A 12-foot ladder is leaning against a wall. The top of the ladder touches the wall 10 fe above the ground. The bottom of the ladder touches the ground n feet from the wall A student states that the distance from the bottom of the ladder to the wall can be determined by solving the equation below. is the student correct? 12² + 10² = n²​

the answer is 56 and 16

Step-by-step explanation:

56 and 16

Justice is using a technique known as chunking.

Short-term memory can function more effectively thanks to chunking, however the quantity of chunks that can be stored efficiently declines as chunk size grows.

Large pieces of information may be divided into smaller bits and then grouped together using relevant information or attributes before being stored in order to improve retention of that information in the short term memory. To establish relational information or similarity between the information to be stored in order to improve retention and recall in the short term memory, information must be broken down before being regrouped. However, as chunk size grows, so does the efficiency of information chunking.

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The equation of the circle with the centre at origin and having the radius 2 is; x² + y² = 4.

The standard circle's equation is-

(x – h)² + (y – k)² = r².

Centre (h,k) = (0,0) origin

radius r = 2

Circle's equation is-

(x – 0)² + (y – 0)² = 2²

Circle's equation is-

(x )² + (y)² = 4

Thus, the equation of the circle with the centre at origin and having the radius 2 is; x² + y² = 4.

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Answer:

for 3. the answer is 9

for 4. the answer is 12

Step-by-step explanation:

hope this helped!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

g(x) = 3x - 4

g(-4) means x = -4

g(-4) = 3(-4) - 4 = -12 - 4 = -16

The equation obtained for Kim will be t = x/2

Equation obtained for Jake will be t = (x - 6)/1.5

As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.

Kim moves at a 2-meter-per-second running pace.

Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)

Jake gets 6 meters ahead of Kim.

To get equations for the same case to both persons we should get it as,

Let x be the complete race distance and t be either Kim's or Jake's total race time.

Time = Speed/Distance

Kim's time equation is t = x/ 2.

The time equation that Jake uses is t = (x - 6)/1.5.

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Answer: 1) 8x + 2 = 90 1a. 11 2. 13x-10= 133 2a. 11

Both solve for 11.

Step-by-step explanation: 1) they’re both the same measure so they equal each other

Subtract 2 from each side 8x = 88 and x is 11

13x - 10 = 133 they’re both the same measures so they equal each other.

Add 10 to both sides because it’s already negative and 13x = 143 and you get 11

Answer:

11 for both

Step-by-step explanation:

[Cr(NH3)4Cl2]NO3 The name of the given coordination compound [Cr(NH3)4Cl2]NO3 is Tetrakis (ammine)chromium(III) chloride nitrate. A coordination compound is a compound in which a metal atom is bound to a group of surrounding atoms.

In [Cr(NH3)4Cl2]NO3, the ligands are ammonia (NH3) and chloride (Cl-). When naming coordination compounds, follow these steps:

Write the name of the ligands in alphabetical order.

Do not use prefixes if the ligand name has only one. Indicate the oxidation state of the metal ion by using Roman numerals in parentheses after the name of the metal, as well as the suffix "-ate."

Write the name of the anion, including any necessary prefixes and suffixes.

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Answer:

7 minutes

Step-by-step explanation:

The computation of the time taken for downloading the second file is given below:

Given that

The combined size for both files is 696 megabyres

And, the size of the first file is 290 megabytes

So, the size of the second file is

= 696 - 290

= 406

Now for the first file it took 5 minutes to download

So for the second file, it would took

= 406 × 5 minutes ÷ 290

= 7 minutes

Answer:

7 minutes

Step-by-step explanation:

The computation of the time taken for downloading the second file is given below:

Given that

The combined size for both files is 696 megabyres

And, the size of the first file is 290 megabytes

So, the size of the second file is

= 696 - 290

= 406

Now for the first file it took 5 minutes to download

So for the second file, it would took

= 406 × 5 minutes ÷ 290

= 7 minutes

The limits are  `(i + (3/2)j - k)`

We need to substitute the value of t in the function and simplify it to get the limits. Substitute `π/2` for `t` in the function`lim_(t→π/2)(cos(2t)i−4sin(t)j+2tπk)`lim_(π/2→π/2)(cos(2(π/2))i−4sin(π/2)j+2(π/2)πk)lim_(π/2→π/2)(cos(π)i-4j+πk).Now we have `cos(π) = -1`. Hence we can substitute the value of `cos(π)` in the equation,`lim_(t→π/2)(cos(2t)i−4sin(t)j+2tπk) = lim_(π/2→π/2)(-i -4j + πk)` Answer: `(-i -4j + πk)` Now let's evaluate the second limit`lim_(t→ln2)(2eti6e−tj−4e−2tk)`.We need to substitute the value of t in the function and simplify it to get the answer.Substitute `ln2` for `t` in the function`lim_(t→ln2)(2eti6e−tj−4e−2tk)`lim_(ln2→ln2)(2e^(ln2)i6e^(-ln2)j-4e^(-2ln2)k) Now we have `e^ln2 = 2`. Hence we can substitute the value of `e^ln2, e^(-ln2)` in the equation,`lim_(t→ln2)(2eti6e−tj−4e−2tk) = lim_(ln2→ln2)(4i+6j−4/4k)` Answer: `(i + (3/2)j - k)`

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Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Answer:

Answer at the bottom

Step-by-step explanation:

The smallest average will occur when the numbers are as small as possible. The four smallest distinct positive even integers are 2, 4, 6, and 8 and their average is 5.

Hope this helps!!

Answer: to the right

Step-by-step explanation:

Answer:

y = 10/11 x + 2.45

Step-by-step explanation:

Equation of the line

First find the gradient

formula = \(\frac{y2-y1}{x2-x1}\)

= \(\frac{-3-7}{-6-5}\)

=\(\frac{-10}{-11}\)

= 10/11

m is the gradient

equation of a line

y- y1 = m(x-x1)

y-7 = 10/11 (x-5)

y-7 = \(\frac{10}{11}x\) - \(\frac{50}{11}\)

y = 10/11 x + 2.45

NB i rounded of -50/11 +7  = 2.4545..... to 2.45

Answer:

how many brothers do you have?

Answer: 110 degrees

Step-by-step explanation:

Answer:

C, at 0/25, 1/20, 2/15, 3/10,...

Answer:

C

Step-by-step explanation:

The numbers that are in the range are:

\(\displaystyle\sf -3, -2, -1, 0, 1, 2\).

Answer:The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

Step-by-step explanation:

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

Describe a formula. To create the expression known as an equation, two sides are connected by the equals symbol (=). The variables in the equation 2x+1 = 9 are 2x+1 on the left and 9 on the right (RHS).

To simplify the equation 2/3x + 5 = 1/5 - 2x, we can start by getting rid of the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators of the fractions, which is 15.

So, we have:

15 * (2/3x + 5) = 15 * (1/5 - 2x)

Expanding the left-hand side, we get:

10x + 75 = 3 - 30x

Bringing all the x terms to one side and all the constant terms to the other, we get:

10x + 30x = 3 - 75

Combining like terms, we get:

40x = -72

Dividing both sides by 40, we get:

x = -72/40 = -9/5

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

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To determine if W is a vector space, we need to check whether it satisfies the closure axioms of a vector space.

In particular, we need to check whether W is closed under vector addition and scalar multiplication.

Let's first consider vector addition. Suppose that u = (4a, 3b, 0) and v = (a, b, c - 2a) are two arbitrary vectors in W. Then their sum is given by:

u + v = (4a, 3b, 0) + (a, b, c - 2a) = (5a, 4b, c - 2a)

We see that the sum is also of the form shown in the definition of W, which means that W is closed under vector addition.

Now, let's consider scalar multiplication. Suppose that u = (4a, 3b, 0) is an arbitrary vector in W, and let c be an arbitrary real number. Then their scalar product is given by:

c * u = c * (4a, 3b, 0) = (4ca, 3cb, 0)

We see that the scalar product is also of the form shown in the definition of W, which means that W is closed under scalar multiplication.

Therefore, we have shown that W is closed under both vector addition and scalar multiplication, and is thus a vector space.

To find a set S of vectors that spans W, we can find a set of vectors such that every vector in W can be written as a linear combination of the vectors in S. One possible set S is:

{(4, 0, 0), (0, 3, 0), (0, 0, 1), (-2, 0, 0)}

We see that any vector in W can be written as a linear combination of these four vectors, as follows:

(4a, 3b, 0) = 4(a, 0, 0) + 3(0, b, 0) + 0(0, 0, 1) + (-2)(-2, 0, 0)

(a, b, c - 2a) = 1(4, 0, 0) + 0(0, 3, 0) + 1(0, 0, 1) + (-2)(-2, 0, 0)

Therefore, the set S = {(4, 0, 0), (0, 3, 0), (0, 0, 1), (-2, 0, 0)} spans W.

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Answer:

125 over 343 as a fraction and 0.364431 as a decimal

Step-by-step explanation:

hope this helps dont know if its right

Answer:

125/343

Step-by-step explanation:

The selection chances and the required probability for 9 women and 6 men is given by ,

Different groups of applicants selection = 3003

Selection of trainee entirely of women = 126

Probability of selection of entirely women from 15 people = 4.19%

Total number of women = 9

Total number of men = 6

Total = 9 + 6

        = 15

The total number of groups of applicants that can be selected for the positions can be calculated using the combination formula,

nCr = n! / r!(n-r)!

where n is the total number of applicants (15),

And r is the number of positions to be filled (5).

Number of different groups of applicants that can be selected for the positions is,

15C5

= (15! )/(15-5)!5!

=(15! )/(10)!5!

= 3003

Number of different groups of trainees that consist entirely of women can be calculated by selecting 5 women from the 9 available,

9C5

= (9! )/(9-5)!5!

=(9! )/(4)!5!

= 126

Probability of selecting a group of five trainees ,

Consist entirely of women can be calculated by dividing the number of different groups of all-women trainees (126) by the total number of different groups of trainees (3003),

Required probability

= 126/3003

≈ 0.0419

Probability that the trainee class will consist entirely of women is approximately 0.0419, or 4.19% (rounded to four decimal places).

Therefore, for a group of 15 people,

Selection of different groups of people = 3003

Selection of trainee represents entirely women =126

probability of selecting entirely women = 4.19%

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$$\boxed{y=\frac{ce^{x}}{\sqrt{3e^{2x}-1}}}$$

The given differential equation is $\frac{dy}{dx}-y=y^{2}e^{-x}$. To find the general solution in explicit form to the differential equation, we need to find the integrating factor of the differential equation.

Step 1: Finding the integrating factorThe differential equation can be written in the standard form,$$\frac{dy}{dx}+p(x)y=q(x)$$where $p(x)=-1$ and $q(x)=y^{2}e^{-x}$ The integrating factor of the differential equation is defined as$$I=e^{\int p(x)dx}$$Here, $p(x)=-1$. Hence, the integrating factor is$$I=e^{\int(-1)dx}=e^{-x}$$

Step 2: Multiplying both sides by the integrating factor. Multiplying both sides of the differential equation by the integrating factor $e^{-x}$, we get$$(e^{-x}\frac{dy}{dx})-(ye^{-x})=y^{2}$$. We can simplify this as$$\frac{d}{dx}(ye^{-x})=y^{2}$$

Step 3: Integrating both sides. Integrating both sides of the equation above with respect to x, we get$$\int\frac{d}{dx}(ye^{-x})dx=\int y^{2}dx$$$$ye^{-x}=\frac{y^{3}}{3}+c$$where c is a constant of integration.

Step 4: General solutionThe general solution of the differential equation in explicit form is given by$$y=\frac{ce^{x}}{\sqrt{3e^{2x}-1}}$$Hence, the required general solution of the given differential equation in explicit form is given by $$\boxed{y=\frac{ce^{x}}{\sqrt{3e^{2x}-1}}}$$

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a) Here is a sketch of the region D:

            |\

            | \

            |  \

            |   \

            |    \

            |     \

            |      \

            |       \

   _________|________\_________

            |        \

            |         \

            |          \

            |           \

            |            \

            |             \

b) Possible way to set up this integral is:

∫[0,2π] ∫[1,2] y r dr dθ

(a) The region D is an annulus (a ring-shaped region) with inner radius 1 and outer radius 2. It is neither a type z nor a type y region.

Here is a sketch of the region D:

            |\

            | \

            |  \

            |   \

            |    \

            |     \

            |      \

            |       \

   _________|________\_________

            |        \

            |         \

            |          \

            |           \

            |            \

            |             \

(b) The integral to find the volume under the surface z = y over the region D is:

∬D y dA

where D is the region given by 1 < x² + y² < 4. One possible way to set up this integral is:

∫[0,2π] ∫[1,2] y r dr dθ

where we integrate first with respect to r, the radial variable, and then with respect to θ, the angular variable. Note that the limits of integration for θ are 0 to 2π, the full range of angles, and the limits of integration for r are the radii of the annulus

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The dimensions that minimize the cost subject to the volume constraint are \(L = 4 ft, W = 2 ft,\) and \(H = 2 ft\) using surface area.

Assuming that the cost of material is proportional to the surface area, we can write the cost function as:

\(C = k(2LW + 2LH + WH)\)

where k is a constant of proportionality that depends on the cost of the material. We are given that the cost of the material for the top and bottom is twice the cost of the material for the sides, so we can take k = 3 for simplicity (since the cost of the material for the sides is then 1).

Using the volume constraint as before, we can eliminate one of the variables:

\(H = 16/LW\)

When this is used as a cost function substitution,

\(C = 3(2LW + 2LH + WH) = 6LW + 96/L + 48/W\)

To find the critical points of C, we need to find where the partial derivatives are zero:

\(dC/dL = 6W - 96/L^2 = 0\)

\(dC/dW = 6L - 48/W^2 = 0\)

When we simultaneously solve these equations, we obtain:

L = 4 ft

W = 2 ft

H = 2 ft

Therefore, the dimensions that minimize the cost subject to the volume constraint surface area are L = 4 ft, W = 2 ft, and H = 2 ft.

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Answer:

7x+12y

Step-by-step explanation:

Equation 1: 2x+4y        Equation 2: 5x+8y

(2x+4y)+(5x+8y)

1. Move and add like terms:   (2x+5x)+(4y+8y)

2. Remove parentheses:   (7x)+(12y)

7x+12y