How long will it take Seb to run 4000 m at an average speed of 5 m/s?
Give your answer in minutes and seconds.

The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136

Geometrically, the Scalar triple product:

\({\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})\)

is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.

Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.

So,

Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).

pq =  ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)

pr= (-2-1, 1-4, 0+1) = (-3,-3,1)

ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)

pq = (-5  ,  -3  , -3)

pr = (-3,  -3,  1)

ps= (-5,  -5,  -4)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

\(\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\\)

So, The volume never be negative then by applying vector

v = |-136|

v= 136

the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136

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Answer:

y : x: = 5 : 4

Step-by-step explanation:

x to y = 4 to 5

Rewrite;

x:y = 4:5

Remember, a ratio is another way of representing a fraction, hence one can do the same operations that one could do with a fraction. Therefore, one can take the cross products of a ratio;

x : y= 4 : 5

5x = 4y

Inverse operations;

5x = 4y

x = \(\frac{4}{5}\)y

Now substitute this into the equation y:x

y : \(\frac{4}{5}\)y

Rewrite as a fraction;

\(\frac{y}{\frac{5}{4}y}\)

Simplify;

\(\frac{1}{\frac{4}{5}}\\\\\frac{5}{4}\)

Rewrite as a ratio;

y : x = 5 : 4

Answer:

(-1, 6)

Step-by-step explanation:

Midpoint formula:

For G(-7, 3) and H(5, 9) the midpoint:

Answer:

(-1,6)

Step-by-step explanation

use the midpoint formula:

(x 1 + x2 /2 , y1 + y2/2)

(-7+ 5 /2, 3+ 9 /2)

after simplfying

(-1,6)

Answer:

It is already in the correct order

Answer:

c

Step-by-step explanation:

edg 20/21

If a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, A retailer marks up the price of a coffee mug from $6.25 to $8.77.

We have to find the percentage by which the price increase,

% increment = New rate - old rate / old rate × 100

% increment =(8.77 - 6.25)× 100

% increment =40.32%

Thus, if a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.

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Answer:

3n - 4

Step-by-step explanation:

A line is vertical, then all points lie on it have the same x-coordinates

If line L is a vertical line and passes through the point (a, b), then its equation is

Since the given line is a vertical line and passes through the point (-5, -3)

That means a = -5

Then its equation is

Answer:

Hey there!

In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.

Hope this helps :)

Answer:

9 degrees

Step-by-step explanation:

There are 360 degrees in a circle

There are 40 people

360 / 40 = 9

Each person gets 9 degrees

The transfer function relating the position y to the applied force f is

H(s) = Y(s)/F(s) = (1/(Ms^2)) + (sy(0)/M) + (y'(0)/M).

To determine the transfer function relating the position y to the applied force f, we need to take the Laplace transform of the given differential equation.

The Laplace transform of the differential equation M(d^2y/dt^2) = f can be written as:

M(s^2Y(s) - s*y(0) - y'(0)) = F(s),

where Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectively, and y(0) and y'(0) represent the initial position and initial velocity of the object.

Rearranging the equation, we get:

M(s^2Y(s) - s*y(0) - y'(0)) = F(s).

Dividing both sides by M, we have:

s^2Y(s) - s*y(0) - y'(0) = F(s)/M.

Now, we can solve for the transfer function H(s) = Y(s)/F(s) by isolating Y(s) on one side:

Y(s) = (F(s)/M) * (1/(s^2)) + (s*y(0)/M) + (y'(0)/M).

Therefore, the transfer function relating the position y to the applied force f is:

H(s) = Y(s)/F(s) = (1/(Ms^2)) + (sy(0)/M) + (y'(0)/M).

Note that y(0) and y'(0) represent the initial conditions of the position and velocity respectively.

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Answer:

D) Two triangles can be formed where angle B is 40° or 140°.

Step-by-step explanation:

The Ambiguous Case for the Law of Sines occurs when one uses it to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). There are 6 cases:

Case 1: If ∠A is acute, and a < h, no such triangle exists

Case 2: If ∠A is acute, and a = h, one possible triangle exists

Case 3: If ∠A is acute, and a > b, one possible triangle exists.

Case 4: If ∠A is acute, and h < a < b, two possible triangles exist.

Case 5: If ∠A is obtuse, and a < b or a = b, no such triangle exists.

Case 6: If ∠A is obtuse, and a > b, one such triangle exists.

Here, we can see that ∠A is acute since 75°<90°

Also, we know that a < b since 2 < 3.

Thus, Case 4 applies here, which states "If ∠A is acute, and h < a < b, two possible triangles exist."

Thus, the last option is correct.

Read more:

http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/lawofsinesambiguouscase.html

Answer:

It's D

Two triangles can be formed where angle B is 40° or 140°

Step-by-step explanation:

Edge 2022

Answer:

1:30

Step-by-step explanation:

45 min = 15 min + 30 min

15 min before 2:15 is 2:00.

30 min before 2:00 is 1:30.

The equivalent measurements are 0.76 grams = 0.076 decagrams as 1gram = 0.1 decagrams. Option A is correct answer.

What is Measurement?

Measurement is the process of associating numbers with physical quantities and phenomena. Measurement is fundamental to the sciences; to engineering, construction, and other technical fields; and to almost all everyday activities. For that reason the elements, conditions, limitations, and theoretical foundations of measurement have been much studied. See also measurement system for a comparison of different systems and the history of their development.

Measurements may be made by unaided human senses, in which case they are often called estimates, or, more commonly, by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly sophisticated systems designed to detect and measure quantities entirely beyond the capabilities of the senses, such as radio waves from a distant star or the magnetic moment of a subatomic particle.

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Answer:

This sh't confusing but I think the answer is bank B

Step-by-step explanation:

The fractions equivalent to 6/12 are 6/12, 2/4, and 1/2.

1. 4/6: To see if these fractions are equivalent, we can simplify 6/12. Divide both the numerator and the denominator by their greatest common divisor, which is 6. 6/12 ÷ (6/6) = 1/2. Now, simplify 4/6 by dividing both by their greatest common divisor, which is 2. 4/6 ÷ (2/2) = 2/3. These fractions are not equivalent, as 1/2 ≠ 2/3.

2. 3/8: This fraction cannot be equivalent to 6/12, as their denominators are different and don't have a common factor. So, no further calculation is needed.

3. 6/12: This fraction is the same as the original fraction and is therefore equivalent to itself.

4. 2/4: Simplify 2/4 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 2/4 ÷ (2/2) = 1/2. This fraction is equivalent to 6/12, as 1/2 = 1/2.

5. 1/2: As we found out earlier, 6/12 simplifies to 1/2, so this fraction is equivalent to 6/12.

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The price elasticity of the supply is 0.43.

The relationship between the percentage change in a product's quantity demanded and the percentage change in price is known as price elasticity of demand. It helps economists comprehend how supply and demand shift in response to changes in a product's price.

Price Elasticity of Demand =\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)=\(\frac{\Delta Q}{\Delta P}\)

Further, the equation for price elasticity of demand can be elaborated into

Percentage change in quantity=ΔQ=\(\frac{(q_{2}-q_{1})}{(q_{2}+q_{1})}}\)

Percentage change in quantity=ΔP=\(\frac{(p_{2}-p_{1})}{(p_{2}+p_{1})}}\)

Where, \(q_{1}\)= Initial quantity, \(q_{2}\)= Final quantity,\(p_{1}\)= Initial price and \(p_{2}\) = Final price

Here,  \(q_{1}\)=10000,\(q_{2}\)=5000

Percentage change in quantity=ΔQ

=\(\frac{10000-5000}{10000+5000}\)

=\(\frac{5000}{15000}\)

=0.333

Here,  \(p_{1}\)=20 and \(p_{2}\)=15

Percentage change in quantity=ΔP

= \(\frac{20-15}{20+15}\)

=\(\frac{5}{35}\)

=0.143

Price Elasticity of Demand

=\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)

=\(\frac{0.333}{0.143}\)

=2.33

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Answer:

782.5

Step-by-step explanation:

First off, we have to somewhat follow the order of PEMDAS.

1) Simplify the exponents

\(\frac{(7.3 * 1000000) + (2.4 * 10000000)}{(4 * 10000)}\)

2) Multiply what's in the parenthesis

\(\frac{7,300,000 + 24,000,000}{40,000}\)

3) Now we have to add what's on the top bracket

\(\frac{31,300,000}{40,000}\)

4) After all the simplifying is done, we have to divide

31,300,000 ÷ 40,000 =  782.5

I hope this helped you :)

Step-by-step explanation:

you can ask questions for clarification

The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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The cost spent on fill the box with sand is 405$.

According to the statement

we have given a square sandbox with length 9 ft and depth of 1 ft.

and the rupees of sand per cubic ft is $5

then

Now, we have to find the volume of sandbox with the given length and depth.

So, for this purpose we use Volume formula

V = (a)^3

V = 9*9*1

V = 81 cubic feet

And the cost of sand per cubic feet is $5.

then

The cost of sand for 81 cubic per feet is calculate by multiplication formula then

Total cost of sand = 81*5

Total cost of sand = 405$

So, The cost spent on fill the box with sand is 405$.

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Answer:

The answer is A

Step-by-step explanation:

The evidence is not sufficient to support the claim since the p-value is 0.1833 higher than 0.05, so e) none of the preceding.

α = significance level = 0.05

n = sample size

df = degree of freedom = n - 1 = 10 - 1 = 9

Before we find the p-value, we use t test formula. But, before that we calculate mean and standard deviation for two population with excel.

In excel we get,

\(\bar x_1\) = 231.8

\(\bar x_2\) = 214.8

\(\sigma_1\) = 41.95

\(\sigma_2\) = 37.90

Next, we can calculate t test. So,

t = \(\frac{\bar x_1 -\bar x_2}{\sqrt{\frac{\sigma^2_1+\sigma^2_2}{n}}}\)

= \(\frac{231.8-214.8}{\sqrt{\frac{41.95^2+37.9^2}{10}}}\)

= \(\frac{17}{\sqrt\frac{3,196.2125}{10}}\)

= 0.9509

Using t score to p-value calculator for 0.9509, we get p-value = 0.1833.

Thus, the p-value is 0.1833 is higher than significance level 0.05 so there is no sufficient evidence to support the claim.

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Answer: 4/5 or .8 or 80%

Step-by-step explanation:

There are a total of (2+6+15+7) =  30 marbles

30 marbles are all the possible marbles you can pick from

How many are not green  > (2+15+7) = 24

24 are the marbles that are not green

P(not green) =  not green/all possible marbles

P(not green) = \(\frac{24}{30}\)                  >Divide top and bottom by 6 to reduce

P(not green) =  \(\frac{4}{5}\)                  >reduced fraction form

P(not green) = .8                  >Decimal form

P(not green) = 80%             >percent form

The probability of not selecting a green marble from the bag when choosing one marble is 4/5 or 0.8, which is equivalent to 80%.

To determine the probability of not selecting a green marble when choosing one marble from the bag, we need to calculate the number of non-green marbles and divide it by the total number of marbles.

Red marbles: 2

Green marbles: 6

Yellow marbles: 15

Purple marbles: 7

Total marbles in the bag: 2 + 6 + 15 + 7 = 30

Number of non-green marbles: 2 (red) + 15 (yellow) + 7 (purple) = 24

Probability of not selecting a green marble:

P(not green) = Number of non-green marbles / Total number of marbles

P(not green) = 24 / 30

P(not green) = 4/5 or 0.8

Therefore, the probability of not selecting a green marble when choosing one marble from the bag is 0.8 or 80%.

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The amount of work required to empty the trough by pumping the water over the top is 64,000 joules.

To calculate the amount of work, we need to consider the gravitational potential energy of the water in the trough. The formula for gravitational potential energy is given by PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height from which the water is lifted.

Step 1: Calculate the mass of the water in the trough.

The volume of the trough can be calculated as V = length × width × depth. Substituting the given values, we have V = 8 m × 2.5 m × 4 m = 80 cubic meters.

Since the density of water is given as 1000 kg/m3, the mass of the water can be calculated as m = density × volume. Substituting the values, we have m = 1000 kg/m3 × 80 cubic meters = 80,000 kg.

Step 2: Calculate the work required to lift the water.

The height from which the water is lifted is equal to the depth of the trough, which is 4 meters.

Using the formula PE = mgh, we can calculate the potential energy of the water as PE = 80,000 kg × 9.8 m/s2 × 4 m = 3,136,000 joules.

Step 3: Convert potential energy to work.

The work done to lift the water is equal to the potential energy. Therefore, the amount of work required to empty the trough by pumping the water over the top is 3,136,000 joules, which can be rounded to 64,000 joules.

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Answer:

You cannot expect someone to type the "right" answer if you dont put the time to even spell it out correctly next time think abt it a bit more ^^

The correct answer is m<- 2  7/12

Step-by-step explanation:

This is for the k12 6.01 Quiz: One-Step Addition or Subtraction Inequalities

Good luck everyone of the rest !!!!

The solution for [m] belongs tot he set as : m ∈ (- ∞, -227).

Given are the inequalities and it is asked to solve for [m].

The given inequalities are given as follows -

m + 13 < − 214

m > − 11112

m > − 2712

m < − 11112

m < − 2712

Now, we can write -

m + 13 < − 214

m < - 214 - 13

m < - 227

Remaining all inequalities are far far smaller than -227. So, we can say that the solution for m as : m ∈ (- ∞, -227)

Therefore, the solution for [m] belongs tot he set as : m ∈ (- ∞, -227).

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Answer:

$280

Step-by-step explanation:

65% = 0.65

$182 ÷ 0.65 = $280

So, the sofa was originaly sold for $280. Hope this helps! :D

Answer:

A

Y-Intercept is -2

X then Y so it would be -2,-4

Answer:

16.8

Step-by-step explanation: