What is 0.524 In scientific notation

Answer:

75% = 3/4

3/4 of 20 = 15

Ratio - 15:20 (A)

The ratio that would show the number of questions answered correctly to the total number of questions as 15 : 20.

A ratio between two variables {x} and {y} can be expressed in the following form → {x : y} = {x}/{y}.

We can write the relation between two ratios using the proportion as -

{x : y} :: {a : b}

Given is that a student received a 75% on an exam. There were 20 questions on the exam.

It is given to find that which ratio would show the number of questions answered correctly to the total number of questions.

Total number of questions = 20

Number of questions answered correctly = 75%

75% of 20

75/100 x 20

75/5

15

We can write the ratio that would show the number of questions answered correctly to the total number of questions as 15 : 20.

Therefore, the ratio that would show the number of questions answered correctly to the total number of questions as 15 : 20.

To solve more questions on ratio, visit the link-

https://brainly.com/question/21138916

#SPJ7

(i) The area of the region is 4 square units.

(ii) The area of the region bounded by the curves is,

1 + (sin(π/2)cos(π/5) + cos(π/2)sin(π/5)) + (cos(π/2)cos(π/5) - sin(π/2)sin(π/5))

(i) The area of the region bounded by the curves f(x) = x and g(x) = x - 2 in the first quadrant,

we need to compute the definite integral:

∫[0, 2] (x - (x - 2)) dx

= ∫[0, 2] 2 dx

= [2x] from 0 to 2

= 4

Therefore, the area of the region is 4 square units.

ii. The area of the region bounded by the curves f(x) = sin(x) and g(x) = cos(x) in the interval [4π/5, 4π], we need to compute the definite integral:

∫[4π/5, 4π] (cos(x) - sin(x)) dx

= [-sin(x) - cos(x)] from 4π/5 to 4π

= [-sin(4π) - cos(4π)] - [-sin(4π/5) - cos(4π/5)]

= [0 - 1] - [-sin(4π/5) - cos(4π/5)]

= 1 + sin(4π/5) + cos(4π/5)

Using the angle sum identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b), we can simplify the expression:

= 1 + sin(4π/5) + cos(4π/5)

= 1 + sin(π/2 + π/5) + cos(π/2 + π/5)

= 1 + (sin(π/2)cos(π/5) + cos(π/2)sin(π/5)) + (cos(π/2)cos(π/5) - sin(π/2)sin(π/5))

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ4

Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:

F(x) = x*(x + 1)*(x - 2)

For a polynomial with the zeros:

x₁, x₂, x₃, ..., xₙ

The polynomial can be written as:

y = (x - x₁)*(x - x₂)*...*(x - xₙ)

In this case, the zeros are:

0, -1, and 2

Then we can write the polynomial as:

y = (x - 0)*(x + 1)*(x - 2)

If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)

Learn more about polynomials:

https://brainly.com/question/4142886

#SPJ1

Answer:$2.50

Step-by-step explanation: You will take $49.95 times 0.05 or 5% and you get 2.497 and round that to $2.50.

The order of visit for DFS and BFS will differ based on the structure of the graph or tree and the starting node. DFS will typically visit nodes in a deeper order, while BFS will visit nodes in a breadth-first order.

Both  algorithm depth-first search and algorithm breadth-first search are used to traverse or search a graph or tree data structure. The difference between them lies in their traversal strategy.
Depth-first search (DFS) starts at a root node and explores as far as possible along each branch before backtracking. It follows a content-loaded algorithm, meaning that it prioritizes exploring deeper into the structure before considering other branches. In terms of visit order, DFS starts at the root node, then moves to its first child node, and continues to explore its descendants until it reaches a leaf node. Once it has visited all descendants of the current node, it backtracks to the previous node and repeats the process until it has visited all nodes.
On the other hand, breadth-first search (BFS) starts at the root node and explores all the neighboring nodes at the current depth level before moving on to the next depth level. It follows a breadth-first algorithm, meaning that it prioritizes exploring all nodes at a given depth level before moving on to deeper levels. In terms of visit order, BFS visits all nodes at a given depth level before moving on to the next level.

learn more algorithm about here:

https://brainly.com/question/28724722

#SPJ11

Answer:

tan(X) = 1.05

Step-by-step explanation:

The triangles WXY and VTU are similar using the case AA (angle-angle).

The angle X is equal the angle T, therefore they have the same tangent value.

The tangent value is given by the opposite side to the angle divided by the adjacent side to the angle, so we have that:

\(tan(T) = UV / UT\)

\(tan(T) = 21 / 20 = 1.05\)

\(tan(X) = tan(T) = 1.05\)

The categories of the ordered pairs are

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

f = {(3, -4). (6, 5), (-4,3), (5,7)}

g = {(-4,8), (5,-3), (-3,-4),(7, 4)}

In the above, we have

[f . g](x) = f(g(x))

So, we have

[f . g](x) = f(g(6))

This gives

[f . g](x) = f(g(6))

Next, we have

[g . f](x) = g(f(x))

So, we have

[g . f](6) = g(f(6))

[g . f](6) = g(5)

[g . f](6) = -3

This means that

(6, -3) = [g . f](x)

Next, we have

[f . g](-3) = f(g(-3))

This gives

[f . g](-3) = f(-4) = 3

This means that

(-3, 3) = [f . g](x)

Next, we have

[f . g](7) = f(g(7))

This gives

[g . f](7) = f(g(7)) = f(4)

[g . f](7) = Neither

Next, we have

[f . g](5) = f(g(5)) = f(-3) =

[g . f](5) = g(f(5)) = g(-3) = -4 = Neither

Read more about composite functions at

https://brainly.com/question/10687170

#SPJ1

Answer:

d=8

Step-by-step explanation:

Okay we've got 68/17 and d/2

68/17 = 4 meaning d/2 is also 4. Since 4 × 2 is 8, we know the answer is 8.

Answer:

sec 0 = 5/(2√6)

Step-by-step explanation:

sin 0 = -1/5

Fourth quadrant Cos positive Rest negative

cos²0 + sin²0 = 1

cos²0 = 1-sin²0

cos²0 = 1 - (1/5)²

cos²0 = 1- 1/25

cos²0 = 24/25

cos0 = ±(2√6)/5

quadrant IV cos is positive.

Therefore cos0 = (2√6)/5

Now, sec0 = 1/cos0

sec0 = 1/{(2√6)/5)}

sec0 = 5/(2√6)

.

Hope it helps

The standard deviation of the given random sample is approximately 0.351.

To find the standard deviation of a random sample, we need to calculate the standard deviation of the underlying distribution.

In this case, the distribution has a density function:

f(x) = x² + 2/3 (0 ≤ x ≤ 1)

To find the standard deviation, we first need to find the mean (μ) and variance (σ²) of the distribution.

The mean can be calculated as follows:

μ = ∫(x × f(x)) dx

where the integral is taken over the range [0, 1].

μ = ∫(x × (x² + 2/3)) dx

= ∫(x³ + 2/3 × x) dx

= (1/4 × x⁴ + 1/3 × x²) |[0, 1]

= (1/4 × 1⁴ + 1/3 × 1²) - (1/4 × 0⁴ + 1/3 × 0²)

= 1/4 + 1/3

= 7/12

Next, we calculate the variance (σ²):

σ² = ∫((x - μ)² × f(x)) dx

σ² = ∫((x - 7/12)² × (x² + 2/3)) dx

= ∫((x⁴ - 7/6 × x³ + 49/144 × x² - 7/36 × x + 49/432) dx

= (1/5 × x⁵ - 7/24 × x⁴ + 49/432 × x³ - 7/72 × x² + 49/432 × x) |[0, 1]

= 1/5 - 7/24 + 49/432 - 7/72 + 49/432

= 145/432

Now, we can calculate the standard deviation (σ) by taking the square root of the variance:

σ = √(145/432)

≈ 0.351

Therefore, the standard deviation of the given random sample is approximately 0.351.

Learn more about standard deviation click;

https://brainly.com/question/29115611

#SPJ1

pH = 5.28; Percent ionization = 0.0945%.

To determine the pH and percent ionization for a hydrocyanic acid (HCN) solution of concentration 5.5×10−3 M, we are given that the value of Ka for HCN is 4.9×10−10. We can use the formula of Ka to find the pH and percent ionization of the given hydrocyanic acid solution.

\(Ka = [H3O+][CN-]/[HCN]\)

\(Ka = [H3O+]^2/[HCN]\)

Since the concentration of CN- is equal to the concentration of H3O+ because one H+ ion is donated by HCN, we can take [H3O+] = [CN-]

\(Ka = [CN-][H3O+]/[HCN]\)

Substituting the values given in the question

\(Ka = x^2/[HCN]\)

where x is the concentration of H3O+ ions when the equilibrium is established.

Let the concentration of H3O+ be x. Thus, [CN-] = x

[\(Moles of HCN] = 5.5×10^-3 M\)

Volume of the solution is not given. However, it is safe to assume that the volume is 1 L since it is not mentioned otherwise.

Number of moles of HCN in 1 L of solution = \(5.5×10^-3 M × 1 L = 5.5×10^-3 moles\)

Now,

\(Ka = x^2/[HCN]\)

\(4.9×10^-10 = x^2/5.5×10^-3\)

\(x^2 = 4.9×10^-10 × 5.5×10^-3\)

\(x^2 = 2.695×10^-12\)

\(x = [H3O+] = √(2.695×10^-12) = 5.2×10^-6\)

\(pH = -log[H3O+]\)

\(pH = -log(5.2×10^-6)\)

pH = 5.28

Percent ionization = [H3O+]/[HCN] × 100

[H3O+] = 5.2×10^-6, [HCN] = 5.5×10^-3

Percent ionization =\((5.2×10^-6/5.5×10^-3) × 100\)

Percent ionization = 0.0945%

Answer: pH = 5.28; Percent ionization = 0.0945%.

Know more about percent ionization

https://brainly.com/question/1619653

#SPJ11

The pH of a hydrocyanic acid (HCN) solution with a concentration of 5.5×10^−3 M can be calculated to be approximately 2.06. The percent ionization of the HCN solution can be determined using the Ka value of 4.9×10^−10.

To calculate the pH of the HCN solution, we first need to determine the concentration of H+ ions in the solution. Since hydrocyanic acid (HCN) is a weak acid, it will undergo partial ionization in water. The concentration of H+ ions can be obtained by calculating the square root of the Ka value multiplied by the initial concentration of HCN.

[H+] = sqrt(Ka * [HCN])

[H+] = sqrt(4.9×10^−10 * 5.5×10^−3)

[H+] ≈ 2.35×10^−7 M

Using the concentration of H+ ions, we can calculate the pH of the solution by taking the negative logarithm (base 10) of the H+ ion concentration:

pH = -log[H+]

pH ≈ -log(2.35×10^−7)

pH ≈ 2.06

The percent ionization of the HCN solution can be determined by dividing the concentration of ionized H+ ions ([H+]) by the initial concentration of HCN and multiplying by 100:

Percent Ionization = ([H+] / [HCN]) * 100

Percent Ionization = (2.35×10^−7 / 5.5×10^−3) * 100

Percent Ionization ≈ 0.00427%

Therefore, the pH of the HCN solution is approximately 2.06, and the percent ionization is approximately 0.00427%.

To calculate the pH of the HCN solution, we first need to determine the concentration of H+ ions in the solution. Since hydrocyanic acid (HCN) is a weak acid, it will undergo partial ionization in water. The concentration of H+ ions can be obtained by calculating the square root of the Ka value multiplied by the initial concentration of HCN.

[H+] = sqrt(Ka * [HCN])

[H+] = sqrt(4.9×10^−10 * 5.5×10^−3)

[H+] ≈ 2.35×10^−7 M

Using the concentration of H+ ions, we can calculate the pH of the solution by taking the negative logarithm (base 10) of the H+ ion concentration:

pH = -log[H+]

pH ≈ -log(2.35×10^−7)

pH ≈ 2.06

The percent ionization of the HCN solution can be determined by dividing the concentration of ionized H+ ions ([H+]) by the initial concentration of HCN and multiplying by 100:

Percent Ionization = ([H+] / [HCN]) * 100

Percent Ionization = (2.35×10^−7 / 5.5×10^−3) * 100

Percent Ionization ≈ 0.00427%

Therefore, the pH of the HCN solution is approximately 2.06, and the percent ionization is approximately 0.00427%.

Know more about solution:

brainly.com/question/1619653

#SPJ11

Answer:

18.3 yards

Step-by-step explanation:

6 yards = 18 feet

1/3 yards = 0.3333...

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

4

Step-by-step explanation:

The number of 2/3's in 6 can be found by dividing 6 by 3 and then multiplying the result by 2. The answer is 4.

x - Ernie, y - Kaylin, z - Tria

x = y + 121.50

z = 3y - 35

x + y + z = 579

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

z = 3 y - 35      =>   - 3 y + z = -35

y + 121.50 + y + z = 579

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

- 3 y + z = - 35        / · ( -1 )

 2 y + z = 457.50     (we will use the elimination method) 

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

3 y - z = 35

2 y + z = 457.50

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

5 y = 492.5,            y = 492.5 : 5 = 98.5

z = 3 · 98.5 - 35

z = 260.5

Tria earned $260.5 

The correct statement regarding the rate of change of the functions is given as follows:

The amount of wood required has a constant rate of change, but the amount of glass does not.

The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.

For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.

For the glass function, we have that:

Hence the rate of change is not constant, and then the second statement is the correct statement.

The table is given by the image shown at the end of the answer.

More can be learned about the rate of change of a function at https://brainly.com/question/11627203

#SPJ1

Answer:

B & D

Step-by-step explanation:

You can use PEMDAS (exponets go first)

7x7x7x7x7x7=7^6 times 7=7^1

42

7^12=7x7x7x7x7x7x7=13841287201 divided by 7x7=49

13841287201/49=282475249

Answer:

$5000

Step-by-step explanation:

800/16=50

50*100=5000

Answer:

ΔABC ~ ΔDEF

Step-by-step explanation:

If the given triangles ΔABC and ΔDEF are similar,

Their corresponding sides will be proportional.

\(\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}\)

By substituting the measures of the given sides,

\(\frac{4}{2}=\frac{6}{3}=\frac{2}{1}\)

2 = 2 = 2

Since, corresponding sides of both the triangles are proportional, both the triangles will be similar.

ΔABC ~ ΔDEF

The height of water left in the cylindrical can is 9.9 cm.

Darius pours sparkling water from the can into the paper cup until it is completely full.

Therefore, the height of the water in the can can be calculated as follows:

volume of water in the cylindrical can = πr²h

volume of water in the cylindrical can = 4.6² × 13.5π

volume of water in the cylindrical can = 285.66π cm³

volume of the water the cone shaped paper can take = 1 / 3 πr²h

volume of the water the cone shaped paper can take = 1 / 3 × 5.1² × 8.7 × π

volume of the water the cone shaped paper can take = 75.429π

Therefore,

amount of water remaining in the cylindrical can = 285.66π - 75.429π = 210.231π

Therefore, let's find the height of the water as follows:

210.231π = πr²h

r²h =  210.231

h = 210.231 / 21.16

h = 9.93530245747

h = 9.9 cm

Therefore,

height of the water in the can = 9.9 cm

learn more on height here: https://brainly.com/question/27209837

#SPJ1

Therefore, The solution of the given initial value problem is;y(t) = 5.9334h(t) - 2.0666h(t - 2π) + 8e'cost + 10e'sint.

The given initial value problem is;

8(1) +2y-g(r), y(0)-8,

y (0) - 2 #≤1<2n - 16 0,

0≤1<1>2m  y(t) = unh(tr)- u₂h(t - 2n) + 8e cost + 10e sint 1

where

h(t) = - -(e-¹cost cost + e-'sint)

The given initial value problem is solved as follows:The equation in the given initial value problem is;

y(t) = unh(tr)- u₂h(t - 2n) + 8e cost + 10e sint

where

h(t) = - -(e-¹cost cost + e-'sint)

The corresponding characteristic equation is obtained as;

r = u1(u - h(π)) - u2(u - h(2π))

Therefore;

r = u1(1 - e-ir) - u2(1 - e-2ir)

r = u1 - u1e-ir - u2 + u2e-2iru1 - u2

= r(1 - e-ir) + u2(1 - e-2ir)

Since; y(0) = 8, we can solve for u1 and u2 using the given equation.The values of u1 and u2 are obtained as;

u1 = 5.9334 and u2 = 2.0666

The solution to the initial value problem is thus;

y(t) = 5.9334h(t) - 2.0666h(t - 2π) + 8e'cost + 10e'sint

Therefore, The solution of the given initial value problem is;y(t) = 5.9334h(t) - 2.0666h(t - 2π) + 8e'cost + 10e'sint.

To know more about equations visit:

https://brainly.com/question/22688504

#SPJ11

The required Answer that will help in the selection of the correct option from the given statement is True.

A string builder is considered a class in JAVA API where it provides the mutual sequence of characteristics. It is used for the requirement of dynamic string manipulation. Using it to form new characters in an existing string.

In comparison with string, the following points help in differentiating the ability, function, and purpose of their creation,

To learn more about string builder,

https://brainly.com/question/12905682

#SPJ4

Answer:

9.5

Step-by-step explanation:

Note the place values:

9 ones place value

.

5 tenths place value

2 hundredths place value.

You are solving for the nearest tenths. To solve, look at the place value directly next (the hundredths place value). If the value of the number is 5 or greater, round up. If it is 4 or less round down.

In this case, it is 2, so you will round down.

9.52 rounded to the nearest tenths is 9.5

~

Answer:

9.5

Step-by-step explanation:

I used Rounding Numbers calculator on calculator soup.

The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using set builder notation, the domain of this function shown in the graph above can be written as follows;

Domain = {-4, ∞}

Domain = {x|x ≥ -4}

Read more on domain here: brainly.com/question/17812730

#SPJ1