(like Section 9.4, #9) Given these functions: z = 2x3y, x = s cost, y = s sint Find dz/ds and dz/dt. Remember to substitute for x and y so that they do not appear in your final answer.

Answer:

(3x+1)(x+3) is the factorised form for the expression.

Step-by-step explanation:

:3

x

2

+

10

x

+

3

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like  

a

x

2

+

b

x

+

c

, we need to think of 2 numbers such that:

N

1

⋅

N

2

=

a

⋅

c

=

3

⋅

3

=

9

and,

N

1

+

N

2

=

b

=

10

After trying out a few numbers we get:

N

1

=

9

and  

N

2

=

1

9

⋅

1

=

9

, and  

9

+

(

1

)

=

10

3

x

2

+

10

x

+

3

=

3

x

2

+

9

x

+

1

x

+

3

=

3

x

(

x

+

3

)

+

1

(

x

+

3

)

(

3

x

+

1

)

(

x

+

3

)

is the factorised form for the expression.

is the factorised form for the expression.

Answer:

140 hamburgers

Step-by-step explanation:

to find the answer we must first use a let statement and write an equation

let x = hamburgers

hamburgers * 2 is cheeseburgers and added together that is 420

so

x + 2x = 420

now solve

3x = 420

x = 140

140 hamburgers were sold

Answer:

Step-by-step explanation:

240 divided by 3= 80

80+80=160

160 hamburgers sold altogether on Wednesday.

The value of the definite integral is -28/3

Using the power rule of integration, we can find the antiderivative of t^2 - 5 as follows:

∫(t^2 - 5) dt = (1/3)t^3 - 5t + C

where C is the constant of integration.

To evaluate the definite integral, we substitute the limits of integration into this expression and take the difference:

∫^-1_1 (t^2 - 5) dt = [(1/3)(1^3) - 5(1)] - [(1/3)(-1^3) - 5(-1)]

= (1/3 - 5) - (1/3 + 5)

= (-14/3)  (16/3)

= -28/3

Therefore, the value of the definite integral is -28/3.

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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Answer:

The domain = 1, 3, 5, 7 and the range = 5, 15, 25, and 35

Step-by-step explanation:

The given parameters are;

The life expectancy of a monkey = 15 years

The life expectancy of an African elephant = 35 years

The life expectancy of a beaver = 5 years

The life expectancy of a grizzly bear = 25 years

Therefore, if the  life expectancy of a beaver = X, we have;

The life expectancy of a monkey = 3 × The life expectancy of a beaver = 3·X

The  life expectancy of a beaver = X

The life expectancy of an African elephant = 7 × The life expectancy of a beaver = 7·X

The life expectancy of a grizzly bear = 5 × The life expectancy of a beaver = 5·X

Therefore;

The domain = 1, 3, 5, 7 and the range = 5, 15, 25, and 35.

Answer:

Relation = {(Monkey, 15), (African elephant, 35), (Beaver, 5), (Grizzly bear, 25)}

Domain = {Monkey, African elephant, Beaver, Grizzly bear}

Range = {5, 15, 25, 35}

Step-by-step explanation:

Relation is just (x,y).

{(Monkey, 15), (African elephant, 35), (Beaver, 5), (Grizzly bear, 25)}  

I like to put domain as least ---> greatest, but in this case, it's just the names

{Monkey, African elephant, Beaver, Grizzly bear}

The numbers.

{5, 15, 25, 35}

Hope this helped! Please mark brainliest :)

~~ SUMMER ~~

Based on the given side lengths, one of the quadrilaterals (A or B) cannot be a scaled copy of the other.

Yes, one of the quadrilaterals could be a scaled copy of the other. In order for two quadrilaterals to be scaled copies of each other, their corresponding side lengths must be proportional. To determine if the two quadrilaterals are scaled copies of each other, we need to check if the ratios of their corresponding side lengths are equal.

Let's compare the side lengths of quadrilateral A and quadrilateral B:

Quadrilateral A: 2, 3, 5, 6

Quadrilateral B: 4, 5, 8, 10

Now, let's find the ratios of the corresponding side lengths:

Ratio of the first side: 2/4 = 1/2

Ratio of the second side: 3/5

Ratio of the third side: 5/8

Ratio of the fourth side: 6/10 = 3/5

As we can see, the ratios of the corresponding side lengths are not equal for the two quadrilaterals. Therefore, quadrilateral A and quadrilateral B are not scaled copies of each other.

In conclusion, based on the given side lengths, one of the quadrilaterals (A or B) cannot be a scaled copy of the other.

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Based on the given side lengths, one of the quadrilaterals (A or B) cannot be a scaled copy of the other.

Yes, one of the quadrilaterals could be a scaled copy of the other. In order for two quadrilaterals to be scaled copies of each other, their corresponding side lengths must be proportional. To determine if the two quadrilaterals are scaled copies of each other, we need to check if the ratios of their corresponding side lengths are equal.

Let's compare the side lengths of quadrilateral A and quadrilateral B:

Quadrilateral A: 2, 3, 5, 6

Quadrilateral B: 4, 5, 8, 1

Now, let's find the ratios of the corresponding side lengths:

Ratio of the first side: 2/4 = 1/2

Ratio of the second side: 3/5

Ratio of the third side: 5/8

Ratio of the fourth side: 6/10 = 3/5

As we can see, the ratios of the corresponding side lengths are not equal for the two quadrilaterals. Therefore, quadrilateral A and quadrilateral B are not scaled copies of each other.

In conclusion, based on the given side lengths, one of the quadrilaterals (A or B) cannot be a scaled copy of the other.

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Answer:

Because the solution is 12.5 so he need to teach about 13 lessons

Step-by-step explanation:

There are 198 passengers in each car.

What is division?

The division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication.

To determine the number of passengers in each car, we need to divide the total number of passengers by the total number of cars.

We know that:

There are 4,752 passengers in total

There are 8 cars per train and 3 trains

So, the total number of cars is 8 cars/train x 3 trains = 24 cars

To find the number of passengers per car, we divide the total number of passengers by the total number of cars:

4,752 passengers / 24 cars = 198 passengers per car.

Hence, there are 198 passengers in each car.

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the distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ.

What is Equivalence relation?

An equivalence relation is a relation between elements of a set that satisfies three properties: reflexivity, symmetry, and transitivity.

a) To prove that R is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we need to show that m R m, i.e., 4 |\((m^2 - m^2).\) Since the difference of squares is 0, which is divisible by 4, the relation is reflexive.

Symmetry: For any integers m and n, if m R n, then we need to show that n R m. If 4 | \((m^2 - n^2)\), then \((m^2 - n^2)\) is divisible by 4. Taking the negative of both sides, we have\((-n^2 + m^2) = (m^2 - n^2)\), which is also divisible by 4. Therefore, n R m, and the relation is symmetric.

Transitivity: For any integers m, n, and p, if m R n and n R p, then we need to show that m R p. Suppose 4 |\((m^2 - n^2)\)and 4 \(| (n^2 - p^2)\). This means \((m^2 - n^2) and (n^2 - p^2)\)are both divisible by 4. Adding these two divisibility statements, we get (m^2 - p^2) is also divisible by 4, which implies m R p. Hence, the relation is transitive.

Since the relation R satisfies reflexivity, symmetry, and transitivity, it is an equivalence relation.

b) The distinct equivalence classes of the relation R can be described by the set of all integers that are congruent modulo 4. In other words, each equivalence class contains integers that have the same remainder when divided by 4.

The distinct equivalence classes can be denoted as follows:

[0] = {..., -8, -4, 0, 4, 8, ...}

[1] = {..., -7, -3, 1, 5, 9, ...}

[2] = {..., -6, -2, 2, 6, 10, ...}

[3] = {..., -5, -1, 3, 7, 11, ...}

Each equivalence class consists of integers that satisfy the condition 4 | (m^2 - n^2), and within each class, any two integers have their squares yielding the same remainder when divided by 4.

c) The distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ. A partition of a set is a collection of non-empty, pairwise disjoint subsets whose union is the entire set.

In this case, the equivalence classes [0], [1], [2], and [3] are non-empty and pairwise disjoint because no integer can simultaneously belong to two different equivalence classes. Also, the union of all the equivalence classes covers the entire set of integers, as each integer belongs to exactly one of the equivalence classes.

Therefore, the distinct equivalence classes [0], [1], [2], and [3] form a partition of ℤ.

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Answer:

185

Step-by-step explanation:

14.8 / 0.08 = 185

Best of Luck!

Answer:

185

Step-by-step explanation:

next time you get a question like that use symbolab

Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

\(72 = 2^3 * 3^2\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\\)

The GCD of the crayons is \(2^3 * 3\), which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = \(2^3 * 3 * 5\)

The GCD of the drawing paper is also \(2^3 * 3\), which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

Gobi Desert and karakum desert

Step-by-step explanation:

Several pairs of items (x, y) have a support of at least 100. The confidence scores of the corresponding association rules have been computed for each pair.

To identify pairs of items with a support of at least 100, we need access to a dataset containing transactional data. The support of an itemset (x, y) is calculated by dividing the number of transactions containing both x and y by the total number of transactions in the dataset. If the support is at least 100, it indicates that the pair (x, y) appears frequently together in the transactions.

Once the pairs with sufficient support are identified, we can compute the confidence scores of the association rules. Confidence is a measure of the strength of an association rule. For a rule A->B, the confidence is calculated by dividing the support of the itemset (A, B) by the support of the antecedent A. A high confidence score indicates a strong association between A and B.

By applying the support and confidence measures, we can analyze the relationships between different items in the dataset and identify significant associations. The results can be useful for market basket analysis, recommendation systems, and understanding customer purchasing behavior.

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Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

10 meters away is the bus from the bus stop after 10 seconds.

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.

In this way bus forms an arithmetic sequence

10, 20, 30, 40........up to 10 terms.

nth term of an arithmetic sequence is represented by

\(T_{n}\) = a+ (n - 1)d

Here a = 10 and d = common difference = 10

Therefore 10th term = 10 + (10-1)10

                                  = 10 + 90

                                  = 100

Therefore after 10 seconds bus will be 10 meters away from the bus stop.

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The image after the sequence of transformations is (30, -14)

We start with the point (9, 4), first we need to translate it up 3 units, then right 6 units, dilate it by a scale factor of 2, and finally reflect it across the x-axis.

Let's write all these transformations in a general way and then let's apply them.

For a general point (x, y)

A vertical translation up of 3 units gives: (x, y + 3)

A horizontal translation of 6 units to the right gives: (x + 6, y)

A dilation of scale factor 2 gives: (2x, 2y)

A reflection across the x-axis gives: (x, -y)

Then if we apply all that to our point (9, 4) we will get:

A vertical translation up of 3 units gives: (9, 4 + 3) = (9, 7)

A horizontal translation of 6 units to the right gives: (9 + 6, 7) = (15, 7)

A dilation of scale factor 2 gives: (2*15, 2*7) = (30, 14)

A reflection across the x-axis gives: (30, -14)

That is the image after the sequence of transformations.

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Answer:

-11f +15

Step-by-step explanation:

-f-5(2f-3)

Distribute

-f -10f +15

Combine like terms

-11f +15

Answer:

B

Step-by-step explanation:

We apply distributive property first on the 2f thingie.

The negative 5 is applied on both the 2f and the negative 3 to get

-10f + 15 since two negatives equals a positive in math.

Then we subtract an "f" from the current data to get your answer since the original question was

-f -5 ( 2f - 3 )

So we get

-11f + 15 or B.

Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be

Then,

Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.

However, we can algebraically find x and y, although it would not make any sense geometrically speaking.

Solving for x,

Similarly, solving for y,

Answer:

T=50.99

Step-by-step explanation:

Given:

I=3,875.78

P=1,900

R=4% I.e 4/100 , 0.04

T=?

I=PRT

3,875.79=($1,900)(0.04)t

3,875.79=76t

3,875.79/76= t

T=50.99

Answer:

Step-by-step explanation:

Given equation:

Solve for variables:

Answers:

Answer:

sin B= square root of 3/ 2

Cos B= 1/2

tan B= square root of 3/1

Sin C=1/2

cos C square root of 3/2

tan C= 1/square root of 3

Step-by-step explanation:

Answer:

\(\angle ABC\) corresponds to the \(\angle D EF\)

\(\angle BCA\) corresponds to the \(\angle EFD\)

Segment AC corresponds to segment DF.

Segment BA corresponds to segment ED.

Step-by-step explanation:

As per the given statements, kindly refer to the attached figure for the diagrammatic representation of the situation.

Given two triangles: \(\triangle ABC, \triangle D EF\).

Horizontal sides are AB and DE with points B and E are on the right side of A and D respectively.

Points C and F are directly above the corresponding sides AB and DE respectively.

Kindly refer to the attached diagram for the representation as per the given situation.

Scaled version of a figure and the original figure are similar to each other.

It means that corresponding sides and angles are equal to each other.

\(\angle ABC\) corresponds to the \(\angle D EF\)

\(\angle BCA\) corresponds to the \(\angle EFD\)

Segment AC corresponds to segment DF.

Segment BA corresponds to segment ED.

If the statement is "The difference of four times a number and seven is ten times the number." then an algebraic equation is 4x-7= 10+x and the solution is -7/6.

Given the statement "The difference of four times a number and seven is ten times the number." We have to translate the statement in an algebraic equation and then solve it.

Let, the number be x.

This difference of four times a number and seven is 4x-7 and ten times the number is 10x

According to the question, the equation is,4x-7= 10x

4x-7=10x

6x=-7

x=-7/6

x=-7/6

Hence the value of the x is -7/6.

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The number of glasses of lemonade that can be poured from the cooler is 45.

Given that, an insulated cooler holds 558 ounces of lemon.

We need to find how many full 12.4-ounces glasses of lemonade can be poured from the cooler.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, the number of glasses of lemonade = 558/12.4

=45

Hence, the number of glasses of lemonade that can be poured from the cooler is 45.

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Explanation:

The probability of picking red is 0.13

The probability of picking orange is 0.20

The probability of picking either of these is 0.13+0.20 = 0.33

So the probability of picking neither of them is 1 - 0.33 = 0.67

There's a 67% of this happening.

Answer:

0.34

Step-by-step explanation:

because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.

(A) Algorithms are mathematical formulas placed in software that performs an analysis on a data set.

Therefore, (A) algorithms are mathematical formulas placed in software that performs an analysis on a data set.

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