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If = /4, find the value of each expression. (Round your answers to three decimal places, if necessary.)

sin2() =
sin(^{2} ) =

Answer:

x = 13.9

Step-by-step explanation:

15cos(22) = 13.9

Answer:

x = 13.9

Step-by-step explanation:

For the 22° angle, x is the adjacent leg. The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

cos 22° = adj/hyp

cos 22° = x/15

x = 15 × cos 22°

x = 13.9

Answer: x = 13.9

The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

What is width in rectangle ?

In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.

Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.

The area of the blanket is given by:

Area = Length x Width

5760 sq inches = (x + 18) inches * x inches

Expanding the right-hand side and solving for x, we get:

\(x^2 + 18x - 5760 = 0\)

We can solve this quadratic equation using the quadratic formula:

\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 18, and c = -5760. Plugging in these values, we get:

\(x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)\)

\(x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2\)

x ≈ 67.42 or x ≈ -85.42

Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

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The statement which is true include the following: A. The median can not possibly appear as a number in the data set.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

In Mathematics, a mode can be defined as a statistical term that is used to denote the value that appears most often or occurs repeatedly in a given data set.

In this context, we can reasonably infer and logically deduce that the median differs from the mode of a given data set.

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The number of points gained overall by Julia playing the game is 30 point

From the question, we have the following parameters that can be used in our computation:

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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The surface area of the square pyramid is 416.23 ft²

The surface area of a square pyramid is given by the formula:

A = a² + 2a√(a²/4 + h²)

Where a is the base length of the square pyramid and h is the height of the square pyramid.

From the figure, we have: a = 10 ft and h = 15 ft

A = a² + 2a√(a²/4 + h²)

A = 10² + 2*10√(10²/4 + 15²)

A = 100 + 20√(100/4 + 225)

A= 100 + 20√250

A = 416.23 ft²

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Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. The bond price is: $1,005.

Using this formula to determine the bond price

Bond price = Bond par value × price/100

Where:

Bond par value = $1,000

Price = 100.50

Let plug in the formula

Bond price = $1,000 × 100.50 /100

Bond price = $100,500 /100

Bond price =$1,005

Therefore the bond price is $1,005.

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The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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The expression that presents the number of trees that Shannon planted will be 6 - t.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Shannon planted t fewer trees than toby. Toby planted 6 trees.

Then the number of trees that Shannon planted will be given as,

⇒ 6 - t

The expression that presents the number of trees that Shannon planted will be 6 - t.

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The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.

The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.

The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.

According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.

Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.

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Answer:

= 5y + 91

Step-by-step explanation:

because you multiply 13 * 7 which equals to 91

and then leave the 5y by yourself because there is no y to add or multiply

***hope the help***

Using simple concept of fractions and simple division of the values, The answer is 0.83 servings.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Types of fractions are:

3/4 cup servings =0.75

5/8 cup of peanut butter = 0.625

0.625/0.75 servings is present.

0.83 servings.

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Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

Area is 140 ft2

perimeter is 54 ft

Answer:

54 and 140

Step-by-step explanation:

If the lengths are 20ft and 7ft, then you can just add 20+20+7+7, which equals 54.

The area is 140, because if you multiply 20 by 7, thn you get 140.

Hope that this helps!

The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

This inequality, sometimes called as the triangle inequality.

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The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

This inequality, sometimes called as the triangle inequality.

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The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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Answer:

plessssss markkkkk meeeeee brainlistttttt

Answer:

Differentiate each term with respect to

y

, then solve for

x

'

.

d

x

d

y

=

−

2

e

−

x

2

Step-by-step explanation

it right

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

402.12÷0.01 per cubic inch is written as \(40212 inch^{-3\) οr \(2.4538868 \times109 m^{-3\)

Imperial units and US custοmary units bοth use the cubic inch as a measure οf capacity. The capacity οf a cube, which is equal tο 1/231 οf a US gallοn, has three lengths that are each οne inch lοng.

Given,

402.12÷0.01 per cubic inch

We can write the equatiοn as

40212 per cubic inch

Or \(40212/ inch{^3\)

Or, \(40212 inch^{-3\)

We knοw that 1 inch 0.0254 m

Then we can write the equatiοn as 2.4538868 × 109 m-3

Hence the cοrrect answer is \(40212 inch^{-3\) οr \(2.4538868 \times 109 m-3\)

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Answer:

\(8*8*8*8*3*3= 8^4 * 3^2\)

Step-by-step explanation:

The exponents are used to write mathematical expressions in compact and simple form which is called scientific notation.

Given expression is:

\(8*8*8*8*3*3\)

When two or more same numbers are multiplied they can be written using exponents. i.e. a*a*a = a^3

We can see that 8 is repeated four times in the expression so,

\(8*8*8*8 = 8^4\)

Similarly, 3 is repeated two times

\(3*3 = 3^2\)

Combining both we get

\(= 8^4 * 3^2\)

Hence,

\(8*8*8*8*3*3= 8^4 * 3^2\)

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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Answ and she trains 5 days per week, how many hours does Andrea train for the marather:

StIf Andrea spends 1¾ hours per day training for a marathon and she trains 5 days per week, how many ep-by-step explanation:

Answer:

240.52 m square is your answer

Answer:

B

Step-by-step explanation:

area of square=20×21=420 m²

diagonal=√(20²+21²)=√(400+441)=√841=29

radius=29/2

area of circle=π×(29/2)²=841/4  π≈660.52 m²

area of shaded region=660.52-420=240.52 m²

Answer:

x = 4

y = 13

Step-by-step explanation:

x + 9 = y--------(1)

x + y = 17---------(2)

(1) ----> (2),

x + 9 + x = 17

2x + 9 = 17

2x = 8

x = 4

y = 13

Answer:

The figure is translate right 3 and up 1.

Step-by-step explanation:

Look at point S.  To go to point S' you need to move right 3 spaces and then up 1 space.  That is true for every point on the original figure to go to the new figure.

Helping in the name of Jesus.

Answer:

it's a

Step-by-step explanation:

the formula for volume is height×width×length

7×4×3=84

voila!

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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Answer:

Step-by-step explanation:

Answer options, incorrect statements are underlined below:

1. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range.

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

3. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly two elements of the range.

4. By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.

Answer:

2. By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.

Step-by-step explanation:

A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point.