What is the step by step formula for figuring out a home mortgage?

The percent of decrease in the cost of each ticket is 26%

We know that last year, the cost of a seat was $68.50, then we can write the relation:

$68.50 = 100%

So the original cost is the 100% in our calculations.

The cost now is $50.69, and this is equivalent to a percentage X, so we can write:

$50.69 = X

Now we can write the quotient between these two equations to get:

X/100% = $68.50/ $50.69

X = ($50.69/ $68.50)*100% = 74%

Then the percentage decrease is:

100% - 74% = 26%

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The coordinate grid shows two endpoints M and N.

The distance between two endpoints on a coordinate grid is calculated as;

The length of MN therefore is 5.8 units (approximately)

By working with the exponential function, we will see that after 13.68 years the value of the card will be $27.09.

We know that the original value is $5.75, and it increases a 12% per year, then the value of the card is given by the exponential function:

\(f(x) = \$ 5.75*(1 + 0.12)^x\)

We want to find the value of x such that:

f(x) = $27.09, so we need to solve:

\(f(x) = \$ 5.75*(1 + 0.12)^x = \$ 27.09\\\\(1.12)^x = 27.09/5.75\)

Now we can apply the natural logarithm to both sides:

\(ln(1.12^x) = ln(27.09/5.75)\\\\x*ln(1.12) = ln(27.09/5.75)\\\\x = \frac{ln(27.09/5.75)}{ln(1.12)} = 13.68\)

This means that after 13.68 years, the value of the card will be $27.09.

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Answer: 3/2

Step-by-step explanation:

Answer:

3/2 or 1 1/2

Step-by-step explanation:

\(2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}\)

Answer:

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

Y-intercept: 3

Equation:  \(y =-\frac{1}{2} x + 3\)

Step-by-step explanation:

The line intercepts the y-axis at the point (0, 3).

The line appears to be rising by -1 and running by 2. This gives us the slope, \(-\frac{1}{2}\).

We can use these two parts to put together the equation: \(y =-\frac{1}{2} x + 3\)

Hope this helps! Let me know.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 2000/2500 = 0.80

Number of samples n = 2500

Confidence interval = 95%

z-value(at 95% confidence) = 1.96

Substituting the values we have;

0.80+/- 1.96√(0.80(1-0.80)/2500)

0.80+/- 1.96√(0.000064)

0.80+/- 0.01568

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)

Answer: \(67\)

Step-by-step explanation:

\(0+1+3=4, \\\\ 4+10=141+3+4=8 \\8+20=283+4+8=15 \\\\ 15+30=454+8+15=27 \\\\ 27+ 40=67\)

Answer:

{4, 4, 8, 13, 16}

Step-by-step explanation:

If we have a set of N numbers in order:

{x₁, x₂, ..., xₙ}

The median is the middle number of the set.

The mode is the value that is repeated more times in the set

The mean is computed as:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

And the range is the difference between the largest value and the smallest value.

Here we want 5 positive integers, so we have something like:

{x₁, x₂, x₃, x₄, x₅}

We know that the median is 8.

Then the middle value, x₃, is equal to 8.

We also know that the mode is 4, then we can have the number 4 repeated two times, and because 4 is smaller than 8 and this must be in order, then we can have:

x₁ = x₂ = 4

Replacing these in the set we have:

{4, 4, 8, x₄, x₅}

Now we know that the range is 12, and this was the difference between the largest and smallest value.

We know that the smallest value is 4, and the largest value is x₅, then we will have:

x₅ - 4 = 12

x₅ = 12 + 4 = 16

Then our set is:

{4, 4, 8, x₄, 16}

Finally, we know that the mean is 9.

Remember that the equation for the mean is:

\(M = \frac{4 + 4 + 8 + x_4 + 16}{5}\)

Then we need to solve:

\(9 = \frac{4 + 4 + 8 + x_4 + 16}{5}\)

\(9*5 = 4 + 4 + 8 + x_4 + 16}\)

\(45 = 32 + x_4\)

\(45 - 32 = x_4 = 13\)

Then the set of five positive integers is:

{4, 4, 8, 13, 16}

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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The fraction which is closest to 1/2 is, 3/8. So option B is correct

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

A fraction number 1/2

In decimal form = 0.5

Closest fraction number = ?

Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,

Lets take, A fraction 1/6

In decimal form it can written as,  0.167

Difference 1 =  0.5 - 0.167

                  =   0.333

Similarly, For numbers 3/8, 3/4, -1/2

Difference 2 =  0.5 - 0.375  = 0.125

Difference 3 =  0.5 - 0.75  = -0.25

Difference 4 =  0.5 - (-0.5)  =  1.0

It can be seen that,

Magnitude of difference in case of 3/8 is very less

Hence, the closest number is 3/8

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The threes solutions to the given equation sec²x - secx = 2 are:

To solve: sec²x - secx = 2 on interval [0,2\(\pi\))

When we set t = sec x, we get the quadratic equation:

As a result, we must seek solutions to the equations:

\([1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;\)

Therefore, the three solutions are:

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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2\(\pi\))

Answer:

12

Step-by-step explanation:

We know that ,

So that ,

Answer:

No

Step-by-step explanation:

B/c trinomial has exactly 3 terms and binomial only have 2

9514 1404 393

Answer:

  0.9114

Step-by-step explanation:

The multiplier for a series of changes is the product of the multipliers for each of the changes:

  (1 -2%)(1 -7%) = (0.98)(0.93) = 0.9114

The rate of change of the area of the triangle after two seconds have passed is 16 cm².

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Area of a right angled triangle = \(\frac{1}{2}\) × base × height

Given that, the lengths of the right sides of a right triangle were 12 cm and 16 cm.

Initial area of the triangle = \(\frac{1}{2}\) × 12 × 16

                                          = 96 cm²

The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec.

After 2 seconds, length of base = 12 + (2 × 2) = 16 cm

After 2 seconds, length of height = 16 - (2 × 1) = 14 cm

Area of the triangle after 2 seconds = \(\frac{1}{2}\) × 16 × 14

                                                            = 112 cm²

Rate of change of area = 112 cm² - 96 cm² = 16 cm²

Hence the rate of change of area is 16 cm².

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Answer:

yes it will......I'm not to sure

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

-2

Step-by-step explanation:

Slope equals rise over run. The line goes forwards by two and down by 4 between the two charted points, so the slope would be -4/2 or -2.

Answer:

12 ÷ 0.03 move two places to the right

12÷3

4

Step-by-step explanation:

It's just asking you to rewrite it in vertex form. Which would be

\((x + 10) ^{2} - 4\)

Step-by-step explanation:

Solve the inequality for x.

10x > 9(2x - 5) - 11

10x > 18x - 45 - 11

10x > 18x - 56

subtract 18x from both sides:

10x - 18x > 18x - 56 - 18x

-8x > - 56

divide both sides by -8 and remember to flip the sign:

-8x/-8 < - 56/-8

x < 7

This means that x can be any number below 7.

In set builder notation: (-∞ , 7).

To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

the answer is 2 hours

Step-by-step explanation:

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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