what is the difference in meaning between |-3| and -3.

Answer:

See below.

Step-by-step explanation:

\(\frac{1+cos(\theta)}{sin(\theta)} +\frac{sin(\theta)}{1+cos(\theta)}=2csc(\theta)\)

\(\frac{(1+cos(\theta))(1+cos(\theta))}{sin(\theta)((1+cos(\theta))} +\frac{(sin(\theta))(sin(\theta))}{(1+cos(\theta))(sin(\theta))}=2csc(\theta)\)

\(\frac{(1+cos(\theta))(1+cos(\theta))+(sin(\theta))(sin(\theta))}{sin(\theta)((1+cos(\theta))}=2csc(\theta)\)

\(\frac{(1+2cos(\theta)+cos^2(\theta)+sin^2(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)\)

Recall the identities:

\(sin^2(\theta)+cos^2(\theta)=1\)

\(\frac{1+2cos(\theta)+1}{sin(\theta)(1+cos(\theta))} =2csc(\theta)\)

\(\frac{2+2cos(\theta)}{sin(\theta)(1+cos(\theta)}=2csc(\theta)\)

\(\frac{2(1+cos(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)\)

\(\frac{2}{sin(\theta)} =2csc(\theta)\)

\(2csc(\theta)=2csc(\theta)\)

\(\displaystyle\\\\Answer:\ \\x=\frac{3}{2} \pi +2\pi \mathbb N \\\\x=\frac{2}{3}\pi +2\pi \mathbb N\\\\x=\frac{4}{3} \pi +2\pi \mathbb N\)

Step-by-step explanation:

\(\displaystyle\\sin(2x)+sin(x)+2cos(x)+1=0\\\\2sin(x)cos(x)+sin(x)+2cos(x)+1=0\\\\2sin(x)cos(x)+2cos(x)+sin(x)+1=0\\\\2cos(x)(sin(x)+1)+(sin(x)+1)=0\\\\(sin(x)+1)(2cos(x)+1)=0\\\\a)\ sin(x)+1=0\\\\sin(x)=-1\\\\x=\frac{3}{2} \pi +2\pi \mathbb N\\\\b)\ 2cos(x)+1=0\\\\2cos(x)=-1\)

Divide both parts of the equation by 2:

\(\displaystyle\\cos(x)=-\frac{1}{2} \\\\x=\frac{2}{3}\pi +2\pi \mathbb N\\\\x=\frac{4}{3} \pi +2\pi \mathbb N\)

Answer:

b is equal to negative a and a is also equal to negative b

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

Answer:

\(\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }\)

Step-by-step explanation:

Hello, please find below my work.

\(2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0\)

\(\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Since the number of trials is not fixed, an inverse binomial distribution is used.

For each car, there are only two possible outcomes, either they use a blinker during lane change, or they do not. The probability of a car using a blinker during lane change is independent of any other car, which means that the number of cars that do not use a blinker during a lane change is a binomial variable.

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Answer:

(15 ÷ n) + (n ÷ 15)

Step-by-step explanation:

The sum of 15 divided by a number and that number divided by 15.

15 divided by a number

= (15 ÷ n)

15 is being divided by an unknown number (put n as a variable)

that number divided by 15

= (n ÷ 15)

An unknown number (put n as a variable) is being divided by 15.

The sum

Add (15 ÷ n) and (n ÷ 15)

(15 ÷ n) + (n ÷ 15)

Hope this helped and have a lovely rest of your day! :)

Answer:

\(y=2x+3\)

Step-by-step explanation:

1. Approach

Slope intercept form is a way of expressing an equation of a line using the slope of a line, and its y-intercept. The general format for the equation of a line in slope-intercept form is the following,

\(y=mx+b\)

Find each of the missing pieces of information and substitute it into the equation to find the equation of the line.

2. Find the slope

The slope of a line is the change in the line is can be found using the following formula,

\(\frac{y_2-y_2}{x_2-x_1}\)

As one can see on the given graph, two points on the line are the following,

\((-2, -1), (-1, 1)\)

Substitute the points into the formula and solve for the slope,

\(\frac{(1)-(-1)}{(-1)-(-2)}\)

\(=\frac{2}{1}\\\\=2\)

3. Find the y-intercept

The y-intercept of a line is where the line intersects the y-axis. As one can see this point is the following,

\((0,3)\)

Thus the y-intercept is (3).

4. Put the information together

Putting all of this information together, substitute the found information into the general equation for slope-intercept form. One can see that the equation of a line is the following,

\(y=2x+3\)

Answer:

X= 2, -5

Step-by-step explanation:

Take the root of both sides

Answer:

-5

Step-by-step explanation:

In order to solve this equation, we can do the following steps:

1) Add -6 to both sides of the equation:

2) Multiply the equation by -1:

3) Divide both sides by 2:

So the value of x is -1.

Answer:

12

Step-by-step explanation:

You simplify root 72 as much as possible which would be root 36 times root 2.

This would have then equaled 6 root 2.

You do 6 × root 2 × root 2.

This would then be 6 × 2, which would then equal 12.

Hope this helps :)

The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.

The correct answer is 4.

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.

Given information:

- Circle C (cats): 15

- Circle D (dogs): 21

- Circle F (fish): 12

- Overlap of C and F: 2

- Overlap of F and D: 0

- Overlap of D and C: 3

- Overlap of all 3 circles: 1

- Number outside of circles: 14

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.

From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.

To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.

Therefore, from the options given correct one is 4.

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Answer: 4

Step-by-step explanation:

trust me bro

The given inequality has the following solution set

9.52 ≤ x ≤ 22.22

If we express this as an interval, we get [9.52, 22.22].

Here is the inequality which is Kali's earning potential

200 ≤ 15.75x + 50 ≤ 400

To solve the inequality, we must isolate the variable in the center; if we remove 50 from each of the three sides, we get:

200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50

150 ≤ 15.75x ≤ 350

Now we must divide both totals by 15.75, yielding:

150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75

9.52 ≤ x ≤ 22.22

This is the inequality's solution; the solution set expressed as an interval will be [9.52, 22] or 9.52 ≤ x ≤ 22.22

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The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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\(d(f-4)=2(1-f)\\\\frac{d(f-4)}{d} =\frac{2(1-f)}{d} \\f-4=\frac{2(1-f)}{d} \\f=\frac{2(1-f)}{d} +4\)

Attached is the solution

Answer:

Step-by-step explanation:

d= 2(1-f) / f-4

d = 2 - 2f / f-4

d = 1/2 - 2f - f

d = 1/2 - f

0=1/2-f-d

f = 1/2 - d

Answer: D

Step-by-step explanation:

Thus, the probability that either blue or green or purple will appear on the next spin is 63%.

The proportion between the number of likely occurrences and the total number of potential occurrences.

Given result for the spinner:

probability = favourable outcome / total outcome

probability (blue) = 4/35

probability (Purple) = 3/35

probability (Green) = 15/35

So, probability (either blue or green or purple) = 4/35 + 3/35 + 15/35

= 22/35

= 0.6285

= 62.85

= 63%

Thus, the probability that either blue or green or purple will appear on the next spin is 63% (nearest whole number).

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*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

Answer:

  24 inches each

Step-by-step explanation:

The base of the triangle in the truck is 2 times that in the automobile, hence the similar triangle will have sides that are 2 times 12.0 inches each.

The two equal sides of the truck triangle are 24.00 inches each.

Answer:

10 meters

Step-by-step explanation:

Answer:

The rectangle is 5 inches long by 19 inches wide.

Step-by-step explanation:

Let's start by listing what we know:

Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.

\(\left \{ {{2w + 2l = 48} \atop {w = 3l + 4}} \right.\)

Now, let's solve the system of equations using substitution:

\(2w + 2l = 48\)

\(2 (3l + 4) + 2l = 48\)

\(6l + 8 + 2l = 48\)

\(8l + 8 = 48\)

\(8l = 40\)

\(l = 5\)

The length of the rectangle is 5 inches.

Now, let's use this to solve for the width.

\(w = 3l + 4\)

\(w = 3(5) + 4\)

\(w = 15 + 4\)

\(w = 19\)

The width of the rectangle is 19 inches.

Let's check our work:

\(2w + 2l = 48\)

\(2(19) + 2(5) = 48\)

\(38 + 10 = 48\)

\(48 = 48\)

The results match, so our answer is correct.

The rectangle is 5 inches long by 19 inches wide.

Answer:

y=-2x-2

Step-by-step explanation:

If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:

\(\frac{-4-4}{-9-7}\) = \(\frac{-8}{-16}\)=\(\frac{1}{2}\). For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of \(\frac{1}{2}\), which is -\(2\). The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.

Now we find the equation!

y=mx+b. Plug in -\(2\)     as the "m", or slope:

y=-\(2\)x+b

Now, plug in the point (-1, 0):

0=-\(2\)*-1+b

0=\(2\)+b

b=-\(2\)

So, we have m=-\(2\) and b=-\(2\) and we can form our equation!

y=-\(2\)x-\(2\)

Hope this helps!! :D

Answer:

Gary is now 24years

Step-by-step explanation:

let the age of Jan be x and that of Gary be x+15

in six years time they will be as follows

Jan =x+6

Gary=x+15+6=x+21

2(x+6)=x+21

2x+12=x+21

collect the like terms

2x-x=21-12

x=9

Gary =9+15=24years

An angle that opens one-third of a whole circle is 120 degrees. To find the angle of a triangle given two sides, use the Law of Cosines. The total degree of a triangle is 180 degrees.

To calculate the angle for the first case is to divide 360 degrees (the total amount of degrees in a circle) by 3 (the number of parts the circle is being divided into). 360 divided by 3 is equal to 120. Therefore, the angle is 120 degrees. To find the angle of a triangle given two sides, use the Law of Cosines. The Law of Cosines states that for any triangle ABC, we have the equation c2 = a2 + b2 - 2abcos(C), where c is the length of the side opposite the angle C, a and b are the lengths of the other two sides, and C is the angle opposite the side c.  The total degrees of a triangle is 180°. This is because of the Triangle Angle Sum Theorem which states that the sum of the angles of any triangle is equal to 180°.

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Answer:

We can use three solution and they are

(1)completing the square

(2)quadratic formula

(3) factorisation method

The quadratic equation 2x^2 - 4x = -2 has  two values .

   (1)completing the square

   (2)quadratic formula

   (3) factorization method

Given,

           quadratic equation 2x^2 - 4x = -2

                   2x² - 4x + 2 =0

Now solve this equation by factor,

                    2x² - 4x + 2 = 0

                    2x² - ( 2+2)x +2 = 0

                    2x² - 2x -2x + 2 = 0

                    2x(x- 1 ) -2 ( x -1) = 0

                    (2x - 2) ( x- 1) =0

                  2x - 2 = 0   or  x - 1 = 0

                   x = 1 or x = 1

So, this equation has 2 value of x.

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Answer:

5.25 miles

Step-by-step explanation:

The line segment which is a ray shown in the drawing include the following: B. BC.

In Mathematics and Geometry, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In Mathematics and Geometry, parallel lines refer to two (2) lines that are always the same (equal) distance apart and never meet.

By critically observing the parallel lines cut by a transversal above, we can reasonably infer and logically deduce that line segment BC represents a ray.

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