solve for w: k = 3pw
please help i have no clue

When the angle of elevation from a point on the structure to its top is 40°, the building has a height to the nearest foot of 758 feet.

Offered that it has sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. When the three points are not collinear, a unique rectangle and triangle in Trigonometry are discovered. Triangles are polygons because they have three sections and three corners. The points where the four sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

Using the triangles OBD and OAD and the SOH CAH TOA identity

OAD in triangle

Divide the two resulting equations to obtain the value of "x" for the triangle OBD.

The building's height must then be determined to the closest foot.

Just to refresh your memory, H = xtan50 H = 636tan50

H = 636(1.1918)

H = 757.96 feet.

Consequently, the building is 758 feet tall to the nearest foot.

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The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are  6 and -10.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point Q( -1, a )

Point P( 3, -2 )

To find the numerical value of a, plug the given coordinates into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )

Square both sides

( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²

( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²

( 4√5 )² = ( 4 )² + ( -2 - a )²

80 = 16 + ( -2 - a )²

80 - 16 = ( -2 - a )²

64 = ( -2 - a )²

( -2 - a )² = 64

Expand the parenthesis

( -2 - a )( -2 - a ) = 64

a² + 4a + 4 = 64

a² + 4a + 4 - 64 = 0

a² + 4a - 60 = 0

solve for a

( a - 6 )( a + 10 ) = 0

a - 6 = 0, a + 10 = 0

a = 6, a = -10

Therefore, the values of a are 6 and -10.

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The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Answer:

14.8

Step-by-step explanation:

4(2)+3.4(2)

8+6.8

14.8

Detailed solution attached!~

\(\rule{300pt}{3pt}\)

The second attachment contains the part of trapezium that we have used to find the length of AC...

The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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In order to determine the sample size needed to achieve a desired margin of error for the population proportion, you will need to use a formula that takes into account the confidence level, the margin of error, and an estimate of the population proportion (p*).

However, since you do not have a reliable estimate of p*, you can use a conservative estimate of 0.5 to calculate the sample size. This will ensure that you have a large enough sample size to capture any changes in the population proportion, while still maintaining a reasonable level of precision in your estimate. Once you have collected your data, you can use the sample proportion as an estimate of the population proportion in any subsequent analyses.

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Answer:

29.75 unit ^2

Step-by-step explanation:

Base * height /2 =

8.5 *7 /2 = 29.75

You just have to count the block for height and base.

Answer:

7/8,5/6

Step-by-step explanation:

Two fractions are equivalent when their division is equal to one.

When we are dividing fractions, we multiply the numerator by the inverse of the denominator.

1/9,2/18

7/8,5/6

The division is not 1, so this par of fractions is not equivalent.

3/16, 9/48

6/15, 4/10​

Answer:

Step-by-step explanation:

Given that:

cos(x) = x³

f(x) = cos (x) - x³

f(x) is continuous on the interval (0, 1)

when;

f(0) = cos (0) - (0)

f(0) = 1 - 0

f(0) = 1 > 0

f(1)  = cos (1) - 1³

f(1) = 0.5403 - 1

f(1) = -0.4597

f(1) = - 0.46

f(1) = - 0.46 < 0

Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)

such that f(c) = 0

By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)

b) Given that:

The interval length = 0.01; this implies that it is 0.005 length from its root.

f(0.865) = 0.0014

f(0.87) = - 0.013

The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.

Answer:

V = 2388.16 in3

Step-by-step explanation:

\(V=\pi (4)^{2} (9)+(16)(11)(11)=452.16+1936=2388.16in.^{3}\)

Hope this helps

Answer:

The pressure level will rise. The pressure increases as the volume decrease. This demonstrates that a gas's pressure is inversely proportional to its volume.

Using the Central Limit Theorem, it is found that the correct option is:

(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.

By the Central Limit Theorem, for a distribution with mean \(\mu\) and standard deviation \(\sigma\), considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:

\(s = \frac{\sigma}{\sqrt{n}}\)

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Answer:

i got 6.6? maybe that helps (:

Answer: 623 /18

Step-by-step explanation:

The roots of the quadratic equation ax^(2) + bx + c = 0 are real and irrational.

This can be proven using the quadratic formula, which states that the roots of a quadratic equation of the form ax^(2) + bx + c = 0 are given by:

x = (-b ± sqrt(b^(2) - 4ac)) / 2a

Since b^(2) - 4ac is positive but not a perfect square, the square root term in the above formula is irrational. Therefore, the roots of the quadratic equation are real and irrational.

To understand why this is the case, consider the discriminant b^(2) - 4ac. This term determines the nature of the roots of a quadratic equation. If the discriminant is positive and a perfect square, then the roots are rational.

If the discriminant is negative, then the roots are complex conjugates. If the discriminant is zero, then there is only one real root.

In this case, since b^(2) - 4ac is positive but not a perfect square, we know that the roots are real and irrational. This means that they cannot be expressed as a ratio of two integers and do not terminate or repeat in decimal form.

In summary, if a, b, and c are rational numbers and if b^(2) - 4ac is positive but not a perfect square, then the roots of the quadratic equation ax^(2) + bx + c = 0 are real and irrational.

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Answer:

b

Step-by-step explanation:

Answer:

The answer is "\(\bold{668 + 7x > 2,000}\)"

Step-by-step explanation:

7x = x is the cans obtained within 7 days 668 is the number of cans that are already obtained. Its number for goal cans is 2000. So, the equation is:

\(\to 7 x + 668 < 2000\)

subtract and add the value 668:

         \(- 668 \ \ \ \ \ -668\)

\(\to 7x +0 < 1332\)

Divide the value 7:

    \(7 \ \ \ \ \ \ 7\)

\(\to x < 190.30 \\\\OR\\\\\to x < 190\\\\\)

The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

False

Rise is the vertical change not the horizontal

Step-by-step explanation:

Answer:

press x button to close the tab

Step-by-step explanation:

Answer:

\(4 (d+3)\)

Answer:

4(d+3)

Step-by-step explanation:

look to see what can be factored from both sides

in this example it is 4

so 4 comes to the front

and what times to make the expression is d + 3 so they go inside the brackets

The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the circumference of the circle is 12.56 units, which means that the radius is half of this, or  1.99 units which is approximately 3.90 units .

Step 1: Determine the circle's radius.

The formula for circumference is C = 2πr, where r is the radius of the circle.

2πr = 12.56

r = 12.56 / (2π)

r = 1.99 units

Step 2: Calculate the area of the circle

The formula for area of a circle is A = πr2

A = π(1.99)2

A = 3.90 units2

The area of a circle can be calculated by using the formula A = π\(r^2,\) where r is the radius of the circle. The radius of a circle is half of its circumference, so if the circumference of a circle is 12.56 units, the radius is 6.28 units. By plugging this value into the formula, the area of the circle can be found. To calculate the area of the circle, we would multiply π (3.141592654) by \(6.28^2\), which would give us 122.58 units. This is the approximate area of the circle with a circumference of 12.56 units. It is important to note that the value of π is an approximate value, and can be rounded up or down depending on the precision desired. Additionally, the value of π can be substituted with other values such as 22/7 or 3.14 to obtain a more accurate result.

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Answer:

1. so the express of the shaded region would be

10x*6 which gives 60x the area of the whole thing subtract 2x*4 =8x

so 60x-8x

2.

the perimeter is 6*2 bc two sides so 12

and 10x *2 bc two sides 20

so 20x+12 would be the perimeter

Answer:

A. 7w + 60 = 5w + 120; w = 30

Step-by-step explanation:

Answer:

cardioid

Step-by-step explanation:

r=2+2 sin(theta)​

This is of the form

r =a+b theta

This is a limacon

When a = b, it is called a cardioid.

Answer:

Where: 28 is the old value in 36 is the new value in this case we have a positive change increase of 28.571142857

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

To find the number in the given problem, we can translate the statement into the equation \(x - 7 = 4(x+2).\)

Let's break down the problem step by step. We are given that "Seven less than a number" can be represented as x−7.

The phrase "the product of four and two more than the number" can be expressed as 4(x+2), where x+2 represents "two more than the number" and multiplying it by 4 gives us "the product of four and two more than the number."

Therefore, we can write the equation as \(x-7=4(x+2)\) to represent the given problem mathematically.

Solving this equation will give us the value of the number (x) that satisfies the given conditions.

It's important to note that the equation \(x-7=4(x+2)\) assumes that the number being referred to is x.

If the problem specifies a different variable, the equation would be adjusted accordingly.

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The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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