find the dimensions of a cylinder of maximum volume that can be contained inside of a square pyramid sharing the axes of symmetry with a height of 15 cm and a side of the base of 6 cm.

Answer:

5.35

Step-by-step explanation:

9-3.65=5.35

The probability of more than 3 of the flips turn up tails is 0.0528 i.e 5.28%.

The binomial distribution in contains n independent Bernoulli trials. A Bernoulli trial is a trial that happens to succeed (probability p) or fail (probability 1- p = q )

Suppose we have a variable X for a Bernoulli distribution with parameters n and p, which is written as The probability of x successes in n trials is P(X = x)

= ⁿCₓ pˣ(q)ⁿ ⁻ ˣ

Toss a fair coin 12 times.

Next is the probability that 3 or more flips will be a number.

The probability of success is (P) = 1/2 = 0.5

total number of tosses (n) = 12

we have x = 3

P(X = 3) = ¹²C₃(0.5)³x (1 - 0.5)¹²⁻³

= 220 (0.5)³ (1 - 0.5)⁹

P(X = 3) = 0.0528

P(X = 3) = 5.28%

Hence, the probability that more than 3 of flips turn up tails is 0.0528.

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Answer:

x² + 9x + 8

Step-by-step explanation:

Given dimensions of the figure :

Area of rectangle

The correct answer is D. All of the above. When the spread of scores around the arithmetic mean gets smaller, it means that the data points are closer to the mean.

This has several implications:
A. The coefficient of variation (CV) gets smaller: The coefficient of variation is the ratio of the standard deviation to the mean. When the standard deviation decreases (due to smaller spread of scores), the CV also decreases.
B. The interquartile range (IQR) gets smaller: The IQR represents the range between the first quartile and the third quartile. When the spread of scores decreases, the values at the first and third quartiles are closer together, resulting in a smaller IQR.
C. The standard deviation gets smaller: The standard deviation measures the average distance of data points from the mean. As the spread of scores decreases, the data points are closer to the mean, resulting in a smaller standard deviation.
In summary, when the spread of scores around the arithmetic mean gets smaller, the coefficient of variation, interquartile range, and standard deviation all decrease.

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To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

The angle of impact for the blood droplet can be calculated using the trigonometric formula: tan(angle) = opposite/adjacent. In this case, the opposite side is 2.5 cm and the adjacent side is 5 cm.

Trigonometry is a branch of mathematics that studies relationships between angles and sides of triangles. It is used to determine angles, distances, and other properties of a triangle. Trigonometry is also applied in the fields of engineering, physics, astronomy, and other sciences. By understanding the relationships between angles and sides of triangles, trigonometry is used to solve problems involving angles, lengths, and areas of triangles.

the angle of impact is tan(angle) = 2.5/5 = 0.5. Converting this to degrees, the angle of impact is tan-1(0.5) ≈ 26.6°.

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Answer:

Mai and Clare  will complete the fourth and third signs respectively at 24 minutes after beginning  the task

Mai and Noah won´t finish signs at the same time

Clare and Noah won´t finish signs at the same time

Step-by-step explanation:

A)  During half an hour of work

Mai will finish signs at:

6     12    18    24           32  ( out of the range of 1/2 hour)

for Clare finishing time are:

8     16     24                 32 out

And Noah

5  10  15  20  25  30     no more

Mai and Clare  will complete the fourth and third signs respectively at 24 minutes after beginning  the task

Mai and Noah won´t finish signs at the same time

Clare and Noah won´t finish signs at the same time

We can give answers to that type of question, just by examining the products of time making the sign * each different sign, as we did.

In fact, 24 is the minimum common multiple of 6 and 8

6 * 4  =  24

8 * 3  =  24

And that is the required condition to get  finished signs at the same time.

Answer:

10 x 15 feet

Step-by-step explanation:

Possible answers

1 x 150

2 x 75

3 x 50

5 x 30

10 x 15  seems the most reasonable size for a patio

If the difference between the squares of two consecutive odd number be 48 then the first number is 11 and the second number is 13.

Given that the difference between the squares of two consecutive odd number be 48.

We are required to find the numbers.

Odd numbers are basically those numbers which are not divisible by 2.

Consecutive numbers are those numbers which come one after other.

Suppose the first number be x.

In this way the second number be x+2.

We are given that the difference between the squares of these numbers is 48. So,

\((x+2)^{2} -x^{2}\)=48

\(x^{2} +4+4x-x^{2}\)=48

4+4x=48

4x=48-4

4x=44

x=11

Put the value of x in x+2 to get the other number.

Second number=11+2=13

Hence if the difference between the squares of two consecutive odd number be 48 then the first number is 11 and the second number is 13.

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The height of the water tank given the volume, length and width is 40 cm

Volume of the water tank= 40 liters

Length of the water tank= 50 cm

Width of the water tank= 20 cm

Height of the water tank= x

convert liters to centimeters

1 liter= 1000 cm

40 liters= 40,000 cm

Volume of the water tank= length × width × height

40,000 = 50 × 20 × x

40,000 = 1000x

divide both sides by 1000

x = 40,000 / 1000

x = 40 cm

Therefore, the height of the water tank is 40 cm

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The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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Answer:

$44.4.

Step-by-step explanation: To find the new price, we would simply perform "37 + 20%" yielding 44.4, or forty four dollars and 40 cents. Hope this answered your question.

Answer: 44.4

Step-by-step explanation:

To calculate the original price of a discounted or sale item, you need to know the sale price and the discount percentage. The calculations include a simple formula that divides the sale price by the result of 1 minus the discount in percentage form. Use this formula to calculate the original or list price of an item.

52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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The expected value 'w' for the total raffle tickets sold for $1.00 with other conditions is equal to $0.784.

Number of raffle tickets sold for $1.00 = 2000

Expected value of w is ,

= Expected value of the prize won - cost of a single ticket $1.00

The probability of winning a $25 prize is

=  20/2000

= 0.01.

The expected value of winning this prize is equal to

= (25 - 1) × 0.01

= 0.24

The probability of winning a $50 prize is

= 10/2000

= 0.005.

The expected value of winning this prize is equal to

=  (50 - 1) × 0.005

= 0.245

The probability of winning a $300 prize is

= 2/2000

= 0.001.

The expected value of winning this prize is,

= (300 - 1) × 0.001

= 0.299

This implies,

The expected value of w is equal to

= 0.24 + 0.245 + 0.299

= 0.784

Therefore, the expected value of winning a prize minus the cost of the ticket is $0.784.

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Therefore, the measure of the central angle whose radii define the given arc is approximately 83.077 degrees.

The length of an arc on a circle is given by the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, we know the arc length is 6π centimeters, and the radius of the circle is 13 centimeters. The circumference of the circle can be calculated using the formula:

Circumference = 2π * Radius

Substituting the radius value, we get:

Circumference = 2π * 13

= 26π

Now we can use the arc length formula to find the central angle:

6π = (Central Angle / 360°) * 26π

Dividing both sides of the equation by 26π:

6π / 26π = Central Angle / 360°

Simplifying:

6 / 26 = Central Angle / 360°

Cross-multiplying:

360° * 6 = 26 * Central Angle

2160° = 26 * Central Angle

Dividing both sides by 26:

2160° / 26 = Central Angle

Approximately:

Central Angle ≈ 83.077°

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The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

The function f(x1, x2) = 2x1 + 3x2  defined from Real Number to Real Number is both one-to-one and onto.  

Let's assume we have two input pairs (x1, x2) and (y1, y2) such that f(x1, x2) = f(y1, y2). Then, we have 2x1 + 3x2 = 2y1 + 3y2. To show that f is one-to-one, we need to prove that if the equation 2x1 + 3x2 = 2y1 + 3y2 holds, then it implies x1 = y1 and x2 = y2. we can see that the equation holds only if x1 = y1 and x2 = y2. Therefore, f is one-to-one.

For any real number y in R, we need to find input pairs (x1, x2) such that f(x1, x2) = y. Rewriting the function equation, we have 2x1 + 3x2 = y. By solving this equation, we can express x1 and x2 in terms of y: x1 = (y - 3x2)/2. This shows that for any given y, we can choose x2 freely and calculate x1 accordingly.

Therefore, every real number y in the codomain R has a preimage in the domain RxR, indicating that f is onto.

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No, Khaleed's  claim not correct the distribution is uniform with mean equal to 8 interviews if a random variable y represent the number of interviews conducted for job openings at a certain company.

A discrete random variable is one that can have any whole number of values as the result of a random experiment. The discrete random variable has  countable number of possible outcomes,represented as 0, 1, 2, 3, 4,... The values of discrete random variables are represented by probability distributions. A stochastic variable is another name for a discrete random variable. A binomial random variable and a Poisson random variable are two examples of discrete random variables.

Data can be of two types: discrete and continuous. Also, do not confuse a discrete random variable with an algebraic variable.

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Answer:

C

Step-by-step explanation:

i used the substitution method to find it out

Answer: Number of kids who attended the party = 12 / 0.60

Step-by-step explanation:

60% = 12

x 0.60 = 12

Number of kids attending =  x = 12 / 0.60

Answer:

12 is 60

Step-by-step explanation:

Answer: 12 is 60 percent of 20. (60% of 20 = 12) Percentages are fractions with 100 as the denominator.

An equation in point-slope form that can be used to describe the relationship between x and y is y - (-1) = 3/4(x - 1).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 1)/(5 - 1)

Slope (m) = 3/4

At data point (1, -1) and a slope of 3/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = 3/4(x - 1)  

y + 1 = 3/4(x - 1)  

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Alanna will therefore receive $2,560 in commission for a $32,000 transaction.

A ratio or figure expressed as a fraction of 100 is called a percentage. Since "percent" is a slang term for "per hundred," when we discuss percentages, we actually mean parts per hundred. It is frequently represented by the sign %. To express your score as a percentage, divide your real score by the range of possible scores, multiply the result by 100, for instance, if you received an 80 out of 100.Your percentage result in this situation would be: % equals (80/100) times 100. Number equals 80%

given

We must multiply the transaction amount by the commission rate in order to determine the commission that Alanna will receive.

Sale amount x Commission percentage equals commission.

The fee rate is stated as 8%, which is equivalent to 0.08 in decimal form.

Consequently, Alanna's commission on a $32,000 transaction is as follows:

$32,000 multiplied by 0.08 of a commission equals $2,560.

Alanna will therefore receive $2,560 in commission for a $32,000 transaction.

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Answer:

a) 7/4 b) 5 c) 2

Step-by-step explanation:

Logrithmic Rule for a and b

Let a, M, N be positive real numbers.

a)  

logaM - logaN = loga(M/N)

log9(7) - log9(4) = log9 (7/4)

b)

logaM + logaN = logaMN

log2 (x) + log2(9) = log2(45)

x9=45

(x9)/9 = 45/9

x = 5

c)

Change of base formula.

logb​(x)=logd​(b)/logd​(x)​

x log6(5) = log6(25) divide each term by log6(5)

x log6(5) / log6(5) = log6(25) / log6(5)   Cancel common factor log6(5)

x = log6(25) / log6(5)

x = log6(5^2) / log6(5)

Expand log6(5^2) by moving 2 outside the logarithm.

x = 2log6(5) / log6(5) cancel the like term log6(5)

x = 2

Answer:

x=1/4

Step-by-step explanation:

4(1/4)=1

1/3=1/3

Answer:

Step-by-step explanation:

36/$15 = $2.04 per pound

Answer:

36/$15 which equals $2.04 per pound

Step-by-step explanation:

Jane Height will be = 56 (4.7) inches

What is Height?

Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

we have to calculated jared height first

Jared height= he would be 1 3/8 inches taller then jack at 54  3/4 inches

= 54   3/4 + 1   3/8

= 55 ( 3/4 + 3/8)

= 55 ( 24+12)/8

= 55 (36 /8)

= 55 (4.5) inches

Then jane is 1   1/5 inches taller than jared

= 55 ( 36/8) + 1    1/5

= 55 ( 36/ 8 + 1/5)

= 56 ( 180 + 8 )/40

= 56 (4.7) inches

Jane height is 56( 4.7) inches

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Answer:

One pound of beef is $3.2

Step-by-step explanation:

14.40 / 4.5

= 3.2

CHECK:

3.2 * 4.5

=14.40

Answer:

Step-by-step explanation:

The unit rate for this beef is:

$14.40

---------- = $3.20/lb

4.5 lb