A Triangular Prism with equilateral triangle faces has Volume of 84cm³ and a Length of 12cm. Find the base area of this prism.

Got this on my test, don't know how to do it lol.

Answer:

$44

Step-by-step explanation:

What we know:

$5.50 = 1 hour

average day's work = 8 hours

Question:  How much money for eight hours?

To figure this out, 5.50 and multiply it by 8.

This gives us 44.

So, Michaela makes $44 dollars in an average eight-hour day.

17 students played cricket more than basketball.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

Pie chart showing the preference of the students is given below.

Total number of students = 300

We know that total degree of the circle = 360°

Students who played cricket = 90°

Number of students who played cricket will be (90° / 360°)th of 300.

Number of students who played cricket = (90° / 360°) × 300

                                                                   = 75

Students who played basketball = 70°

Number of students who played basketball = (70° / 360°) × 300

                                                                         = 58.33 ≈ 58

Students played cricket - Students played basketball = 75 - 58 = 17

Hence there are 17 students more in cricket than that in basketball.

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Answer:

Below

Step-by-step explanation:

Pick any two points on the graph   say  2,70   and  3 , 105

  rise is   70 to 105 = 35     run is   2 to3 = 1

     rise/run = 35/1 = 35

Answer:

35

Step-by-step explanation:

gradient= rise/run

= 70-35/2-1

= 35

The amount of time it takes for E to increase by 10%. it takes 4.81 seconds.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given that,

Let the amount of time it takes for E to increase by 10% be x.

Thus, after (t + x) seconds, E is increased by 10%.

E(t + x) = E(t) + 10% of E(t)

= E(t) + 10/100 E(t)

= E(t) + 0.1 E(t)

E(t + x) / E(t) = 1.1

As,

[tex]E(t) = 6(1.02)^t\\\\E(t + x) = 6(1.02)^{t + x}\\\\\frac{E(t + x)}{E(t)} = \frac{6(1.02)^{t + x}}{6(1.02)^{t}}\\\\\frac{E(t + x)}{E(t)} = (1.02)^{t + x - t}\\\\(1.02)^x = 1.1[/tex]

Taking log on both sides:

x = log (1.1) / log (1.02)

x = 4.81 seconds.

Hence, the amount of time it takes for E to increase by 10%.

it takes 4.81 seconds.

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Answer:

see explanation

Step-by-step explanation:

W(2) = 5 , means

a puppy of 2 months has a weight of 5 pounds.

W(6) > W(4) , means

a puppy at 6 months has a greater weight than a puppy of 4 months

W(12) = W(15) , means

a puppy at 12 months is the same weight as a puppy of 15 months

The expectation values are <x> = 1.25 x 10⁻¹⁰ ,  <x²>  =  2.07 x 10⁻²⁰

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

We need to find expectation value of <x> and < x²>

average value for <x>   is given by a/2   where a = length of box

hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰

hence <x²> = (1.25 x 10⁻¹⁰)²  = 1.56 x 10⁻²⁰

<x²> = ( a/2 x 3.14 x n)²   x ( 4 x 3.14² x n² /3  -2)

hence <x²>  = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)²   x ( 4 x 3.14² x 5² /3  -2)

  <x²>  =  2.07 x 10⁻²⁰

<x²>  is not equal to <x>²

The expectation values are <x> = 1.25 x 10⁻¹⁰,  <x²>  =  2.07 x 10⁻²⁰

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Answer:

100 liters is equal to 100,000 milliliters.

Step-by-step explanation:

(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Here,

An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.

The distance between two complex numbers a + bi and c + di can be found using the formula:

√((c - a)² + (d - b)²)

So, the distance between 3-2i and 6-i is:

√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10

And the distance between 3-2i and c is:

√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)

Since these distances must be equal, we have:

√((c - 3)² + (c + 2)²) = √10

Squaring both sides:

(c - 3)² + (c + 2)² = 10

Expanding both sides:

c² - 6c + 9 + c² + 4c + 4 = 10

Combining like terms:

2c² + 10c + 5 = 10

Subtracting 10 from both sides:

2c² + 10c - 5 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

c = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 10, and c = -5. Plugging these values into the formula:

c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2

c = (-10 ± √(100 + 40)) / 4

c = (-10 ± √(140)) / 4

c = (-10 ± 10√2) / 4

So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.

The product of these two solutions is:

c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)

= (100 - 100√2 + 100) / 16

= (200 - 100√2) / 16

(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.

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Answer:

if marip has a piece of string. He cuts off six-eights of it's length. how much is left it's 2

x = (300 - p) / 20

According to the equation, the quantity of kilos (x) of snig that will be sold is equal to the difference between 300 and p, divided by 20.

The price-demand connection for roast snig at the harvest festival on the planet Bozone can be represented by the equation p=300 - 20x. The formula specifies that 300 minus 20 times the number of kilogrammes (x) of snig sold is the price per kilogramme of snig (p) in the local currency (Bozats).

Using this equation, one can determine how much of the price must be reduced in order to sell 1 extra kilogramme of snig. The equation can be rewritten to solve for x in terms of p in order to accomplish this. This can be done by taking 300 off of both sides of the equation, multiplying both sides by 20, and then solving for x = (300 - p) / 20. This rearrangement has the effect of dividing the number of kilogrammes of snig that will be sold in terms of price per kilogramme by the difference between 300 and p. This equation can be used to calculate the price reduction required to sell an extra kilogramme of snig.

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Answer:

53/63

Step-by-step explanation:

It is already in simplest form

Answer:

61

Step-by-step explanation:

√(2+3)^2+(2+4)^2

=√5^2+6^2

=√25+36

=√61

So the number is 61

The equations Ax = b are not compatible.

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.

If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.

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To find the instantaneous speed of an object, we must make the time interval very small, so that the speed does not change appreciably.

How to find the speed?

Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction.

To find the instantaneous speed of an object, we must make the time interval very short, so that the speed does not change appreciably. The formula for the instantaneous speed of an object is given by the limit as time approaches zero of the change in distance divided by the time over which that change occurs. The formula for average speed is simply the total distance traveled divided by the total time elapsed.

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The probability of having a 4 in a 30 roll is 5 times

The expected value, μ, of rolling a 4 on a fair number cube (with faces numbered 1 to 6) can be found by using the formula μ = np, where n is the number of trials (30 in this case) and p is the probability of success for an individual trial (rolling a 4).

The probability of rolling a 4 on a fair number cube is 1/6. Therefore, the expected value of rolling a 4 30 times can be calculated as follows:

μ = 30 * (1/6) = 5

So, Mr. Jackson can expect to roll a 4 approximately 5 times in 30 rolls of his number cube.

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Answer: 154.28 feet

Step-by-step explanation:

The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

[tex]\rm P=P_o \times e^{rt}[/tex]

The initital amount is $15,000 and the interest rate is 4.75% annually.

A. If the interest is compounded quarterly. Then the amount is given as,

[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]

A = $15,000 x 1.1319

A = $16,979.44

B. if the interest is compounded continuously. Then the amount is given as,

[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]

A = $15,000 x 1.1808

A = $17,713.02

C. The difference in the amount of interest earned is given as,

Differenece = $17,713.02 - $16,979.44

Differenece = $733.58

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The probability that daily production is between 28 and 45.9 liters is 0.024.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Given that, x₁=28, x₂=45.9, μ=38 and σ =4.3

We know that, Z=(x-μ)/σ

Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample

z =(38-28)/4.3= 2.32 and probability on the z-table is 0.9896

z = (38-45.9)/4.3 = -1.83 and probability on the z-table is 0.9656,  

Now, P(2.32<z<-1.83) = 0.9896-0.9656

= 0.024

Therefore, the probability that daily production is between 28 and 45.9 liters is 0.024.

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A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel. Hence, the vertices ABCD form a parallelogram.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel.

B. The opposite sides of the parallelogram are parallel and equal, and their slopes are equal.

C. The given vertices of a parallelogram are:

A(-2, 0), B(0, 9), C(2, 0) and D(0, -9).

Calculate the slope of segment AB and CD.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

For AB:

m = (9 - 0) / (0 + 2) = 9/2

For CD:

m = (-9 - 0) / (0 - 2) = 9/2

Since the slopes of the segments AB and CD are equal the two lines are parallel to each other. Hence, the vertices ABCD form a parallelogram.

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A basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) =  is {p(x) = x² - 1, q(x) = x² + x - 2}

The vector space {f(x) € P3[x] | f'(1) = f(1)} consists of polynomials of degree less than 3 with the property that their derivative at x = 1 is equal to the polynomial itself evaluated at x = 1. To find a basis for this space, we can start by finding a set of two polynomials that satisfy this property, and that are linearly independent.

One possible choice for p(x) is x² - 1, and one possible choice for q(x) is x² + x - 2. These polynomials satisfy the required property (i.e., their derivatives at x=1 are equal to the polynomials themselves evaluated at x=1), and they are linearly independent because their leading terms (x² in both cases) are distinct.

Thus, {p(x) = x² - 1, q(x) = x² + x - 2} is a basis for the vector space {f(x) € P3[x] | f'(1) = f(1)}.

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The equation 15 - x = 7 models the scenario because it represents the decrease in the number of cats that the zoo now nurses. It can be read as "15 (the number of cats originally) minus x (the number of cats moved) equals 7 (the number of cats the zoo now nurses)".

Notably, this response comes the nearest to choice A (83.3 wins). The right response is thus A.

A mathematical statement that shows the equivalence of two mathematical equations is what a solution in algebra means. For instance, the two numbers 3x + 5 and 14 make up the expression 3x + 5 = 14, which is separated by the sign "equal."

We can change x to 17 in the regression model y = 4.9x + 15.2 and calculate for y to get the number of victories for a squad with 17,000 spectators: y = 4.9(17) + 15.2 = 83.5

Consequently, 83.5 victories are expected for a squad with a 17,000-fan attendance.

To predict the number of wins for a team with an attendance of 17,000, we can substitute x = 17 into the regression equation y = 4.9x + 15.2 and solve for y:

y = 4.9(17) + 15.2 = 83.5

Therefore, the predicted number of wins for a team with an attendance of 17,000 is 83.5 wins.

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The total production of both countries when they did not specialize was 91 million / day.

Given the information that when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68, we can calculate the total production of both countries with the following equation:

Total Production = Chinos (23 million pairs / day) + Pistachios (68 million / day)

Therefore, the total production of both countries when they did not specialize was 91 million / day. This can be calculated as:

Total Production = 23 million pairs + 68 million = 91 million / day

Hence, the total production of both countries when they did not specialize was 91 million / day. This calculation can be represented by the following formula:

Total Production = Chinos (x) + Pistachios (y)

Where x = 23 million pairs and y = 68 million.

Therefore, the total production of both countries when they did not specialize was 91 million / day.

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A. The velocities are given as follows:

B. The graph is given by the image presented at the end of the answer.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the table, Devron's rate is given as follows:

k = 180/4

k = 45 miles per hour.

Hence the equation is of:

y = 45x.

For Avery's equation of y = 60x, the rate is of 60 miles per hour.

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1. The two equations have different slopes.

2. The two equations have different intercepts.

3. The system of equations has one solution.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

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