Compute the product using​ (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as​ weights, and​ (b) the​ row-vector rule for computing Ax. If a product is​ undefined, explain why.

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

A

Hope This Helps! :)

Answer:

B. 4 inches

Step-by-step explanation:

(24)(1) / 6 = 4

Answer:

Step-by-step explanation:

4ox-16=4[10x-4]this is because 4 is the common factor in both 40and 16

16x-24x-4±12=4[4x-6x-1±3]

-8x-8=8[-1-1]

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

The correct equation that matches the given graph is y = cos(x) + 1.

To determine the equation that matches the given graph, we can observe the key features and points provided.

The waveform starts from the y-axis at 1 unit: This suggests that the function has a vertical shift of 1 unit upwards.

The waveform passes through (π, -1), (2π, 1), and (3π, -1): This indicates that the function oscillates between the values of -1 and 1 as x increases.

The waveform intercepts the x-axis at π/2, 3π/2, 5π/2, and 7π/2: This suggests that the function has zeros or x-intercepts at these values.

Based on these observations, the function can be represented as a cosine function.

The cosine function with a vertical shift of 1, oscillating between -1 and 1, and having zeros at π/2, 3π/2, 5π/2, and 7π/2 is:

y = cos(x) + 1

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Answer:

1/8 paintings per week

Step-by-step explanation:

If the artist completes 1/4 of a painting in 2 weeks, then in half the time (1 week), the artist will complete half the work which is 1/8.

Hope this helps :)

Answer:

Step-by-step explanation:

The smallest perfect square that has three different prime numbers as factor is 900

900 = 30 * 30

Factors = 2² * 3² * 5² = 900

The graph will have a slope of 15 and is attached with the answer below.

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

When y and x are two quantities that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

Given that Nicole had a collection of 60 stuffed animals. She gave away 5 stuffed animals per month until all her stuffed animals were gone.

The equation can be written as:-

y = kx

The value of k will be calculated as :-

60 = k x 5

k = 60 / 5

k = 12

The equation will be:-

y = 12x

The graph of the linear relation is attached with the answer below.

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The amount of sample after 25 years and the half life are given as 51.8 g and 12.83 years respectively.

An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.

The given function for the decay of an isotope is given as A(t) = 200\(e^-0.054t\).

Now, the given problem can be solved as follows,

(a) The amount of sample after 25 years is given as,

A(25) = 200\(e^{-0.054 \times 25}\)

         = 200\(e^{-1.35}\)

         = 200 × 0.259                      

         = 51.8

(b) The half life can be calculated as,

100 =  200\(e^{-0.054t}\)

=> \(e^{-0.054t}\) = 1/2

=> t = 12.83        

Hence, the sample left after 25 years will be 51.8 g and it will take 12.83 years for the sample to decay to half of its amount.

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Answer:

24

Step-by-step explanation:

\(\frac{3}{4} *32\\=\frac{3}{4}*\frac{32}{1} \\=\frac{96}{4} =24\)

Answer:

Following are the answer to the given question:

Step-by-step explanation:

Following are the null and alternative Hypothesis:

\(Null \ Hypothesis: \mu = 4\\\\Alternative \ Hypothesis: \mu < 4\)

Rejection Zone

This is left tailed test, for α = 0.2 and df = 39

\(critical\ value(t) = -0.851\\\\reject\ H_0 \ when = t < -0.851\)

Testing statistic:

\(t = \frac{(\bar{x} - \mu)}{( \frac{s}{\sqrt{n}})}\)

  \(= \frac{1.5 - 4}{\frac{5}{\sqrt{40}}}\\\\= \frac{-2.5}{\frac{5}{6.32}}\\\\= \frac{-2.5}{0.79}\\\\ = -3.162\)

\(P-value = 0.0015\)

P-value < 0.2, reject the null hypothesis.

Approach to the Rejection Zone:

The null hypothesis is rejected since the test statistic t is outside of the critical range value. Only at the 0.200 significance mark, there's significant evidence that its new shrub's growth rate is less than 4 cm per week.

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

The number of fours divided by the total number of possibilities. If there are two fours and 8 spaces, the probability is 2/8 = 1/4.

Step-by-step explanation:

Answer:

21> 2x+ 15

Step-by-step explanation:

The expression is 21 > 15+ 2x

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Twenty-one is greater than the sum of fifteen and two times a number​

let the number be x.

two times a number​ = 2x

and, sum of fifteen and two times a number​ = 15 + 2x

So, Twenty-one is greater than the sum of fifteen and two times a number​

21 > 15+ 2x

Hence, the expression is 21 > 15+ 2x.

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Answer:

3 with a remainder of 15

Step-by-step explanation:

Long division

y = 3x + 13

y = 7x + 17

Using the elimination method. Multiply both equations by common their common factors, 7 and 3. In order to cancel out the x variable.

7y = 21x + 91

3y = 21x + 51

Subtract the equation.

4y = 40

y=10

substitute 10 to either one of the equations to solve for x

10=3x+13

x=-1

Answer:

7y=21×+91

3y=21×+51

subtract the equation

4y=40

y=10

Answer:

41 adults and 82 kids

Step-by-step explanation:

divide 123 by 3 two parts are kids one part is adults.

Answer:

D.

Step-by-step explanation:

To  find the mean you add all the numbers together then divide by the total of number so 5

The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Answer:

21.67

Step-by-step explanation:

look at the number next to 7 to determine how it will change.

The number is 3 which is under 5 so the 7 stays the same while 3 is gotten rid of

Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

Answer:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Step-by-step explanation:

Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.

For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 29.2 g

Biscuit mass = 43.8 g

For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Answer:

A

Step-by-step explanation:

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Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.

In geometry, parallel lines are coplanar unlimited lines that never cross. In a particular three-dimensional space, the parallel planes represent the ones that never cross. Parallel curves are those with a constant minimum separation between them and no places of contact or intersection. In geometry, parallel lines are two lines which run in the exact same plane, evenly spaced apart, and hadn't cross. Both vertical and horizontal can be used. In commonplace items like train tracks, stacks of notebooks, and crossings for pedestrians, straight lines can be seen.

The form of Jackson's poster is best described as a rhombus. A quadrilateral with a rhombus has opposing sides that are parallel and all of its sides are equal. Additionally, it has congruent opposing angles. In addition to having parallel opposing sides, a parallelogram also has non-congruent sides and angles. Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.

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Answer:

\( \cos(x) = - \frac{5}{ \sqrt{41} } \)

\( \csc(x) = \frac{ \sqrt{41} }{4} \)

\( \tan(x) = - \frac{4}{5} \)

Step-by-step explanation:

We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.

We need to find the cos, csc, and tan measure of this point.

We can find cos by using the formula of

\( \cos(x) = \frac{adj}{hyp} \)

The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.

\( { - 5}^{2} + {4}^{2} = \sqrt{41} \)

So using the info the answer is

\( \cos(x) = \frac{ - 5}{ \sqrt{41} } \)

We can find tan but first me must find sin x.

\( \sin(x) = \frac{opp}{hyp} \)

\( \sin(x) = \frac{4}{ \sqrt{41} } \)

So now we just use this identity,

\( \tan(x) = \sin(x) \div \cos(x) \)

\( \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} \)

So tan x=

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

We can find csc by taking the reciprocal of sin so the answer is easy which is

\( \frac{ \sqrt{41} }{4} \)

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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