Dave ran 10km in 40 minutes. He rested for 5 minutes then ran a further 8 km in 35 minutes. Work out his average speed for the whole journey. (Give your answer in km/h)

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

To know more about orthogonal visit

https://brainly.com/question/32250610

#SPJ11

a) The price of fuel A is decreasing by a rate of 12% per month.

b) The greater percentage change over the previous month was of Fuel A.

A decreasing exponential function is modeled as follows:

y = a(1 - r)^x.

In which the parameters are given as follows:

The function for fuel A is given as follows:

f(x) = 2.27(0.88)^x.

As 0.88 < 1, the function is decreasing, and the percentage is obtained as follows:

1 - r = 0.88

r = 1 - 0.88

r = 0.12 = 12%.

The rate for fuel B is given as follows:

3.04/3.17 = 0.96 (approximately).

Hence the change is of 4%, meaning that fuel A has the greater percentage change.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

0.77 is bigger than 0.08

Step-by-step explanation:

0.77 > 0.08

You have to compare tenth place. In tenth place 7 is greater than 0. so 0.77 is bigger than 0.08

The equation that represents Jacob's age is  x = y + z + 2

From the question, the following information was provided :

Jacob's age is two years more than the sum of the ages of his siblings Becky and Micah.

This above information can be represented with the equation below

Jacob = 2 + ( Becky + Micah) (equation 1)

If :

x represents Jacob's age

y represents Micah's age

z represents Becky's age

Equation 1, can be rewritten as x = y + z + 2

Micah's age can be determined by making Micah the subject of the formula in the above equation

Micah = Jacob - Becky - 2   (equation 2)

If :

x represents Micah's age

y represents Becky's age

z represents Jacob's age

Micah's age can be rewritten as :

x = z - y - 2

Becky's age  age can be determined by making Becky the subject of the formula in the first equation.

Becky = Jacob - Micah - 2 (equation 3)

If:

x represents Becky's age

y represents Jacob's age

z represents Micah's age

Equation 3 can be rewritten as :

x = y - z - 2

Check here for a related question : https://brainly.com/question/21843246?referrer=searchResults

Using a system of equations, it is found that the correct equation is given by:

\(x = y + z + 2\), which is option B.

---------------

\(x = y + z + 2\)

Which is given by option B.

A similar problem is given at https://brainly.com/question/24233433

Answer:

Same as other person

3

Step-by-step explanation:

We find the Y intercept by getting x to zero and in this case it is already zero

if it wasn't then we would need slope to solve it

A parabola is a U-shaped curve that is symmetrical about a specific axis. It is a conic section defined by a quadratic equation and has applications in various fields, including mathematics, physics, and engineering.

To find the coefficient b, we need to use the given points to form a system of equations. Substituting (0,3), (1,4), and (2,3) into the equation y=ax²+bx+c, we get:

3=c
4=a+b+c
3=4a+2b+c

Substituting c=3 into the second equation, we get:

4=a+b+3

Substituting c=3 into the third equation, we get:

3=4a+2b+3

Simplifying the third equation, we get:

1=2a+b

Now we have two equations:

4=a+b+3
1=2a+b

Solving for b, we get:

b=1-2a

Substituting b=1-2a into the first equation, we get:

4=a+(1-2a)+3

Solving for a, we get:

a=0

Substituting a=0 into b=1-2a, we get:

b=1

Therefore, the coefficient b is 1.

To know more about parabola visit:

https://brainly.com/question/29267743

#SPJ11

System of Equations

Let:

x = number of small pizzas

y = number of medium pizzas

z = number of large pizzas

They sold 47 pizzas, thus:

x + y + z = 47

They received 7x for the small pizzas, 10y for the medium pizzas, and 11z for the large pizzas, thus:

7x + 10y + 11z = 469

The last condition states they sold 17 more large than small pizzas, thus:

z = 17 + x

Rearranging the system of equations:

x + y + z = 47

7x + 10y + 11z = 469

x + 0y - z = -17

Now we write the expanded matrix of the system:

Apply Gauss-Jordan Elimination Method.

Multiply row 1 by -7 and add it to row 2:

Divide row 2 by 3:

Multiply row 2 by -1 and add it to row 1:

Multiply row 1 by -1 and add it to row 3:

Multiply row 3 by -3/2:

Multiply row 3 by 1/3 and add it to row 1:

Multiply row 3 by -4/3 and add it to row 2:

Now we have the identity matrix 3x3 to the left and the column of solutions to the right:

x = 9, y = 12, z = 26

They sold 9 small pizzas, 12 medium pizzas, and 26 large pizzas

∑ Hey, jillianwagler ⊃

Answer:

\(\left(x+3\right)\left(x-15\right)\)

Step-by-step explanation:

Given info:

Factor completely: \(x^2 -12x -45\)

Solve:

Break the expression to : \(\left(x^2+3x\right)+\left(-15x-45\right)\)

Factor out x from x²+ 3x :x ( x +3 )

Factor out -15 from -15x - 45 : -15( x + 3 )

Put them together:

\(x\left(x+3\right)-15\left(x+3\right)\)

Now factor  x + 3

Answer~: \(\left(x+3\right)\left(x-15\right)\)

xcookiex12~

8/19/2022

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

Know more about derivative here:

https://brainly.com/question/25324584

#SPJ11

Answer:

This would bring you to $160.00. This is because you initially had $20.00, because of the $13 and $7. Then, your family gave you a total of $140.00, and 140 + 20 = 160.

Step-by-step explanation:

The total amount of money he had is $160 and this can be determined by using the arithmetic operations and the given data.

Given :

The arithmetic operations can be used in order to determine the total amount of money he had.

The initial amount of money he had is:

= $13 + $7

= $20

His Mom gave him $10.00. So, the total amount of money now he had is:

= $20 + $10

= $30

His Dad gave him $30.00. So, the total amount of money now he had is:

= $30 + $30

= $60

His Aunt, Uncle, and Grandma gave him $100. So, the total amount of money now he had is:

= $60 + $100

= $160

For more information, refer to the link given below:

https://brainly.com/question/25277954

Weighing using a tared container is not appropriate due to the potential for errors and inaccuracies. This method can impact the results by introducing uncertainties in the measurements.

Using a tared container involves placing the substance to be weighed on a container that has already been weighed and then subtracting the weight of the container to obtain the weight of the substance alone. While this method is commonly used for qualitative analysis or when the accuracy requirements are not strict, it is not suitable for quantitative preparation where precise measurements are essential.

The use of a tared container introduces several potential sources of error. First, the accuracy of the tare weight might not be exact, leading to uncertainties in subsequent measurements. Additionally, the tare weight may change over time due to factors like evaporation or contamination, further affecting the accuracy of subsequent measurements. Moreover, the process of transferring the substance to the tared container introduces the risk of loss or gain of material, leading to errors in the final measurements.

Overall, relying on weighing with a tared container for quantitative preparation can result in inaccurate quantities of the substance being weighed, compromising the reliability and reproducibility of experimental results. Therefore, more precise weighing techniques, such as using calibrated weighing balances or analytical techniques, should be employed for quantitative preparations.

Learn more about error analysis here:

https://brainly.com/question/29261280

#SPJ11

Answer: y=-1x-8

Step-by-step explanation:

The first step is to: Move the 'X' to the right side of the equation.

The second step is to: Divide the 'Y'

But since the 'X' is already on the right side you will just divide the 'Y'. If the 'X' was on the left then you will follow those steps that I gave you at the beginning in order to get it in the y=mx+b.  

So it will look like this:

2y=-1x-8

y=-1x-8

y= -1(is the slope)x-8(is the Y-intercept)

So, if you have to graph this you will graph it starting with negative 8 as the y-intercept. Then you will go down one and over 1.

Answer:

\(198\:\mathrm{m^3}\)

Step-by-step explanation:

The volume of a cylinder is given by \(V=r^2\pi\cdot h\), where \(r\) is the radius of the cylinder and \(h\) is the height.

What we're given:

Substituting given values, we get:

\(V=3^2\pi\cdot 7,\\V=9\cdot 3.14\cdot 7,\\V\approx 197.82\:\mathrm{m^3}=\boxed{198\:\mathrm{m^3}}\), rounded the nearest cubic meter as requested in question.

Answer:

Volume of cylinder is 197.82 m ³.

Step-by-step explanation:

Here,

Diameter of cylinder = 6 m

So, Radius of cylinder, r = 6 / 2 = 3m

Height of cylinder , h = 7 m

Value of π = 3.14

Volume of cylinder

We know that,

Volume of cylinder = π × r ² × h

Substitute the values

Volume of cylinder = 3.14 × ( 3m ) ² × 7 m

volume of cylinder = 3.14 × 9m² × 7 m

Multiply , we get

Volume of cylinder = 197.82 m ³

Therefore, The volume of cylinder id 197.82 m ³.

Answer:

820 square meters

With that information we can create the equation

10x + 5000 = 20x

where x is the number of earphones produced

10x is the cost to make each earphone, 5000 being the fixed costs of manufacturing, and 20x being the total revenue of selling each earphone for $20

Now to solve the equation:

subtract both sides by 10x

10x - 10x + 5000 = 20x - 10x

5000 = 10x

Now divide both sides by 10

5000/10 = 10/10 x

500 = x

Answer: D

Hope it helps :)

500 earphones must be produced to get the cost price of one ear phone of $20.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

The start-up costs for manufacturing earphones is $5,000.

Also, the cost to make earphones is $10.

Let x number of  earphones will produced to get a cost per unit of $20.

From the given conditions, we will get a linear equation in one variable

10x + 5000 = 20x

⇒ 5000 = 20x -10x

⇒ 5000 = 10x

⇒ x = 500

Hence, 500 earphones must be produced to get the cost of earphone of $20.

Learn more about linear equation in one variable here:

https://brainly.com/question/17139602

#SPJ2

The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

Now,

Hence, amongst all the given options, The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

To learn more about experimental design, refer to the link:https://brainly.com/question/17274244

#SPJ4

correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40

Children for adoption

Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.

learn more about of biological here

https://brainly.com/question/14510435

#SPJ4

Answer:

a. 20,40,60,80,100,120,140 continue adding 20 each time

b. 30 pages left to read

Step-by-step explanation:

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

Answer:

x^2+10

Step-by-step explanation:

2x^2+3-(x^2-7)

2x^2+3-×^2+7

x^2+10

The probability of none of the graduates having a summer job is 0.262, which is calculated using the binomial probability distribution.

The probability of none of the graduates having a summer job can be calculated by using the formula of a binomial probability distribution. The formula is P(x) = nCx * p^x * q^(n-x). In this case, n represents the number of graduates, x represents the number of successes, p is the probability of success, and q is the probability of failure.

For this example, n = 6, x = 0, p = 0.2 (the probability of a graduate having a summer job is 0.2), q = 0.8 (the probability of a graduate not having a summer job is 0.8).

Plugging these values into the formula, we get P(x) = 6C0 * 0.2^0 * 0.8^6 = 0.262. Therefore, the probability of none of the graduates having a summer job is 0.262.

Therefore, The probability of none of the graduates having a summer job is 0.262, which is calculated using the binomial probability distribution. This is calculated by using the formula P(x) = nCx * p^x * q^(n-x), where n = 6, x = 0, p = 0.2 and q = 0.8.

Learn more about graduates  here:

https://brainly.com/question/12640798

#SPJ4

If a group of 6 graduates is selected at random, what is the probability that none of the graduates have a summer job assuming a binomial distribution?

Answer:

Step-by-step explanation:

Hope this helps! <3

( Pic Below )

Answer:

The total coat of the jeans and t - shirt is $39.00

Answer:

It is the second one $39.00

The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

Learn more about Equation click here :brainly.com/question/13763238

#SPJ11

From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

To learn more about equation from the given link

https://brainly.com/question/28871326

#SPJ1