Express in the form 1:n.
Give n as a fully simplified fraction.
12:2

Answer:

Step-by-step explanation:

Given the expression;

secθ − tan θ = cosθ

We are to find the solution in the interval [0, 2π).This is as shown;

From trigonometry identity;

secθ = 1/cosθ

tanθ = sinθ/cosθ

Substitute into the formula;

secθ − tan θ = cosθ

1/cosθ-sinθ/cosθ = cosθ

Multiply through by cosθ

1 - sinθ = cos²θ

1-sinθ = (1-sin²θ)

1-sin²θ-1+sinθ =0

-sin²θ+sinθ = 0

sin²θ = sinθ

sinθ = 1

θ = arcsin 1

θ = 90

θ = π/2

Hence the solution is π/2

The equation is an illustration of trigonometry ratios and identities

The solution in the interval  [0, 2π) is [tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]

The equation is given as:

[tex]\mathbf{sec\theta - tan \theta = cos\theta}[/tex]

In trigonometry identity, we have:

[tex]\mathbf{sec\theta = \frac{1}{cos\theta}}[/tex]

and

[tex]\mathbf{tan\theta = \frac{sin\theta}{cosθ}}[/tex]

So the equation becomes

[tex]\mathbf{\frac{1}{cos\theta} -\frac{sin\theta}{cos\theta} = cos\theta}[/tex]

Multiply through by cosθ

[tex]\mathbf{1 - sin\theta = cos\²\theta}[/tex]

In trigonometry,

[tex]\mathbf{cos\²\theta = 1 - sin^2\theta }[/tex]

So, we have:

[tex]\mathbf{1-sin\theta = 1-sin\²\theta}[/tex]

Subtract 1 from both sides

[tex]\mathbf{sin\theta = sin\²\theta}[/tex]

Divide both sides by [tex]\mathbf{sin\theta}[/tex]

[tex]\mathbf{1 = sin\theta}[/tex]

Rewrite as:

[tex]\mathbf{sin\theta = 1}[/tex]

Take arc sin of both sides

[tex]\mathbf{\theta = sin^{-1}(1)}[/tex]

This gives

[tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]

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Answer:980,507

Step-by-step explanation:

Answer:

980,507

Step-by-step explanation:

hope this helps :)

Answer:

y= -4

Step-by-step explanation:

Edge 2020 :)

Answer:

The graph of the solution to inequality is shown in the attached figure.

Step-by-step explanation:

Considering the inequality

[tex]b< 6[/tex]

As this inequality could simply further

so

[tex]b<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:b<6\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:6\right)\end{bmatrix}[/tex]

As the interval notation indicates that b is less than 6, hence 6 will not be included on the graph.

Therefore, the graph of the solution to inequality is shown in the attached figure.

Answer:

6 cups of lemon juice

Step-by-step explanation:

Answer:

It’s confusing

Step-by-step explanation:

Answer:

2 < x < 4

Step-by-step explanation:

Based on Lauren's spending patterns and the balance in her account, her new balance must be an overdraft of $180.

Her balance after the vacation can be found as:

= Balance before vacation - ( Amount spent)

= 60 - ( 80 x 3)

= 60 - 240

= -$180

In conclusion, she will have a bank overdraft of $180.

Find out more about bank overdrafts at https://brainly.com/question/8283687.

Answer:

The answer is "50".

Step-by-step explanation:

Let,

[tex]\to p(200) = 400[/tex]

If we assume the $20 reduction would raise the number of items sold to $40 so the increment is (x - 200) if x is the number of units sold.

[tex]\to (\frac{1}{40}) \times 20 = 0.5[/tex]

[tex]\to D(x) = 400 - 0.5 \times ( x - 200 ) \\\\ \ and \\ \to R(x) = x \times (D(x) \\\\[/tex]

            [tex]= x \times [ 400 - 0.5\times ( x - 200 )]\\\\ = x\times[400 - 0.5x - 100]\\\\= x\times [300 - 0.5 x]\\\\= 300x - 0.5 x^2[/tex]

[tex]R(x)= 300x- \frac{1}{2} x^2\\\\R'(x)=300-x\\[/tex]

if R'(x)=0

x=300

if  0 < x  < 300  and R(x) > 0 then R(x) for maximum x is = 300

[tex]D(300) = 400 - 0.5\times ( x - 200 )\\\\[/tex]

            [tex]= 400 - 0.5\times ( 300- 200 )\\\\ = 400 - 150+ 100\\\\ = 500 - 150 \\\\=350[/tex]

The rebate must be  : 400 - 350  = 50

Answer:

2

Step-by-step explanation:

Answer:

100 inches

Step-by-step explanation:

Given

20 inch ≈ 0.5 m

Required

Determine the equivalent of 2.5m in inches

The question illustrated conversion between units of same measurements.

And we have that:.

20 in ≈ 0.5 m

Which can be rewritten as:

0.5 m ≈ 20 in

To solve further, we multiply both sides by 5

0.5 m * 5 = 20 in * 5

2.5 m ≈ 100 in

Hence, we can conclude that the 2.5m rope is approximately 100 inches long

The 2.5m rope is approximately 100 inches long

We have to given that,

20 inch ≈ 0.5 m

And, To Determine the equivalent of 2.5m in inches.

Since, It is illustrated conversion between units of same measurements.

And we have that;

20 in ≈ 0.5 m

Which can be rewritten as:

0.5 m ≈ 20 in

we multiply both sides by 5

0.5 m x 5 = 20 in x 5

2.5 m ≈ 100 in

Hence, we can conclude that the 2.5m rope is approximately 100 inches long.

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Answer: The answer is C.

Step-by-step explanation:

Remember that the formula for the area of a rectangle is [tex]lw[/tex]. This gives you 12x as the length and 4+x as the width. You just need to multiply those two number together, and you get 12x(4+x) which is C.

Answer:

y=5x+(-19)

Step-by-step explanation:

Refer to the picture that given

Answer:

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.) PEAKS: Graphs often display peaks, or local maximums.

Answer: It is Skewed

Step-by-step explanation: More positive space than negative. So it is positively skewed.

Answer:

1/5

Step-by-step explanation:

Answer:

Answer:

C=0.15y+7.89

Step-by-step explanation:

The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We define a linear equation. Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.

When two linear expressions are equal, there is a linear equation in one variable. Or, to put it another way, a graph would be one method of solving this equation.

Given ,

Average price of movie ticket =$7.89

Increased average tickets =$0.15

So Simplifying the equation is

C=0.15y+7.89

Therefore The linear equation represents the cost C of a movie ticket y is C=0.15y+7.89.

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9514 1404 393

Answer:

  110 units

Step-by-step explanation:

Fill in the given value and solve for x.

  c = x^2 -10x +35

  11035 = x^2 -10x +35

  11025 = x^2 -10x +25 = (x -5)^2 . . . . subtract 10 to complete the square

  x = 5 +√11025 = 5 +105 . . . . find the positive solution

  x = 110

The number of units manufactured at a cost of 11,035 is 110 units.

Answer:

Your answer would be 92 Hours

Step-by-step explanation:

4 x 115 = 460

460 x 12 = 5,520

5,520 ÷ 60 = 92

Therefore your answer would be 92

Answer:

D

Step-by-step explanation:

If its right let me know I think this is right

Answer:

Step-by-step explanation:

If MQ also bisects angle ∠LMP, then;

<LMQ + <QMP = <LMP

Also <LMQ = <QMP

The equation becomes <QMP + <QMP = <LMP

2<QMP = <LMP

Let <LMP be 8x+40° (This is an assumed value)

2(5x+10) = 8x+40

Open the parenthesis

10x+20 = 8x+40

10x-8x = 40-20

2x = 20

x = 20/2

x = 10

Find <QMP

Since <QMP = 5x+10

<QMP = 5(10)+10

<QMP = 50+10

<QMP = 60 degrees

Note that the angle <LMP was assumed. Any other function can be used depending on the question

Answer:

44,55,77

Ratio is 11/1

Step-by-step explanation:

176=4x+5x+7x

176=16x

11=x

44,55,77

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

There are 104 kids and 162 adults

Step-by-step explanation:

104x1.5=156 Dollars from the kids

162x4=648 dollars from adults

648+156=804

Can I get brainiest now?

Answer:

1) Let's suppose that you go in a straight line, in a car that moves at a constant speed of 80km/h.

Then the distance from your house (assuming that you start the drive in your house) can be modeled with a linear equation:

D(t) = 80km/h*t

where t is time in hours.

This will be a linear function.

2) Suppose that you have a population of some animal, that grows by 2% each month, and initially, there are 100 individuals of that animal.

Then the first month, the population is 100.

The second month the population increased by a 2%, then it will be:

100 + 100*0.02 = 100*(1.02)

The third month, the population will be 100*(1.02) + 0.2*100*(1.02) = 100*(1.02)^2.

and so on, this is an exponential relation, where the population as a function of the number of months, can be written as:

P(m) = 100*(1.02)^(m - 1)

3) Suppose that you have $100 saved, and each month you can save another $80, let's find a function that says the amount of money that you have saved as a function of the number of months. S(m)

The month number zero (before you started saving) you had $100 saved.

S(0) = $100.

One month after, you have saved $80 more, then you have:

S(1) = $100 + $80

Another month after, you have:

S(2) = $100 + $80 + $80 = $100 + 2*$80

And so on, you already can see the pattern, after m months, you will have:

S(m) = $100 + m*$80 saved.

Answer:

20%

Step-by-step explanation:

To find the percent decrease, we do old number subtracted from the new numbers over old.

We do

40 - 32 = 8

Then we put the 8 over the old and get

8/40

In percentage form it would be 20%

Answer:

5 [tex]\frac{1}{2}[/tex]  

Step-by-step explanation:

[tex]2\frac{4}{5}[/tex] + [tex]3\frac{7}{10}[/tex] = [tex]2\frac{8}{10}[/tex] + [tex]3\frac{7}{10}[/tex] = [tex]5\frac{15}{10}[/tex] = [tex]6\frac{1}{2}[/tex]  

12 - [tex]6\frac{1}{2}[/tex] = (12 - 6) - [tex]\frac{1}{2}[/tex] = 6 - [tex]\frac{1}{2}[/tex] = 5 [tex]\frac{1}{2}[/tex]

Answer: -4/15

Step-by-step explanation: To add these two fractions together,

we start by finding their Least Common Denominator (LCD).

Since our denominators of 5 and 3 have no factors in common,

our least common denominator is 5 · 3 or 15.

In order to get a denominator of 15 in each fraction,

we multiply top and bottom of the first fraction by 3

and top and bottom of the second fraction by 5.

That gives us -9/15 + 5/15 which simplifies to -4/15.

As your last step, make sure that the fraction

that you end up with doesn't reduce.

In this case, -4/15 does not reduce but watch out for this last step.

Answer:

0.12995

0.47508

0.0841

0.738

Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

Zscore = −1.378

P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04

-1.378 ≤ z ≤ 0.924

Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

P(Z ≤ - 1.378) = 0.084102

0.82226 - 0.084102

= 0.738