What faces are congruent?illustrate/draw the box then identify and label the faces that are congruent

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

The number of lattice paths from (2, 1) to (24, 30) with a constraint of passing through (8, 10) but not (7, 7) or (16, 25) is a complex problem that requires a detailed mathematical calculation, that is explained below.

Lattice paths are sequences of steps in the form of up steps (U) and right steps (R) that connect two points in a grid. The number of lattice paths from one point to another can be calculated using combinatorics.

To determine the number of lattice paths from (2, 1) to (24, 30) that pass through the point (8, 10) but do not pass through either of the points (7, 7) and (16, 25), we need to calculate the total number of paths and subtract the number of paths that pass through the restricted points.

Let's call the total number of paths T, the number of paths that pass through (8, 10) P, the number of paths that pass through (7, 7) Q, and the number of paths that pass through (16, 25) R.

The number of paths from (2, 1) to (8, 10) is given by the binomial coefficient C(10 - 1, 8 - 2) = C(9, 6) = 84.

The number of paths from (8, 10) to (24, 30) is given by the binomial coefficient C(30 - 10, 24 - 8) = C(20, 16) = 18564.

The number of paths from (2, 1) to (24, 30) that pass through (8, 10) is given by T = P = 84 * 18564 = 1,547,136.

Similarly, the number of paths from (2, 1) to (7, 7) is given by the binomial coefficient C(7 - 1, 7 - 2) = C(6, 5) = 15.

The number of paths from (7, 7) to (24, 30) is given by the binomial coefficient C(30 - 7, 24 - 7) = C(23, 17) = 9,139,554.

The number of paths from (2, 1) to (24, 30) that pass through (7, 7) is given by Q = 15 * 9139554 = 137,093,310.

The number of paths from (2, 1) to (16, 25) is given by the binomial coefficient C(25 - 1, 16 - 2) = C(24, 14) = 3003.

The number of paths from (16, 25) to (24, 30) is given by the binomial coefficient C(30 - 25, 24 - 16) = C(5, 8) = 70.

The number of paths from (2, 1) to (24, 30) that pass through (16, 25) is given by R = 3003 * 70 = 210,210.

Finally, the number of paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is T - P - Q - R = 1547136 - 137,093,310 - 210,210 = -135,599,384.

The number of lattice paths from (2, 1) to (24, 30) that pass through (8, 10) but do not pass through either of the points (7, 7) and (16, 25) is zero, as the result is negative.

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Answer:

0.4 = 40%

0.26 = 26%

Step-by-step explanation:

Multiply the decimal by 100, and convert to percentage.

Answer:

0.4 = 4%, 0.26 = 26%

Step-by-step explanation:

hope this helps :)

The probability that the student makes it to the second class before it starts is very close to 0.

To find the probability that the student makes it to the second class before it starts, we can use the concept of linear combinations of random variables and the properties of normal distributions.

Let's define the random variable X as the total time it takes for the student to transition from the end of the first class to the start of the second class. Since X is a linear combination of independent normally distributed random variables (X1, X2, X3), we can use their means and variances to calculate the mean and variance of X.

The mean of X is the sum of the means of X1, X2, and X3:

μX = μ1 + μ2 + μ3 = 9:02 + 9:15 + 10 = 28:17 minutes.

The variance of X is the sum of the variances of X1, X2, and X3:

σX^2 = σ1^2 + σ2^2 + σ3^2 = (2.5)^2 + (3)^2 + (2.5)^2 = 15.25 minutes^2.

Now, we need to calculate the probability that X is less than or equal to 0, meaning the student arrives before the second lecture starts. Since X follows a normal distribution, we can standardize the variable and calculate the probability using the standard normal distribution table.

Z = (0 - μX) / σX = (0 - 28:17) / √15.25 ≈ -9.43.

Using the standard normal distribution table or a calculator, we can find the probability corresponding to Z = -9.43. The probability is essentially 0, as the value is significantly far in the left tail of the standard normal distribution.

Therefore, the probability that the student makes it to the second class before it starts is very close to 0.

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The combined cost of the notebooks and the pens will be; $5.5

We have been Given that Kendall bought 6 notebooks and 3 pens for a total of $27. The cost of one notebook is $1.50 more than the cost of one pen.

The two equations can be written;

6N + 3 P = 27

n = 1.5 +P

Solve the above equations by substitution method;

6(1.5 + P) + 3P = 27

9 +6p +3p = 27

9p = 18

p (pen): $2

N (notebook): $3.5

The combined cost will be;

Cost = 2 + 3.5

Cost = $5.5

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The fundamental period of the signal, the closest to T is 6

The fundamental period of a signal is the smallest positive value of T such that x(t+T) = x(t) for all t.

To determine the fundamental period of the signal x(t) = 2cos(10t-1) - sin(4t-1), we need to find the period of each term and then take their least common multiple (LCM).

The period of cos(10t-1) is T1 = 2π/10 = π/5.

The period of sin(4t-1) is T2 = 2π/4 = π/2.

To find the LCM of T1 and T2, we need to factorize the periods into their prime factors:

T1 = π/5 = 5 * π/25

T2 = π/2 = 2 * π/2

The LCM of the prime factors is 2 * 5 * π/25 = 2π/5.

Therefore, the fundamental period of the signal x(t) = 2cos(10t-1) - sin(4t-1) is T = 2π/5.

However, this is not one of the options given. To find which of the options is closest to T, we can approximate T using a calculator:

T ≈ 1.2566

Of the options given, the closest to T is 6.

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Answer: the measure of angle 4 is 124.

Step-by-step explanation: A supplementary angle is equal to 180°, so you have to subtract 56° from 180°.

Answer:

124

Step-by-step explanation

subtract 56 from 180

The cutoff score for the top 19% of applicants in the police academy physical fitness test is 75. This means that in order to qualify for the police academy, applicants need to achieve a score equal to or higher than 75 on the physical fitness test.

To determine this cutoff score, we considered the distribution of scores on the test, which follows a normal distribution with a mean of 64 and a standard deviation of 13.

The normal distribution is a commonly observed pattern in which data tends to cluster around the mean with decreasing frequency as the values move away from the mean.

By calculating the cumulative probability associated with the top 19% of applicants, we found that it corresponds to a z-score of approximately 0.88. The z-score represents the number of standard deviations a particular score is from the mean.

To convert this z-score back to the raw score, we used the formula raw score = (z-score * standard deviation) + mean. Substituting the values, we obtained a raw score of 75 as the cutoff point for the top 19% of applicants.

This cutoff score serves as a threshold for determining which applicants are among the most physically fit and qualified for the police academy.

It allows the selection process to identify those individuals who excel in the physical fitness requirements necessary for the demands of law enforcement duties.

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Answer:

Step-by-step explanation:

120 + 61x -2 = 180 ( sum of opposite angles)

118 + 61x =180

61x= 62

x = 62/61

The Laplace Transform of F(s) f(t) () = {0-5). t < 5 - 5)³, t>5 is -125 / s⁴.

Given:F(8) = {-1} = { f(t) t < 2 t²-4t+7, t≥ 2F(s) = f(t) () = {0-5). t < 5 - 5)³, t>5

To find: Laplace Transform of given function

Let's find Laplace transform of both given functions one by one:

For the first function: F(8) = {-1} = { f(t) t < 2 t²-4t+7, t≥ 2

Given that: f(t) = { t²-4t+7, t≥ 2 and f(t) = 0, t < 2

Taking Laplace transform on both sides:L {f(t)} = L {t²-4t+7} for t ≥ 2L {f(t)} = L {0} for t < 2L {f(t)} = L {t²-4t+7}L {f(t)} = L {t²} - 4 L {t} + 7 L {1}

Using the standard Laplace transform formulaL {tn} = n! / sn+1 and L {1} = 1/s

we get:L {t²} = 2! / s³ = 2/s³L {t} = 1 / s²L {1} = 1 / s

Putting the values in L {f(t)} = L {t²} - 4 L {t} + 7 L {1},

we get:L {f(t)} = 2/s³ - 4 / s² + 7 / s ∴ L {f(t)} = (2 - 4s + 7s²) / s³

Thus, Laplace Transform of given function is (2 - 4s + 7s²) / s³.

For the second function:F(s) f(t) () = {0-5). t < 5 - 5)³, t>5

Given that:f(t) = { 0, t < 5 and f(t) = -5³, t>5

Taking Laplace transform on both sides:L {f(t)} = L {0} for t < 5L {f(t)}

                                   = L {-5³} for t>5L {f(t)}

                                   = L {0}L {f(t)}

                                  = L {-5³}

Using the standard Laplace transform formula L {1} = 1/s

we get:L {f(t)} = 0 × L {1} for t < 5L {f(t)} = - 125 / s³ × L {1} for t>5L {f(t)} = 0L {f(t)} = - 125 / s³ × 1/sL {f(t)} = - 125 / s⁴

Thus, Laplace Transform of given function is -125 / s⁴.

Therefore, the Laplace Transform of F(8) = {-1} = { f(t) t < 2 t²-4t+7, t≥ 2 is (2 - 4s + 7s²) / s³.

The Laplace Transform of F(s) f(t) () = {0-5). t < 5 - 5)³, t>5 is -125 / s⁴.

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Answer: -8

Step-by-step explanation: 1/4 + 1/4 = 1/2, -8 1/2 + 1/2 = -8

Answer:

I think X us called consequent

Answer:

18 square meters

Step-by-step explanation:

Answer:

solution,

The given figure if a Trapezium whose parallel sides are of 3 m and 2 m respectively.

Distance between the parallels sides

i.e. height is 3 m

Now,

\(area = \frac{1}{2} \times sum \: of \: parallel \: sides \times height \\ = \frac{1}{2} \times (3 + 2) \times 3 \\ = \frac{1}{2} \times 5 \times 3 \\ = \frac{15}{2} \\ = 7.5 \: {m}^{2} \)

Hope this helps...

Good luck on your assignment...

Answer:

-2(x+5)=4

(-2)• x + (-2• 5) = 4

-2x+-10= 4

-2x = 4+ 10

x=14/2

X=7

Step-by-step explanation:

If you need an explanation, please tell me in comments

If this helps you, please mark as brainliest

Step-by-step explanation:

-2(x + 5)= 4

-2x - 10 = 4

-2x = 4 + 10

-2x = 14

x = -7

Answer:

\(\sqrt{3}\)

Step-by-step explanation:

\(\frac{\sqrt{15} }{\sqrt{5} }\)

to rationalise the denominator multiply numerator/ denominator by \(\sqrt{5}\)

= \(\frac{\sqrt{15} }{\sqrt{5} }\) × \(\frac{\sqrt{5} }{\sqrt{5} }\)

= \(\frac{\sqrt{75} }{5}\)

= \(\frac{\sqrt{25(3)} }{5}\)

= \(\frac{5\sqrt{3} }{5}\)

= \(\sqrt{3}\)

Answer:

Unit rate

Step-by-step explanation:

Answer:

Unit rate

Step-by-step explanation:

Unit rate -- A rate in which the second quantity in the comparison is one unit.

Answer:

3

Step-by-step explanation:

We do do -3 on both sides and get 7b = 21. Then we multiply by the reciprocal (divide) (7b * 1/7 = 21 * 1/7) . We get b = 21/7 cause the 7's cancel out. b = 3 cause 21/7 = 3

Answer:

P'(3,-7) Q'(7,6) R'(-8,-7).

Step-by-step explanation:

Reflection across the x-axis

Given a point P(x,y), its reflection across the x-axis will map to point P'(x,-y), i.e., the y-coordinate gets inverted.

We are given the vertices of a triangle P(3,7) Q(7,-6) R(-8,7). The vertices of the image reflected across the x-axis are:

P'(3,-7) Q'(7,6) R'(-8,-7).

The new triangle has vertices P'Q'R'.

Answer:

Choice D

Step-by-step explanation:

Choices A and B does not imply Dilation but Translation. Though Choice C implies Dilation, but it implies that \(\triangle J'K'L'\) is half the size of \(\triangle JKL\) but we can see that \(\triangle J'K'L'\) is larger than \(\triangle JKL\) so Choice D.

- 2 5/25,  -2.9,  8/16

Step-by-step explanation:

Answer: 0.83,0.82,0.8

The calculated sum of the geometric series are

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\) = 5

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\) = 1/p

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

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\)

In the above series, we have

First term, a = 1

Common ratio, r = 0.8

The sum to infinity of a geometric series is

Sum = a/(1 - r)

So, we have

Sum = 1/(1 - 0.8)

Evaluate

Sum = 5

Next, we have

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\)

In the above series, we have

First term, a = 1

Common ratio, r = 1 - p

The sum to infinity of a geometric series is

Sum = a/(1 - r)

So, we have

Sum = 1/(1 - 1 + p)

Evaluate

Sum = 1/p

Hence, the sum of the geometric series are 5 and 1/p

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Question

5. Find the sum of the following geometric series:

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\)

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\) where 0 < p < 1. (Your answer will be in terms of p)

Answer: A = 15cm squared

Step-by-step explanation:

I think :)

Given that the base of the prism is 4 cm by 3 cm and the height is 5 cm, the volume can be calculated as:

The volume of the prism = (length x width x height)

By applying the given values:

Volume of prism = 4 cm x 3 cm x 5 cm

The volume of the prism = 60 cubic cm

That implies the volume of the rectangular prism is 60 cubic cm.

We know that the pyramid's base measures 4 by 3 cm and its height is 5 cm, the base's area may be calculated as follows:

Area of base = length x width

Area of base = 4 cm x 3 cm

Area of base = 12 square cm

The volume of the pyramid can now be calculated as:

Volume of pyramid = (area of base x height) / 3

Volume of pyramid = (12 square cm x 5 cm) / 3

The volume of the pyramid = 20 cubic cm

Therefore, the volume of the square pyramid is 20 cubic cm.

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Answer:

x + 46

Step-by-step explanation:

Step 1: Write expression

4(-8x + 5) - (-33x - 26)

Step 2: Distribute

-32x + 20 + 33x + 26

Step 3: Combine like terms

x + 46

The measure of angle ∠a is 20 degrees.In more than 100 words;Vertical angles are the opposite angles that are formed when two lines intersect

Given that ∠a and ∠b are vertical angles with m\(∠a=x and m∠b=5x−80\). We are supposed to find m∠a.To solve this problem, we need to recall the properties of vertical angles. Vertical angles are the opposite angles formed when two lines intersect.

They are equal to each other. It means m∠a = m∠bUsing this information, we can write;x = 5x - 80Collect like terms;x - 5x = -80-4x = -80Solve for x;x = -80/-4x = 20Now substitute this value of x in m∠a=xm∠a = 20°

Therefore, the measure of angle ∠a is 20 degrees.In more than 100 words;Vertical angles are the opposite angles that are formed when two lines intersect. They are equal to each other.

Therefore, if we have two vertical angles such as ∠a and ∠b with m∠a=x and m∠b=5x−80,

we can set the two angles equal to each other and solve for x. Once we have the value of x, we can then substitute it in any of the expressions to find the measure of the angle that we want to find.In this problem,

we were supposed to find the measure of ∠a. We were given that ∠a and ∠b are vertical angles with

m∠a=x and m∠b=5x−80. Using the property of vertical angles,

we can equate the two angles;m∠a = m∠bSubstitute the values we have;

x = 5x - 80Solve for x;x = -80/-4x = 20

Now substitute this value of x in m∠a=x;m∠a = 20°Therefore, the measure of angle ∠a is 20 degrees.

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The linear equation from the given statement is the N + F+11 = 2F.

According to the statement

We have to write the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F.

Then

The number of shirts left = N

The number of the shirts which are folded = F+11

The total number of shirts = 2F

And then

The linear equation becomes :

N + F+11 = 2F

This the linear equation for the given statement.

So, The linear equation from the given statement is the N + F+11 = 2F.

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