What is the estimated answer to 8 x 7 divided by 0.5

If the zero vector \(\vec{O}\) is an element of the set \(S\), then \(S\) is linearly dependent.  If the set \(S\) contains only one vector \(\vec{V}\), then \(S\) is linearly independent.

a) If the zero vector \(\vec{O}\) is an element of the set \(S\), then \(S\) is linearly dependent. This is because the presence of the zero vector in a set automatically makes it linearly dependent, as we can always find coefficients to satisfy the linear combination \(\vec{O} = 0\vec{V}\) where \(\vec{V}\) is any vector in \(S\).

b) If the set \(S\) contains only one vector \(\vec{V}\), then \(S\) is linearly independent. This is because for a set to be linearly dependent, there must exist non-zero coefficients such that the linear combination of the vectors in the set equals the zero vector. However, with only one vector in the set, the only way to satisfy this condition is by setting all coefficients to zero, which implies linear independence.

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The perimeter of the figure is 4d+6c - 6

The distance around the outside of a 2D shape is known as its perimeter. Add together the lengths of all the sides to determine the perimeter.

We have been given a figure. We are asked to write an expression for the perimeter of our given figure.

We know that perimeter of a solid is sum of all of its side.

We can see that opposite side of our given figure are equal and our given figure is a rectangle.

We know that perimeter of rectangle is two times the length and width of rectangle, so the perimeter of our given figure would be:

2×(2d- 3+3c)

Use distributive property:

2 × 2d - 2 × 3 + 2 × 3 c

4d -6+6c

4d+6c-6

Therefore, the perimeter of our given figure is 4d+6c - 6

The complete question is : Write and simplify an expression for the perimeter of each figure

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The average amount of fluid consumed is 35.7 oz of fluid each day.

We have to note that in this case of the question, we have the following information;

When we convert the galloons to oz, we can see that the amounts of the milk and the water are actually 64 oz and 128 oz respectively.

Total fluid consumed in the week = 64 oz + 6 0z + 128 oz + 52 oz

= 250 oz

The average amount of fluid that is consumed per day is; 250 oz/7

= 35.7 oz of fluid each day.

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115.

The point estimate for the average IQ score of the population of 3000 college students based on a simple random sample of 150 students with an average IQ score of 115 and a standard deviation of 10 is 115.

Therefore, the correct option is 115.

A point estimate is an estimate of a population parameter based on a single value or point. It is obtained by using statistics collected from a sample to infer population values. It can be a single value or a range of values that best represents the unknown population parameter.

Based on the given information, a simple random sample of 150 students is drawn from a population of 3000 college students.

Among sampled students, the average IQ score is 115 with a standard deviation of 10. The point estimate, in this case, is the average IQ score of the population, which is estimated to be 115 based on the sample data.

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Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

The slope of the line m = 1

The equation of the straight line x -y -7=0

Step-by-step explanation:

Explanation:-

In the given graph

The points are ( 7,0) and ( 0, -7)

The slope of the line

            \(m = \frac{y_{2}- y_{1} }{x_{2}-x_{1} } = \frac{-7-0}{0-7} = \frac{-7}{-7} = 1\)

The equation of the straight line passing through the point (7,0) and slope m=1

    y - y₁ = m (x - x₁)

    y - 0 = 1( x-7)

   y = x -7

   x - y -7=0

Final answer:-

The slope of the line m = 1

The equation of the straight line x -y -7=0

Answer:

3

Step-by-step explanation:

\(18*\frac{1}{6} \\\\3\)

Answer:

=3x

Step-by-step explanation:

18x^1 / 6

=3x

Answer:

\(f(x)\geq -2\)

Step-by-step explanation:

Range corresponds to the values of y on the y-axis. If we see the graph the minimum value of the y-coordinate is -2 and then it tends to increase from it. We do not know till where the y values will increase in the figure it shows 6 but it's still actually increasing we keep on tracing the graph but the minimum value will always remain the same which is -2 . So we can say that the range of the function is

\(f(x)\geq -2\\\)

Where f(x) is the function and since the values of y on the y-axis increase from -2 we can say that the function has the range of values greater than or equal to -2

Depreciation are represented by exponential function

You have lost $3603 of the motorcycle's value after 4 years

The given parameters are:

The function to represent the depreciation is calculated as:

\(y = a(1 - r)^n\)

So, we have:

\(y = 9000 * (1 -12\%)^4\)

Multiply

\(y = 5397\)

The above represents the new value of the motorcycle.

The depreciated value is then calculated as:

\(Value = 9000 - 5397\)

\(Value = 3603\)

Hence, you have lost $3603 of the motorcycle's value after 4 years

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The only possible dimension for the third side of the triangle is 7 inches, as it is the only option given that satisfies the above conditions.

The properties of the triangle are:

Every side of a triangle must be shorter than the total length of the other two sides. Hence, the third side of the triangle in this instance must be more than the difference between 10 and 4 inches but less than the product of 10 and 4 inches.

The third side must be larger than 6 inches since 10 inches and 4 inches differ by 6 inches.

The third side must be shorter than 14 inches since the total of 10 inches and 4 inches is 14 inches.

Therefore, 7 inches is the only choice presented that meets the aforementioned requirements, it follows that this measurement is the only one that may be used for the third side of the triangle.

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Answer:

(x - 3)^2 + (y + 5)^2 = 64

Step-by-step explanation:

We can find the equation of the circle in standard form, which is

\((x-h)^2+(y-k)^2=r^2\), where

Step 1:  We see that the center is (3, -5).  Thus, in the formula, 3 becomes -3 for h and -5 becomes 5 for k since -(-5) becomes 5.

Step 2:  We know that the diameter is equal to 2 * the radius.  Thus, if we divide the diameter of 16 by 2, we see that the radius of the circle is 8 units

Step 3:  Now, we can plug everything into the equation and simplify:

(x - 3)^2 + (y + 5)^2 = 8^2

(x - 3)^2 + (y + 5)^2 = 64

Answer:

\(c \: 5dollar \: each\)

Answer:

its avocados cost $5.00 each ( its c)

Answer:

35

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Range = Highest number - lowest number

range = 6 - 6

range = 0

It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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The price of a computer increase from £631 to £776. 13. The percentage change is 81.3%

As per the given data:

Old value of computer is £631

New value of computer is £776. 13

Percentage Change: Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100.

The phrase percent change says the difference in the percent of the earlier and present quantity.

Percentage change formula is

Percentage Change \(=\frac{{New Value - Old Value} }{{Old Value}} \times 100\)

If the result is positive, then it is an increase.

If the result is negative, then it is a decrease.

\(=\frac{631}{776.13} \times 100\)

= 0.813 × 100

= 81.3%

Therefore the increase in percentage is 81.3%

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Answer:

2y + 2x = 0

Step-by-step explanation:

First you have to find the slope of the line.

Parallel lines have same slope

2y = -2-2x

y=-1-1x, y=-1x-1

slope = -1

Use point slope formula

y-y=m(x-x)

y-(-9) = -1(x-9)

y+9 = -1(x-9)

y+9 = -1x+9

y = -x

y + x = 0

2y + 2x = 0

The reason for this is because the round off had not been completed correctly as the correct digit will be 182.9.

Estimation is a sort of rounding off. Estimation is employed in daily life as well as in areas such as mathematics and physics. Many physical values, such as money, distance traveled, length measured, and so on, are approximated via rounding off the exact figure to the next whole number.

The following are the decimal rounding-off rules:

Now, according to the question;

The given added vales are-

7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815

Round-off the values in the following manner

= 8 + 8 + 79 + 8 +  79 + 0.9

= 182.9

As a result, the clustered point of three numbers is incorrect.

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The correct question is-

A student estimated the sum

7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as:

All the numbers begin with a 7 or 8, so use cluster estimation.

8 + 8 + 80 + 8 + 80 + 0.8 = 184.8

Explain why this reasoning is not accurate.

Answer: The numbers are not clustered around a common number. Two of the numbers are very large and one is very small.

Step-by-step explanation:

Answer:

a: 14,299.2 b: 153.1

Step-by-step explanation:

Answer:

The answer is the first choice and the last choice.

Step-by-step explanation:

The first one is already solved for y, so when you plug 9 into the equation in the x spot since 9 is the x-coordinate of the point, you get -2, which is correct because it is the corresponding y-value.

The second one is a mess when trying to solve and it clearly doesn't yield the right answer.

For the last one, when you solve for y and then plug in 9 for x, you get -2, the y-value making it correct.

(2x + 3) (x^2 - 6x + 9)

Answer:

1

Step-by-step explanation:

definite integral from 0-2 of root x dx

root x = x^½

integral of x^½ = ⅔x^(3/2)

3x-12y=6

Lets convert to slope intercept form

Slopes are equal so lines are parallel

Hence no solutions

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: Useful if you simply need a broad answer or are certain that the intersection takes place at an integer location. To find where the two lines intersect, just plot them.

(2) The Substitution Approach: To begin, a linear equation for y must be resolved in terms of x. Substitute that expression for y in the other linear equation after that. A formula will be given to you in x. You'll know the intersection's x-coordinate if you can figure this one out. Insert x into either equation to get the equivalent y-coordinate.

(3) Using a linear combination: Add (or subtraction) a multiple of one equation to (or from) the other equation to make the x-terms or y-terms cancel out. Solve for x (or y, depending on which is left) before substituting to get the other coordinate.

(4) The Matrix Approach: This is actually just a streamlined notation of the Linear Combination approach.

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Answer:

56/34 = \(\frac{28}{17}\) or \(1\frac{11}{17}\) or 1.65

Answer:

56/34=1.65 or 1 \(\frac{13}{20}\)

Step-by-step explanation: