \sqrt{12^{2}+(-5)^{2}}\)

\(\|\vec v\| = 13\)

The vector is now determined:

\(\vec u = \frac{3}{13} \cdot (12\,\hat{i}-5\,\hat{k})\)

\(\vec u = \frac{36}{13} \,\hat{i}-\frac{15}{13}\, \hat{k}\)

The vector of magnitude 3 in the direction of \(\vec v = 12\,\hat{i}-5\,\hat{k}\).

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

Step-by-step explanation:

For each computer, there are only two possible outcomes. Either it works beyond 6 years, or it does not. The probability of a computer working beyong 6 years is independent of any other computes. This means that the binomial probability distribution is used to solve this question.

As the lifetime of a computer is an exponential variable, the probability of a computer working beyond 6 years is found using the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

Probability of a computer working beyong 6 years:

Mean of 5 years means that \(m = 5, \mu = \frac{1}{5} = 0.2\)

The probability is:

\(P(X > 6) = e^{-0.2*6} = 0.3012\)

What is the probability that at least 6 computers are functioning beyond 6 years?

10 computers means that \(n = 10\)

0.3012 probability of a computer working beyond 6 years means that \(p = 0.3012\)

This probability is:

\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 6) = C_{10,6}.(0.3012)^{6}.(0.6988)^{4} = 0.0374\)

\(P(X = 7) = C_{10,7}.(0.3012)^{7}.(0.6988)^{3} = 0.0092\)

\(P(X = 8) = C_{10,8}.(0.3012)^{8}.(0.6988)^{2} = 0.0015\)

\(P(X = 9) = C_{10,9}.(0.3012)^{9}.(0.6988)^{1} = 0.0001\)

\(P(X = 10) = C_{10,10}.(0.3012)^{10}.(0.6988)^{0} \approx 0\)

\(P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0374 + 0.0092 + 0.0015 + 0.0001 + 0 = 0.0482\)

0.0482 = 4.82% probability that at least 6 computers are functioning beyond 6 years

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Assuming that f(x)=x, we need to shift f(x) to the left by 5 and up by 2 in order to get g. (x). The equation g(x) may be written in mathematical terms as

G(x)=(x+5)+2

This is further explained below.

Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

In conclusion, Assuming f(x)=x, f (x) is shifted left 5 and shifted up 2 to create g(x).  the equation g(x) is mathematically given as

G(x)=(x+5)+2

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Answer:

8

Step-by-step explanation:

6 5/6 divided by 5/6 = 41/5 which is slightly more than 8.

hope this helps you

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Answer:  9.22

Step-by-step explanation:

distance in x direction:  ║-4║ + 2 = 6

distance in y direction:  5 + ║-2║ = 7

Use pythagorean theorem to find hypotenuse of triangle with legs of 6 and 7:

\(d^{2} = 6^{2} + 7^{2} = 85\\d = \sqrt{85} = 9.2195 = 9.22\)