3/2 (as a fraction) by the power of 2

Answer:

We know that:

sin^2a + cos^2a = 1 (1)

Also, we have:

cos a + sin a = 1/2

Squaring both sides of the above equation, we get:

cos^2a + 2cos a sin a + sin^2a = 1/4

Using equation (1), we can simplify this to:

1 + 2cos a sin a = 1/4

Subtracting 1 from both sides, we get:

2cos a sin a = -3/4

Squaring both sides, we get:

4cos^2a sin^2a = 9/16

Using the identity:

sin^2a = 1 - cos^2a

We can rewrite the above equation as:

4cos^2a (1 - cos^2a) = 9/16

Expanding and rearranging, we get:

4cos^4a - 4cos^2a + 9/16 = 0

Multiplying both sides by 16, we get:

64cos^4a - 64cos^2a + 9 = 0

Letting x = cos^2a, we can rewrite this as a quadratic equation:

64x^2 - 64x + 9 = 0

Solving for x using the quadratic formula, we get:

x = (64 ± √16384)/128

x = 1/2 or x = 9/64

Since 0 < a < 2π, we know that cos a is positive, so we can take the positive square root:

cos a = √(1/2) = 1/√2

Substituting this into the equation sin a + cos a = 1/2, we get:

sin a = 1/2 - cos a = 1/2 - 1/√2 = (√2 - 1)/2

Therefore:

sin^2a - cos^2a = ((√2 - 1)/2)^2 - (1/√2)^2

= (3 - 2√2)/4

Therefore, sin^2a - cos^2a = (3 - 2√2)/4.

Given that radius (r) = 7 cm.

We know that the circumference of the circle = [tex]2\pi r[/tex]

So, the circumference of the semicircle = [tex]\frac{1}{2} \times2\pi r=\pi r[/tex]

[tex]=\dfrac{22}{7} \times7 \ \text{cm}[/tex]

[tex]=22 \ \text{cm}[/tex]

So, the diameter of the circle = [tex]2r=2\times7 \ \text{cm}=14 \ \text{cm}[/tex]

Thus, the perimeter of each semicircular dis = [tex]22 \ \text{cm}+14 \ \text{cm}=36 \ \text{cm}[/tex].

For pyramid, ABCDE with square base ABCD, of side length 10, the total surface area of frustum ABCDMNPQ of pyramid, is equals to the 245 square units.

We have a pyramid, ABCDE, with base abcd, is a square with side length 10.

Total surface area of pyramid= 260

Let m,n,p and q are mid points of AE, BE, CE and DE, respectively. We have to determine total area of frustum ABCDMNPQ. See the above figure, we get [tex]\frac{ \bar{EM }}{\bar {EA }} = \frac{ \bar{EN }}{\bar {EB }} = \frac{ \bar{EP}}{\bar {EC }} = \frac{ \bar{EQ}}{\bar {ED }} =\frac{1}{2} [/tex] MQ

here, k = 1/2 or 1/k² = 1/4

MN = NP = PQ = MQ = k( 10 ) = 5

Now, Area of frustum, ABCDMNPQ = Area of ABMN + Area of BDMQ + Area of CDPQ + Area of BNPC + Area of square MPNQ + Area of square ABCD. There are four trapezoid and two squares.

Now, Area of ABMN + Area of BDMQ + Area of CDPQ + Area of BNPC

= ( 1 - k²) ( 260 - 100)

= 120

Total surface area of frustum ABCDMNPQ = 120 + 100 + 25 = 245. Hence, required area is 245 square units.

For more information about frustem of pyramid , visit:

https://brainly.com/question/30591530

#SPJ4

Complete question:

The above figure completes the question. let ABCDE be a pyramid, where the base ABCD is a square of side length 10. the total surface area of pyramid abcde (including all five faces) is 260. let M,N,P and Q be the midpoints of $\overline{AE}$, $\overline{B}$, $\overline{CE}$, and $\overline{DE}$, respectively. find the total surface area of frustum ABCDMNPQ.

The area of the given shaded region is 0.1587 which can be calculated using the cumulative area of the normal distribution.

The z-score is the number of standard deviations a data point is away from the mean. It can be calculated by subtracting the mean from the data point, and then dividing by the standard deviation.

To calculate the area of the shaded region, the z-score for the value of 115 must first be determined.

In this case, the z-score= (115 - 100)/15, or 1.

The area of the shaded region is then calculated using the cumulative area of the normal distribution.

As the area of the shaded region is the probability of a data point being greater than 115, the cumulative area of the normal distribution should be subtracted from 1 to get the area of the shaded region.

The cumulative area of the normal distribution for a z-score of 1= 0.8413,

as z-score= x - μ/σ

so the area of the shaded region

=1 - 0.8413

= 0.1587.

For more questions related to standard deviation

https://brainly.com/question/24298037

#SPJ1

Answer:

its to sloppy i cant make out what it says  

Step-by-step explanation:

The minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.

what is circuit?

In graph theory, a circuit is a closed path in a graph that starts and ends at the same vertex. In other words, a circuit is a sequence of vertices and edges that starts and ends at the same vertex, and every vertex in the sequence (except the first and last vertex) is visited exactly once.

In the given question,

To find the minimum cost Hamilton Circuit using the brute-force method, we need to try all possible Hamilton circuits and choose the one with the minimum cost. Since there are only 3 vertices in this graph, there are only 3! = 6 possible Hamilton circuits. We can enumerate all of them and calculate their costs to find the minimum.

Here are the 6 possible Hamilton circuits, starting with vertex A:

A -> B -> C -> A

Total cost = 26 + 20 + 20 = 66

A -> C -> B -> A

Total cost = 20 + 8 + 26 = 54

A -> B -> D -> A

Total cost = 20 + 8 + 20 = 48

A -> D -> B -> A

Total cost = 20 + 26 + 8 = 54

A -> C -> D -> A

Total cost = 8 + 20 + 26 = 54

A -> D -> C -> A

Total cost = 26 + 20 + 8 = 54

Therefore, the minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.

To know more about Hamilton Circuit , visit:

https://brainly.com/question/31034797

#SPJ1

‍‍‍Answer : -0.65

:)

Answer: Circumference - 37.68

Area of the circle - 113.04

Step-by-step explanation:

We have to remember that the formula for the circumference of a circle is Pi X Diameter, and since the diameter is 2 times the radius, we would have 3.14x12, which would be 37.68. For the area, we would do Pi times R squared, meaning 6x6=36, 36x3.14=113.04. I hope you understand this.

Using trigonometric ratio and trigonometric identities, the angle of elevation is 19.5 degrees and [tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]

To determine the angle of elevation, we will need to apply trigonometric ratio here;

Length of cable = hypothenuse = 300ft

Distance of parasailer to surface = opposite = 100 ft

Since we have the value of opposite side and hypothenuse, we can use the sine ratio;

sinθ = opposite / hypothenuse

sinθ = 100/300

sinθ = 1/3

θ = sin⁻¹(1/3)

θ = 19.5°

2. Let;

[tex]\theta = \arcsin(-\sqrt{2}/2)$. Then, $\sin\theta = -\sqrt{2}/2[/tex]

Since θ is in the fourth quadrant, cos θ is positive. To find cos θ, we can use the trigonometric identity

[tex]\sin^2\theta + \cos^2\theta = 1[/tex]

\begin{align*}

[tex]\cos^2\theta &= 1 - \sin^2\theta \\&= 1 - \left(-\frac{\sqrt{2}}{2}\right)^2 \\&= 1 - \frac{1}{2} \\&= \frac{1}{2}[/tex]

Taking the positive square root, we get:

[tex]\cos\theta = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}[/tex]

Therefore,

[tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]

Learn more on trigonometric ratio here;

https://brainly.com/question/17155803

#SPJ1

Answer:

Step-by-step explanation:

Given system of equation to us is ,

3a + 2c = 38.65

1a + 2c = 22.75

Here the given system of equation are linear equations in two variables. We can use various methods to solve them like substitution method, elimination method, etc . Here i will make use of elimination method. For that ;

Subtract both the equations , that would result to ;

3a + 2c - ( 1a + 2c ) = 38.65 - 22.75

3a + 2c - 1a - 2c = 15.9

2a = 15.9

a = 15.9/2

a = 7.95

To find out the value of c , plug in a = 7.95 in any of the two equations, as ;

a + 2c = 22.75

2c = 22.75 - 7.95

2c = 14.8

c = 14.8/2

c = 7.4

Hence the value of a is 7.95 and that of c is 7.4 .

The pοlynοmial that is a difference οf squares is: x² - 36 factοred as: (x + 6)(x - 6)

A pοlynοmial is a mathematical expressiοn that cοnsists οf οne οr mοre terms, where each term is a prοduct οf a cοefficient and οne οr mοre variables raised tο nοn-negative integer pοwers. Pοlynοmials can be used tο mοdel variοus real-wοrld phenοmena and are fundamental tο many areas οf mathematics and science.

The pοlynοmial that is a difference οf squares is: x² - 36

This pοlynοmial can be factοred as: (x + 6)(x - 6)

Tο see why this wοrks, we can write x² - 36 as (x)² - (6)², which is a difference οf squares. Then, we can use the fοrmula fοr the difference οf squares, which states that a² - b² = (a + b)(a - b), tο factοr x² - 36 as (x + 6)(x - 6).

To learn more about Polynomials from the given link

https://brainly.com/question/4142886

#SPJ1

There is a significant difference in stress levels between dog owners and non-dog owners.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves techniques for designing experiments, surveys, and observational studies to gather data, as well as methods for summarizing, visualizing, and drawing conclusions from the data.

Step 1: State the null and alternative hypotheses:

Null hypothesis: There is no significant difference in stress levels between dog owners and non-dog owners.

Alternative hypothesis: There is a significant difference in stress levels between dog owners and non-dog owners.

Step 2: Determine the level of significance (alpha) and the degrees of freedom :

Alpha = 0.01 (given in the problem)

Degrees of freedom = n₁ + n₂ - 2, where n1 and n2 are the sample sizes of the two groups.

n₁ = 20 (from the table)

n₂ = 15 (from the table)

Degrees of freedom = 20 + 15 - 2 = 33

Step 3: Calculate the sample means and standard deviations:

For dog owners:

Sample mean (x₁) = 28.25

Sample standard deviation (s₁) = 9.24

For non-dog owners:

Sample mean (x₂) = 36.20

Sample standard deviation (s₂) = 7.96

Step 4: Calculate the t-statistic:

t = (x₁ - x₂) / √[(s₁²/n₁) + (s₂²/n₂)]

t = (28.25 - 36.20) / √[(9.24²/20) + (7.96²/15)]

t = -2.75

Step 5: Determine the critical t-value:

Using a t-table with 33 degrees of freedom and a one-tailed alpha of 0.01, the critical t-value is -2.449.

Step 6: Make a decision:

Since the calculated t-value (-2.75) is less than the critical t-value (-2.449), we reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in stress levels between dog owners and non-dog owners.

To know more about hypotheses, visit:

https://brainly.com/question/18173488

#SPJ9

The maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1, is equals to the 1/27.

Volume of something is defined as the amount of space it takes up inside. When we measure inside of something then we measure volume. We have, a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x + y + z = 1 --(1)

First from the above equation, z = 1 -x- y.

The volume of the box is, V = xyz --(2)

Plug the value of z from equation (2),

=> V = xy(1 − x − y)

=> V = xy - x²y - xy²

Now, we determine the partial derivatives to determine the critical points, Vₓ = y − 2xy − y² , Vᵧ = x - x² - 2xy

For maxima and minima we equate the partial derivatives equal to zero, Vₓ = 0 and Vᵧ = 0

=> y − 2xy − y² = 0

=> y² + y( 2x - 1) = 0

=> 2x + y = 1 --(3)

Also, x - x² - 2xy = 0

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

=> x + 2y = 1 --(4)

Solving equations (3) and (4), x = 1/3 and y = 1/3.

So, from equation (1), z = 1 - 1/3 - 1/3 = 1/3. Therefore, volume of box is V

= (1/3)(1/3)(1/3)

= 1/27

Hence, required volume is 1/27 cubic units.

For more information about maximum volume, visit :

https://brainly.com/question/28950621

#SPJ4

Answer:

C. -1/4

The negative value are smaller then 0

Answer: C. -1/4

Step-by-step explanation: 0 and -1 is greater than -1/4. -1/2 is also greater than -1/4 as -1/4 goes to the left of a number line and going to the left of a number line makes the number smaller

if it's wrong, im sorry

hope this helps!!

A. To solve the quadratic equation 2x² - 17x + 8 = 0, we can use the factoring method. We need to find two numbers whose product is 16 (the product of the coefficients of x² and the constant term) and whose sum is -17 (the coefficient of x). These two numbers are -1 and -16, so we can rewrite the equation as:

2x² - 17x + 8 = (2x - 1)(x - 8) = 0

Setting each factor equal to zero, we get:

2x - 1 = 0 or x - 8 = 0

Solving for x, we get:

2x = 1 or x = 8

x = 1/2 or x = 8

Therefore, the roots of the quadratic equation are x = 1/2 and x = 8.

B. To solve the quadratic equation x² - 4x - 12 = 0, we can use the factoring method. We need to find two numbers whose product is -12 (the product of the coefficients of x² and the constant term) and whose sum is -4 (the coefficient of x). These two numbers are -6 and 2, so we can rewrite the equation as:

x² - 4x - 12 = (x - 6)(x + 2) = 0

Setting each factor equal to zero, we get:

x - 6 = 0 or x + 2 = 0

Solving for x, we get:

x = 6 or x = -2

Therefore, the roots of the quadratic equation are x = 6 and x = -2.

Answer:

18 km

Step-by-step explanation:

43.2/2.4 = 18

Helping in the name of Jesus.

Therefore , the solution of the given problem of probability comes out to be , the occurrence that is UNLIKELY is P (failing math).

Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

From most likely to least likely, the following occurrences are most likely to occur:

=> P(Honor score) = 100% Spanish class = 60%

=> P(left-handedness) = 33% P(math failure) = 0%

Because there is no chance of it happening, the occurrence that is UNLIKELY is P (failing math).

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer:-14

Step-by-step explanation:

Answer:

Step-by-step explanation:

The roots of this discriminant x=0 or x=-14

The equation for given coordinates are A) p(x) = |x - 9| C), r(x) = |x + 9| O) ,t(x) = |x| - 9

What are coordinates ?

Coordinates are sets of numbers used to locate points on a grid or map. In mathematics, the most common type of coordinates are Cartesian coordinates, which consist of an ordered pair of numbers (x, y). The x-coordinate represents the horizontal position of the point on the x-axis, and the y-coordinate represents the vertical position of the point on the y-axis.

For example, in a two-dimensional coordinate system, the point (2, 3) has an x-coordinate of 2 and a y-coordinate of 3. This means that the point is located 2 units to the right and 3 units up from the origin, which is the point (0, 0) where the x-axis and the y-axis intersect.

According to the question :

We can determine which equation corresponds to each set of vertex coordinates by observing the general form of the equation of an absolute value function and how the vertex coordinates affect it. The general form of an absolute value function is:

f(x) = |x - h| + k

where (h, k) represents the vertex coordinates of the graph.

The vertex coordinates are (-9, 0). The value of h is -9, which means the equation involves a shift to the right by 9 units. The absolute value of x is the distance from x to 0, so when x is less than -9, the absolute value of x - (-9) will be positive, and when x is greater than -9, the absolute value of x - (-9) will be negative. Therefore, the equation with vertex coordinates (-9, 0) is:

C) r(x) = |x + 9|

The vertex coordinates are (9, 0). The value of h is 9, which means the equation involves a shift to the left by 9 units. The absolute value of x is the distance from x to 0, so when x is less than 9, the absolute value of x - 9 will be negative, and when x is greater than 9, the absolute value of x - 9 will be positive. Therefore, the equation with vertex coordinates (9, 0) is:

A) p(x) = |x - 9|

The vertex coordinates are (0, -9). The value of k is -9, which means the equation involves a vertical shift downwards by 9 units. The absolute value of x is the distance from x to 0, so the equation with vertex coordinates (0, -9) is:

O) t(x) = |x| - 9

To know more about coordinates visit:
https://brainly.com/question/30574507
#SPJ1

Answer: 36 cm^2

Step-by-step explanation:

The right part of this shape is a triangle so we just need to find the area of a triangle and the area of the rectangle and add them to get the total area.

Area of a triangle:

We know the height is 4. The base will be 10 - 8 = 2 since the 10 includes the 8cm which need to be subtracted.

A = b*h/2

= 4*2/2

= 4 cm^2

Area of rectangle:

The height is 4 and the base is 8.

A = b*h

= 4*8

= 32 cm^2

Now we add them to get the total area

A = 4 + 32

A = 36 cm^2

On solving the provided question we can say that Mr. and Mrs. Hawell, unitary assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return.

what is income tax return

An income tax return is a document or form filed by an individual or a business with the tax authorities, such as the Internal Revenue Service (IRS) in the United States or the HM Revenue and Customs (HMRC) in the United Kingdom.

to report their income, expenses, and other relevant financial information for the purpose of calculating and paying their income taxes.

The income tax return typically includes information such as the taxpayer's income from various sources, deductions, and credits that they may be eligible for, and the amount of taxes owed or overpaid.

Filing an income tax return is generally required by law, and failure to do so can result in penalties or legal consequences.

Mr. and Mrs. Hawell, assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return:

In general, most married couples file jointly since it results in reduced taxes and greater tax advantages. Yet, there may be times when filing separately is preferable, such as when one spouse has large medical costs or there are issues about the veracity of the other spouse's tax record.

Therefore, To identify the optimal filing status for a certain scenario, it is always preferable to speak with a tax specialist.

Learn more about tax here:

https://brainly.com/question/30111603

#SPJ1

An IQR of 17.25°F suggests that there is some variation in the record high temperatures across North America, but it is not extremely large.

What is temperature?

Temperature is a measure of the average amount of thermal energy or heat in a substance or system. It is a physical quantity that describes how hot or cold something is relative to some standard or reference point. Temperature is typically measured in degrees Celsius (°C) or degrees Fahrenheit (°F) in everyday life, or in kelvins (K) in scientific contexts.

The interquartile range (IQR) is a measure of how much the record high temperatures vary in North America. It is calculated as the difference between the 75th percentile and the 25th percentile of the data set. In this case, the IQR is given as 17.25°F, which means that the range of record high temperatures between the 25th and 75th percentile is 17.25°F.

The IQR is a measure of variability that is less sensitive to extreme values than the range. It provides a measure of how much the data is spread out from the middle 50% of the values. A larger IQR indicates that the record high temperatures vary more widely in North America, while a smaller IQR indicates that the temperatures are more consistent or clustered around a central value.

In this case, an IQR of 17.25°F suggests that there is some variation in the record high temperatures across North America, but it is not extremely large.

To learn more about temperature visit:

https://brainly.com/question/25677592

#SPJ1

Answer:

[tex]7 \: is \: a \: constant. \\ 4u \: and \: 3u \: are \: like \: terms[/tex]

Answer:

A. 3 . 2 > 0 . 32  

C. 2 . 6 > 2 . 59  

Step-by-step explanation:

YES -  A. 3 . 2 > 0 . 32  

3.2 is greater than .32

NO - B. 4 . 7 < 4 . 70  

these are the same so they are =

YES - C. 2 . 6 > 2 . 59

2.6 is greater than 2.59

NO - D. 2 . 09 = 2 . 9

these two are not equal, 2.09 < 2.9

Answer: 30

Step-by-step explanation: 15x2=30 6x5=30 so: the least common multiple is:30

know the meaning of least multiple

Answer:

$220,150 depreciates each year and increases in value with inflation of 7.2% per year? the useful life of the oven is considered 7 years. 10. The manager of a hotel bought...

Step-by-step explanation:

If it's wrong report the answer.........XD

Answer:

x=-5

Step-by-step explanation:

(8x+4)/2=6x+12

4x+2=6x+12

-2x=10

x=-5

Answer:

x = -5

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{2}(8x+4)=6(x+2)[/tex]

Multiply both sides of the equation by 2 to eliminate the fraction on the left side:

[tex]\implies 2\cdot\dfrac{1}{2}(8x+4)=2\cdot6(x+2)[/tex]

[tex]\implies (8x+4)=12(x+2)[/tex]

[tex]\implies 8x+4=12(x+2)[/tex]

Distribute the right side of the equation:

[tex]\implies 8x+4=12\cdot x+12 \cdot 2[/tex]

[tex]\implies 8x+4=12x+24[/tex]

Switch sides:

[tex]\implies 12x+24=8x+4[/tex]

Subtract 8x from both sides of the equation:

[tex]\implies 12x+24-8x=8x+4-8x[/tex]

[tex]\implies 4x+24=4[/tex]

Subtract 24 from both sides of the equation:

[tex]\implies 4x+24-24=4-24[/tex]

[tex]\implies 4x=-20[/tex]

Divide both sides of the equation by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{-20}{4}[/tex]

[tex]\implies x=-5[/tex]

Therefore, the value of x is -5.

The resistance of the electric blanket is approximately 80 ohms.

Ohm's law, a fundamental tenet of physics, explains how voltage, current, and resistance interact in an electrical circuit. It claims that the voltage across two locations and the resistance between them determine the relationship between the current flowing through a conductor between those two sites.

Ohm's law is mathematically represented as:

V = IR

where the three variables are voltage (V), current (I), and resistance (R). Given the values of the other two variables, this equation may be rewritten to account for any one of the three variables.

The resistance is given as:

R = V / I

Substituting the values of voltage and current we have:

R = 120 / 1.5

R = 80 ohms

Hence, the resistance of the electric blanket is approximately 80 ohms.

Learn more about ohms law here:

https://brainly.com/question/1247379

#SPJ1