The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.

Answer:

  10.309 in²/s

Step-by-step explanation:

Given A³ = 36πV² and V' = 18 in³/s, you want to know A' when A=153.24 in² and V=178.37 in³.

Using implicit differentiation, we have ...

  3A²·A' = 36π·2V·V'

  A' = (36π·2)/3·V/A²·V' = 24πV/A²·V'

  A' = 24π·(178.37 in²/(153.24 in²)²·18 in³/s

  A' ≈ 10.309 in²/s

The surface area is increasing at about 10.309 square inches per second.

__

Additional comment

There are at least a couple of ways a calculator can be used to find the rate of change. The first attachment shows evaluation of the expression we derived above. The second attachment shows the rate of change when the area is expressed as a function of the volume.

The result rounded to 5 significant figures is the same for both approaches.

The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .

The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.

In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).

To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:

`P(E) = n(E) / n(S)`

where, P(E) = Probability of an event

n(E) = Number of favorable outcomes

n(S) = Total number of outcomes

Total number of outcomes = 52

First card will be a diamond

Number of diamonds in a deck of 52 cards = 13

Total number of outcomes after drawing the first card = 52

Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52

Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`

Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`

Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`

Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.

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Keenan's z-score is 0.71, rounded to the nearest hundredth.

The z-score measures how many standard deviations an individual's score is from the mean, and can be calculated using the formula:

z = (x - μ) / σ

where x is the individual's score, μ is the mean score, and σ is the standard deviation.

For Keenan's exam:

z = (80 - 77) / 4.2

z = 0.71

Therefore, Keenan's z-score is 0.71, rounded to the nearest hundredth.

Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.

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Answer: $22.50

Step-by-step explanation:

Let x be the cost per pound of the secret-formula coffee beans.

The total cost of the secret-formula beans is 12x dollars.

The total cost of the other beans is 15 × 18 = 270 dollars.

The total cost of the mix is (12 + 15) × 20 = 540 dollars.

Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.

We can set up an equation based on the total cost of the mix:

12x + 270 = 540

Subtracting 270 from both sides:

12x = 270

Dividing both sides by 12:

x = 22.5

Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.

Answer:

- 1 and 7

Step-by-step explanation:

to find h(0) substitute x = 0 into h(x)

h(0) = 4(0) - 1 = 0 - 1 = - 1

to find h2) substitute x = 2 into h(x)

h(2) = 4(2) - 1 = 8 - 1 = 7

Answer:

To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.

We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.

So we have:

556 = 16 x 34 + 48 + 4

This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.

Simplifying the remainder, we have:

48 + 4/16 = 48 + 1/4 = 48.25

Therefore, the quotient of 556 and 16 is:

556/16 = 34 1/4

The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.

When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.

Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.

Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.

There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.

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The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

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Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares

Given that

4 triangles to 16 squares

When expressed as ratio, we have

Triangle : Square = 4 : 16

To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.

So, we have

Triangle : Square = 4 : 16

Divide both sides by 4:

Triangle/4 : Square/4 = 1 : 4

So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.

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Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

Answer:

Step-by-step explanation:

The answer to the question is 334 kittens.

Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.

First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g

Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.

Therefore, the answer to the question is 334 kittens.

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The Length of AB in square ABCD is 30 feet.

Since the squares ABCD and EFGH are similar, their corresponding sides are proportional, so we can set up the following relation:

AB/EF = 1/4

We can also use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore,

AB²/EF² = (Area of square ABCD)/(Area of square EFGH)

Substituting the given values:

AB²/EF² = (Area of square ABCD)/(14400)

Since the areas of squares are proportional to the square of their sides, we can write,

Area of square ABCD/Area of square EFGH = (AB/EF)²

Substituting this into the above equation and solving for AB, we get,

AB²/EF² = (AB/EF)²

AB² = (AB/EF)² * EF²

AB² = (1/4)² * 14400

AB² = 900

AB = 30 feet

Therefore, the length of the side AB of square ABCD is 30 feet.

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As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is  $43,200. (option d).

To calculate this, we can use the formula for future value of an annuity:

FV = PMT x (((1 + r)⁻¹) / r)

where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).

Plugging in the numbers, we get:

FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60

Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.

Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:

$200 x 12 x 18 = $43,200

Hence the correct option is (d).

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In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.

The correct answer is option (C).

Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).

The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:

t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)

The vector's magnitude is given by:

|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296

The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.

θ = tan⁻¹ (–9/–5) ≈ 60.945°

In trigonometric form, the vector t is thus represented as follows:

t = [t|cos|i] + [t|sin|j]

We get the following by altering the values of |t| and:

t = 10.296 cos I + 10.296 sin j of angle 60.945

As a result, the following is the proper trigonometric representation of the vector t:

t = 10.296 cos I + 10.296 sin j of angle 60.945

Thus, alternative is the right response (C).

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Answer:

To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:

P = (3B + 1A) / 4

where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.

Substituting the values, we get:

P = (3*(-1, -5) + 1*(-5, 3)) / 4

P = (-3, -7)

Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).

Step-by-step explanation:

To perform matrix multiplication in MIPS, we can use nested loops to iterate over the rows and columns of the matrices.

The outer loop iterates over the rows of the first matrix, while the inner loop iterates over the columns of the second matrix. We then perform the dot product of the corresponding row and column, which involves multiplying the elements and summing the products.

To perform multiplication efficiently, we can use MIPS registers to store intermediate values and avoid accessing memory unnecessarily. We can also use assembly instructions like "lw" and "sw" to load and store values from memory, and "add" and "mul" to perform arithmetic operations.

In summary, matrix multiplication in MIPS involves nested loops, efficient use of registers and assembly instructions, and arithmetic operations.

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Answer: profit

Step-by-step explanation:

3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit

The position of C on the number line is 1/8th position.

A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.

From the given number line, there are total 8 points between 0 to 1

That means, it's fractions of 8.

Location of point C is on the 1st point,

So, position of C on this number line = (1/8) ÷ (1-0) = 1/8

Therefore, In the number line, C is located in the 1/8th place.

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the triangles are similar, corresponding parts of the triangles are equal in measure. Thus, it is reasonable to conclude that [tex]AB ≅ DE.[/tex]

It is reasonable to conclude that [tex]AB ≅ DE[/tex]because triangles ABC and DEF are similar.

This means that corresponding parts of the two triangles are equal in measure. Specifically, ∠A and ∠D are equal in measure, as are ∠B and ∠E.

Therefore, the corresponding sides AB and DE are equal in measure.

A way to show that the two triangles are similar is by using the AA Similarity Postulate.

This postulate states that if two angles of one triangle are equal in measure to two angles of a second triangle, then the two triangles are similar. In this case, [tex]∠A ≅ ∠D and B ≅ ∠E[/tex], which means the two triangles are similar.

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The three examples of contracts are:

Contracts are legal agreements between two or more parties that involve the exchange of goods, services, or money. They can be classified as unilateral or bilateral, express or implied, executed or executory.

Here are three examples of contracts that a person can be a part of:

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Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.

Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)

To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.

One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)

To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)

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Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

They cover almost equal distances from their starting points:

24 miles ≈ √12²+21² miles

b) They encounter each other.

c) The angle at one vertex measures 30 degrees.

d) e) As shown in the attached picture, it is an almost right triangle.

f) Together, they cover a total distance of 57 miles (12+21+24).

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Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is

∠BCD = ∠BAD ⇒ ∠BCD = 106°