The value of x in the equation 14(12x−36)=5x+18 is?

The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.

The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.

The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.

We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.

Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.

Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.

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Answer:

the area of the shaded region is 0.9525 (rounded to four decimal places).

Step-by-step explanation:

Since IQ scores above 75 are shaded, we need to find the area to the right of 75 on the normal distribution curve with mean 100 and standard deviation 15.

Using a standard normal table or calculator, we can find the z-score corresponding to 75 as follows:

z-score = (75 - 100) / 15 = -1.67

The area to the right of this z-score is the probability that an IQ score is above 75, which is the shaded area in the graph.

Using a standard normal table or calculator, we find that the area to the right of a z-score of -1.67 is 0.9525 (rounded to four decimal places).

Therefore, the area of the shaded region is 0.9525 (rounded to four decimal places).

According to the tax tables below, Melvin would have to pay in federal income taxes if filing separately $5,131 and Sylvia $6,750. The total would be $11,881

To identify how much Melvin and Sylvia have to pay in taxes, we must look carefully at the table. In this, the different incomes are classified and on the right side are shown how much the tax is depending on the condition of the citizen. These options are: single, married filling jointly, married filling separately and head of a household.

In accordance with the above, we must look at which number coincides in the row of married filling separately with the value of the income of each one of them. According to the above, Melvin has to pay 5,131 in taxes while Sylvia has to pay 6,750.

Note: This question is incomplete. Here is the complete information:

Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $35,750 last year, while Sylvia had a gross income of $41,700.

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Answer:

-10x+18=-15x-18+5x

-10x+18=-10x-18

18=-18

Since the equation is inconsistent and has no solution, there is no value of x that would make it true.

Step-by-step explanation:

Answer:

P(5) ≈ 0.0537.

Step-by-step explanation:

La fórmula para la distribución binomial es:

P(K) = (n choose k) * p^k * (1-p)^(n-k)

donde "n" es el número de ensayos, "p" es la probabilidad de éxito en cada ensayo, "k" es el número de éxitos y "n choose k" representa el número de formas de obtener k éxitos en n ensayos.

(a) Para n = 5, p = 1/4 y k = 2:

P(2) = (5 choose 2) * (1/4)^2 * (3/4)^3

= 10 * 1/16 * 27/64

= 0.2637

Por lo tanto, P(2) ≈ 0.2637.

(b) Para n = 10, p = 1/2 y k = 7:

P(7) = (10 choose 7) * (1/2)^7 * (1/2)^3

= 120 * 1/128 * 1/8

= 0.0820

Por lo tanto, P(7) ≈ 0.0820.

(c) Para n = 8, p = 2/3 y k = 5:

P(5) = (8 choose 5) * (2/3)^5 * (1/3)^3

= 56 * 32/243 * 1/27

= 0.0537

Por lo tanto, P(5) ≈ 0.0537.

The two points of tangency are (-1,3) and (1,-3).

What is the equation of a tangent to the circle?

The equation of a tangent to a circle is a linear equation that describes a line that touches the circle at exactly one point, without crossing it. A tangent line is perpendicular to the radius of the circle at the point of contact.

Since the line T is tangent to the circle, the radius of the circle drawn to the point of tangency (-1,3) is perpendicular to the line T. Therefore, the center of the circle must lie on the line perpendicular to T at (-1,3).

The equation of the tangent line T can be found by taking the derivative of the equation of the circle and evaluating it at the point of tangency (-1,3):

2x + 2y(dy/dx) = 0

dy/dx = -x/y

At the point (-1,3), dy/dx = -(-1)/3 = 1/3. Therefore, the equation of the tangent line T is:

y - 3 = (1/3)(x + 1)

y = (1/3)x + 10/3

The slope of any line perpendicular to T is -3 (the negative reciprocal of 1/3). The point-slope form of the equation of a line with slope -3 passing through (-1,3) is:

y - 3 = -3(x + 1)

y = -3x

To find the points of tangency, we need to solve the system of equations consisting of the equation of the circle and the equation of the tangent line:

x² + y² = 10

y = -3x

Substituting y = -3x into the first equation, we get:

x² + (9x²) = 10

10x² = 10

x² = 1

x = ±1

Substituting these values of x into y = -3x, we get:

(-1,3) and (1,-3)

Therefore, the two points of tangency are (-1,3) and (1,-3).

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Answer:

0

Step-by-step explanation:

Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)

In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).

The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.

Therefore, the expected value is:

Expected Value = (1/6) x $15 + (5/6) x (-$3)

Expected Value = $2.50 - $2.50

Expected Value = $0

The average rate of change of a function f(x) over the interval [a, b] is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, the function is f(x) = 2x^3 - x and the interval is [4, 6]. So we have:

f(4) = 2(4)^3 - 4 = 124

f(6) = 2(6)^3 - 6 = 330

Therefore, the average rate of change of f(x) over [4, 6] is:

(330 - 124) / (6 - 4) = 103

So the average rate of change of the function f(x) over the interval [4, 6] is 103.

Answer:

151

Step-by-step explanation:

Average Rate of Change Formula

[tex]\frac{f(b)-f(a)}{b-a}\\\frac{f(6)-f(4)}{6-4} \\\frac{((2*6^3)-6)-((2*4^3)-4)}{2} \\\frac{(432-6)-(128-4)}{2} \\\frac{426-124}{2}\\\\ \frac{302}{2} = 151[/tex]

If you have trouble remembering the rate of change formula, it's the same as the slope formula.

[tex]f(b) = y_2\\f(a) = y_1\\b = x_2\\b = x_1\\slope = \frac{y_2-y_1}{x_2-x_1} \\[/tex]

Similarly to the slope formula, it doesn't matter which point you set up to be the second coordinate, as long as it is consistent across the numerator and denominator.

Answer:

d = kw²

Step-by-step explanation:

The equation that expresses the relationship "d varies directly with the square of w" is:

d = kw² (or kw^2 if you prefer to write it that way!)

where k is the constant of proportionality.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

Answer: B) 2

Step-by-step explanation:

In the image, we see a box and whisker plot. The middle line represents the median. Looking at the numbers on the side, and the placement of the middle line, we can see that the median in this situation is 2.

Answer: We can simplify the given expression as follows:

9√64 - 2√125

Since √64 = 8, we can substitute to get:

9(8) - 2√125

Since √125 = √(25 × 5) = √25 × √5 = 5√5, we can substitute again to get:

9(8) - 2(5√5)

Simplifying further:

72 - 10√5

Therefore, the expression 9√64 3 − 2√125 simplifies to 72 - 10√5.

Step-by-step explanation:

When x = 5, y =  9 / 11

When x = 0, y = -1 / 6

when x = -6, y = -13

When x = 5

we would have

[tex]y = \frac{2(5) - 1}{5 + 6}[/tex]

y = 10 - 1 / 11

y = 9 / 11

when the value of x = 0

[tex]y = \frac{2(0) - 1}{0 + 6}[/tex]

y = -1 / 6

When the value of x = -6

[tex]y = \frac{2(-6) - 1}{-6 + 6}[/tex]

y = -12 - 1 / 0

y = -13 / 0

y = -13

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Answer:

To find out how many patients smoke, you can multiply the total number of patients by the percentage of smokers:

8500 x 25% = 2125

Therefore, there were 2125 patients who smoke last month in the trust.

Step-by-step explanation:

2125 of the patients are smoker.

Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.

Given that, there were 8500 patients in total last month in the trust. 25% of these are smokers.

We need to find the number of the patients who smoke.

So,

25% of 8500

= 0.25 × 8500

= 25 × 85

= 2125

Hence, 2125 of the patients are smoker.

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The rate of change is $1.25 per premium movie watched.

A. $1.25 / 1 premium movie

The rate of change in this scenario is the increase in cost for each additional premium movie watched.

In this case, the rate of change is constant, since the cost per premium movie remains the same regardless of the number of premium movies watched.

Therefore, the rate of change is simply the additional cost per premium movie, which is $1.25.

So, for example, if you watched 10 premium movies, the total cost would be:

$35 + (10 * $1.25) = $47.50

And if you watched 20 premium movies, the total cost would be:

$35 + (20 * $1.25) = $60.00

rate of change = (60 - 47.5) / (20 - 10) = 1.25

In both cases, the rate of change is still $1.25 per premium movie watched.

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The transformations that compares the functions y = 1/x and y = 5/(x + 6) are

What are transformations?

Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.

Since we have the functions

We want to see how the graphs of

We proceed as folows.

Looking at the functions

We compare the transformations and see that

So, the functions compare by

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Answer:

I think the answer is 63%

Step-by-step explanation:

9/10 * 7/10 = 63/100 = 63%

(I am not fully sure.)

Answer: they small angel is 12

Step-by-step explanation:because the third angle is 36 and 12 times three is 36  

The measure of angle x to the nearest tenth of a degree is 51.8°

The figure in the image is a right triangle.

From the image;

To solve for the measure of angle x, we use one of the six (6) trigonometric ratio.

Sine = Opposite / Hypotenuse.

Plug in the given values and solve for angle x.

sin( x ) = 11 units / 14 units.

Take the sine inverse.

x = sin⁻¹( 11/14 )

x = 51.7867

x = 51.8 degrees.

Therefore, the value of x is 51.8 degrees.

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From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.

The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:

P(rolling a 3) = Number of times 3 was rolled / Total number of rolls

P(rolling a 3) = 45 / 100

P(rolling a 3) = 0.45 or 45%

Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.

The linear regression equation for the data-set in this problem is given as follows:

y = -1.04x + 9.57.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.

The seven points that represent the data-set for this problem are given as follows:

(1, 10), (2,6), (3, 3), (4,10), (5, 4), (6, 3), (7, 2).

Inserting these points into the linear regression calculator, the linear regression equation for the data-set in this problem is given as follows:

y = -1.04x + 9.57.

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The Tοtal number οf tickets tο play will be 15.

Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.

At a schοοl fair, there are different games tο play that each require 5 tickets tο play.

Jοrdan wants a bag οf pοpcοrn that requires 26 tickets and tο use the rest οf the tickets tο play games.

Jοrdan has 101 tickets.

Fοr tickets tο play will be 101-26 = 75

Sο the Tοtal number οf tickets tο play will be 75/5 = 15.

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In response to the given question, we can state that As a result, the square answer is (D) 1 square yard.

In Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is also known as a rectangle with two adjoining sides that have the same length. A square is an equilateral quadrilateral because it has all four equal sides and all four equal angles. Square angles are 90 degree or straight angles. Moreover, the square's diagonals are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. A quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides that create a right angle. Rhombus with straight sides.

Then, calculate the length of each side of the square enclosure.

Vanessa utilised the garage's outer wall for one of the sides, so she only needed to create three more sides. She utilised three yards of fence for these three sides, therefore each must be three-thirds of a yard long.

As a result, the area of the enclosure is equal to the length of one side squared:

Area = side length + 1 yard + 1 yard = 1 square yard

As a result, the answer is (D) 1 square yard.

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Answer:

105 mi

Step-by-step explanation:

distance = speed x time

total distance = (62 mi/hr)(1.5 hr) + (24 mi/hr)(0.5 hr) = 105 mi

30 min = 0.50 hr

Answer:104

Step-by-step explanation:

The 5 foot 5 tall lady will cast a shadow of approximately 4.4 ft.

Given that, a 6 foot 2 man casts a shadow of 5 feet. Also, a lady is 5 foot 5 and we find the shadow she casted.

We can solve this problem by setting up a proportion:

The height and shadow length are proportional, so we can write:

6 feet 2 inches : 5 feet = 5 feet 5 inches : x

where x is the length of the shadow cast by the lady.

To solve for x, we can cross-multiply:

(6 feet 2 inches) × x = (5 feet) × (5 feet 5 inches)

To simplify the calculation, we can convert all the lengths from feets to inches:

Note: 1 ft = 12 in

(74 inches) × x = (60 inches) × (65 inches)

Now we can solve for x:

x = (60 inches)  × (65 inches) / (74 inches)

x = 3900/74

x = 52.70 inches

Convert back to ft

x = 4.4 ft

Therefore, the lady will cast a shadow of approximately 4.4 ft.

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The answer is [tex]\sqrt{58} = 7.62[/tex]

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).

Use the Pythagorean theorem:

[tex]c^2 = a^2 + b^2[/tex]

[tex]a = 3[/tex]

[tex]b = 7[/tex]

[tex]c^2 = 3^2 + 7^2[/tex]

[tex]c^2 = 9 + 49[/tex]

[tex]c^2 = 58[/tex]

[tex]c = \sqrt{58}[/tex]

[tex]c = 7.62[/tex]

Answer:

Step-by-step explanation:

a. To find the rate at which the x-coordinate of the bug is increasing when the bug is at the point (4, 16), we need to differentiate the equation y=x with respect to time t:

dy/dt = dx/dt

Since the bug is moving along the right side of the parabola y=x, the bug's position can be described by the equation y=x^2. Taking the derivative of both sides with respect to time t, we get:

2y(dy/dt) = 2x(dx/dt)

Simplifying and plugging in the given values for y and dy/dt:

2(16)(9) = 2(4)(dx/dt)

dx/dt = 36 cm/min

Therefore, the x-coordinate of the bug is increasing at a rate of 36 cm/min when the bug is at the point (4, 16).

b. The equation y=x^2 can be rewritten as x=sqrt(y). Differentiating both sides with respect to time t, we get:

dx/dt = 1/(2sqrt(y)) * dy/dt

Substituting y=16 and dy/dt=9, we get:

dx/dt = 1/(2sqrt(16)) * 9

dx/dt = 9/8 cm/min

c. We can use the same equation from part (a) to find the rate at which the y-coordinate of the bug is increasing when the bug is at the point (4, 16):

2y(dy/dt) = 2x(dx/dt)

Substituting y=16, x=4, and dx/dt=36, we get:

2(16)(dy/dt) = 2(4)(36)

Solving for dy/dt:

dy/dt = 18 cm/min

Therefore, the y-coordinate of the bug is increasing at a rate of 18 cm/min when the bug is at the point (4, 16).

d. Let D be the distance the bug is from the origin. We can use the Pythagorean theorem to relate D to x and y:

D^2 = x^2 + y^2

Substituting y=x^2, we get:

D^2 = x^2 + x^4

Taking the derivative of both sides with respect to time t, we get:

2D(dD/dt) = 2x(dx/dt) + 4x^3(dx/dt)

Simplifying and substituting x=4, dx/dt=36, and y=16:

2sqrt(16+16^2)(dD/dt) = 2(4)(36) + 4(4^3)(36)

Solving for dD/dt:

dD/dt = (836 + 44^3*36) / (2sqrt(16+16^2))

dD/dt = 72/(sqrt(17))

Therefore, the distance between the bug and the origin is increasing at a rate of 72/(sqrt(17)) cm/min when the bug is at the point (4, 16).

Answer:

b

Step-by-step explanation:

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