Girish left his home at 7 45 and travelled to Muar, which was 120 km away. He arrived
at Muar 2 h later. After staying 1 2/3 hours in Muar, he travelled from Muar back to his home
along the same route at a speed which was 20 Km/h slower than his previous speed.
At what time did Girish reach home?

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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Answer:

It would be 2,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Looking at the y-values, it seems a geometric progression with the common ratio of 5. Therefore it can be exponential relationship.

By trying the values in the table we get the equation:

Answer: 2.4

Step-by-step explanation: obviously not anywhere close to 3 trust

Answer:

\(s = 4\pi {r}^{2} \\ \frac{ds}{dr} = 8\pi r =8\pi(2) = 16\pi \\ from \: chain \: rule \\ \frac{ds}{dr} = \frac{ds}{dt} . \frac{dt}{dr} \\ but \: \frac{ds}{dt} = 1 \\ 16\pi = 1 \times \frac{dt}{dr} \\ \frac{dt}{dr} = 16\pi \\ \frac{dr}{dt} = ( \frac{dt}{dr} ) ^{ - 1} \\ \frac{dr}{dt} = \frac{1}{16\pi} \)

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:

The probability that X is between 1.48 and 15.56 is \(P(1.48 \leq X \leq 15.56) = 0.919\)

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.

This means that \(\mu = 8, \sigma = 4\)

The probability that X is between 1.48 and 15.56

This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So

X = 15.56

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{15.56 - 8}{4}\)

\(Z = 1.89\)

\(Z = 1.89\) has a pvalue of 0.9706

X = 1.48

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1.48 - 8}{4}\)

\(Z = -1.63\)

\(Z = -1.63\) has a pvalue of 0.0516

0.9706 - 0.0516 = 0.919

Write out the probability notation for this question.

\(P(1.48 \leq X \leq 15.56) = 0.919\)

The probability that X is between 1.48 and 15.56 is \(P(1.48 \leq X \leq 15.56) = 0.919\)

Answer:

CD = 8 cm

Step-by-step explanation:

Given

See attachment

\(AE=6 cm,\ ED=4 cm,\ AB=4.5 cm,\ BE=4.8 cm.\)

Required

Find CD

To calculate CD, we first calculate BC using the following equivalent ratio

\(AB : BC = AE:ED\)

Substitute values for AB, AE and ED

\(4.5 : BC = 6 : 4\)

Express as fraction

\(\frac{4.5 }{ BC} = \frac{6 }{ 4}\)

Cross Multiply

\(BC * 6 = 4.5 * 4\)

\(BC * 6 = 18\)

Divide through by 6

\(BC = 3\)

To calculate CD,

We make use of the following equivalent ratio

\(AB : BE = AC : CD\)

Where

\(AC = AB + BC\)

\(AC = 4.5 + 3\)

\(AC = 7.5\)

So, we have:

\(AB : BE = AC : CD\)

\(4.5 : 4.8 = 7.5 : CD\)

Express as fraction

\(\frac{4.5 }{ 4.8 }= \frac{7.5 }{ CD}\)

Cross Multiply

\(4.5 * CD = 7.5 * 4.8\)

Divide through by 4.5

\(CD = \frac{7.5 * 4.8}{4.5}\)

\(CD = \frac{36}{4.5}\)

\(CD = 8\)

Answer:

11 degrees

Step-by-step explanation:

All the angles of a triangle add up to 180 degrees. Subtract (3+47-17) from 180 and divide by three. Therefore, you get 11 degrees.

Answer:

y=3x-19

Step-by-step explanation:

If y=mx+b, then you would input the x and y of (6, -1) into the equation. Therefore,

-1=18+b

Therefore,

b=-19

Therefore the answer would be:

y=3x-19

Answer:C

Step-by-step explanation:

Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer

Roy has $0.92 or 92 cents on him.

Explanation

We need to lnow the worth of each of those coins before knowing the total worth of money that Roy has.

1 nickel = 5 cents = $0.05

1 quarter = 25 cents = $0.25

1 dime = 10 cents = $0.10

1 penny = 1 cent = $0.01

Roy has 3 nickels, 2 quarters, 2 dimes, and 7 pennies.

3 nickels = 3 × $0.05 = $0.15

2 quarters = 2 × $0.25 = $0.50

2 dimes = 2 × $0.10 = $0.20

7 pennies = 7 × $0.01 = $0.07

All of Roy's money is then

(3 nickels) + (2 quarters) + (2 dimes) + (7 pennies)

$0.15 + $0.50 + $0.20 + $0.07

= $0.92

Hope this Helps!!!

After reflecting the quadrilateral EFGH across the line y = 2, the x-coordinates of the corresponding points in the image and the preimage will be the same.

Generally,  Reflection is an isometry, which means that it preserves distance and angles. Therefore, the x-coordinates of the points in the image and the preimage will not be changed by the reflection. The y-coordinates will change since the reflection flips the points over the line of reflection.

For example, if quadrilateral EFGH has a vertex at (x, y), then the corresponding vertex in the image will be at (x, 2 - y). The x-coordinate remains the same, but the y-coordinate is reflected across the line y = 2.

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One characteristic of a well-defined probability density function of a continuous random variable X is that the area under the curve, f(x) over all values of x is equal to one.

Probability density functions are a group of functions commonly used in statistical theory to describe the behavior of theoretical probability distributions. A function satisfies a criterion like the function if its values are always positive for all horizontal axes and its primitives are probability distributions. This means that this function is non-negative for all abscissa values and its definite integral product in the range -∞ to +∞ is equal to 1. Apart from being called the probability density function, it is also called the probability density function or probability density function in the literature.

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On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.03357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

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False

Explanation

let's remember some properties of the exponents

so

when dividing two variables with the same base, you subtract the exponents

Therefore, the answer is

False

I hope this helps you

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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Answer:

≈ 404.6666667

Step-by-step explanation:

70 - 8 ÷ 6 + 8 x 42

70 - 1.33333333 + 8 x 42

70 - 1.33333333 + 336

68.6666667 + 336

404.6666667

Answer: KL = KN LM=NO=9 Side-Side-Side

Step-by-step explanation:

The required answers to the question is given below.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

Use the following figure to understand the answer.

The Proof is

1. KM=KO=5 (GIven)

2. MN=3 (Given)

3. KN=KM+MN=8 (because the lengths are equal to the sum of their parts.)

4. KL=8 (Given)

5. KL=KN (from 3,4 substitution)

6. NO=ML=9 (Given)

7. ΔKLM=ΔKNO the congruence criterion used is SSS congruence.

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Answer:

Below

Step-by-step explanation:

245.8 = .872 x      where x is the theoretic airflow

245.8 / .872 = x = 281.9 cfm

First, let's define our variables.

Let:

• M, be the number of ,math, teachers and ,m, be the number of math students.

• B, be the number of ,biology, teachers and ,b, be the number of ,biology, students.

• H, be the number of ,history, teachers and ,h, be the number of ,history, students.

Similarly, we'll have that:

• Cm, will be the number of students in a ,math, class.

• Cb, will be the number of students in a ,biology, class.

• Ch, will be the number of students in a ,history, class.

Now, we'll traslate what each dean said into mathematic expressions, so we can work on them and get our solution.

FOR MATH:

The dean said:

1. "We divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."

2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 1.”

Now, let's clear Cm from equation 2 and equal both equations, as following:

Solving for m, we'll get an expression for the number of students asigned to a certain number of teachers:

Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.

For instance, we can choose 10 teachers, and we'll get that:

• There were 10 teachers and 120 students in the fall semester

• There were 11 teachers and 121 students in the fall semester

FOR BIOLOGY:

The dean said:

1. "...we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."

2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 2."

Similarly, we'll clear Cb from equation 2 and equal both equations, as following:

Solving for b, we'll get an expression for the number of students asigned to a certain number of teachers:

Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.

For instance, we can choose 10 teachers, and we'll get that:

• There were 10 teachers and 230 students in the fall semester

• There were 11 teachers and 231 students in the fall semester

FOR HISTORY:

The dean said:

1. "...we divided all the students evenly among all the professors in the fall semester, and each class had exactly the same number of students."

2. "In the spring semester, we hired one additional professor and our student enrollment went up by exactly 1, and it turned out that our class size in the spring went down by exactly 3."

Just as we did, we'll clear Ch from equation 2 and equal both equations, as following:

Solving for h, we'll get an expression for the number of students asigned to a certain number of teachers:

Now, we can choose any number of teachers that we want, and we'll get the corresponding number of students that make the dean's statements correct.

For instance, we can choose 10 teachers, and we'll get that:

• There were 10 teachers and 340 students in the fall semester

• There were 11 teachers and 341 students in the fall semester

Step-by-step explanation:

To find the numerical limits for a D grade, we need to determine the cutoff points for the top 77% and bottom 8% of scores.

Using a standard normal distribution table or a calculator, we can find that the z-score cutoff points for the top 77% and bottom 8% are approximately 0.61 and -1.41, respectively.

To find the corresponding raw scores, we use the formula:

raw score = (z-score x standard deviation) + mean

For the top 77%, we have:

raw score = (0.61 x 7.2) + 81.6 = 86.392, which we can round up to 87

For the bottom 8%, we have:

raw score = (-1.41 x 7.2) + 81.6 = 70.848, which we can round down to 70

Therefore, the numerical limits for a D grade are scores below 87 and above 70.

Step-by-step explanation:

we need to use the standard normal distribution table for mean = 0, standard deviation = 1.

to use it for our normal distribution with mean = 81.6 and standard deviation = 7.2 we need to find the transformation from the standard normal distribution to our normal distribution.

this is done by the z-scores of the interval limits (the z-score tells us how many standard deviations the desired value is away from the mean value).

and to correlate the given %-values to the distribution interval limits, we need to look up the corresponding p-value (probability value) in the table.

and then we need to calculate backwards to get our specific interval limits.

for the D-grade we are looking for the upper limit to "below the top 77%", which is "below the bottom 23%".

we have to assume this means "below or equal to the bottom 23%", just in case.

the lower level will be "above the bottom 8%".

so, the p-value for 23% = 0.2300.

that gives us the z-score ≈ -0.74.

z-score = (interval-limit - mean-value)/standard-deviation

-0.74 = (interval-limit - 81.6)/7.2

-0.74×7.2 = interval-limit - 81.6

-5.328 = interval-limit - 81.6

interval-limit = 76.272 ≈ 76

the p-value for 8% = 0.0800.

that gives us the z-score ≈ -1.41

-1.41 = (interval-limit - 81.6)/7.2

-1.41×7.2 = interval-limit - 81.6

-10.152 = interval-limit - 81.6

interval-limit = 71.448 ≈ 71

the students with a score s

71 < s <= 76

get a D.

(greater than 71 but lower or equal to 76).

The quartic function with only two real zeros of x=0 and x=4 is x² - 4x = 0

A quartic function is a quartic polynomial, that is, a polynomial with integer coefficients whose highest degree is four. The coefficient of the variable to the fourth degree cannot be zero. Examples of quartic functions include

From the roots;

a = 0 ; b = 4

From the polynomial expressions

x² - (a +b)x + ab = 0

x² - (0 +4 )x + 0*4 = 0

x² - 4x = 0

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The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Given the bag contains mulch at a amount of,

Used fraction of mulch is,

To find the amount of mulch used.

At first we need to convert the given improper fraction into proper fraction. so we get,

So to find the amount of mulch used, we multiply the fraction used with the total amount of mulch.

So the amount of mulch used is,

By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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