Write the following values in ascending order (smallest to largest):
0.1, 0.09, 2%,7/10,19/100

Satisfying all the given situations, there were 156 candidates in the examination.

We can use the principle of inclusion-exclusion to solve the problem.

The principle of inclusion-exclusion states that the total number of elements in the union of two or more sets is equal to the sum of the number of elements in each set, minus the number of elements in their intersection.

Here, let A be the set of candidates who offered biology, B be the set of candidates who offered history, and C be the set of candidates who offered mathematics.

Using the principle of inclusion-exclusion, the total number of candidates, N, can be found as follows:

N = (A U B U C) = (A + B + C) - (A ∩ B + B ∩ C + A ∩ C) + (A ∩ B ∩ C)

where A U B U C is the union of the three sets, A ∩ B is the intersection of A and B, and so on.

Given that:

|A| = 52, |B| = 60, |C| = 96

|A ∩ B| = 21, |A ∩ C| = 22, |B ∩ C| = 16

|A ∩ B ∩ C| = 7

Therefore,

N = (52 + 60 + 96) - (21 + 22 + 16) + 7

N = 156

Hence, there were 156 candidates in the examination.

The problem seems incomplete, it must have been

"In a certain examination, 52 candidates offers biology,60 offers history,96 offers mathematics, if 21 offered both biology and history,22 offered mathematics and biology, and 16 offered mathematics and history. If 7 candidates offered all the subject. how many candidates were there for the examination​?"

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Answer:

in *42* days it will be 45 seconds behind

Step-by-step explanation:

it is already 3 behind and if its only 1 second everyday then you add 1 day until you get to 45 which 42+3 is 45 so the correct answer is 42 days.

Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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The relation R is transitive, as demonstrated through the matrix method where every pair (x, y) and (y, z) in R implies the presence of (x, z) in R, based on the matrix representation.

To demonstrate this using the matrix method, we construct the matrix representation of the relation R. Let's denote the elements of the set {a, b, c, d} as rows and columns. If an element exists in the relation, we place a 1 in the corresponding cell; otherwise, we put a 0.

The matrix representation of relation R is as follows:

\(\left[\begin{array}{cccc}1&1&1&1\\1&1&1&1\\0&0&1&0\\1&1&1&1\end{array}\right]\)

To check transitivity, we square the matrix R. The resulting matrix, R^2, represents the composition of R with itself.

\(\left[\begin{array}{cccc}4&4&3&4\\4&4&3&4\\2&2&1&2\\4&4&3&4\end{array}\right]\)

We observe that every entry \(R^2\) that corresponds to a non-zero entry in R is also non-zero. This verifies that for every (a, b) and (b, c) in R, the pair (a, c) is also present in R. Hence, the relation R is transitive.

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You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.

Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.

The slope of the line is then

\(\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}\)

which means that 1 in ≈ 2.5 cm.

So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)

\(64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}\)

Answer:

a) 1/4

b) 1/6

c) 1/12

Step-by-step explanation:

Let S be the sample space.

S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

n(s) =12

Events

A: coin with head and die with prime number .

B:coin with head and die with composite number.

C:coin with tail and die with even prime number.

a) A={H2,H3,H5}

n(A) = 3

P(A) =n(A)/n(S)

=3/12

= 1/4

b) B={H4,H6}

n(B)= 2

P(B) = n(B)/n(S)

= 2/12

= 1/6

c) C ={T2}

n(C) = 1

P(C) = n(C)/n(S)

= 1/12

The total number of students in the seminar is 258, with 98 boys and 160 girls given a ratio of 8:5 between boys and girls.

We can begin by using the given ratio of boys to girls, which is 8:5, and the information that there are 160 girls to find the number of boys in the seminar.

If the ratio of boys to girls is 8:5, then we can say that for every 8+5=13 students, there are 8 boys and 5 girls.

To find the number of boys, we can set up a proportion

8/13 = x/160

where x is the number of boys.

Simplifying this proportion, we get

x = 8/13 × 160

x = 98.46

Therefore, the number of boys in the seminar is approximately 98.

To find the total number of students in the seminar, we can add the number of boys and girls

Total number of students = Number of boys + Number of girls

Total number of students = 98 + 160

Total number of students = 258

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From the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

From the given equations, the equation which has no solution has to be found out. When the value, does not equate for the expression, then the expression has no solution.

The first equation given in the problem is,

\(6 (x +2) > x-3\)

Solve it further,

\(6 x +12 > x-3\\6x-x > -3-12\\5x > -15\\x > -3\)

The second equation given in the problem is,

\(3+ 4x \leq 2 (1 +2x)\)

Solve it further,

\(3+ 4x \leq 2 +4x\\4x- 4x \leq 2-3\\0\leq-1\)

The value of 0 is greater than the number -1. Thus, this inequality has no solution.

The option 3 and 4 has a solution. Hence, from the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

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Answer:

Below

Step-by-step explanation:

Z score is the ± standard deviations from the mean

For 93.6% confidence level, the value of α is (100-93.6) / 2 = 3.2To find zα/2, we look up the z-table and find the area that is closest to 0.5 + α/2. At 3.2, the closest value to 0.5 + α/2 is 0.4987.

This corresponds to the value of zα/2, which is 1.81. Hence, the zα/2 value for 93.6% confidence level is 1.81. The level of confidence, 1 - α, in any confidence interval denotes the area that is bounded by the critical value or values and the probability distribution. This probability is 1 - α and is called the level of confidence.If the value of α is to be found, we first find the level of confidence and then subtract it from 1.

Then divide it by 2. The result is the value of α divided by 2. This is because of the distribution's symmetry.For example, if the level of confidence is 93.6%, thenα = (1 - 0.936) / 2= 0.032Find zα/2 using a normal distribution table: Look up 1 - α/2 in the normal distribution table, where α is the significance level.

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Some safety functions of a modern car include: Anti-lock braking system (ABS), Electronic stability control (ESC), Airbags, Seat belts, Adaptive cruise control (ACC), Lane departure warning (LDW) and lane-keeping assist (LKA), Forward collision warning (FCW) and automatic emergency braking (AEB).

Anti-lock braking system (ABS): ABS prevents the wheels from locking up during braking, allowing the driver to maintain steering control and reducing the risk of skidding.

Electronic stability control (ESC): ESC helps maintain vehicle stability by detecting and reducing skidding or loss of control. It applies selective braking to individual wheels and may also reduce engine power to prevent accidents.

Airbags: Airbags provide additional protection to occupants in the event of a collision. They deploy rapidly upon impact, reducing the risk of severe injury.

Seat belts: Seat belts are crucial safety devices that restrain occupants during sudden stops or collisions, minimizing the risk of ejection or severe injuries.

Adaptive cruise control (ACC): ACC uses radar or sensors to maintain a safe distance from the vehicle ahead. It automatically adjusts the car's speed, reducing the need for constant braking and acceleration.

Lane departure warning (LDW) and lane-keeping assist (LKA): LDW alerts the driver if the vehicle deviates from its lane, while LKA actively assists in keeping the vehicle within the lane, enhancing safety on highways.

Forward collision warning (FCW) and automatic emergency braking (AEB): FCW warns the driver of an imminent collision, and AEB automatically applies brakes to mitigate or avoid a collision.

Modern cars are equipped with various safety functions to enhance driver and passenger safety. The mentioned safety functions address different aspects of vehicle safety, such as braking, stability control, occupant protection, and collision avoidance.

The safety functions mentioned above are important features of modern cars that contribute to reducing the risk of accidents and enhancing the safety of occupants. Each function serves a specific purpose in mitigating risks associated with braking, stability, collision, and occupant protection. These safety functions work collectively to improve the overall safety of modern vehicles and play a significant role in preventing accidents and minimizing the severity of injuries in case of unavoidable incidents.

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Answer:

1. Sine ratio of angle ∠C = 12/13

2. cos ratio for ∠C = 6/10

Step-by-step explanation:

1. sin = perpendicular /hypotuse

=> 12/13

2. cos = base / hypotuse

=> 6/10

The Laplace transform of the periodic function f(t) is F(s) = 8 [1/s - e^(-3s)s].

The given function f(t) is periodic with a period of 6. Therefore, we can express it as a sum of shifted unit step functions:

f(t) = 4[u(t) - u(t-3)] + 4[u(t-3) - u(t-6)]

Now, let's find the Laplace transform F(s) using the definition:

F(s) = ∫[0 to ∞]e^(-st)f(t)dt

For the first term, 4[u(t) - u(t-3)], we can split the integral into two parts:

F1(s) = ∫[0 to 3]e^(-st)4dt = 4 ∫[0 to 3]e^(-st)dt

Using the formula for the Laplace transform of the unit step function u(t-a):

L{u(t-a)} = e^(-as)/s

We can substitute a = 0 and get:

F1(s) = 4 ∫[0 to 3]e^(-st)dt = 4 [L{u(t-0)} - L{u(t-3)}]

     = 4 [e^(0s)/s - e^(-3s)/s]

     = 4 [1/s - e^(-3s)/s]

For the second term, 4[u(t-3) - u(t-6)], we can also split the integral into two parts:

F2(s) = ∫[3 to 6]e^(-st)4dt = 4 ∫[3 to 6]e^(-st)dt

Using the same formula for the Laplace transform of the unit step function, but with a = 3:

F2(s) = 4 [L{u(t-3)} - L{u(t-6)}]

     = 4 [e^(0s)/s - e^(-3s)/s]

     = 4 [1/s - e^(-3s)/s]

Now, let's combine the two terms:

F(s) = F1(s) + F2(s)

    = 4 [1/s - e^(-3s)/s] + 4 [1/s - e^(-3s)/s]

    = 8 [1/s - e^(-3s)/s]

Therefore, the Laplace transform of the periodic function f(t) is F(s) = 8 [1/s - e^(-3s)/s].

Regarding the minimal period T for the function f(t), as mentioned earlier, the given function has a period of 6. So, T = 6.

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Hey there!

\(Answer:\boxed{n<-1}\)

\(Explanation:\)

\(3<-5n+2n\)

Start by simplifying both sides of the inequality.

\(-3n>3\)

Now divide both sides by -3.

\(\frac{-3n}{-3} >\frac{3}{-3}\\n<-1\)

\(\boxed{n<-1}\text{ is the answer.}\)

Also here is a graph below.

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

$24

Step-by-step explanation:

$36 divided by 3 = 12

12 x 2 = 24

24 = 2/3 of 36

The inverse property of logarithms states that log base b of x is equal to y if and only if b raised to the power of y is equal to x.

The correct equations that use the inverse property of logarithms are:

   8^7 = 87, so log8(87) = 7.

   7^7 = 7, so 8log7(7) = 7.

   7^8 = 8, so 7log7(8) = 8.

   8^7 = 78, so log8(78) = 7.

Therefore, the correct answers are:

   log8(87) = 7

   8log7(7) = 7

   7log7(8) = 8

   log8(78) = 7

Hence, the options (a), (b), (d), and (f) are correct.

The equations that correctly use the inverse property of logarithms are: log8(87) = 7, 8log8(7) = 7, and 8log7(8) = 7.

The inverse property of logarithms states that if log base a of b equals c, then a raised to the power of c equals b. In the given options, the equations that satisfy this property are:

log8(87) = 7: This equation can be rewritten as 8^7 = 87, which holds true

8log8(7) = 7: This equation can be simplified as 7 = 7, which is true.

8log7(8) = 7: This equation can be rewritten as 7^7 = 8, which is correct.

The other equations, 8log7(7) = 7, log8(78) = 7, and 7log7(8) = 8, do not satisfy the inverse property of logarithms as they do not yield the original values of the bases when raised to the powers indicated by the logarithms.

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Transforming the equation into a quadratic equation, we have:

The measure of the lableled angles are x = 202 and  (x - 44) = 158

Before we can solve this question, we need to understand the geometry of the shape.

The shape we have here is a pentagon. The sum of angles in a pentagon is 540.  The angle with a red square is a right angle and the value is 90.

Therefore:

x + 90 + 90 + (x - 44) = 540

x + 180 + x - 44 = 540

2x + 136 = 540

2x = 540 - 136

2x = 404

x = 404/2

x = 202

Also:

(x - 44) = 202 - 44 = 158

Therefore, the angles x and (x - 44) measure 202 and 158 respectively.

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The unknown value x in the polygon is equal to 112 degrees.

The sum of angles in the given polygon be equal to 360 degrees. This implies that when we add all the total sides together, we must have a total of 360 degrees.

Since one of the indicated sides is a right angle, we can sum everything up and solve for x

Mathematically;

\(90 + 90 + x +(x - 44) = 360\)

Solving the equation above;

\(180 + x + x - 44 = 360\\180 + 2x - 44 = 360\\x = 112\)

The value of x in the figure given is 112.

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The factored expression of the expression given as xy - 9x - 3y + 27 is (x - 3)(y - 9)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

xy - 9x - 3y + 27

Factor out the common factor from the expression

So, we have

xy - 9x - 3y + 27 = x(y - 9) - 3(y - 9)

Factor out (y - 9) from the expression

So, we have

xy - 9x - 3y + 27 = (x - 3)(y - 9)

The expression above cannot be further simplified

This means that the expression has been completely factored and cannot be further factored

Hence, the equivalent expression of the expression given as xy - 9x - 3y + 27 when it is factored by grouping is (x - 3)(y - 9)

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Answer:

The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.

Step-by-step explanation:

Since E is the midpoint of diagonals AD and BC (see attachment). That is:

\(AD = 2 \cdot AE\)

\(BC = 2\cdot BE\)

The vectorial distances of AE and BE are, respectively:

\(\overrightarrow{AE} = \vec E - \vec A\)

\(\overrightarrow {AE} = (-2,4) -(1,7)\)

\(\overrightarrow{AE} = (-2-1, 4-7)\)

\(\overrightarrow {AE} = (-3,-3)\)

\(\overrightarrow{BE} = \vec E - \vec B\)

\(\overrightarrow {BE} = (-2,4) - (-3,5)\)

\(\overrightarrow {BE} = (-2+3, 4-5)\)

\(\overrightarrow {BE} = (1,-1)\)

Now, the relative vectorial distances to C and D are now obtained:

\(\overrightarrow {AD} = 2\cdot \overrightarrow {AE}\)

\(\overrightarrow {AD} = 2 \cdot (-3,-3)\)

\(\overrightarrow{AD} = (-6, -6)\)

\(\overrightarrow {BC} = 2 \cdot \overrightarrow {BE}\)

\(\overrightarrow{BC} = 2 \cdot (1,-1)\)

\(\overrightarrow {BC} = (2,-2)\)

Lastly, the coordinates are found by the following vectorial equations:

\(\vec C = \vec B + \overrightarrow {BC}\)

\(\vec C = (-3,5) + (2,-2)\)

\(\vec C = (-3+2, 5 -2)\)

\(\vec C = (-1,3)\)

\(\vec D = \vec A + \overrightarrow {AD}\)

\(\vec D = (1,7) + (-6,-6)\)

\(\vec D = (1-6, 7 -6)\)

\(\vec D = (-5, 1)\)

The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.

The amount obtained for the daily compounding for the given APR is $4121.28.

The formula for compounding is-

A = P*\((1 + r/n)^{n *1}\)

In which;

Principal P = $3,200

r = 0.2531

time t = 1 year

Compounding time n = 365 days

Then,

A = 3,200*\((1 + 0.2531/365)^{365}\)

A = 3,200*1.2879

A = 4121.28

Thus, the amount obtained for the daily compounding for the given APR is $4121.28.

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what is the decimal form of 100/3 100/5 and 100/6? determine whether each repeats or terminates ​

to know the decimal form, just make the division

Step 1

every time you divide you will have a residual number (1),

so

100=(33*3)+1

when you divide the 1 by 3, you will have

1=(3*0.3)+0.1

and

10=3*3 +1

,so the 3 will repeat forever

Step 2

so the decimal form of 100/5 is 20

Step 3

when you divide 100 by 6 you have

I hope it helps you.

Answer:

t=-61.1

Step-by-step explanation:

You first want to isolate t. You have to multiply both sides by 6.5 to make t by itself. 6.5x9.4=61.1. This will make the equation -t=61.1. You wan to make t positive so we have to divide each side by -1. t=-61.1. This means that t=-61.1

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The given quantity log(5/sqrt(7)) can be expressed in terms of a and b as 2a - (1/2)b.

To understand how we arrive at this expression, let's break it down step by step. We start with the given quantity log(5/sqrt(7)).

First, we can use the logarithmic property that states log(a/b) is equal to log(a) - log(b). Applying this property, we can rewrite the expression as log(5) - log(sqrt(7)).

Next, we can use another logarithmic property that states log(sqrt(x)) is equal to (1/2)log(x). Applying this property to log(sqrt(7)), we get (1/2)log(7).

Now we substitute the values of a and b into the expression: log(5) - (1/2)log(7) = a - (1/2)b.

Therefore, the given quantity log(5/sqrt(7)) can be expressed in terms of a and b as 2a - (1/2)b.

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He will make $61.20 for 72 muffins in three hours.

Answer:

That's alot of words, kinda hard to understand

Answer:

15.20,15.50

Step-by-step explanation: