Find the dot product of the vectors u = [2, 3, 4] and v = [5, 6, 7].

Step-by-step explanation:

The pool is 10 feet long and 4 feet deep. This means the pool has a volume of 40 cubic feet (10 feet x 4 feet x 1 foot). To calculate the width of the pool, divide the total volume (40) by the length (10) to get 4 feet. Therefore, the width of the pool is 4 feet.

The given mixed fraction can be written in decimal form as 1.5.

These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)

The given mixed fraction is [tex]1\frac{1}{2}[/tex].

Now, the given mixed fraction can be written as 3/2

3/2 can be written in decimal number as 1.5.

Decimal number 1.5 is between 1 and 2.

Therefore, the given mixed fraction can be written in decimal form as 1.5.

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Los intervalos numéricos para la recta numérica en el punto x=2, con 2>x<7, son: (2,7) e (2,∞).

Esto significa que los valores de x pueden oscilar entre 2 y 7, o bien entre 2 y el infinito.

Por ejemplo, el intervalo numérico (2,7) incluiría todos los números entre 2 y 7, incluyendo 2 y 7, pero excluyendo los números menores que 2 y mayores que 7. El intervalo numérico (2, ∞) significa que todos los números mayores que 2 están incluidos, mientras que los números menores que 2 no están incluidos.

Versión en inglés:

The numerical intervals for the number line at the point x=2, with 2>x<7, are: (2,7) and (2,∞).

This means that the values of x can range from 2 to 7, or from 2 to infinity.

For example, the numerical interval (2,7) would include all numbers between 2 and 7, including 2 and 7, but excluding numbers less than 2 and greater than 7. The numerical interval (2, ∞) means that all numbers greater than 2 are included, while numbers less than 2 are not included.

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Answer:

7 packs of floorboards

Step-by-step explanation:

total area of floor= (4.5×2)+(2×3)

= 9+6

= 15m2

15÷2.25= 6.6666666

~7 packs (rounded up to the nearest whole no.)

Answer:

Step-by-step explanation:

36 divided by 4 is 9, so the answer would be 9

According to the given data, Ryan walked 12 small dogs.

Let x be the number of small dogs that Ryan walked.

The number of large dogs that Ryan walked would then be y = 4 - x.

Using the information given, we can set up the following equation:

x * 2 + (4 - x) * 5 = 40

Expanding and solving for x, we get:

2x + 4 - 5x = 40

-3x = 36

x = 12

So, Ryan walked 12 small dogs.

In this problem, we used a system of equations to solve for the unknown variable, x, which represents the number of small dogs that Ryan walked. By substituting this value back into the equation for the number of large dogs, we were able to confirm that Ryan walked 4 - x = 4 - 12 = 4 large dogs.

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13. a. To the ones: 26. 5

b. To the tenths: 26. 52

c. To the hundredths: 26. 519

14. 7x + 5 - 1. Terms = 3. coefficients: 1, constants: 1, variables: 1

3a - 5c + 9 - 1. Terms = 4, coefficients = 2 , constants = 2 , variables = 2

15. Collecting like terms;

a. 2b + 6

b. 9c + 3b + 7

16a. 2(8 - 7) = 2(1) = 2

16 - 14 = 2

b. 10(8 + 4) = 10(12) = 120

80 + 40 = 120

They are defined as expressions comprising of terms, coefficients, variables, constants and factors.

They are also composed of mathematical operations.

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21 is 18.75% of 112. Percentage is widely used to represent a difference or contrast between two numbers.

A percentage is a way to express a number as a fraction of 100. It is often used to express a change or a comparison between two numbers. The symbol for percentage is %, and it represents the fraction of 100. For example, 50% means 50 out of 100, or 1/2.

Percentages are often used to represent increases or decreases in a quantity, as well as ratios and proportions. For example, if the price of a product increases by 20%, it means the new price is 120% of the original price, or 1.2 times the original price. If a student scores 80% on a test, it means they answered 80 out of 100 questions correctly.

Percentages can be easily converted to decimals or fractions by dividing by 100. For example, 50% can be written as 0.5 as a decimal or 1/2 as a fraction. Similarly, 75% can be written as 0.75 as a decimal or 3/4 as a fraction.

To find what percent 21 is of 112, we can use the formula:

Percent = (Part ÷ Whole) x 100

In this case, the part is 21 and the whole is 112, so:

Percent = (21 ÷ 112) x 100

Percent = 0.1875 x 100

Percent = 18.75

Therefore, 21 is 18.75% of 112.

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Answer:

I only

Step-by-step explanation:

any point and its coordinates is an ordered pair of (x, y).

in other words, we get the x value used for the function and the resulting y value.

if the equation is true for such a pair, then the point is on the line. if it is false, then not.

y = (-5/4)x + 5

(4, 0)

0 = (-5/4)×4 + 5 = -5 + 5 = 0

true.

(0, 5)

5 = (-5/4)×0 + 5 = 0 + 5 = 5

true.

y + 5 = (-5/4)(x - 4)

(4, 0)

0 + 5 = (-5/4)(4 - 4)

5 = (-5/4)×0 = 0

false.

so, II is not containing (4, 0).

therefore, only I is contains both points.

Step-by-step explanation:

=01000101

is the answer

The binary value of the given expression is 111101.

To multiply binary numbers, we use the same process as with decimal numbers, but using only 0s and 1s. We can use the distributive property of multiplication to break down the problem into simpler multiplication and addition operations.

First, we multiply 1101 by 101:

                                  1101

                                x  101

                                  -----

                                  1101

                                  1101

                                ------

                              111001

Next, we add 100 to the result:

                              111001

                            +    100

                               -------

                              111101

The decimal value of 111101 is given by,

                              (111101)₂ = (61)₁₀

Therefore, the product of 1101 and 101, plus 100, is 111101 in binary.

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Answer: 0.75

Step-by-step explanation:

With a volume of 700 cubic feet and a height of 9 feet , the radius of cylinder is 3.49 feet after rounding to nearest hundredth.

To find the radius of a right cylinder, you need to know its volume and height. The formula for the volume of a cylinder is given by:

V = πr^2h

Where r is the radius, h is the height, and π is approximately equal to 3.14.

Given that the volume is 700 cubic feet and the height is 9 feet, we can substitute these values into the formula:

700 = πr^2 * 9

Dividing both sides by π * 9:

700 / (π * 9) = r^2

Taking the square root of both sides:

√(700 / (π * 9)) = r

Using a calculator and rounding to the nearest hundredth, we find that:

r ≈ 3.49

So the radius of the cylinder is approximately 3.49 feet.

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A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association.

0.8 - Strong Association

0.25 - Weak Association

0.9 - Strong Association

0.65 - Moderate Association

The strength of a correlation is determined by its correlation coefficient. A correlation coefficient of 0.8 or higher is considered strong, a correlation coefficient between 0.5 and 0.7 is considered moderate, and a correlation coefficient of 0.4 or lower is considered weak. A correlation coefficient of 0.8 indicates a strong association between two variables, a correlation coefficient of 0.25 indicates a weak association, a correlation coefficient of 0.9 indicates a strong association, and a correlation coefficient of 0.65 indicates a moderate association.

A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association. For the given correlation coefficients, 0.8 and 0.9 indicate strong associations, 0.25 indicates a weak association, and 0.65 indicates a moderate association.

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The cost of nails can be represented as 12.99n, and the cost of screws can be represented as 14.99s.

The cost of buying nails and screws can be represented by a system of inequalities where "n" represents the number of boxes of nails and "s" represents the number of boxes of screws.

The cost of one box of nails is $12.99 and the cost of one box of screws is $14.99. Hence, the cost of "n" boxes of nails is represented by 12.99n and the cost of "s" boxes of screws is represented by 14.99s. The carpenter has a budget of $60 and can spend no more than that.

Therefore, the combined cost of buying nails and screws must be less than or equal to $60. This requirement can be represented by the inequality 12.99n + 14.99s <= 60.

To make the calculation easier, we can also express the inequality as n + s <= 4.62, where 4.62 is obtained by dividing $60 by $12.99. This system of inequalities represents the carpenter's budget constraint and helps to determine the number of boxes of nails and screws that can be purchased within the budget.

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Answer:

Step-by-step explanation:

The formula of volume is length x width x height.

Answer:

Below

Step-by-step explanation:

3/4 (1/6 x +16) = 3/7 (4 3/8 - 21)      expand L side and compute R side

3/24 x + 12 =  - 7.125        Subtract 12 from both sides of the equation

3/24 x = -19.125             Multiply both sides by 24/2

x = -153

THIS EQUATION DOES SHOW x = -153

PERHAPS you MEANT this :

3/4 (1/(6x) +16) = 3/7 (4 3/8 - 21)       Expand L side  and compute R side

3/(24x) + 12 = - 7.125       subtract 12 from both sides

3/(24x) = -19.125      re-arrange

3 / (-19.125)    = 24 x      divide both sides by 24

3/ (-19.125 * 24) = x = - 1/153      

     Don't know how to find a different answer......check the equation you posted......

Answer:

Below

Step-by-step explanation:

a)  DIRECT variation    y = k  x

                                    10 = k (4)

                                      10/4 = k = 2.5

                y = 2.5 x

b)    y = 2.5 x

       y = 2.5 (10) = 25

Answer:

60

good luck!

The slope of the linear function in this problem is given as follows:

m = -4.

The slope of a linear function represents the rate of change of the linear function, hence it is calculated as the change in y divided by the change in x, taking two points.

From the graph of the function, when x increases from 0 to 3, y decays from 5 to -7, hence the slope is calculated as follows:

m =(-7 -5)/3

m = -4.

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The average speed of whole trip was 6.7 mile per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, the total distance =6+6=12 miles and total time

=58+49= 107 minutes

So, number of hours = 107/60

= 1.8 hours

Now, the average speed = 12/1.8

= 6.7 mile per hour

Therefore, the average speed is 6.7 mile per hour.

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The sales tax of the car is $1960

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

Price of car = $28000

Given that the sales tax on the new car is 7%, we have

Sales tax amount = 7% * Cost of new car

Substitute the known values in the above equation, so, we have the following representation

Sales tax amount = 7% *  $28000

Evaluate

Sales tax amount = $1960

Hence. the Sales tax amount is $1960

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Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.

A relationship or collection of numbers without the equal sign is known as a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two factors are not equal. Differences exist between variable equity and inequality. Because the digits are not identical or similar, the most typical symbol was selected (). Any difference, regardless of how small or large, can be used to evaluate values.

Here,

If each side of the frame can be at most 12 inches long, then the perimeter of the frame can be at most 4 x 12 = 48 inches.

So, the inequality that describes the problem is:

x ≤ 48.

Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.

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Step-by-step explanation:

It is translated up 6 units, with the y value is vertical (up and down). The y value is 5, (x, y). Because it only moves up you would keep the x value, -3, and add 6 to the y value. So 5+6=11

The new coordinates are now (-3,5)

Hope this helps :)

In linear equation, the store will get $468.72 from the sale of the couch.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

a.

Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.

Commission is calculated as follows:

Total commission = Total Sales * Commission Percentage

Given

Total Sales = $495

Commission Percentage = 5½%

Substitute in, the above values

Total Commission = $496 * 5½%

Total Commission = $496 * 5.5%

Total Commission = $496 * 0.055

Total Commission = $27.28

Hence, the total commission is calculated as $27.28

b. The amount remitted to the store is calculated as

Amount = Total Sales - Total Commission

Where Total Sales = $496

Total Commission = $27.28

Amount = $496 - $27.28

Amount = $468.72

Hence, the store will get $468.72 from the sale of the couch.

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The complete question is -

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.

A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?

Answer:

a. The total commission is $27.28

b. The store will get $468.72 from the sale of the couch

The expression which is equivalent is 2x + 5y - 3.

The equivalent expressions to 3x + 5y - x + 2 - 5 are:

2x + 5y - 3

3x + 5y - 3x + 2 - 5 = 3x - 3x + 5y + 2 - 5 = 2x + 5y - 3

So, both options are equivalent to 3x + 5y - x + 2 - 5.

Equivalent expressions" refer to mathematical expressions that have the same value for all values of the variables involved, regardless of the order or the grouping of the operations. For example, the expressions "2 + 3" and "3 + 2" are equivalent because they both equal 5.

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a) The sine and the cosine are given as follows:

b) The tangent is given by the sine divided by the cosine, as follows:

tan(Φ) = sin(Φ)/cos(Φ) = (8/17)/(15/17) = 8/15.

The three trigonometric ratios are defined as follows:

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 8² + 15²

h = sqrt(8² + 15²)

h = 17.

Considering that 8 is the opposite side and 15 is the adjacent side to the angle, the sine and the cosine are given as follows:

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Check the picture below.

let's recall that on an isosceles triangle, twin sides make twin angles.

Answer:

yes Priya's conclusion is incorrect

Step-by-step explanation:

x square will always be greater than the actual value of x

but in this expression

f (x ) = 10 * x²

g (x) = 3 * 2raise to the power x

priya's conclusion is incorrect because in the other expression the power of x is increasing exponentially so eventually g(x) will be greater than f(x)

as for x = 10

f(x) = 10 * 10² = 1000

g(x) = 3 * 2raise to power 10 = 3 * 1024 = 3072

The expected time (also known as the expected value or the mean) Is approximately 12.5 days.

The expected time for an activity is the average time it is likely to take, taking into account its optimistic, most likely, and pessimistic estimates. The three-point estimate formula is used to calculate the expected time by weighting the most likely estimate four times as much as the optimistic and pessimistic estimates. In this case, the optimistic time is 15 days, the most likely time is 18 days, and the pessimistic time is 27 days. By plugging these values into the formula, the expected time is calculated to be 12.5 days. This means that, on average, the activity is likely to take 12.5 days to complete.

The expected time (also known as the expected value or the mean) can be calculated using the three-point estimate formula, which is:

Expected time = (Optimistic time + 4 * Most likely time + Pessimistic time) / 6

Plugging in the values, we get:

Expected time = (15 + 4 * 18 + 27) / 6 = (75) / 6 = 12.5

So the expected time for this activity is 12.5 days.

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Answer: To happen before

Step-by-step explanation: