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The value of the cross product of two given vectors is = 6i-7j.

We only want to think about a portion of the rod. We first wish to think about a narrow slice of the rod. We can solve a straightforward equation if the thermal energy density is constant across the volume.

A *B stands for the vector product or cross product of two vectors A and B, and the resulting vector is perpendicular to the original two. While the dot product is used to identify the length of a vector or the angle between two vectors, the cross product is typically employed to determine the vector that is perpendicular to the plane surface spanned by two vectors. In three dimensions, the cross product of two vectors, such as A B, equals a vector at right angles to both.

we have a = i - 6k and b= j + k then find a×b

[tex]a*b=\left[\begin{array}{ccc}i&j&k\\1&0&-6\\1&0&1\end{array}\right] \\\\a*b=(6)i-(1+6)j+(0k)\\\\a*b=6i-7j[/tex]

The value of the cross product of two given vectors is = 6i-7j.

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Based on the information, we can infer that after 20 days there will be 153 plants and after 65 days there will be 498 plants.

To find the number of plants that will be after 20 and 65 days we must take into account the number of initial plants and the number of days required for the plantation to double.

According to the above, we must make a rule of 3 as shown below:

12 - 92

20 -

= 20 * 92 / 12 = 153

12 - 92

65

= 65 * 92 / 12 = 498

According to the above, after 20 days there will be 153 plants and after 65 days there will be 498 plants.

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Answer:

2500 people

Step-by-step explanation:

There are several ways of figuring this one out, we could do a proportion

[tex] \frac{10\%}{100\%} = \frac{250}{x} [/tex]

Cross multiply and divide

10x = (250)(100)

10x = 25000

Dividing both by 10

x = 2,500 people were at the stadium

Answer:

2500

Step-by-step explanation:

The solution of all the measures of the angles are,

1) m ∠A = 63°

2) m ∠B = 138°

3) m ∠C = 117°

4) m ∠D = 137.22°

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

In figure 1;

Measure of angle A and angle B are vertically opposite angle and hence both are equal to each other.

⇒ ∠A = ∠B

⇒ 2x + 35 = 8x - 49

⇒  35 + 49 = 8x - 2x

⇒ 84 = 6x

⇒ x = 14

Thus, The value of m ∠A = 2x + 35

                                       = 2×14 + 35

                                       = 28 + 35

                                       = 63°

2) By the figure, the sum of both indicated angle is 180°.

Hence, We get;

⇒ 10x - 18 + 15x + 48 = 180

⇒ 25x + 30 = 180

⇒ 25x = 180 - 30

⇒ 25x = 150

⇒ x = 6

Thus, The value of m ∠B = 15x + 48

                                       = 15×6 + 48

                                       = 90 + 48

                                       = 138°

3) By the figure, Both angles are alternate angle of parallel lines and hence both are equal.

So, We get;

⇒ 7x + 5= 12x - 75

⇒ 5 + 75 = 12x - 7x

⇒ 80 = 5x

⇒ x = 16

Thus, The value of m ∠C = 7x + 5

                                       = 7×16 + 5

                                       = 112 + 5

                                       = 117°

4) By the figure, the sum of both indicated angle is 180°.

Hence, We get;

⇒ 27x - 21 + 10x - 16 = 180

⇒ 37x - 37 = 180

⇒ 37x = 180 + 37

⇒ 37x = 217

⇒ x = 217/37

⇒ x = 5.86

Thus, The value of m ∠D = 27x - 21

                                       = 27×5.86 - 21

                                       = 158.22 - 21

                                       = 137.22°

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According to the information, Maria has to add a unit in the second bar that corresponds to the vacations that have between 7 and 9 days.

To complete the graph correctly we must identify what information is in it. First of all we see that there are ranges of duration of vacations on the X axis, then, there are 4 bars that represent the following ranges:

According to the above, since she has not added her last vacation that lasted 7 days, we must add a unit that represents these vacations in the second column, to complete the graph.

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Answer:

[tex]c^6 -7[/tex]

Step-by-step explanation:

c to the sixth power is [tex]c^6[/tex], and this minus 7 is [tex]c^6 -7[/tex].

Answer:

7 - c^6

Step-by-step explanation:

First, calculate the value of c raised to the 6th power: c^6

Then, subtract the result from 7: 7 - c^6. The expression represents the calculation of raising c to the 6th power, and then subtracting the result from 7.

The probability that at least 5000 dropouts will receive the flyer is 0.7852

The probability of high school dropouts is p₀ = 20.2% or 0.202

We, know that probability is the number of favourable outcomes divided by the number of possible outcomes.

Total number of flyers sent to persons between the ages of 18 and 24 = 25000 = Total number of possible outcomes

Number of dropouts who receive the flyer = 5000 = number of favourable outcomes

Probability(p) = No. of favourable outcomes/ No. of possible outcomes

                   p = 5000/25000

                   p = 0.2

Now,

                                 z = (p - p₀)/( (p₀ (1 - p₀) ) / n)^0.5

                                 z = (0.2 - 0.202)/( (0.202 (1 - 0.202) ) / 25000)^0.5

                                 z = - 0.79

Hence, P(z > −0.79) = P(z < 0.79) = 0.7852

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The probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].

As per the given data:

A bag contains 19 balls numbered 1 through 19.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19

The total number of outcomes is 19.

Here we have to determine the probability that a randomly selected ball has a number less than 10.

Numbers on the balls less than 10 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.

A ball is randomly selected.

The favorable outcomes are 9.

The likelihood of every event depends on the overall number of positive outcomes as well as the number of favorable outcomes.

The formula for probability:

The number of favorable outcomes is divided by the total number of outcomes.

= [tex]$\frac{9}{19}[/tex]

Therefore the probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].

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Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Inequality Form:

x≤−16/7

Interval Notation:

(−∞,−16/7]

The solution to the linear inequality given as -6 + 7x ≤ -22 is determined as x ≤ -16/7.

The value of x in the inequality -6 + 7x ≤ -22, is determined by applying the following method.

The given inequality expression;

-6 + 7x ≤ -22

Solve the inequality by collecting similar terms together as shown below;

-6 + 7x + 6 ≤ -22 + 6

Simplify further as follows;

7x ≤ -16

Divide both sides of the inequality by 7 to solve for x as shown below;

(7x)/7 ≤ (-16)/7

x ≤ -16/7

Therefore, the solution to the inequality is x ≤ -16/7.

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Work Shown:

[tex]\frac{33.5 \text{ rev}}{1 \text{ min}} *\frac{360 \text{ deg}}{1 \text{ rev}}*\frac{1 \text{ min}}{60 \text{ sec}} \\\\[/tex]

[tex]=\frac{33.5 \not{\text{r}}\not{\text{e}}\not{\text{v}}}{1 \text{ min}} *\frac{360 \text{ deg}}{1 \not{\text{r}}\not{\text{e}}\not{\text{v}}}*\frac{1 \text{ min}}{60 \text{ sec}} \ \text{ ... 'rev' units cancel}\\\\[/tex]

[tex]=\frac{33.5}{1 \text{ min}} *\frac{360 \text{ deg}}{1}*\frac{1 \text{ min}}{60 \text{ sec}} \\\\[/tex]

[tex]=\frac{33.5}{1 \not{\text{m}}\not{\text{i}}\not{\text{n}}} *\frac{360 \text{ deg}}{1}*\frac{1 \not{\text{m}}\not{\text{i}}\not{\text{n}}}{60 \text{ sec}} \ \ \text{ ... 'min' units cancel}\\\\[/tex]

[tex]=\frac{33.5}{1} *\frac{360 \text{ deg}}{1}*\frac{1}{60 \text{ sec}}\\\\[/tex]

[tex]=\frac{33.5*360}{60} \text{ degrees per second}[/tex]

[tex]=201 \text{ degrees per second}[/tex]

Notes:

Buyers get a percentage off on any purchase above the Minimum Basket Price. It will also be capped at the Maximum Discount Price if you choose to set a limit. E.g. "10% OFF with Min.

Since the unit price per pound of the dog food we bought is lesser than that of Target, we got a better buy.

To find the unit price per pound, we need to divide the price paid by the amount bought (in pounds)

`Now we have paid $53.99 for 40 pounds

Target charges $28.99 for 20 pounds.

Hence the unit price per pound we paid will be

53.99/40

= $1.34975 /lb

Now the unit price per pound charged by Target is

$28.99/20 lb

= $ 1.4495 /lb

Hence here we can clearly see 1.34975 < 1.4495

Hence, we bought the dog food at a better price than that at Target.

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Complete Question

I paid $53.99 for a 40 lb bag of dog food at Costco. At Target, they are selling the same dog food for $28.99 for a 20 lb bag. Find the unit price in dollars per pound. Then state which bag of dog food is the better buy based on the unit price.

a. Water in the pail at the end = 12.2 gallons

b. Water poured in the pail = 7.7 gallons

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

Given,

Water in tank = 35 gallons

Water in pail = 4.5 gallons

Ratio of the water in the tank to pail became 7:2 after pouring same amount of water in both.

Let the amount of water poured in the tank and the pail is x

Then ratio of water in tank to pail

(35 + x)/(4.5 + x) = 7/2

70 + 2x = 31.5 + 7x

5x = 38.5

x = 38.5/5

x = 7.7

Water poured in pail and tank = 7.7 gallons

Total water in pail = 4.5 + 7.7 = 12.2 gallons

Hence,

a. there was 12.2 gallons of water in the pail at the end

b. 7.7 gallons of water was poured into the pail.

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Answer: 40 and 50-2x.

Step-by-step explanation: you multiply 5*2=10, and subtract that from 50. You would do the same with x, to get 2*x=2x. but you can't subtract 2x from 50 without knowing x, so you leave it as 50-2x.

The value of the equations are

a₃ = -1

a₄ = -4

a₅ = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of aₙ = - aₙ₋₁ - aₙ₋₂

The value of a₁ = -4

The value of a₂ = 5

So , when n = 3

Substitute the value of n = 3 in the equation , we get

a₃ = -a₂ - a₁

On simplifying the equation , we get

a₃ = -5 - ( -4 )

a₃ = -5 + 4

a₃ = -1

Substitute the value of n = 4 in the equation , we get

a₄ = -a₃ - a₂

On simplifying the equation , we get

a₄ = - ( -1 ) - ( 5 )

a₄ = + 1 - 5

a₄ = -4

Substitute the value of n = 5 in the equation , we get

a₅ = -a₄ - a₃

On simplifying the equation , we get

a₅ = - ( -4 ) - ( -1 )

a₅ = 4 + 1

a₅ = 5

Hence , the equations are solved

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The product of two numbers whose sum is 10 and whose product is 24 is 4 and 6. 10x can be written as (4x6)x3 and factored by grouping as (4x3)+(6x3).

a. The product of two numbers is 24, and the sum is 10. This means that 4 and 6 must be the numbers, because 4x6=24 and 4+6=10.

b. 10x can be written as (4x6)x3, since 4x6=24 and 24x3=10x.

c. 10x can be factored by grouping as (4x3)+(6x3). This is because 4x3=12 and 6x3=18, and 12+18=30, which is the same as 10x.

The product of two numbers whose sum is 10 and whose product is 24 is 4 and 6. 10x can be written as (4x6)x3 and factored by grouping as (4x3)+(6x3).

The complete question is :

Find two numbers whose product is 8•3=24 and whose sum is 10, write 10x using the factors from part (a), and factor by grouping. The answer is that the two numbers are 4 and 6, 10x can be written as (4x6)x3, and factored by grouping as (4x3)+(6x3).

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Tom first makes an error in step 4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3,912 ÷ 12

12 ) 3912 ( 326

      36

        312

        240

           72

           72

             0

Step 1.

There are 300 12s in 3,912

Step 2.

3,912 − 3,600 = 312

Step 3.

There are 20 12s in 312

Step 4.

312 − 240 = 72

Step 5.  
There are 7 12s in 72

Step 6.

72 − 72 = 0

Step 7.

Quotient = 300 + 20 + 7 = 326 with a remainder of 0

Thus,

Step 4 is an error.

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Answer:

below

Step-by-step explanation:

We need to eliminate oneof the variables....I'll choose 'y'

x+ y = 60      <======multiply this equation - 22 to get

-22x -22y = -1320

44x  =22y = 2024        Now add the two equations together to eliminaty 'y'

22x = 704     then x = 32     x+y = 60   so y = 28

The value of completing a centerline perimeter calculation is vast, as it helps in various fields by providing precise and accurate information on the length of a curved structure.

The centerline perimeter calculation is a mathematical formula used to find the length of a circular arc, and it is widely used in engineering, construction, and surveying.

One of the most significant values of centerline perimeter calculation is its use in the construction industry.

Architects and engineers use the formula to determine the amount of material required to build a curved structure, such as a bridge or a circular building.

It helps them to determine the length of the curved portion of the structure and the number of materials needed to construct it.

This information is critical for budgeting, scheduling, and ensuring that the structure is built to the specified standards.

This information is necessary for the construction of new roads and the improvement of existing ones.

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Answer:

∠ HLK = 29°

Step-by-step explanation:

the measure of the inscribed angle HLK is half the measure of its intercepted arc, that is

∠ HLK = [tex]\frac{1}{2}[/tex] × HB = [tex]\frac{1}{2}[/tex] × 58°= 29°

Answer: The table that represents blueberries that are more expensive than those represented by the equation p = 3.25b is the one where the prices listed are higher than what would be calculated using the equation p = 3.25b.

Step-by-step explanation:

To determine this, we can substitute different values of b into the equation p = 3.25b and compare the results to the prices listed in each table. For example, if b = 2 (2 pounds of blueberries), the price p would be 3.25 x 2 = 6.5 dollars, according to the equation. If any of the prices in the table is higher than 6.5 dollars for 2 pounds of blueberries, then that table represents blueberries that are more expensive than those represented by the equation p = 3.25b.

It's important to note that the equation given represents a linear equation with a slope of 3.25 and a y-intercept of 0. It's a linear equation that relates the price and weight of blueberries and can be used for any value of weight.

Answer:

1) 111, 112

2) 12, 9

3) -12

4) 31, 32, 33

Step-by-step explanation:

1)   n + (n+1) = 223

2n + 1 = 223

2n=222

n = 111              numbers: 111, 112

2)  n + (n-3) = 21

2n - 3 = 21

2n=24

n=12                    numbers: 12, 9

3)   2*(n+5) = n-2

2n + 10 = n - 2

n = -12               number: -12

4)   n + (n+1) + (n+2) = 96

3n + 3 = 96

3n = 93

n=31                numbers: 31, 32, 33

Answer:

It will cost R1725

The ratio for this problem is 5: 575.

(litres of paint: price)

We first need to figure out how to go from 5 to 15.

To go from 5 to 15, we multiply the 5 by 3.

Now that we have this, we need to multiply the other side of the ratio (575) by 3.

The ratio now looks like this:

15: 1725

Therefore, for every fifteen litres of paint, it will cost R1725.

Answer: look below love :))

Step-by-step explanation: To find out how much Amir will have in the account after 23 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the initial principal (the amount Amir deposited)

r is the annual interest rate (2.25%)

n is the number of times the interest is compounded per year (let's assume it is compounded annually)

t is the number of years

So, we can plug in the given values:

A = 1390(1 + 0.0225)^(1*23)

A = 1390(1.0225)^(23)

A = 1390 * 2.6388955

A = 3655.922

So Amir will have £3655.922 in the account after 23 years with 2.25% compound interest.

Answer:

To find the constant of proportionality between the cost of the game tickets and the number of tickets purchased, we can write an equation that represents the relationship between the two values. Let's call the constant of proportionality "k".

Step 1: Write an equation for Rocko's purchase:

12.50 = k * 25

Step 2: Solve for k:

k = 12.50 / 25 = 0.50

Step 3: Write an equation for Louisa's purchase:

17.50 = k * 36

Step 4: Substitute the value of k from step 2 into the equation:

17.50 = 0.50 * 36

Step 5: Check if the value of k is the same for both equations:

17.50 / 36 = 0.50

The constant of proportionality is 0.50, which means that for each additional game ticket purchased, the cost increases by $0.50.

Using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

So, we have:

Hypotuenese is 70ft long and Height is 25ft long.

Then, the base would be:

c² = a² + b²

70² = 25² + b²

b² = 4,900 - 625

b² = 7,275

b = √7275

b = 85ft

Therefore, using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.

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Answer: The data shows an association between the type of instructor and a certification in CPR. The association is that swimming instructors are less likely than tennis instructors to be certified in CPR. This can be seen from the frequency table, where all the swimming instructors are not certified in CPR, while only 4 out of 12 tennis instructors are not certified in CPR, so yes, the data does show an association between the type of instructor and a certification in CPR.

Step-by-step explanation:

The two-way frequency table shows the number of instructors who are certified or not certified in CPR, broken down by type of instructor (swimming or tennis). The data in the table allows us to see the relationship between the two variables (type of instructor and certification in CPR) and whether there is an association between them.

An association means that the values of one variable are related to the values of another variable in some way. In this case, the type of instructor (swimming or tennis) is related to whether or not the instructor is certified in CPR. The data shows that the proportion of swimming instructors who are not certified in CPR (100%) is higher than the proportion of tennis instructors who are not certified in CPR (33%). This indicates that there is an association between type of instructor and certification in CPR, with swimming instructors being less likely to be certified in CPR than tennis instructors.

It is important to note that this association does not necessarily imply causation, meaning that being a swimming instructor does not cause one to not be certified in CPR, but it could be the other way around, or it could be due to some other factors that the data does not show.

Answer:

x=108

Step-by-step explanation:

180-58-14=108