1). On a Friday night 18 pupils were in detention from a school of 800 pupils.
What percentage of the school were in detention that Friday night?
2). 360 buses run from a depot, but 72 are being repaired.
What percentage of the total are in service ?
3). One day 132 trains arrive at a railway station and 99 are on time. What percentage of them
are late ?
4). In an exam a pupil gets 54 out of 72 marks. What percentage of the exam does he get wrong?
5). A dentist looks at Jean's 32 teeth, 12 of them have fillings.
What percentage don't have fillings?
6).
Billy has 250 school meals in a year. He has chips for 195 meals.
What percentage of school meals does Billy not have chips?

a) is the graph of inverse sine function.

The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal. It produces the angle's value.

When the opposing side and hypotenuse of a right triangle are known, the angles can be determined using the inverse sine function. That is, angle = sin-1. The inverse sine function, which is represented as sin-1 or arcsine, is one of the inverse trigonometric functions that calculates the inverse of the sine function. Each restricted domain inverse of a trigonometric function, such as cosine, tangent, cosecant, or cotangent, exists. The trigonometric ratios from the right-angle triangle are utilized to compute the angles using the inverse function formulas.

Given,

a) is the graph of inverse sine function.

Function - inverse sine

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Answer:

A

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

240 divided by 2 = 120

120 x 5 = 600

The lowest common denominator for the rational expressions \(\frac{3}{x+2}$ and $\frac{4}{2x+4}$ is $2(x+2)^2$\).

The lowest common denominator (LCD) of a rational expression refers to the smallest expression that is evenly divisible by each of the denominators in the expression.

To compute the lowest common denominator of a rational expression, you should take the following steps:

Find the prime factorization of each denominator

Find the highest power of each factor that appears in any of the denominators

Multiply all the factors found in Step 2 together to find the lowest common denominator (LCD)

Let's look at an example:

Find the lowest common denominator for the rational expressions \(\frac{3}{x+2}$ and $\frac{4}{2x+4}$\)

Factor each denominator \($x+2$\) is already factored \($2x+4 = 2(x+2)$\)

The highest power of each factor that appears in any of the denominators \($x+2$\) appears once in the first denominator \($2(x+2)$\) appears once in the second denominator

Multiply all the factors found in Step 2 together to find the lowest common denominator \((LCD)$LCD\) = (x+2) \(\cdot 2(x+2) = 2(x+2)^2$\)

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Answer:

the G graph runs straight through the middle while the F does not

If Tamika receives 20 rewards points just for signing up and she earns 10.5 points for each visit to the movie theater and she needs 167 points for a free movie ticket, then an equation to determine x, the number of visits Tamika must make to earn a free movie ticket is 10.5x + 20 = 167 and the value of x is calculated to be 14.

The number of visits Tamika must make can be determined by using a linear equation with one variable.

As,

reward points for signing up = 20

points for each visit = 10.5

points needed for free movie ticket = 167

If we consider x to be the number of visits required, then the linear equation can be given as,

10.5x + 20 = 167

Solving for x,

10.5x = 167 - 20

10.5x = 147

x = 147/10.5 = 14

Hence, the number of visits Tamika must make to earn a free movie ticket is equal to 14.

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Answer:

Step-by-step explanation:

Answer:

20 red sweets

Step-by-step explanation:

do two thirds of 30 and the part that cane out is the red sweets

Answer:

12

Step-by-step explanation:

Sum the parts of the ratio, 2 + 3 = 5 parts

Divide the number of sweets by 5 to find the value of one part of the ratio

30 ÷ 5 = 6 sweets ← value of 1 part of the ratio, thus

2 × 6 = 12 ← number of red sweets

Answer:

Step-by-step explanation:

It’s A

The triangles EFG and HJK are congruent as all three sides of triangle EFG are given equal to the three sides of triangle HJK.

The postulate applied here is Side-Side-Side (SSS) postulate.

Thus, we can select option A. Congruent - SSS.

Two triangles are congruent when their shape is identical and their size is equal, that is, the three sides are equal and the three angles are also equal.

Congruency in triangles can be proven by the following postulates:

In the question, we are asked if EFG - HJK (EFG is congruent to HJK), when we are given that:

EF = HJ

EG = HK

FG = JK.

And if they are congruent, by which postulate it is so.

The triangles EFG and HJK are congruent as all three sides of triangle EFG are given equal to the three sides of triangle HJK.

The postulate applied here is Side-Side-Side (SSS) postulate.

Thus, we can select option A. Congruent - SSS.

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Answer:

B

Step-by-step explanation:

A)  The function in factored form is -5(x - 1)² and the vertex is (1, 0).

B)  The zeroes are x = 1, the axis of Symmetry is x = 1 and the direction of the opening is downward.

C)  The domain of the function is all real numbers and the range is

(-∞, 0].

We have,

A)

Factoring out the common factor (-5):

f(x) = -5(x² - 2x + 1)

The equation x² - 2x + 1 can be factored as (x - 1)(x - 1) or simply (x - 1)²:

f(x) = -5(x - 1)²

The equation of a quadratic function:

f(x) = a(x - h)² + k

In this case,

a = -5, h = 1, and k = 0 (since there is no constant term).

So, the vertex of the function is (h, k) = (1, 0).

B)

To find the zeros of the function, we set f(x) = 0 and solve for x:

-5(x - 1)² = 0

(x - 1)² = 0

Taking the square root of both sides:

x - 1 = 0

x = 1

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

In this case, the axis of symmetry is x = 1.

The direction of the Opening:

Since the coefficient of the x² term is negative (-5), the parabola opens downward.

C)

The domain of the function f(x) is all real numbers since there are no restrictions or limitations on the possible input values of x.

The parabola opens downward and the vertex is at (1, 0), the range of the function is all real numbers less than or equal to 0.

The range can be expressed as (-∞, 0].

Thus,

A) The function in factored form: -5(x - 1)², Vertex: (1, 0).

B) Zeros: x = 1, Axis of Symmetry: x = 1, Direction of Opening: Downward.

C) Domain: All real numbers, Range: (-∞, 0].

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Step-by-step explanation:

Hope this image helps you!!

It is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.

As given in the question,

Maximum error on the reading of speedometer =1.6%

Speed limit on a road is 65 miles per hour

Reading of a speedometer = 63 miles per hour

As per the error in the speedometer it can be more or less by 1.6%

To check speed limit

If it more

Speed limit  = 63 + (1.6% of 63)

                   = 63 + 1.008

                   = 64.008 miles per hour < 65 miles per hour

If it less

Speed limit = 63 - (1.6% of 63)

                   = 63 -1.008

                   = 61.992 miles per hour < 65 miles per hour

Therefore, it is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.

The complete question is:

The reading on a car speedometer has 1.6% maximum error the speed limit on a road is listed 65 miles per hour.

The car’s speedometer reads 63 miles per hour. Is it possible that this car is going over the speed limit?

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If "A" denotes the event that student takes statistics and B denotes event that the student is senior, the probability of P(A' or B) is (c) 0.82.

To find P(A' or B), we want to find the probability that a student is not a senior or take statistics (or both).

We know that the total number of students surveyed is 100, and out of those students : 15 seniors take statistics; 35 seniors take calculus

18 juniors take statistics,  32 juniors take calculus.

The probability P(A' or B) is written as P(A') + P(B) - P(A' and B);

To find the probability of a student not taking statistics, we add the number of students who take calculus (seniors and juniors) and divide by the total number of students:

⇒ P(A') = (35 + 32) / 100 = 0.67;

The probability of student being a senior,

⇒ P(B) = (15 + 35)/100 = 0.50,

Next, to find probability of student who is not take statistics and is a senior, which are 35 students,

So, P(A' and B) = 35/100 = 0.35;

Substituting the values,

We get,

P(A' or B) = 0.67 + 0.50 - 0.35 = 0.82;

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

A student surveyed 100 students and determined the number of students who take statistics or calculus among seniors and juniors. Here are the results.

              Statistics   Calculus

Senior           15              35

Junior           18               32

Let A be the event that the student takes statistics and B be the event that the student is a senior.

What is P(A' or B)?

(a) 0.18

(b) 0.68

(c) 0.82

(d) 0.97

Answer:

8 1/2

Step-by-step explanation:

the volume of the  rectangular prism is 8.5 unit^3.

In mathematics, volume is the space taken by an object.

here, we have,

given a rectangular prism 4  &  2 1/8

now,

the volume of the prism is simply the area of any of the sides times the length, so in this case the shaded area times 4.

i.e. 2 1/8 * 4

=17/8* 4

=17/2

=8.5 unit^3.

hence, the volume of the  rectangular prism is 8.5 unit^3.

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The Laplace transform of the solution y(t) to the given initial value problem y"+y=g(t), y(0) = -4, y'(0) = 0, where g(t) = t, t<6; 5, t>6 is represented by the function Y(s) (in terms of s).

To solve the initial value problem y"+y=g(t) with the given initial conditions, we can take the Laplace transform of both sides of the equation. This transforms the differential equation into an algebraic equation in the Laplace domain.

Applying the initial conditions to the transformed equation, we can find the Laplace transform, Y(s), of the solution y(t). The exact expression for Y(s) can be obtained by using the table of Laplace transforms and the properties of Laplace transforms.

By substituting the Laplace transform of the input function, g(t), into the transformed equation, we can solve for Y(s) in terms of the Laplace variable s.

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Answer: 5.5 inches, 3.5 inches

Step-by-step explanation:

Given

Barry wants to make a drawing i.e. half the size of original

The length and width of the original drawing are  11 inches and 7 inches respectively.

So, the intended drawing is obtained by multiplying the original dimensions by \(\frac{1}{2}\)

The length of barry's drawing is

\(\Rightarrow 11\times \frac{1}{2}\\\\\Rightarrow 5.5\ \text{inches}\)

The breadth of barry's drawing

\(\Rightarrow 7\times \frac{1}{2}\\\\\Rightarrow 3.5\ \text{inches}\)

Answer:

Roadhouse

Step-by-step explanation:

Because

This indicates that approximately 47.7% of the sampled subjects responded definitely or probably not beneficial to family planning.

From the given data, we can analyze the proportions of respondents who considered family planning beneficial and those who did not.

The proportion of respondents who responded definitely or probably beneficial is 651 out of 1245 sampled subjects. Therefore, the proportion can be calculated as:

Proportion = 651/1245 ≈ 0.523

This indicates that approximately 52.3% of the sampled subjects responded definitely or probably beneficial to family planning.

On the other hand, the proportion of respondents who responded definitely or probably not beneficial is 594 out of 1245 sampled subjects. The proportion can be calculated as:

Proportion = 594/1245 ≈ 0.477

This means that roughly 47.7% of the sampled participants indicated that family planning was either definitely advantageous or probably not beneficial.

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\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

The value of x is 36 degrees.

The correct answre is an option (B)

From the attached figure we can observe that angle GHE and angle DHA are opposite angles.

We know that opposite angles are congruent.

So, m∠DHA = m∠GHE

∠DHA = (60 - x)°            ......(as ∠GHE = (60 - x)°)

Here, the line DE is perpendicular to the line HK.

So, the angle DHK measures 90°

We can observe that ∠DHA and ∠AHK are complementary angles.

By definition of complementary angles,

m∠DHG + m∠GHE = 90°

(60 - x) + (2x - 6) = 90

(2x - x) + (60 - 6) = 90

x = 90 - 54

x = 36 degrees

Therefore, the correct answre is an option (B)

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Answer:

you cant solve that y=x-6 is not a solve able question it's just a function,do you mean how to graph it

Answer:

3x³ - 7x² - 2x + 8

Step-by-step explanation:

(x + 1)(3x² - 10x + 8)

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x² - 10x + 8) + 1 (3x² - 10x + 8) ← distribute parenthesis

= 3x³ - 10x² + 8x + 3x² - 10x + 8 ← collect like terms

= 3x³ - 7x² - 2x + 8

The mean of the sampling distribution of proportion is 0.15

The probability the sample proportion will be within 0.04 of the population proportion is 0.9182

The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157

P(Smokers) in Australia= 15/100=0.15

Sample, n =240

Part a, The mean of the sampling distribution of proportion:

μ₂ = P(Smokers)

    = 0.15

The mean of the sampling distribution of proportion is 0.15

The standard deviation of the sampling distribution of proportion is,

δ \(=\sqrt{p\frac{(1-p)}{n} }\)

  \(=\sqrt{0.15\frac{(1-0.15)}{240} }\)

 \(=0.0230\)

The standard deviation of the sampling distribution of proportion is 0.0230

Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:

To find this, we first, compute the z score then find probability based on standard normal table.

For 0.15-0.04,  p=0.11 and converts to:

   \(z=\frac{p-u_{p} }{standard deviation} \\\)

   \(=\frac{0.11-0.15}{0.0230}\)

  = -1.74

For 0.15+0.04, p=0.19, and converts to:

    \(z=\frac{0.19-0.15}{0.0230}\)

     = 1.74

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

     \(=p(-1.74\leq z\leq 1.74)\)

     \(=0.9591-0.0409\)

    \(=0.9182\)  

Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182

Part c, the probability the sample proportion will be within 0.02 of the population proportion:

First, compute the z score then find probability based on standard normal table.

For 0.15-0.02, p=0.13, and converts to:

       \(=\frac{0.13-0.15}{0.0230}\)

       =-0.87

For 0.15+0.02, p=0.17, this converts to:

    \(=\frac{0.17-0.15}{0.0230}\)

    =0.87

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

    \(=p(-0.87\leq z\leq 0.87)\)

   \(=0.8079-0.1922\)

   \(=0.6187\)

Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157

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The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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Hence, the correct answer are Function  f(x)  is  translated  6  units  to  the left and Function  f(x)  is translated 8 units down.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

The absolute value of a number refers to the distance of a number from the origin of a number line. It is represented as |x|,  which defines the magnitude of any integer ‘x’. The absolute value of any integer, whether positive or negative,  will be the real numbers,  regardless of which sign it has.   It is represented by two vertical lines  |x|,  which is known as the modulus of x.

Function  f(x) = ||x||  is  transformed  to  create function  g(x) =  ||x+6||-8.

To  get  from  f(x)  to  g(x),

we  need  to  perform  the  following  transformations:

Therefore,  the correct  statements  are:

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Answer:

∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°

Step-by-step explanation:

l II m and p is their transversal and 1 = 120°

∠1 + ∠2 = 180 °(Straight line)

120° + ∠2 = 180° > ∠2 = 180° - 120° = 60°

∠2 = 60°

But ∠1 = ∠3 (Vertically opposite angles)

∠3 = ∠1 = 120°

Similarly ∠4 = ∠2

(Vertically opposite angles)

∠4 = 60°

∠5 = ∠1 (Corresponding angles)

∠5 = 120°

Similarly ∠6 = ∠2 (Corresponding angles)

∠6 = 60°

∠7 = ∠5 (Vertically opposite angles)

∠7 = 120°

And ∠8 = ∠6 (Vertically opposite angles)

∠8 = 60°

Hence ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°

Marshall is wondering whether he can participate in the LLP again next year. The statement that is true is "He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

The Lifelong Learning Plan is a program that helps Canadian residents finance their post-secondary education through their registered retirement savings plans (RRSP). If an individual is attending school full-time, they can withdraw up to $10,000 a year from their RRSP under the program, or up to $20,000 in total. There are certain rules that must be followed by an individual participating in the LLP. For example, withdrawals must be made within four years of enrolling in an eligible educational program, and repayments must begin within the same period.

Here are the statements: Provided he repays his LLP balance in full by the end of this year, Marshall can participate in the LLP again next year.Marshall can only participate in the LLP once over his lifetime. However, his wife can make a LLP withdrawal from her RRSP on his behalf. He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000. He can only participate in the LLP a second time if he repays his LLP balance in full and waits 5 years before he returns to school.The correct statement is: He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

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