The total surface area of a cube is 294 cm².
Work out the volume of the cube.
Optional working
Answer
7/45
cm³
+

To find the lower quartile of a set of numbers, we need to determine the value that separates the lowest 25% of the data from the rest. In the given set of numbers, the lower quartile can be found by arranging the data in ascending order and identifying the value at the 25th percentile.

First, let's arrange the data in ascending order: 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100.

To find the lower quartile, we need to determine the position of the 25th percentile. Since there are 23 data points, the 25th percentile corresponds to the value at the (25/100) * 23 = 5.75th position.

Since the position is not a whole number, we need to find the value between the fifth and sixth data points. The fifth data point is 7, and the sixth data point is also 7. Therefore, the lower quartile is 7.

The lower quartile represents the value below which 25% of the data lies. In this case, 25% of the data points are less than or equal to 7. It indicates that a quarter of the values in the dataset are smaller than or equal to 7, while the remaining 75% are larger.

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a) the distance in picometers is 135 pm. b) the distance in picometers is 135 pm. c) The answer is 7.0 × 10^4 atoms. d) The volume of a single gold atom is 9.15 × 10^(-24) cm^3.

Part A:

1.35 Å = 0.135 nm (since 1 Å = 0.1 nm)

Therefore, the distance in nanometers is 0.135 nm.

Part B:

1.35 Å = 135 pm (since 1 Å = 100 pm)

Therefore, the distance in picometers is 135 pm.

Part C:

The length of one gold atom is 1.35 Å = 1.35 × 10^(-10) m.

The number of atoms required to span a distance of 9.5 mm = (9.5 × 10^(-3) m) / (1.35 × 10^(-10) m) = 70,370 atoms.

Rounding to two significant figures, the answer is 7.0 × 10^4 atoms.

Part D:

Assuming the gold atom is a sphere, its volume can be calculated as:

V = (4/3)πr^3, where r is the radius of the atom.

Substituting the value of the radius (1.35 Å = 1.35 × 10^(-10) m) gives:

V = (4/3)π(1.35 × 10^(-10))^3 = 9.15 × 10^(-30) m^3.

Expressing this in cubic centimeters gives:

V = 9.15 × 10^(-30) × 10^6 = 9.15 × 10^(-24) cm^3.

Therefore, the volume of a single gold atom is 9.15 × 10^(-24) cm^3.

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Formula Used:-

[tex] \qquad \hookrightarrow{ \underline{ \overline{ \boxed{ \sf{Surface \: Area =3\pi {r}^{2} }}}}}\\[/tex]

[tex] \sf \longrightarrow \: Surface \: Area =3\pi {r}^{2} \: ) \\ [/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times {r}^{2} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times {11}^{2} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times 11 \times 11 \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{3 \times 22 \times 11 \times 11}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{66 \times 11 \times 11}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{66 \times 121}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{7986}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = 1140.8 \: {ft}^{2} \: \\[/tex]

______________________________________________

Therefore, Surface Area of Hemisphere is 1140.8 ft²

Answer:

Step-by-step explanation:

We know that,

[tex]\large {\boxed {\boxed{\bf\leadsto \: surface \: area \: of \: hemisphere \: = 3\pi {r}^{2} }}}[/tex]

Here,

Now

[tex]\large \sf\leadsto3 \times \frac{22}{7} \times 11 {}^{2} [/tex]

[tex]\large \sf\leadsto3 \times \frac{22}{7} \times 121[/tex]

[tex]\large \sf\leadsto \: \frac{66}{7} \times 121[/tex]

[tex]\large \sf\leadsto \frac{7986}{7} [/tex]

[tex] \boxed{\large \bf\leadsto1140.8 \: {ft}^{2} }[/tex]

The type of analysis described in the statement is ratio analysis.

Ratio analysis is a tool used to evaluate the financial performance of a company by comparing different financial ratios over time or between companies. It involves calculating different ratios such as liquidity ratios, profitability ratios, and solvency ratios and comparing them across different periods to identify trends or patterns in the data. The ratio analysis formula mentioned in the statement is used to calculate the percentage change in a ratio between two periods, with the base period amount serving as the denominator.

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first, you distribute, so

4a ([tex]a^{2}[/tex]+7a+4)

[tex]4a^{3}[/tex]+28[tex]a^{2}[/tex]+16a

and that's your answer! :)

thanks in advance for brainliest!!

4a(a^2+7a+4) can be simplified by multiplying 4a to each term inside the parenthesis:

4a(a^2+7a+4) = 4a * a^2 + 4a * 7a + 4a * 4

This gives us:

4a^3 + 28a^2 + 16a

Therefore, 4a(a^2+7a+4) simplifies to 4a^3 + 28a^2 + 16a.

Answer:

We have congruent alternate interior angles.

39° + 96° + x° = 180°

135° + x° = 180°

x = 45

The simplification of the given terms is 14.25 or 114/8

A numerical expression is a piece of algebraic information stated in the form of numbers and variables that are unknown.

We are given that 6 times 2 wholes 3/8

Let the number be x

So,6 times 2 wholes 3/8 means;

x = 6 x 2 3/8

x = 6 x 19/8

x = 14.25 or 114/8

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Answer: t=1

Final Answer=$1,020

t=1/2

Final Answer=$1,009.95

Step-by-step explanation: This is correct

its cammy, im telling that your cheating (and i definitely wasnt looking up this same question)

Answer:

Step-by-step explanation:

The formula for this is:

V = (1/2) x b x h x l

b= base

h=height

l=length

V= (1/2) x 4.2 x 2.8 x 8

so...I think the volume could be 47.04m^3?

PRO TIP: If you want to solve anything with volume, just write down every single formula they have for volume or area. It is good to memorize formulas like that.

The volume of the triangular prism with a height of 2.8, width of 4.2, and a length of 8 is 46.96 cubic unit.

The base area of the triangular cross-section must be multiplied by the prism's height to determine its volume. The triangle cross-section in this instance has a base of 4.2 and a height of 8.

The following is the formula to determine a triangle's area:

(Base * Height) / 2 = Area

When the values are plugged in, we get:

Base = 4.2

Size = 8

Area = (4.2 * 8) / 2 = 33.6 / 2 = 16.8

Next, increase the prism's base area by its height:

Volume = Base Area * Height = 16.8*2.8 = 46.96

The triangular prism therefore has a 46.96 cubic unit volume.

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The amount of the loan Cher took out to buy the motorcycle is $9839.

Here, we have,

To find the amount of the loan, we need to calculate Cher's total assets and then subtract her total liabilities (debts).

Given:

Value of motorcycle = $11,357

Cash = $605

Savings account = $1,811

Net worth =$3,934

Total assets = Value of motorcycle + Cash + Savings account

Total assets = $11,357 + $605 + $1,811

Total assets = $13,773

To find the amount of the loan, we subtract the total assets from the net worth:

Loan amount = Total assets - Net worth

Loan amount = $13,773 -$3,934

Loan amount = $9839

Hence, The amount of the loan Cher took out to buy the motorcycle is $9839.

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Answer:

-x² + 5x - 1

Step-by-step explanation:

separate the x², the x, and the constants (numbers without any x).

3x² - 4x² = -x²

2x - -3x = 2x + 3x = 5x

-5 - -4 = -5 + 4 = -1.

we have -x² + 5x - 1

Alang can buy at most 10 hamburgers if he buys 15 drinks.

Let's say Alang buys x hamburgers. Then, he must buy (18 - x) drinks to meet the requirement of buying a minimum of 18 hamburgers and drinks altogether.

The cost of x hamburgers is 7.5x dollars.

The cost of (18 - x) drinks is 2.5(18 - x) = 45 - 2.5x dollars.

The total cost must be less than or equal to $95:

7.5x + (45 - 2.5x) ≤ 95

Simplifying and solving for x, we get:

5x ≤ 50

x ≤ 10

So Alang can buy at most 10 hamburgers if he buys 15 drinks.

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The 95% confidence interval for the proportion of people who prefer Candidate A is  0.8 ± 0.080.

Confidence Interval = Sample Proportion ± Margin of Error

We first determine the values for each term:

Sample Proportion = Number  / Total sample size

Sample Proportion = 68/85

Sample Proportion  = 0.8

Standard Error = √((Sample Proportion  * (1 -Sample Proportion )) / n)

n =  sample size

Standard Error = √((0.8 * (1 - 0.8)) / 85)

Standard Error = 0.041

We then calculate the Margin of Error = Critical Value * Standard Error Margin of Error = 1.96 * 0.041

Margin of Error = 0.080

We substitute all these values and calculate for :
Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.8 ± 0.080

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Answer:

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

Use a combination formula.

We want to select 2 pennies from a set of 6 and 2 dimes from a set of 8.

The number of ways to do this is:

Therefore, there are 420 possible sets of 4 coins that contain 2 pennies and 2 dimes.

To find the length of the curve y = ln(cos(x)) from 0 to π/3, we can use the arc length formula for a curve defined by a function y = f(x):

L = ∫[a to b] √(1 + (f'(x))²) dx.

In this case, the function is y = ln(cos(x)). Let's first find the derivative:

y' = d/dx ln(cos(x)).

Using the chain rule, we have:

y' = -tan(x).

Now we can calculate the arc length:

L = ∫[0 to π/3] √(1 + (-tan(x))²) dx.

Simplifying the integrand, we have:

L = ∫[0 to π/3] √(1 + tan²(x)) dx.

Using the trigonometric identity tan²(x) + 1 = sec²(x), we can rewrite the integrand as:

L = ∫[0 to π/3] √(sec²(x)) dx.

Taking the square root of sec²(x), we have:

L = ∫[0 to π/3] sec(x) dx.

Integrating sec(x), we get:

L = ln|sec(x) + tan(x)| [0 to π/3].

Evaluating the integral at the upper and lower limits, we have:

L = ln|sec(π/3) + tan(π/3)| - ln|sec(0) + tan(0)|.

Simplifying further, we have:

L = ln|2 + √3| - ln|1 + 0|.

Since ln|1| = 0, the second term on the right-hand side becomes 0, and we are left with:

L = ln|2 + √3|.

Therefore, the length of the curve y = ln(cos(x)) from 0 to π/3 is ln|2 + √3|.

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The only True statement is B: If −2/5r = −20, then r = −50

We can solve each equation to determine which statement is true.

A. If 4/3h = 12, then h = 16.

To solve for h, we can multiply both sides of the equation by 3/4:

4/3h * 3/4 = 12 * 3/4

h = 9

Therefore, statement A is false.

B. If −2/5r = −20, then r = −50.

To solve for r, we can multiply both sides of the equation by -5/2:

-2/5r * -5/2 = -20 * -5/2

r = 50

Therefore, statement B is true.

C. If 1/2 = −3/7q, then q = −116.

To solve for q, we can multiply both sides of the equation by -7/3:

1/2 * -7/3 = -3/7q * -7/3

q = 21/3 = 7

Therefore, statement C is false.

D. If 3/8 = 24c, then c = 9.

To solve for c, we can divide both sides of the equation by 24 * 8/3:

3/8 * 3/24 * 8/3 = 24c * 3/24 * 8/3

c = 1/3 * 8

c = 8/3

Therefore, statement D is false.

Therefore, the only true statement is B: If −2/5r = −20, then r = −50.

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The volume of the box decreases as the cutout length increases over the interval (0, 3.5/2) and increases over the interval (3.5/2, infinity).

Let the dimensions of the rectangular box be x, y, and z. The volume of the box is given by V = xyz. Suppose that the cutout length is along the x-axis, and let it be denoted by w. Then, we have:

V = (x - w)yz

Taking the derivative of V with respect to w, we get:

dV/dw = -yz

The volume of the box will decrease as the cutout length increases if dV/dw < 0, and it will increase if dV/dw > 0. Since y and z are positive, dV/dw will be negative if w is less than x/2 and positive if w is greater than x/2. Therefore, the volume of the box decreases as the cutout length increases over the interval (0, x/2) and increases over the interval (x/2, infinity).

In our case, the largest possible cutout length is 3.5 inches, so the interval over which the volume of the box decreases as the cutout length gets larger is (0, 3.5/2), which is (0, 1.75). The interval over which the volume of the box increases is (3.5/2, infinity), which is (1.75, infinity).

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Doris needs to complete a total of 30 hours of continuing education to renew her real estate license for the first time. As she has already completed 20.5 hours of CE, she needs to complete an additional 9.5 hours of CE.

It's important to note that continuing education requirements vary by state and licensing board, so it's always a good idea to check with the relevant authorities to ensure you meet all the requirements for license renewal. Real estate agents are typically required to complete a certain number of continuing education hours within a specific time frame in order to maintain their license and stay up-to-date with industry developments and best practices. This is important to ensure they are equipped with the necessary knowledge and skills to provide quality services to their clients.
In summary, Doris needs to complete an additional 9.5 hours of CE to meet the 30-hour requirement for renewing her real estate license for the first time.

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Answer:

B

Step-by-step explanation:

203.95 is equal to 4 of the tickets plus 11.95

You can write this as

203.95=4(price of ticket)+11.95

4(price of ticket)=192

Divide by 4

The price of a ticket is 48.

The equation would be 11.95+48t because its 48 times the amount of ticket plus the service fee.

The weight of the melted ice cream would be the same as the weight of the original ice cream, which is 5 ounces.

a quantity or thing weighing a fixed and usually specified amount. : a heavy object (such as a metal ball) thrown, put, or lifted as an athletic exercise or contest. 3. : a unit of weight or mass see Metric System Table.

When the ice cream melts, it undergoes a change in state from solid to liquid, but the total mass or weight remains unchanged. Therefore, the weight of the melted ice cream is still 5 ounces.

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To divide (a-3/7) by (3-a/21), we need to multiply the numerator by the reciprocal of the denominator.

Reciprocal of (3-a/21) is (21/(3-a))

So,

(a-3/7) / (3-a/21) = (a-3/7) * (21/(3-a))

Now, we can simplify by canceling out common factors between the numerator and denominator.

(a-3/7) * (21/(3-a)) = (3-a)(a-3)/(7*21)

= -(a^2 - 6a + 9)/147

= -(a-3)^2/147

Therefore, the quotient is -(a-3)^2/147.

The formula A = πrl represents the curved surface area of a cone, where r is the radius of the base of the cone and l is the slant height.

The curved surface area of a cone is the area of the lateral or side surface of the cone. It is called curved because the surface of the cone is not flat but rather curved, like the surface of a curved cylinder. To derive this formula, we can first imagine a cone with a base that has a circumference of 2πr, where r is the radius of the base. If we cut along a generator line of the cone, we can then unroll the curved surface of the cone to form a sector of a circle with radius l and central angle 2π. The area of this sector is πl^2, which represents the total area of the curved surface of the cone. We can simplify this formula to A = πrl by substituting the value of l with the Pythagorean theorem, l^2 = r^2 + h^2, where h is the height of the cone.

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To find the number of vinyl tiles needed to tile a kitchen measuring 24 ft. by 18 ft. with tiles measuring 8 in. each side, we need to convert all measurements to the same units.

First, we need to convert the kitchen measurements from feet to inches:

- 24 ft. = 24 x 12 = 288 in.
- 18 ft. = 18 x 12 = 216 in.

Next, we need to divide the length and width of the kitchen by the length of each tile to find the number of tiles needed in each direction:

- Length: 288 in. ÷ 8 in. = 36 tiles
- Width: 216 in. ÷ 8 in. = 27 tiles

Finally, we multiply the number of tiles needed in each direction to find the total number of tiles needed:

- Total tiles: 36 tiles x 27 tiles = 972 tiles



To tile a kitchen, it is important to accurately calculate the number of tiles needed to ensure that there is enough material to complete the job. In this case, we converted all measurements to the same units and then used division and multiplication to find the total number of tiles needed.



To tile a kitchen measuring 24 ft. by 18 ft. with vinyl tiles measuring 8 in. each side, we need a total of 972 tiles.

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If circumference of circle is 8 units then the radius of circle is 1.27 units

The circumference of the circle is 8 units.

We have to find the radius of the circle.

The formula for circumference of cirlce is two times of pi and radius.

Circumference = 2πr.

Where r is the radius of the circle.

The value of radius we have to find.

The circumference is 8 units.

Plug in the values of circumference to find r:

8=2×3.14 r

When 2 is multiplied with three point one four we get six point two eight.

8=6.28 r

Divide both sides by 6.28:

r = 8/6.28

When eight is divided by six point two eight we get one point two seven.

r=1.27 units

Hence,  the radius of circle is 1.27 units when circumference is 8 units.

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Complete question

If circumference of circle is 8 units then find the radius of circle?

what do u need help with

The equation of the red graph, g(x) is g(x) = (x + 3)² - 4

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

The functions f(x) and g(x)

In the graph, we can see that

This means that

g(x) = f(x + 3) - 4

Recall that

f(x) = x²

This means that

g(x) = (x + 3)² - 4

This means that the equation of the red graph is g(x) = (x + 3)² - 4

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Hello !

c = the cost

n boxes = 66,12n

c = 66,12n

By using Algebraic methods It will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

The equation is y = -16t^2 + 400, where y represents the height of the rock in feet and t represents the time in seconds.
To find out how many seconds it will take for the rock to hit the ground, we need to set the equation equal to zero because the ground is at a height of zero.
0 = -16t^2 + 400
Now, we can solve for t using  Algebraic methods.
First, we can subtract 400 from both sides of the equation:
-400 = -16t^2
Next, we can divide both sides by -16:
25 = t^2
Finally, we can take the square root of both sides:
t = ±5
Since we can't have negative time, we know that it will take 5 seconds for the rock to hit the ground.
So, to summarize, it will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

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The volume of the composite shaped solid is V = 26,133.33 cm³

Given data ,

To calculate the volume of the composite solid consisting of a cube and a square-based pyramid

Volume of a cube = (edge length)³

V ( cube ) = ( 28 )³

V ( cube ) = 21,952 cm³

Now , The volume of a pyramid is given by the formula:

Volume of a pyramid = (base area * height) / 3

Base area = ( 28 )²

Base area = 784 cm²

Now , V ( pyramid ) = ( 784 x 16 ) / 3

V ( pyramid ) = 4,181.33 cm³

So , volume of composite solid = 21,952 cm³ + 4,181.33 cm³

V = 26,133.33 cm³

Hence , the volume is V = 26,133.33 cm³

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The value of the constants a and b is 2 and -32 respectively.

The complete factorization of the polynomial is (x - 3)(x + 5) (2x - 1).

The value of the constants is calculated as follows;

P(r) = ax³ + 3x² + bx + 15

If x - 1 is factor with a remainder of -12, then x = 1

P(1) = a1³  +  3(1²) + b(1) + 15 = -12

a + 3 + b + 15 = -12

a + b = -30

b = -30 - a

also, if x - 2 is a factor with a remainder of -21, then x = 2;

P(2) = a(2)³  +  3(2²) + b(2) + 15 = -21

8a + 12 + 2b + 15 = -21

8a + 2b = -48

4a + b = - 24

Substitute the value of b into the equation;

4a - 30 - a = - 24

3a = 6

a = 2

b = -30 - a

b = -30 - 2

b = -32

The quadratic equation will become;

P(r) = 2x³ + 3x² -32x + 15

We will factorize the equation as follows;

x - 3 is a factor;

           2x²  + 9x - 5

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

x - 3 √ (2x³ + 3x² -32x + 15)

          - (2x³ - 6x²)

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

                    9x² - 32x + 15

                  - (9x² - 27x )

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

                             -5x + 15

                           - ( -5x + 15)

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

                                     0

We will factorize  2x²  + 9x - 5

= 2x² - x + 10x - 5

= x(2x - 1) + 5(2x - 1)

= (x + 5)(2x - 1)

The complete factor = (x - 3)(x + 5) (2x - 1)

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