The volume of the triangular pyramid below is 240 units. Find the value of a.
Answer: =
12
Submit Answer
15
مومی مرده

Answer:

A. Distance KL = 7.36 m

B. Height ML = 4.25 m

C. The maximum height is 6.96 m

Step-by-step explanation:

A. Determination of distance KL

Hypothenus = KM = 8.5 m

Angle θ = 30°

Adjacent = KL =?

Cos θ = Adjacent / Hypothenus

Cos 30 = KL / 8.5

0.866 = KL / 8.5

Cross multiply

KL = 0.866 × 8.5

KL = 7.36 m

Thus, the distance is 7.36 m

B. Determination of height (ML)

Hypothenus = KM = 8.5 m

Angle θ = 30°

Opposite = ML =?

Sine θ = Opposite /Hypothenus

Sine 30 = ML /8.5

0.5 = ML / 8.5

Cross multiply

ML = 0.5 × 8.5

ML = 4.25 m

Thus, the height is 4.25 m

C. Determination of the maximum height.

Hypothenus = KM = 8.5 m

Angle θ = 55°

Opposite = ML =?

Sine θ = Opposite /Hypothenus

Sine 55 = ML /8.5

0.8192 = ML / 8.5

Cross multiply

ML = 0.8192 × 8.5

ML = 6.96 m

Thus, the maximum height is 6.96 m

Answer:

A. \(n=100\)
B. \(k=0\)

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

Answer:

-4m+10

Step-by-step explanation:

Answer:

-4m+10

explanation:

6m-10=-4m

+10

-4m+10

As described in the algebra the balancing amount is - 1.8375

what is algebra?

Mathematics has several different subfields, including algebra. Algebra, broadly stated, is the study of mathematical symbols and the guidelines for using these symbols in formulas.

Solution;

Balance of account = account amount - account used

                                = 1.10 - 0.25 * ( 47/2)

                                = 1.10 - 0.25* 11.75

                                = 1.10 - 2.9375

Balance of account = - 1.8375

Hence, by algebra the balancing amount of account is - 1.8375

To learn more about Algebra from the given link

https://brainly.com/question/6143254

#SPJ9

The lines of best fit show the relationship between the hours spent on texting and exercising.

(a) The equation of line of best fit

From the graph (see attachment), we have the following points:

\(\mathbf{(x,y) = (5,5),\ (2,7.2)}\)

The slope of the line is:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m = \frac{7.2-5}{2-5}}\)

\(\mathbf{m = \frac{2.2}{-3}}\)

\(\mathbf{m = -0.73}\)

The equation is then calculated as:

\(\mathbf{y = m(x - x_1) + y_1}\)

This gives:

\(\mathbf{y = -0.73(x - 5) + 5}\)

\(\mathbf{y = -0.73x + 3.65 + 5}\)

\(\mathbf{y = -0.73x + 8.65 }\)

Hence, the equation of the line of best fit is \(\mathbf{y = -0.73x + 8.65 }\)

(b) The time spent exercising for a student who spends 6 hours texting

This means that x = 6.

So, we have:

\(\mathbf{y = -0.73 \times 6 + 8.65 }\)

\(\mathbf{y = -4.38 + 8.65 }\)

\(\mathbf{y = 4.27 }\)

Hence, the time spent exercising for a student who spends 6 hours texting is 4.27 hours

Read more about lines of best fit at:

https://brainly.com/question/14279419

Answer:

A

Step-by-step explanation:

Answer:

23 m, South

Step-by-step explanation: He traveled 25 m north then he went 48 m south so that means you would have to subtract 25 from 48 to get 23 m, south

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

Answer:

Step-by-step explanation:

The nomebers are equivalent (true)

opposites. (true)

produt 1 (false)

a positive value (false)

last on don't now but I think it's (false)

The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

Learn more about Stocks here :

https://brainly.com/question/14270259

#SPJ1

Answer:

The average population growth per year is 102.

Step-by-step explanation:

From the given data, we can find the slope which will give us the average rate of change. Our points are:

\((2003, 903)\quad and \quad (2007, 1311)\)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{1311-903}{2007-2003}\\\\m=102\)

Best Regards!

Answer: 42in

Step-by-step explanation: 7in times 6 sides= 42 in

The probability that exactly 3 of those games were won by the colonies is 25%.

We are given that;

Number of colonies= 4

Number of games= 3

Now,

To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:

P(X = 3) = nCx * p^x * q^(n-x)

where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.

P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25

Therefore, by the probability the answer will be 25%.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ1

Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2

Answer:

C=−Ax−By

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The circumference of the pizza is approximately 28.27 inches.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the pizza is 9 inches.

Substituting this value in the formula, we get:

C = πd

C = π(9)

C ≈ 28.27

Therefore,

The circumference of the pizza is approximately 28.27 inches.

Learn more about Circle here:

https://brainly.com/question/11833983

#SPJ2

The value of C in the table will be 24.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, a table of proportional data below,

Part      8    B    D

Part     10   15   45

Whole  A    C    72

Since the two-part will be proportional to the whole.

thus,

=> c /72 = 15/45

=> C = 72/3

=> C = 24

Therefore, the value of C  in the given table will be 24 as pe the proportionality.

Learn more about proportionalities here:

https://brainly.com/question/3254974

#SPJ1

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

Learn more on equation of a line here: https://brainly.com/question/13763238

#SPJ1

Answer:

The check digits

a) x₁₂ ≡ 5( mod 10 )

b) x₁₂ ≡ 2( mod 10 )

c)  x₁₂ ≡ 0( mod 10 )

d)  x₁₂ ≡ 3( mod 10 )

Step-by-step explanation:

Given the data in the question;

We know that the formula for determining the UPCs check is;

3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )

now we will substitute the given values to determine the value of the last bit

a)

73232184434

we substitute into the formula

3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )

                                                                                          x₁₂ ≡ 5( mod 10 )

b)

63623991346

we substitute into the formula

3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂ ≡ 2( mod 10 )

c)

04587320720

we substitute into the formula

3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂  ≡ 0( mod 10 )

d)

93764323341

we substitute into the formula

3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )

                                                                                         x₁₂ ≡ 3( mod 10 )

The series of rigid motion transformations that map polygon A to Polygon A''' are;

A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.

The series of rigid motion transformations that map polygon A to polygon A''' are;

Transformation from A to A'

Transformation from A' to A''

Transformation from A'' to A'''

Learn more about rigid transformations in geometry here:

https://brainly.com/question/2222755

#SPJ1

Sample answer from Edmentum

Answer:

D = (9.6,0). AC is horizontal with y=0 at all points on AC. Also, because BD is an altitude, it forms a right angle with AC, so BD is a vertical line. For all points on BD, x= 9.6.

Hope this helps, have a good day (:

Answer:

i have no idea

Step-by-step explanation:

Answer:

Its the second choice

Step-by-step explanation:

Step-by-step explanation:

yf.bfz

vcg ,kgu nkkgfgvvxvh

The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

To know more about hypotenuse:

https://brainly.com/question/12006293

#SPJ1

∠A = 41.81°

To get measure of angle A, we would apply trigonometry ratio SOHCAHTOA:

opposite = side opposite the angle = 4

hypotenuse = 6

adjacent = base = AC = ?

Since we have been given the opposite and the hypotenuse, we would use the sine ratio:

Sin A = opposite/hypotenuse

Sin A = 4/6

sin A = 0.6667

A = 41.8129 degrees

To the nearest hundredth, ∠A = 41.81°

3 has a mean of 120 and a standard deviation of 3.

Describe standard deviation using an example?

The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

                                The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.

mean of sample means = true mean = 120

std dev of sample mean = true std / sqrt(n)

                                     = 15/5 = 3

Learn more about standard deviation

brainly.com/question/23907081

#SPJ4