2/5 of the pupils in Year 9 say
their favourite colour is red.
There are 75 pupils in Year 9
How many students said red is
their favourite colour?

Hello !

56)

[tex]5 {x}^{2} + 8x = - 1 \\ 5 {x}^{2} + 8x + 1 = 0[/tex]

[tex]\Delta = {b}^{2} - 4ac \\ = {8}^{2} - 4 \times 5 \times 1 \\ = 64 - 20 \\ = 44[/tex]

The value of the discriminant is 44.

57) ∆>0 : there are two solutions.

58)

[tex]x_1 = \frac{ - b + \sqrt{\Delta} }{2a} \\ = \frac{ - 8 + \sqrt{44} }{2 \times 5} \\ = \frac{ \sqrt{11} - 4 }{5} [/tex]

[tex] x_2 = \frac{ - b - \sqrt{\Delta} }{2a} \\ = \frac{ - 8 - \sqrt{44} }{2 \times 5} \\ = \frac{ - \sqrt{11} - 4 }{5} [/tex]

Have a nice day

56. 44

57. 2

58. Image attached.

First, let's simplify some things. Let's make this a quadratic equation.

Moving the -1 (by adding 1 to both sides) gives us 5x^2 + 8x + 1 = 0. Note that this is the standard form of a quadratic, which is ax^2 + bx + c = 0.

Now, the discriminant. The discriminant is helpful because it tells us if we have 2 real solutions, 1 real solution, or if this equation is imaginary and thus impossible to solve using elementary techniques. If the discriminant is greater (>) than 0, then it has 2 solutions. If the discriminant equals (=) 0, it has 1 solution. If the discriminant is less than (<) 0, then it is imaginary.

The discriminant of a quadratic equation is defined as b^2 - 4ac (from the quadratic formula.) We just plug in b, a and c. b will be 8, a will be 5, and c will be 1. Now we just solve. (8)^2 - 4 * 5 * 1 = 64 - 20 = 44. Since 44 is greater than 0, we have 2 solutions for this. 44 is the discriminant. (Answer to 56.) We also have 2 solutions (answer to 57.)

Now, I'll solve the quadratic equation using the quadratic formula. I'll attach my work in an image (answer to 58.)

Hope this helped!

Using the normal distribution, it is found that:

a) [tex]X \approx N(25150, 12050)[/tex]

b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

c) Low: $23,519.65, High: $26,580.35.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 25150, \sigma = 12050[/tex].

Hence the distribution of X can be described as follows:

[tex]X \approx N(25150, 12050)[/tex]

The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:

X = 33950:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33950 - 25150}{12050}[/tex]

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

X = 14200:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14200 - 25150}{12050}[/tex]

Z = -0.91

Z = -0.91 has a p-value of 0.1814.

0.7673 - 0.1814 = 0.5859.

There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = -0.127(12050)

X = $23,519.65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.127 = \frac{X - 25150}{12050}[/tex]

X - 25150 = 0.127(12050)

X = $26,580.35.

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The height of the tree based on the information is 229.23.

Based on the information given,

tan 50 = h/x + 60

h = (x + 60)tan 50°

x tan 60 = (x + 60)tan 50°

x(tan 60° - ta 50°) = 60 ta 60

x = 132.34

Therefore, the height will be:

= x tan60°

= 132.34 × tan 60

= 229.23

Therefore, the height is 229.23.

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The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 <  [tex]\rm \mu[/tex] < 36.907

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]

[tex]\rm \mu[/tex] is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% [tex]\rm \alpha / 2[/tex]  = 0.05

Z = 1.64

34 [tex]\rm \pm[/tex] 1.64 * 8 / √50

34 [tex]\rm \pm[/tex]  1.855

32.145 < [tex]\rm \mu[/tex] < 35.855

(b)  The 99% confidence interval for the population mean

99% [tex]\rm \alpha / 2[/tex]  = 0.005

Z=2.57

34  [tex]\rm \pm[/tex] 2.57 * 8 / √50

34 [tex]\rm \pm[/tex]  2.907

31.093 <  [tex]\rm \mu[/tex] < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

The function in the question is given as

For A:

[tex]F(x) = 4*(1.08)^x[/tex]

For B

[tex]g(x) = 2*(1.08)^x[/tex]

The exponential growth equation that is used to solve this is

[tex]h(x) = A(r)^x[/tex]

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

2. The original population of State A was half of the original population of State B.

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.

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Answer:

Step-by-step explanation:

honestly thats what it is

Answer:

Sir, as for as I can tell that is the correct answer. Maybe you put it in wrong or added a space but that’s correct 100%.

Unless it’s not supposed to be in y = mx + b format?

Step-by-step explanation:

Answer:

y = -x - 1

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

number that describes both the direction and the steepness of the line

slope = rise/run

            b represents the y-intercept  

point where crosses the y-axis

y = mx + b → y = -1x + (-1)

this can be simplified by -x - 1

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Answer:

55,55

Step-by-step explanation:

hereakaigdidjuwjapwwjshd

The length of the model as described in the task content would be; 23 inches.

According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.

On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.

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Step-by-step explanation:

From the conversation of angular momentum

Initial momentum=final momentum

Here,

Since body is initially resting, it's momentum must be zero.

Let v be velocity of third piece. Then

0= 10(-3i+2j) + 18(5i-4j) + 22v

Solving this we get,

v= 4/22(15i+13j).

The velocity of third piece is 2/11(13 j - 15i)

Velocity defines the direction of the movement of the body or the object.

Given:

As the body is at rest so the initial momentum is zero.

Let v be velocity of third piece.

so,

0= 10(-3i+2j) + 18(5i-4j) + 22v

0= -30i + 20j + 90i -72j + 22 v

0= 60i - 52j + 22 v

-60i +52j = 22v

v= 2/11( 13j - 15 i)

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Answer:

The answer is B / y= 10x+25

Step-by-step explanation:

your welcome

Answer:

option C: Asian

explanation:

Asian countries, such as China, produce goods like the European products, but for much cheaper prices.

Answer:

2

Step-by-step explanation:

mum

The measure of the angle x is 53.13 degrees after applying the sin ratio.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Applying sin ratio:

sinx = 12/15

sinx = 0.8

x = 53.13 degrees

Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.

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Answer:

f⁻¹(1/5) = 2

Explanation:

If f(x) = (2x -3)/5

To find inverse of f(x), make x the subject.

[tex]f(x) = \dfrac{2x - 3}{5}[/tex]

[tex]5 f(x) = 2x - 3[/tex]

[tex]2x = 5 f(x) + 3[/tex]

[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]

Then,

[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]

To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]

[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]

which yields

[tex]f^{-1}(0.2) = 2[/tex]

Answer:

csc x - cot x

Step-by-step explanation:

(sinx)/(1+cos x)

Multiplying the numerator and denominator by (1-cos x),

((sinx)(1-cos x))/(1-cos² x)

((sinx)(1-cosx))(sin²x)

(1-cosx)/(sinx)

cscx - cot x

Answer:

49

1

1/6

Step-by-step explanation:

7^2 is just 7 * 7 = 49

4^0 = 1, since anything to the power of 0, is 1.

[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6

Answer:

Step-by-step explanation:

hey

please like my question

The probability of rolling a number less than 14 among {1,2,3,4} is 1.

Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.

Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:

Probability= number of events/ total number of events.

Total likely outcomes=4 {1,2,3,4}

Numbers less than 14 = 4

Probability of rolling a number less than 14=1/4

=0.25 because all number less than 14 is present.

1,2,3,4 are all less than 14.

and because all numbers are included that's why the value of probability is 1.

Hence the probability of rolling a number less than 14 is 1.

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The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.

The given construction involves drawing a parallel line through a given point P to a given line AB.

From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.

Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

The solution of the linear equations will be ( -2, 4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given equations are:-

Solving the equations by elimination method:-

2x +3y = 8

3x+y= -2

Multiply the second equation by 3 and subtract from the first equation.

2x +3y = 8

-9x -3y = 6

----------------

      -7x = 14

         x = -2

Out of the value of x in any one equation, we will get the value of y.

3x+y= -2

3 ( -2) + y = -2

-6 + y = -2

y = 4

The graph of the equations is also attached with the answer below.

Therefore the solution of the linear equations will be ( -2, 4).

The complete question is given below:-

Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.

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The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.

Let

x + 3x = 32

4x = 32

x = 32/4

x = 8

So,

3x = second unknown

= 3(8)

= 24

Check:

x + 3x = 32

8 + 24 = 32

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Answer:

x=-3/2 or-2

Step-by-step explanation:

hope this helps

Step-by-step explanation:

there are a lot of typos and missing info in your problem and answer option definition.

based on what I understood the answer should be

"the second answer option".

this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.

one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.

but I don't think this is really the meaning of this question here.

Answer:

5

Step-by-step explanation:

Anything below 5 is a fail:

3, 2, 0, 1, 3

That's 5 students.

The equation of the function g(x) will be g(x) = - ln (x + 2).

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

Let the equation of the function f will be

f(x) = ln x

If the function is multiplied with negative sign, then the function gets flipped about the x-axis.

And if we add 2 in the variable of the function, then the function gets shifted towards left.

Then the equation of the function g(x) will be

g(x) = - ln (x + 2)

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The average cost per cleaning service call charge by the company is $184.5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the total cost for x number of service calls in a year. Hence:

y = 39x + 349200

For 200 service call, in a year, x = 200 * 12 = 2400

y = 39(2400) + 349200 = $442800

Average cost = $442800 / 2400 = 184.5

The average cost per cleaning service call charge by the company is $184.5.

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Answer:

Area = 49.15

Step-by-step explanation:

area = 0.5 * side a * side b * sin(Angle)

area = 0.5 * 10 * 12 * sin(55)

area = 60 * 0.8192

49.15