simplify [2 1/3-(4 2/5)]-1 1/2​

Answer:

The answer to this question is v= -4

Answer:

v=-4

Step-by-step explanation:

v=-24/6

v=-4

Answer:

3 laps.

Step-by-step explanation:

Hi! I can see how this is tricky, but I was a bit confused by the 4 in "If she runs 4." It says in the problem that the track is a mile long... So if you run the track 3 times, 3 x 1 = 3.

Answer:

A)

2x+5y=37

4x+3y=39

Answer:

A

Step-by-step explanation:

The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.

Here,

The area=2000 m²

xy=2000

x=2000/y

p=4x+2y

p=4*(2000/y)+2y

=8000/y+2y

p'=-8000/y²+2

-8000/y²+2=0

2y²-8000=0

y²-4000=

y²=4000

y= 20 m

p=8000/20+2*20

p=400+40=440 m

Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.

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The center of the circle is (6,7) and the radius of the circle is 1.414 units

The diameter with endpoints = (5, 8) and (7, 6)

The mid point of the diameter = The center of the circle

The center of the circle = \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Substitute the values in the equation

The center of the circle = ( (5+7)/2 , (6+8)/2 )

= (12/2 , 14/2)

= (6, 7)

The radius of the circle = The distance between (6, 7) and (7, 6)

The distance between two points = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The distance between (6, 7) and (7, 6) = \(\sqrt{(7-6)^2+(6-7)^2}\)

= \(\sqrt{1^2+(-1)^2}\)

= \(\sqrt{1+1}\)

= \(\sqrt{2}\)

= 1.414 units

Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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According to the equation for the maximum speed, it is found that the height at the top of the swing of the rider is of 0.8 m.

As stated in the problem, it is given by:

v = 2gh.

In which:

In this problem, the parameters are g = 9.8, v = 15. Hence we can solve for h to find the height.

v = 2gh

2 x 9.8h = 15

19.6h = 15

h = 15/19.6

h = 0.8.

The height at the top of the swing of the rider is of 0.8 m.

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Given the following System of equations:

You need to follow the steps shown below in order to find the solution:

Step 1. Set the equations equal to each other:

Step 2. Solve for the variable "x":

Step 3. Substitute the value of "x" into any original equation and evaluate, in order to find the value of the other variable. This is:

The point is:

Then, the solution is:

Option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two tables shown in the picture.

Table (A) have values of x and a(x)

Table (B) have values of d and r(d)

As we know if the function has an inverse of it and (x, y) satisfies the function then (y, x) must satisfy the inverse of a function.

Thus, the option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.

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Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

The total number of ways to distribute a total inventory of twenty batteries among the six different types is 10 x 120,332,228 = 1,203,322,280.

To determine how many ways a total inventory of twenty batteries can be distributed among the six different types, we need to use the concept of combinations. We know that there are seven different types of batteries, but we are given that there are only ten a7b batteries and at least twenty of each of the other types. This means that the maximum number of batteries that can be used from the other six types is 20 x 6 = 120.

So, to distribute a total of twenty batteries among the six types, we need to consider the number of a7b batteries and the number of batteries from the other six types. Since we are given that there are only ten a7b batteries, we can distribute them in 10 different ways among the six types.

For the other six types, we have a maximum of 120 batteries to use. To distribute 20 batteries among these six types, we can use the formula for combinations, which is nCr = n! / r!(n-r)!. In this case, we have 120 batteries to choose from, and we want to choose 20 batteries, so the formula becomes 120C20 = 120! / 20!(120-20)! = 120,332,228 ways.

Therefore, the total number of ways to distribute a total inventory of twenty batteries among the six different types is 10 x 120,332,228 = 1,203,322,280.

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Answer:

Part A: A

Part B: 1 is the y-intercept and is 0 the horizontal asymptote

Step-by-step explanation:

Using the formula for the population growth with given value of rate and the condition for the population to reach, The answer is 87 years.

The country, territory, or geographic area's yearly average rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and the total population for that year.

The rise in the number of people on Earth is referred to as population growth. The majority of human history saw a relatively steady population size. Energy, food, water, and medical care, however, became more accessible and dependable as a result of innovation and industrialization.

rate = 0.8%

\(2P = P * (1 + \frac {0.8}{100})^{n}\)

\(2= (1.008)^{n}\)

n=86.98 years

approximately 87 years.

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The number of years will be 5 years, will it take for the amount of money in the account to double.

Here, we have,

The number of years will be computed using the excel formula as:

=N per(rate,pmt,pv,fv,type)

where

N per is number of years

rate is 4%

But is compounded quarterly,

So,

rate = 4% × 4

rate = 16%

pmt is $0

pv is Present value which is -$1,000

fv is future value which is $2,000 (as it will get doubled)

Putting the values above:

=N per(4%× 4,0,-1000,2000,0)

= 4.67 years or 5 years

Therefore, the amount will get double in 5 years will it take for the amount of money in the account to double.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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M = log (2.4 - 10⁻¹⁰) is the valid step in the process of calculating the magnitude of an earthquake releasing 2.5 - 10¹⁵ joules of energy.

The equation which gives the magnitude of an earthquake is given as,

M = log (E/Eo)

where E is the energy released by the earthquake in joules and Eo = 1044 is the assigned minimal measure released by an earthquake.

Given, amount of energy released by the earthquake, E = 2.5 - 10¹⁵ joules

We can substitute these values in the given equation to calculate the magnitude of the earthquake.

Magnitude of an earthquake,

M = log (E/Eo)

M = log ((2.5 - 10¹⁵)/1044)

M = log (2.4 - 10⁻¹⁰)

Therefore, M = log (2.4 - 10⁻¹⁰) is the valid step in the process of calculating the magnitude of an earthquake releasing 2.5 - 10¹⁵ joules of energy.

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Answer:

y=bc-abx

Step-by-step explanation:

Given the equation ax + y/b = c, the first thing you'd want to do is isolate the variable that you are trying to solve for.

To do this, you must first subtract ax from both sides, to leave y/b by itself on one side of the equation, resulting in:

y/b = c - ax

Now all you need to do to isolate y, and you can do so by multiplying both sides by b, cancelling out y being divided by b.

b(y/b) = b(c - ax)

y = b(c - ax)

To simplify and fit one of the answer choices, you simply distribute b via multiplication to both c and -ax:

y = bc - abx

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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Answer:

going in the order top to bottom

i)

2

2

2

2 and 2

ii)

2 and 2

2

2

2 and 2

iii)

2

2

2 and 2

2 and 2

Step-by-step explanation:

you have to find out what number you times to get the number they have given you (eg: you have to get 4 and they have given you the number 2, 2 times what makes 4? the answer is 2)

Answer:

y = .25 x 96

y = 24

This is the answer.

Step-by-step explanation:

25% is the same as 0.25

25% = 25/100 = 0.25

Multiply 0.25 with 96

0.25 x 96 = 24

24 is your answer

hope this helps

Answer:

I am going to say that it is option A.

Step-by-step explanation:

I hope this helped out a lot!

False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.

A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.

This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.

Think about these matrices as an illustration:

Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.

A = [1 2; 2 1]

and

B = [1 0; 0 1].

The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.

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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.

Explanation:

Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.

Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.

However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.

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I don't understand the question

The number line of the set C ={x : x ≤ -3} is attached

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

Set C ={x:x<=-3}

Rewrite properly

So, we have

Set C ={x : x ≤ -3}

Remove the curly braces from the set notation

So, we have the following representation

x ≤ -3

There are no multiples and factors to divide or multiply

Also, there are no terms to subtract or add

This means that the inequality to represent on the number line is x ≤ -3

See attachment for the number line

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If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light

The percent transmittance of an IR signal = 45%

The equation of percent transmittance is

Percent transmittance = ( I / Io ) × 100

Where Io is the intensity of the IR signal entering the sample

I is the intensity of the IR signal leaving the sample

If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light

Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample

Therefore, the sample absorbed 55% of the IR light

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Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm